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Simulation and Characterization of Silicon Carbide

Power Bipolar Junction Transistors

BENEDETTO BUONO

Doctoral Thesis

Stockholm, Sweden

TRITA-ICT/MAP AVH Report 2012:08ISSN 1653-7610ISRN KTH/ICT-MAP/AVH-2012:08-SEISBN 978-91-7501-365-7

KTH-ICT,SE-164 40, Kista,

Sweden

Akademisk avhandling som med tillstand av Kungl Tekniska hogskolan framlaggestill offentlig granskning for avlaggande av Teknologie Doktorsexamen inom Mikro-elektronik och Tillampad Fysik. Fredagen den 08 juni 2012, klockan 10:00 i Sal C1,KTH-Electrum, Isafjordsgatan 26, Kista, Stockholm.

c© Benedetto Buono, 08 June 2012

Tryck: US-AB

iii

Benedetto Buono: Simulation and Characterization of Silicon Carbide Power Bipolar Junction

Transistors, School of Information and Communication Technology (ICT), KTH Royal Institute

of Technology, Stockholm 2012.

Abstract

The superior characteristics of silicon carbide, compared with silicon, havesuggested considering this material for the next generation of power semicon-ductor devices. Among the different power switches, the bipolar junctiontransistor (BJT) can provide a very low forward voltage drop, a high cur-rent capability and a fast switching speed. However, in order to competeon the market, it is crucial to a have high current gain and a breakdownvoltage close to ideal. Moreover, the absence of conductivity modulation andlong-term stability has to be solved.

In this thesis, these topics are investigated comparing simulations andmeasurements. Initially, an efficient etched JTE has been simulated and fab-ricated. In agreement with the simulations, the fabricated diodes exhibit thehighest BV of around 4.3 kV when a two-zone JTE is implemented. Fur-thermore, the simulations and measurements demonstrate a good agreementbetween the electric field distribution inside the device and the optical lumi-nescence measured at breakdown.

Additionally, an accurate model to simulate the forward characteristicsof 4H-SiC BJTs is presented. In order to validate the model, the simulatedcurrent gains are compared with measurements at different temperatures anddifferent base-emitter geometries. Moreover, the simulations and measure-ments of the on-resistance are compared at different base currents and dif-ferent temperatures. This comparison, coupled with a detailed analysis ofthe carrier concentration inside the BJT, indicates that internal forward bi-asing of the base-collector junction limits the BJT to operate at high currentdensity and low forward voltage drop simultaneously. In agreement with themeasurements, a design with a highly-doped extrinsic base is proposed toalleviate this problem.

In addition to the static characteristics, the comparison of measured andsimulated switching waveforms demonstrates that the SiC BJT can providefast switching speed when it acts as a unipolar device. This is crucial to havelow power losses during transient.

Finally, the long-term stability is investigated. It is observed that theelectrical stress of the base-emitter diode produces current gain degradation;however, the degradation mechanisms are still unclear. In fact, the analysis ofthe measured Gummel plot suggests that the reduction of the carrier lifetimein the base-emitter region might be only one of the causes of this degradation.In addition, the current gain degradation due to ionizing radiation is investi-gated comparing the simulations and measurements. The simulations suggestthat the creation of positive charge in the passivation layer can increase thebase current; this increase is also observed in the electrical measurements.

Keywords: silicon carbide, power device, BJT, diode, simulation, character-ization, current gain, on-resistance, breakdown voltage, forward voltage drop,degradation.

Contents

Acknowledgments vii

Publications ix

Summary of Included Papers xi

List of Symbols and Acronyms xiii

1 Introduction 11.1 Power Device Characteristics . . . . . . . . . . . . . . . . . . . . . . 21.2 Drift Region for Power Devices . . . . . . . . . . . . . . . . . . . . . 51.3 SiC Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Bipolar Junction Transistor . . . . . . . . . . . . . . . . . . . . . . . 81.5 Thesis Objective and Structure . . . . . . . . . . . . . . . . . . . . . 10

2 Physical Models 132.1 Impact Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Fermi-Dirac Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Incomplete Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 SRH Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.6 Auger Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7 Surface Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . 212.8 Bandgap Narrowing . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.9 Limitations of Physical Models . . . . . . . . . . . . . . . . . . . . . 24

3 Simulation and Characterization of SiC BJTs 273.1 Breakdown Characteristic . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Current Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.1 Influence of the temperature . . . . . . . . . . . . . . . . . . 333.2.2 Influence of the emitter-base geometry . . . . . . . . . . . . . 36

3.3 ON-resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.4 Design Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

iv

CONTENTS v

3.5 Switching Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 473.6 Long-term Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.6.1 Bipolar degradation . . . . . . . . . . . . . . . . . . . . . . . 513.6.2 Current gain degradation . . . . . . . . . . . . . . . . . . . . 523.6.3 Radiation hardness . . . . . . . . . . . . . . . . . . . . . . . . 56

4 SiC diodes 614.1 Design of a 10 kV PiN diode . . . . . . . . . . . . . . . . . . . . . . 61

4.1.1 Reverse characteristic . . . . . . . . . . . . . . . . . . . . . . 614.1.2 Forward characteristic . . . . . . . . . . . . . . . . . . . . . . 65

5 Conclusions and Future Outlook 69

Bibliography 73

Acknowledgments

This thesis summarizes the research work I have conducted as PhD student at KTHRoyal Institute of Technology. During these four years, I have received countlesshelp and support from many people. First of all, I would like to thank my principlesupervisor Dr. Martin Domeij for his continuous supervision and motivation.

I must also express my gratitude to Prof. Mikael Ostling, my co-supervisorand head of the department, who gave me the opportunity to study in his researchgroup, and for his support and guidance on my research.

I am also very grateful to my co-supervisor Dr. Gunnar Malm who has al-ways supported my work with helpful advices about device simulations and devicephysics.

My gratitude is also for Prof. Carl-Mikael Zetterling who has always had time forfruitful scientific discussions that have contributed to give me the research methodon which this thesis is built.

I would also like to thank Prof. Anders Hallen who, with his course, introducedthe field of power semiconductor devices to me.

My deep gratitude also goes to Dr. Reza Ghandi who supported and helpedme when I started my PhD. The scientific collaboration (without his fabricateddevices this work would not be possible) and the friendship has been unique for myresearch.

I would like also to express my gratitude to Dr. Jun Luo who was one of myfirst friends in Stockholm. Our friendship already started when I came to KTH asexchange student, and still continues.

Many thanks also go to all the people who have been and are in the Inte-grated Devices and Circuits department for creating a nice working environment.In particular and as representative of all the uncountable members of the Iraniancommunity, Dr. Henry Radamson, Dr. Mohammadreza Kolahdouz (Mreza), ArashSalemi, who is successfully continuing this research work together with HosseinElahipanah, and Sam Vaziri are thanked for their friendly attitude. I would like tocontinue with the Italian community: Luca Maresca, for the time we spent togetherand for starting the Italian coffee tradition; Luigia (Gina) Lanni, for the fruitfuldiscussions about semiconductor physics and nice time in the office; Eugenio Den-toni Litta, for being a very friendly officemate; and finally Giovanni Fevola, for the

vii

viii Acknowledgments

useful theoretical discussions that criticized my work. In addition, I would like tothank Katarina Smedfors for her friendly attitude.

Indeed, my work has also been possible thanks to all my friend outside thedepartment. I would like to express my deep gratitude to Ana Lopez Cabezas forher support, help for anything I needed, and time we spend together; Reza Sanatiniafor the nice time and fun we have together that has really helped to through thesefour years; Terrance Burk and Mohsin Saleemi for their support and friendship.

Finally, I would like to express my deep and inestimable gratitude to my parents,my three wonderful sisters and lovely Anna for their day-to-day support and forbelieving in me.

Benedetto BuonoStockholm, June 2012

Publications

List of papers included in this thesis:

I High Voltage 4H-SiC PiN Diodes with Etched Junction TerminationExtension, R. Ghandi, B. Buono, M. Domeij, G. Malm, C.-M. Zetterling, M.Ostling, IEEE Electron Device Letters, v. 30, n. 11, pp. 1170-2, 2009.

II Modeling and Characterization of Current Gain versus Temperaturein 4H-SiC Power BJTs, B. Buono, R. Ghandi, M.Domeij, G. Malm, C.-M.Zetterling, M. Ostling, IEEE Transactions on Electron Devices, v. 57, n. 3,pp. 704-11, 2010.

III Influence of Emitter Width and Emitter-Base Distance on the Cur-rent Gain in 4H-SiC Power BJTs, B. Buono, R. Ghandi, M.Domeij, G.Malm, C.-M. Zetterling, M. Ostling, IEEE Transactions on Electron Devices,v. 57, n. 10, pp. 2664-70, 2010.

IV Modeling and Characterization of the ON-Resistance in 4H-SiCPower BJTs, B. Buono, R. Ghandi, M.Domeij, G. Malm, C.-M. Zetterling,M. Ostling, IEEE Transactions on Electron Devices, v. 58, n. 7, pp. 2081-87,2011.

V Investigation of Current Gain Degradation in 4H-SiC Power BJTs,B. Buono, R. Ghandi, M.Domeij, G. Malm, C.-M. Zetterling, M. Ostling, tobe published in Material Science Forum 2012.

VI Impact of Ionizing Radiation on the SiO2/SiC Interface in 4H-SiCBJTs, M. Usman, B. Buono, and A. Hallen, IEEE Transactions on ElectronDevices (submitted).

List of related papers not included in this thesis:

I Simulation of open emitter breakdown voltage in SiC BJTs with non-implantedJTE, B. Buono, H.-S. Lee, M.Domeij, G. Malm, C.-M. Zetterling, M. Ostling,Material Science Forum, vol. 615-17, pp. 841-4, 2009.

ix

x Publications

II Temperature modeling and characterization of the current gain in 4H-SiCpower BJTs, B. Buono, R. Ghandi, M.Domeij, G. Malm, C.-M. Zetterling,M. Ostling, Material Science Forum, vol. 645-48, pp. 1061-4, 2010.

III Surface-passivation effects on the performance of 4H-SiC BJTs, R. Ghandi,B. Buono, M.Domeij, R. Esteve, A. Schoner, J. Han, S. Dimitrijev, S.A. Re-shanov, C.-M. Zetterling, M. Ostling, IEEE Transaction on Electron Devices,vol. 58, n. 1, pp. 259-65, 2011.

IV Current gain degradation in 4H-SiC power BJTs, B. Buono, R. Ghandi,M.Domeij, G. Malm, C.-M. Zetterling, M. Ostling, Material Science Forum,vol. 679-80, pp. 702-5, 2011.

V Removal of crystal orientation effects on the current gain of 4H-SiC BJTsusing surface passivation, R. Ghandi, B. Buono, C.-M. Zetterling, M. Domeij,S. Shayestehaminzadeh, M. Ostling, IEEE Electron Device Letters, vol. 32, n.5, pp. 596-8, 2011.

VI Silicon carbide bipolar power devices, M. Ostling, R. Ghandi, G. Malm,B. Buono, C.-M. Zetterling, ECS Transactions, vol. 41, n. 8, pp. 189-200,2011.

Summary of Included Papers

Paper I

This paper presents an investigation on the blocking capability of implantation-free4H-SiC diodes. The simulations and measurements demonstrate that a breakdownvoltage of around 4 kV can be achieved when the JTE dose is around 1.2 × 1013

cm−2. However, this optimum dose presents a narrow peak, and the breakdownvoltage is strongly reduced especially when the JTE dose is higher than the optimumvalue. Therefore, it is demonstrated that a wider range around the optimum dosecan be obtained implementing a two-zone JTE. This solution demonstrates also ahigher BV of around 4.3 kV.

The author has performed all the device simulations, and contributed tothe electrical characterizations and to writing the manuscript.

Paper II

This paper presents an accurate physical modeling to describe the current gainin 4H-SiC BJTs. The simulations are compared with the measurements at differ-ent temperatures to validate the model and describe the temperature behavior of4H-SiC BJTs. The analysis of the carrier concentration suggests that, at roomtemperature, high injection in the base and internal forward biasing of the base-collector junction cause the reduction of the current gain at high collector current.However, at high temperature, the high injection is alleviated, and only the internalforward biasing occurs. Moreover, this mechanism can explain the reduction of theknee current when the temperature increases.

The author has performed all the device simulations and electrical char-acterizations, and has written the manuscript.

Paper III

This paper presents an accurate description of the influence of the base-emittergeometry on the current gain of 4H-SiC BJTs. Simulations are performed accordingto the physical model presented in paper II. The reduction of the emitter widthcauses an earlier internal forward biasing of the base-collector junction and higherrecombination in the emitter region leading to lower current gain. On the otherhand, placing the base contact close to the emitter edge increases the base current byincreasing the diffusion of the electrons injected from the emitter towards the basecontact. Therefore, the effect of increasing the extrinsic base doping is simulated;

xi

xii Summary of Included Papers

the results suggest that this diffusion can be alleviated; hence, the current gainreduction is avoided.The author has performed all the device simulations and electrical char-acterizations, and has written the manuscript.

Paper IVThis paper presents an accurate description of the on-resistance of 4H-SiC BJTs.Simulated and measured output characteristics are compared at different base cur-rents and different temperatures. The simulations are performed according to thephysical model presented in paper II and III, and they suggest that the surfacerecombination and the material quality play an important role for improving theon-resistance; however, the device design is also crucial. It is shown that it ischallenging to meet the requirement of having a low forward voltage drop, a highcurrent density, and a satisfactory forced current gain. Therefore, based on simu-lations, it is suggested that increasing the extrinsic base doping can contribute tomeet this requirement.The author has performed all the device simulations and electrical char-acterizations, and has written the manuscript.

Paper VThis paper presents an investigation of the current gain degradation in 4H-SiC.Different base-emitter diodes with different emitter widths have been electricallystressed by a fixed current up to 60 hours; during this period, the current gainhas been measured several times. All the devices present current gain degradation.This reduction occurs during the first few hours, and then the current gain becomesstable. The analysis of the recombination in the base region suggests that thedegradation of the carrier lifetime in the base region might be only one of the causesfor this degradation. In fact, the analysis of the ideality factor of the recombinationcurrent in the neutral base region and in the base-emitter depletion region suggeststhat the degradation of the passivation layer might be also involved.The author has planned the experiments, performed the electrical char-acterizations, and, in addition, has written the manuscript.

Paper VIThis paper presents an investigation of the influence of the interface SiC/SiO2 whenthis interface is bombarded with helium ions. The results show that a degradationin the current gain of around 15% is present after high doses of ionizing radiation.This degradation is due to the increase of the base current. Electronic and nuclearstopping simulations and device simulations suggest that the presence of positivecharges, induced in the passivation layer, might cause the degradation of the currentgain.The author has performed all the device simulations, and contributed towriting the manuscript.

List of Symbols and Acronyms

Al Aluminum

BJT Bipolar Junction Transistor

BPD Basal Plane Dislocation

BV Breakdown Voltage

CV Capacitance vs. Voltage

EC Critical Electric Field

EF Fermi Energy

EV Electric Vehicle

F-D Fermi-Dirac

GTO Gate Turn-off Thyristors

HEV Hybrid Electric Vehicle

HVDC High-Voltage Direct-Current

IGBT Insulated Gate Bipolar Transistor

JFET Junction Field-Effect Transistor

JTE Junction Termination Extension

Lp Hole Diffusion Length

MOSFET Metal-Oxide-Semiconductor Field-Effect Transistor

N Nitrogen

RON On-resistance

Runi Unipolar Value

xiii

xiv LIST OF SYMBOLS AND ACRONYMS

SF Stacking Fault

Si Silicon

SiC Silicon Carbide

SIMS Secondary Ion Mass Spectrometry

SiO2 Silicon Dioxide

SRH Shockley-Read-Hall

TED Threading Edge Dislocation

TLM Transfer Length Method

VBE Base-Emitter Voltage

VCB Collector-Base Voltage

VCE Collector-Emitter Voltage

VDROP Voltage Drop

WD Depletion Region

WE Emitter Width

WP Emitter-Base Spacing

β current gain

βFORCED Forced Current Gain

ρc Specific Contact Resistivity

Chapter 1

Introduction

Since the beginning of the industrial revolution, there has been an increasing de-mand of energy to improve the living standards of the population. Unfortunately,these improvements have caused many changes to the environment because mostof the total energy relies on fossil fuel, such as oil, coal and natural gas [1]. Thecombustion of this fossil fuel produces polluting gases, such as CO2, SO2 and CO,that cause global warming. Nowadays the climate change is considered a very im-portant issue, and, generally, energy saving and reduction of the emission of CO2

are considered the challenges for solving this problem.Power electronic systems have a great impact in the daily life because they are

widely used in all the applications that the require conversion of electrical energy.A few examples of this conversion can be (see also Fig. 1.1):

• AC to DC: It is performed by a rectifier, and it is widely used when anelectronic device, such as TV, mobile, computer, is connected to the grid, orin electrical motors.

• DC to AC: It is performed by an inverter, and it finds application in therenewable energy production, such wind and solar, at the high-voltage direct-current (HVDC) converter station, and, in addition, in electric vehicles (EV)and hybrid electric vehicles (HEV).

• DC to DC: It is widely used to maintain constant the output voltage of abattery.

• AC to AC: It converts an AC waveform in another AC waveform with differentvoltage and frequency.

Due to their deep penetration in the society, it can be easily understood thatimproving the efficiency of these power systems is one measure that can contributeto reducing the emission of CO2. In addition, reducing the power losses can havea significant impact on the production of energy from renewable energy.

1

2 CHAPTER 1. INTRODUCTION

101 102 103 104 10510-1

100

101

102

103

104

SiC range

PV and wind turbine

increasing frequencycontrol electronics

electric vehicle

traction

Cur

rent

[A]

Voltage [V]

HVDC

Figure 1.1: Classification of power electronics applications.

Silicon-based power devices have been widely used in power electronic systemssince the 1950s, when the thyristor was introduced, and their technology has beenrapidly improving until the development of the insulated gate bipolar transistor(IGBT) in the 1980s. However, it seems that this technology has reached its limit,and new materials are needed if further improvements are required.

Power devices based on silicon carbide (SiC) have the potential to improvethe energy efficiency due to the suitable properties of this material. Some powerelectronic systems based on SiC have already demonstrated an efficiency of around99% [2, 3, 4]. This means that the wasted energy is largerly reduced; in addition,the problem with removing the heat generated by this wasted energy is largerlyalleviated. Therefore, the size, weigth and cost of these systems can be reducedbecause of the absence or the small size of the cooling systems. This factor isconsidered crucial in applications, such as electric vehicles, in which the size andthe weight is a limiting factor for the overall system.

1.1 Power Device Characteristics

The whole family of power semiconductor devices can be divided in two maingroups: rectifiers and switches. An example of their usage in a power electronicsystem is illustrated in Fig. 1.2 where a schematic of a three-phase inverter is illus-trated. These devices control the flow of power between input (the DC side in theexample) and the output (the AC side); ideally, this operation has to be performedwith no power dissipation. This flow is regulated by switching the devices betweentheir on-state, when they conduct current, and their off-state, when the device isblocking the applied voltage. As can be seen, in order to have no power dissipation,the voltage drop over the devices (VDROP ) and the leakage current through thedevice (ILEAKAGE) - static characteristics - have to be zero during the on-state

1.1. POWER DEVICE CHARACTERISTICS 3

Figure 1.2: Schematic of three-phase inverter. The switches are labeled S, whereasthe diodes D.

and off-state respectively; moreover, the switching between the on and off-state hasto be instantaneous.

An ideal power rectifier provides the static characteristic illustrated in Fig. 1.3a.In other words, it conducts any current with zero voltage drop when it is on, and itsupports any voltage with zero leakage current when it is off. However, an actualrectifier shows a typical characteristic illustrated in Fig. 1.3b. The device exhibitsa non-zero VDROP when it conducts a current ION , and a non-zero ILEAKAGE .

(a) Ideal diode. (b) Actual diode.

Figure 1.3: Comparison between the I-V characteristic of an ideal diode and anactual diode.


(a) Ideal power dissipation. (b) Actual power dissipation.

Figure 1.4: Comparison between ideal and actual power dissipation during thenormal rectifier operation.

Moreover, the device can support only a finite maximum reverse voltage, whichis defined as breakdown voltage (BV). Finally, it has to be mentioned that, inaddition, the actual device shows finite switching times during turn-on and turn-off.These non-ideal components lead to power dissipation during the normal rectifieroperation, as can be seen in Fig. 1.4. In the ideal case, the power dissipationis always zero (see Fig. 1.4a), unlike the actual case where it is present powerdissipation during the off- and on-state, and also a large peak during the transientwhen high voltage and high current are present simultaneously.

(a) Ideal switch. (b) Actual switch.

Figure 1.5: Comparison between the I-V characteristic of an ideal switch and anactual switch.

1.2. DRIFT REGION FOR POWER DEVICES 5

The same considerations can be applied to the switches. An ideal power switchexhibits the static characteristic indicated in Fig. 1.5a. However, an actual switchshows a typical characteristic as in Fig. 1.5b. The switch exhibits a finite resistance(RON ) when it conducts a current ION , thus leading to a finite VDROP ; in the off-state, a non-zero ILEAKAGE is present, and the device can support only a finitebreakdown voltage (BV). The switches can be further divided in two groups: voltagecontrolled devices, such as metal-oxide-field-effect transistors (MOSFET), junctionfield-effect transistors (JFET) and insulated gate bipolar transistors (IGBT), andcurrent controlled devices, such as bipolar junction transistors (BJT) and gateturn-off thyristors (GTO).

The main effort when designing a power device is to obtain characteristics asclose as possible to the ideal case.

1.2 Drift Region for Power Devices

The distinctive characteristic of all the power devices is their blocking voltage capa-bility BV. This capability is determined by the beginning of avalanche breakdownthat occurs when the electric field inside the device approaches the critical electricfield EC . In this case, the carriers, which are generated inside the depletion region,have enough kinetic energy to generate electron-hole pairs when they collide withatoms in the lattice. Since the electron-hole pairs created also participate in thecreation WD of additional carriers, this process is multiplicative and leads to asharp increase of the leakage current during the off-state.

The simplest structure, of which the BV can be analyzed, is a parallel-plane,abrupt pn junction in which the doping concentration of one side is much largerthe other side (see Fig. 1.6).

Figure 1.6: Parallel plane, abrupt pn junction.


In this structure, the WD can be considered to extend only on the lightly-dopedside of the junction. In this situation, the electric field has a triangular shape, andthe BV is reached when the maximum electric field Emax approaches EC (see Fig.1.6). The depletion region under this condition can be expressed as:

WD =2BV

EC, (1.1)

and the doping concentration of the drift region required to obtain this BreakdownVoltage (BV) can be expressed as

ND =ǫsE

2C

2qBV. (1.2)

Combining Eq. 1.1 and Eq. 1.2, the specific RON of the drift layer is

RON,specific =4BV 2

ǫsµnE3C

. (1.3)

The quadratic dependence of the specific RON with the BV indicates that thepower dissipation during the on-state considerably increases when the blocking-voltage capability increases. However, the denominator of Eq. 1.3 suggests that,due to the cubic dependence with the EC , the RON can be largely reduced by usingwide-bandgap semiconductors since they have larger EC compared with Si.

1.3 SiC Material Properties

Among all the wide-bandgap semiconductors, silicon carbide (SiC) is the mostattractive for high-power and high-temperature applications because it has a highbreakdown electric field and a high thermal conductivity. A distinctive property of

0 100 200 300 400 500 600 700 80010-9

10-5

10-1

103

107

1011

1015

4H-SiC

Intri

nsic

Car

rier C

once

ntra

tion

[cm

-3]

Temperature [oC]

Si

Figure 1.7: Comparison of the intrinsic carrier concentration between Si and 4H-SiCas function of temperature

1.3. SIC MATERIAL PROPERTIES 7

102 103 10410-1

100

101

102

103

104

Si

S

peci

fic R

ON [m

cm

2 ]

Breakdown Voltage [V]

4H-SiC

Figure 1.8: Comparison of the RON between Si and 4H-SiC devices as function ofthe designed breakdown voltage

SiC is its polytypism; this compound exists in more than 200 different polytypes.All the polytypes have equal proportion of silicon and carbon atoms, but, since thestacking sequence between the plane differs, the electronic and optical propertiesvary. Among all the polytypes, 4H-SiC has the most suitable properties becauseit has the largest bandgap (3.2 eV) and it shows very small anisotropy in themobility (around 15 % of the maximum). The high bandgap leads to very lowintrinsic carrier concentration (around 10−9cm−3 at room temperature), thus tovery low leakage current even at very high temperature. At around 600C, theintrinsic carrier concentration is only around 1010cm−3, which is still several ordersof magnitude lower than the doping concentration of 1×1015cm−3 that is a typicalvalue for lowly doped regions of power devices (see Fig. 1.7). On the other hand,this limit is reached at already 300 C by silicon.

The large bandgap also leads to a high critical electric field EC of around 2.2× 106 V/cm; therefore, the denominator in Eq. 1.3 can be largely improved, anda much lower RON , around one thousand times lower, for a designed BV, canbe achieved (see Fig. 1.8). Lower RON reduces the power dissipation during theon-state, thus increasing the efficiency of the power system that uses SiC devices.Lower RON also means that, for the same breakdown voltage, no conductivitymodulation is needed; therefore, SiC devices can turn on and off faster reducingthe switching power losses.

In addition to superior electrical characteristics, the thermal conductivity isalso around two times larger than that for Si. This, together with lower powerdissipation during the on-state and during the switching, allows having less stringentrequirements for the cooling systems, thus reducing the size and the weight of theSiC power electronic system.


1.4 Bipolar Junction Transistor

Silicon BJTs have been available for around 40 years and have been chosen inapplications where a high current capability is required. However, these devicespresent very low current gain when they operate at such high current levels dueto conductivity modulation in the collector layer. Therefore, the Si power BJTshave been replaced by IGBTs in high voltage applications. However, the emergenceof SiC as new material for power semiconductor devices has led to consider powerBJTs as a possible candidate for high power and high voltage applications. This isbecause, compared with the other different SiC power semiconductor switches, theSiC BJT has the following benefits:

1. It is a normally off device.

2. It has the potential for a very low specific on-resistance (RON ) due to junctionvoltage cancellation and conductivity modulation.

3. It has a positive temperature coefficient of the RON and a negative one of thecurrent gain. This is very convenient for paralleling of SiC BJTs.

4. It has demonstrated a fast switching speed when it acts as a unipolar device[2, 5, 6].

5. It is free from any gate oxide. Therefore, Silicon Carbide (SiC) Bipolar Junc-tion Transistors (BJTs) are believed to operate at high temperature in areliable way.

However, a few issues, which hinder SiC BJTs to be commercialized, have to becompletely solved. Since it is a current controlled device, the current gain has to

Figure 1.9: Current components during reverse biasing in a base-collector junction.

1.4. BIPOLAR JUNCTION TRANSISTOR 9

be improved to reduce the power required by the drive circuit. In addition, long-term stability can still be problematic, although much progress has been done inthe material quality, and substrates with low BPDs density are now commerciallyavailable. Finally, if the bulk carrier lifetime is improved, conductivity modulationcould be obtained in high blocking-voltage BJTs.

According to the bias condition, different current components flowing inside theSiC BJT are present. As described in section 1.1, power switches operate betweentwo very distinct conditions: off-state and on-state. When the BJT is in its off-state, the base-collector junction is reversed biased, and the current, indicated asJG in Fig. 1.9, is due to the generation of electron-hole pairs. Therefore, thiscomponent mainly depends on the impact ionization coefficients.

On the other hand, when the BJT is in its on-state, the situation becomes morecomplicated by the presence of different components (see Fig. 1.10):

• JpE is the current due to the hole diffusion from the base-emitter depletion re-gion, at the emitter side, towards the emitter contact; it is a component of thebase current. It is dependent on: Schockley-Read-Hall (SRH) recombination;Auger recombination; mobility; incomplete ionization; bandgap narrowing;Fermi-Dirac statistics.

• JrecBE is the current due to the electron-hole recombination in the base-emitter depletion region, and it increases the base current. It depends on theSRH recombination.

• JnB is the current due to the diffusion of the electron injected from emitter to-

Figure 1.10: Current components during forward biasing in a BJT.


wards the depletion region of the base-collector junction. It depends on: SRHrecombination; mobility; incomplete ionization. This is the only componentfor the collector current.

• JSurfRec is the current due to the electron-hole recombination at the inter-face between SiC and the passivation layer. It is dependent on the concentra-tion, capture-cross section, and distribution of the interface traps in the SiCbandgap. It is an additional component for the base current.

• Jn,Diff is the current due to the electrons that, injected from the emitter,diffuse towards the base contact instead of the base-collector depletion region.It depends on: SRH recombination; mobility; incomplete ionization. Thisbecomes a significant additional component for the base current when thebase contact is placed very close to the emitter edge.

• JpC is the current due the holes injected into the collector region when thebase collector junction is forward biased. It depends on: SRH recombinationand mobility. It is a significant component of the base current when the BJToperates in quasi-saturation or saturation region.

• JnB,extrinsic is the current due to the electrons injected from the collector intothe base when the base-collector junction is forward biased. This componentis present only in the extrinsic base region. This is because, when this junctionis forward biased, the carrier concentration in this region has a distributionsimilar to that in a diode due to the presence of the base contact. This com-ponent depends on SRH recombination, mobility and incomplete ionization;it is significant when the BJT operates in the quasi-saturation region and athigh current density.

1.5 Thesis Objective and Structure

The objective of this thesis is to develop an accurate model for the simulations ofSiC BJTs. A proper model can help to investigate the limiting factors for improv-ing current gain, on-resistance and breakdown voltage; in addition, it can help toinvestigate the long-term stability. As suggested in section 1.4, modeling a SiCBJT connotes the prediction of all the different current components inside the de-vice. However, there are uncertainties in the parameters of several physical models,especially in the highly-doped emitter. Therefore, a crucial point to validate thephysical model is to compare the simulations and the measurements. In this thesis,this comparison is performed on test structures and on BJTs with different geome-tries. In addition, the simulations and measurements are compared at differenttemperatures.

This thesis is organized in five chapters. In chapter two, an overview of all thephysical models involved in the simulations are presented. Initially, the impact ion-

1.5. THESIS OBJECTIVE AND STRUCTURE 11

ization model, which is used for breakdown voltage simulations, is presented. Addi-tionally, the models used for simulations of forward characteristics are introduced.These models are: Fermi-Dirac statistics, incomplete ionization, mobility, SRH,Auger and surface recombination, and bandgap narrowing. Finally, the limitationsof incomplete ionization and mobility model, as seen from TLM measurements, arepresented.

In chapter three, the results from the simulations, in particular the breakdownvoltage, the current gain and the on-resistance, are compared with the measure-ments. A detailed analysis of the temperature and geometry influence on the devicecharacteristics is presented. In good agreement with the measurements, the limitingfactor for improving the BJT characteristics are highlighted; consequently, modifi-cations in the BJT design are proposed. In addition, a brief comparison betweenmeasured and simulated switching waveforms is presented. Finally, the degradationof BJT, due to both electrical stress and ionizing radiation, is analyzed.

In chapter four, some considerations about designing a high-voltage SiC diodeare summarized. The design mainly consists of the JTE termination to achieve 10kV, and anode layer to obtain very low forward voltage drop.

In chapter five, conclusions are drawn; moreover, few considerations about fu-ture work are presented.

Chapter 2

Physical Models

Simulation of SiC BJTs consists of solving the partial differential equations thatdescribe the transport of carriers under the influence of external fields. Theseequations are:

−∇ · ǫsE = ∇ · ǫs∇ψ =

= −q(n− p+ND −NA)− ρtrap , (2.1)

Jn = qµnnE + qDn∇n , (2.2)

Jp = qµppE − qDp∇p , (2.3)

∂n

∂t=

1

q∇ · Jn +G−R , (2.4)

∂p

∂t= −1

q∇ · Jp −G+R . (2.5)

In Eq. 2.1, which is the Poisson equation, ǫs is the dielectric constant of thesemiconductor, E is the electric field, ND and NA are ionized donor and acceptorconcentration respectively (section 2.3), n and p are the electron and hole concen-trations, ρtrap includes the charge density contributed by traps and fixed charges(section 2.7), and, finally, ψ is the electrostatic potential. This equation relates thetotal space-charge to the electrostatic potential.

Eq. 2.2 and Eq. 2.3 are the current equations for electrons and holes, respec-tively, according to the the drift-diffusion model. The first term on the right handside represents the drift component, whereas the second term is the diffusion com-ponent. Both the terms are strongly related to the electron (µn) and hole (µp)mobility (section 2.4).

The last two equations, Eq. 2.4 and Eq. 2.5, are the continuity equationsfor electrons and holes respectively. The term G describes generation phenomena,such as the carriers generated by impact ionization (section 2.1), whereas R in-cludes recombination phenomena, such as the Schockley-Read-Hall (SRH), Augerand surface recombination (from section 2.5 to section 2.7). In time-invariant simu-

13

14 CHAPTER 2. PHYSICAL MODELS

lations, the term on the left hand side is equal to zero. In order to have accurate andrealistic simulations, it is crucial to include the appropriate models with the properparameters. In addition, boundary conditions have to be set properly. If ohmiccontacts are used, the recombination velocity is assumed to be infinite; therefore,the boundary conditions at the contacts become:

n = n0 for p type semiconductor , (2.6)

p = p0 for n type semiconductor , (2.7)

ψ = Vapplied + ψ0 , (2.8)

with ψ0 the potential at zero bias.

2.1 Impact Ionization

The ability of power devices to sustain high voltage when they are reverse biasedis established by the beginning of avalanche breakdown in the device.

The avalanche breakdown happens when multiplication factors due to impactionization approach infinity. In this situation, the current, which is due to theelectron-hole that are generate by the impact ionization process, increases sharplyand the device cannot sustain any increment in the applied voltage. The generationrate is expressed according to:

Gii = αenvn + αppvp (2.9)

In Eq. 2.9, αe and αp are the impact ionization coefficients for electrons and holesrespectively, n and p are carrier concentrations, and vn and vp are the electron andhole velocities. The very low intrinsic carrier concentration of SiC leads to numericalinstability when the avalanche breakdown is simulated. Therefore, in this thesis,an elevated temperature of 1000 K is set; however, this prohibits simulating theactual current, and only an estimation of the BV is possible. It is worth to noticethat other methods can be used to increase the intrinsic carrier concentration; anexample can be optical generation.

The impact ionization coefficients are modeled by the van Overstraeten-de ManModel, which is based on the Chynoweth law [7]:

αe = ae exp(−be/E) , (2.10)

αh = ah exp(−bh/E) , (2.11)

where ae, ah, be and bh are fitting parameters, and E is the magnitude of theelectric field.

One of the first work to report measurements of the impact ionization coefficientsis by Konstantinov et. al. in 1997 [8, 9]. In this work, the coefficients were measuredby using the photo-multiplication technique on pn diodes fabricated on a p+-n-n+

and protected by a positive angle bevel. Due to this termination, the avalanche

2.1. IMPACT IONIZATION 15

breakdown is controlled by bulk material properties rather than edge effects. Thecoefficients extrapoled are ah = 1.63 × 107cm−1 and bh = 1.67 × 107V/cm, anda ratio αh/αe = 40. This high ratio indicates that the multiplication process isinitiated by the holes.

Due to the edge termination structure, the measured values represent the impactionization along the < 0001 > direction (‖ c axis), and they are widely used todetermine the ideal breakdown of pn junction. However, it has been reported thatthe impact ionization in 4H-SiC has an anisotropic behavior, and this phenomenonis more more pronounced along the < 1120 > direction (⊥ c axis) [10, 11, 12]. Theionization coefficients reported in [12] are summarized in 2.1.

Table 2.1: Fitting parameters for the electron- and hole-impact ionization coeffi-cients of 4H-SiC reported in [12]

Parameter < 0001 > < 1120 >

ae [cm−1] 1.76× 108 2.10× 108

be [V/cm] 3.30× 107 1.70× 107

ah [cm−1] 3.41× 108 2.96× 107

bh [V/cm] 2.50× 107 1.60× 107

The comparison between the coefficients extrapolated from [8] and [12] is illus-trated in 2.1. It is possible to see that the coefficients for the < 1120 > directionare larger than those for < 0001 > direction; in addition, the difference betweenelectron and hole coefficients is smaller. In section 3.1, the results from these twomodels are compared with BV measured on PiN diodes.

The temperature behavior of the impact ionization coefficient has been studied

2.6 2.8 3.0 3.2 3.4102

103

104

105

106

Electron

Impa

ct Io

niza

tion

Coe

ffici

ent [

cm-1]

Electric Field [x106 V/cm]

Hole

(a) Konstantinov et al.

2.6 2.8 3.0 3.2 3.4102

103

104

105

106

<0001>

Impa

ct Io

niza

tion

Coe

ffici

ent [

cm-1]

Electric Field [x 106 V/cm]

Hole

Electron

<1120>

(b) Hatakeyama et al.

Figure 2.1: Comparison between impact ionization coefficients extrapolated (a)from [8] and (b) from [12].


in [13, 14, 15, 16], and a positive temperature dependence has been reported. Thisis a suitable characteristic for power devices.

Several studies, using Monte Carlo simulations, have investigated the mecha-nisms involved in the electron-hole generation process during the avalanche break-down [17, 18, 19, 20]. In these studies, it has been reported that, due to thecomplicated band structure of 4H-SiC, band-to-band tunneling has to be consid-ered at high electric fields. When this mechanism is included in the Monte Carlosimulation, an accurate estimation for the impact ionization coefficients is obtained.

2.2 Fermi-Dirac Statistics

The Fermi-Dirac (F-D)distribution function represents the probability that an elec-tron has to occupy an electronic state with energy E,

F (E) =1

1 + eE−EF

kT

, (2.12)

and, together with the density of states N(E), gives the electron density in anintrinsic semiconductor, as shown in Eq. 2.13; the electron density in the conductionband is obtained by integrating from the bottom of the conduction band (set equalto zero) to the top of the conduction band Etop.

n =

∫ Etop

0

n(E)dE =

∫ Etop

0

N(E)F (E)dE . (2.13)

In equation 2.12, k is the Boltzmann constant, T is the temperature in degreesKelvin, and EF is the Fermi level.

If the Fermi level is at least 3kT below the conduction band or above the valenceband, then Eq. 2.12 can be simplified as (Boltzmann statistics):

F (E) ∼= e(E−EF )/kT for the conduction band, and (2.14)

F (E) ∼= 1− e(E−EF )/kT for the valence band. (2.15)

SiC BJTs have a very highly-doped emitter layer, usually in the range of 1019;therefore, the Fermi level is very close to conduction, i.e., (EC−EF ) < 3kT . In thiscase, the Fermi-Dirac statistics should be considered in order to have a physically-correct result for the electron concentration in the conduction band. Fig. 2.2illustrates the error obtained if the Boltzmann statistics is used when (E − EF )is less than 3kT . As can be seen, F-D statistics gives a probability of 0.5 when(E − EF ) = 0, as by definition of Fermi energy. In contrast, for this energy, theBoltzmann leads to an inexact probability of one. However, this error becomesinsignificant when (E − EF ) > 3kT .

2.3. INCOMPLETE IONIZATION 17

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.0

0.2

0.4

0.6

0.8

1.0

F(

E)

(E-EF)/kT

Fermi-Dirac Boltzmann

Figure 2.2: Comparison between the Fermi-Dirac distribution function and theFermi-Dirac distribution function for the Boltzmann case.

When the F-D statistics is included in simulations, the carrier concentrationsare derived according to Eq. 2.16 and Eq. 2.17.

n = γnNCexp(EF,n − EC

kT) (2.16)

p = γpNV exp(EV − EF,p

kT) (2.17)

The coefficient γn and γp are function of ηn and ηp respectively:

γn =n

NCexp(−ηn) (2.18)

γp =n

NVexp(−ηp) (2.19)

ηn =EF,n − EC

kT(2.20)

ηp =EV − EF,p

kT(2.21)

In paper II, F-D statistics is included in the BJT simulations to properly modelthe carrier concentration in the highly-doped emitter.

2.3 Incomplete Ionization

Unlike silicon physics, in which most of the dopants can be considered fully ionizedat room temperature, this assumption is not valid for SiC because both nitrogen (N)and aluminum (Al) present an ionization energy relatively larger than the thermalenergy kT . For example, N has an ionization energy of 65 meV, whereas Al has210 meV. These two parameters strongly affect the simulations of current gain forSiC BJTs because they affect the emitter efficiency.


The concentration of the ionized impurities can be modeled in terms of thecarrier concentration as shown in Eq. 2.22 and Eq. 2.23.

ND =ND,0

1 + gDnn1

, (2.22)

NA =NA,0

1 + gApp1

, (2.23)

where ND,0 and NA,0 are the active donor and acceptor concentrations, gD and gAare the degeneracy factors for the impurities, and, n1 and p1 are defined as:

n1 = γnNC exp

(−∆ED

kT

)

, (2.24)

p1 = γpNV exp

(−∆EA

kT

)

. (2.25)

The degeneracy factor for Al (acceptor dopant) is assumed to be 4, whereas theone for N (donor dopant) is equal to 2. The parameters γn and γp are defined inEq. 2.18 and 2.19, and include the F-D statistics, whereas ∆ED and ∆EA are theionization energies for donor and acceptor impurities respectively.

The reduction of the ionization energy has been reported in several studies[21, 22, 23]; in addition, a theoretical description of the several mechanisms forthis reduction has been presented in [24]. In a simplified model, the reduction ofthe average distance between the impurities caused by the increase of the dopingconcentration induces the reduction of the ionization energy. This reduction ismodeled according to:

∆ED = ∆ED,0 − αDN1/3tot , (2.26)

∆EA = ∆EA,0 − αAN1/3tot , (2.27)

where αD = αA = 3.1 × 10−5 meV cm.

It is worth to notice that the assumption of a a single level, 65 meV below theconduction band, for nitrogen is a simplification. In fact, in 4H-SiC, nitrogen cansit in two different C-lattice sites, namely hexagonal (h) or cubic (k). In [25], ithas been reported that N has an ionization energy of 52.1 meV when it sit in theh site, and an energy of 91.8 meV when in the k site.

In paper II, it is suggested that common assumption of complete ionization of thehighly-doped emitter might be weak since the carrier concentration extrapolatedfrom TLM measurements show a positive temperature dependence. In addition,this assumption is discussed in section 2.9 where the incomplete ionization model,coupled with the mobility model, simulates the emitter sheet resistance, and theresults are compared with measurements.

2.4. MOBILITY 19

2.4 Mobility

The electron and hole mobility in SiC can be modeled according to the Arora model[26], as shown in Eq. 2.28 and Eq. 2.29, respectively.

µn =µmax,n ×

(

T300K

)αn

1 +(

ND

Nref,n

)γn=

950×(

T300K

)−2.15

1 +(

ND

1.94×1017

)0.61 , (2.28)

µp =µmax,p ×

(

T300K

)αp

1 +(

NA

Nref,p

)γp=

108.1×(

T300K

)−2.15

1 +(

NA

1.76×1019

)0.34 . (2.29)

The parameters for the doping dependence (Nref,n,p and γn,p) and for the tem-perature dependence (αn,p) are from [27]. The parameter Nref represents the dop-ing concentration at which the contributions to the mobility of lattice scatteringand impurity scattering are equivalent. It is also worth to notice that the tem-perature coefficient αn,p = 2.15 is larger than the ideal coefficient of 1.5 that istheoretically related to lattice scattering. This is dependence is believed to be dueto non-polar optical-phonon scattering.

Due to the incomplete ionization of nitrogen (N), the parameter ND in Eq. 2.28is the ionized donor concentration. However, in this thesis, this assumption is notconsidered for the p doped base. The hole mobility in 4H-SiC has been investigatedin [28]. In this study, it has been concluded that the mobility is mainly affectedby the neutral impurity, and not by the ionized impurities. Since the ionizationenergy of aluminum (Al) in 4H-SiC is very high (210 meV), it can be assumedthat the neutral impurity concentration is equal to the doping concentration. Thisassumption, coupled with ionization energy of 210 meV, is validated comparing the

1015 1016 1017 1018 1019 10200

200

400

600

800

1000

600 oC

300 oC

100 oC

Ele

ctro

n M

obili

ty [c

m2 /V

s]

Ionized Donor / Acceptor Concentration [cm-3]

27 oC

(a) Electron.

1015 1016 1017 1018 1019 10200

20

40

60

80

100

Hol

e M

obili

ty [c

m2 /V

s]

Ionized Donor / Acceptor Concentration [cm-3]

300 oC

100 oC

27 oC

600 oC

(b) Hole.

Figure 2.3: Electron and hole mobility at different temperatures as from (a) Eq.2.28 and (b) Eq. 2.29.


simulated and measured base sheet resistance in the base epilayer. The results areillustrated in section 2.9. In addition, in paper III, this assumption demonstratesa good agreement between the simulated and measured current gain as function ofbase-emitter geometry. In particular, the simulated base sheet resistance properlymodels the base-emitter de-biasing; moreover, the lateral electron diffusion towardsthe base contact is properly predicted.

2.5 SRH Recombination

Indirect recombination is the dominant recombination process in indirect-bandgapsemiconductors, such as silicon and silicon carbide. This process occurs via local-ized energy states in the bandgap, and it is labeled Schockley-Read-Hall (SRH)recombination. This process is crucial in the device physics of bipolar devices. TheSRH recombination rate, when the F-D statistics is considered, can be expressedas:

RSRH =np− γnγpn

2i,eff

τp(n+ γnn1) + τn(p+ γpp1)(2.30)

with: n1 = ni,effexp

(

Etrap

kT

)

(2.31)

and: p1 = ni,effexp

(−Etrap

kT

)

(2.32)

The parameter Etrap is the difference between the defect level and the intrinsiclevel energy, and it is set equal to zero. The parameters γn and γp are definedin Eq. 2.18 and 2.19, respectively. Since Etrap = 0, the recombination process isindependent from the energy levels, concentrations and capture-cross sections of thedefects, and then the minority carrier lifetimes τn and τp become fitting parameters.However, in this thesis, the minority carrier lifetime is modeled according to theScharfetter relation (see Eq. 2.33) for the doping dependence, and according to apower law (see Eq. 2.34) for the temperature dependence.

τdop,n,p =τmax,n,p

1 +(

ND,A

Nref

)γn,p=

=τmax,n,p

1 +(

ND,A

3×1017

)0.3 . (2.33)

τn,p = τdop,n,p

(

T

300K

)α

=

= τdop,n,p

(

T

300K

)1.72

(2.34)

The positive temperature coefficient for the temperature dependence is reportedin [29, 30], whereas the doping dependence is reported in [31, 29]. Due to the lack of

2.6. AUGER RECOMBINATION 21

studies on the parameters for the Scharfetter relation in SiC, the parameters Nref

and γn,p are taken from Si.The effects of the SRH recombination on the BJT current gain have been inves-

tigated in papers II and paper IV. In paper II, it is investigated the effect on themaximum current gain; as expected, longer lifetime decreases the recombinationand, in turn, increases the maximum current gain. In paper IV, it is suggested thatthe forced current gain, which is defined as the current gain when the BJT operatesin the quasi-saturation region, is improved by longer carrrier lifetime.

Although silicon carbide has an indirect band structure, it still suffers from lowbulk carrier lifetime. It is reported that the recombination centers Z1/2 [32] andEH6/7 [33], which are respectively located at 0.65 eV and 1.55 eV below the con-duction band edge, can strongly affect the carrier lifetime [34, 35]. In fact, in [34],it demonstrated that the carrier lifetime is inversely proportional to the concentra-tion of the Z1/2 centers. However, both the Z1/2 and EH6/7 concentrations can bereduced by increasing the C/Si ratio during the epitaxial growth [36]. Therefore,the relation between these centers and carbon vacancies is suggested. This is alsoconfirmed by studies on controlling the lifetime with electron-irradiation [37, 38].Consequently, it has been proposed that the bulk carrier lifetime can significantlyenhanced by either C+ implantation and subsequent annealing [39], or by thermaloxidation [40, 41].

2.6 Auger Recombination

The Auger recombination is a process that involves three particles, and it is animportant process when the carrier concentration is very high. This high con-centration can be due to either very high doping concentration or high injectioncondition. In SiC BJT, the Auger recombination is important to properly modelthe recombination rate in the emitter region. The Auger recombination can bemodeled according to Eq. 2.35.

RAuger = (An n+Ap p)× (n p− n2ieff ) , (2.35)

where An is 5× 10−31cm−6s−1 and Ap is 2× 10−31cm−6s−1 [42].

2.7 Surface Recombination

Surface recombination can be modeled in two different ways:

• By specifying the surface recombination velocity parameter at the SiC/SiO2

interface (see Eq. 2.36), and then in a way similar to Shockley-Read-Hall(SRH) recombination.

• By specifying the trap distribution in the SiC bandgap at the SiC/SiO22interface.


Although the final result is similar because the surface SRH model depends onthe traps implicitly, the second method actually models the traps and consider theoccupation and the space charge stored (see ρtrap in Eq. 2.1).

If the first method is chosen, the following expression is implemented at theinterface:

RSRHsurf =

np− n2i,eff(n+ n1)/sn + (p+ p1)/sp

(2.36)

where sn,p represents the surface recombination velocity, which depends on the trapsimplicitly.

If the second method is chosen, the following trap types can be implemented:

• Fixed charge, which are always completely occupied.

• Acceptor, which are negatively charged when occupied and neutral when un-occupied.

• Donor, which are positively charged when occupied and neutral when unoc-cupied.

In addition, the trap distribution and concentration, and its capture-cross sec-tion can be defined.

In this thesis, the second method is chosen. In paper II, the influence of dif-ferent trap distributions, concentrations and capture-cross sections are investigatedcomparing the simulations of current gain as function of collector current withmeasurements.

For a trap concentration Nt energetically localized at Etrap, the recombinationrate can be expressed as:

Rnet =Ntv

nthv

pthσnσp

(

np− n2i,eff

)

vnthσn (n+ n1/gn) + vpthσp (p+ p1/gp)(2.37)

In Eq. 2.37, vn,pth are the thermal velocities, σn,p are the capture-cross sections,n1 and p1 are defined in Eq. 2.31 and Eq. 2.32, and gn,p are the degeneracy factorsthat are usually equal to one.

Surface recombination is strongly dependent on the surface passivation processcondition. The oxidation process consists of in-diffusion of oxygen atoms and out-diffusion of carbon (C) atoms as CO and CO2 [43]. However, residuals of C atoms atthe interface can degrade the interface between SiC and SiO2 [44, 45]. On the otherhand, it has been reported that incorporation of nitrogen (N) can passivate thesedefects improving the SiC/SiO2 interface. Several methods have been proposed toincorporate N at the interface, such as implanting N prior the oxidation [46, 47], orperforming the post-oxidation annealing in N or N2O ambient [48, 49, 50, 51, 52, 53].In addition, it has been suggested that post-oxidation annealing in POCl3 can alsoimprove the SiC/SiO2 interface [54, 55].

2.8. BANDGAP NARROWING 23

2.8 Bandgap Narrowing

In silicon, it has been reported that, at a high doping level, the band structure ofsemiconductor is altered by three different phenomena [56, 57, 58, 59]:

• The formation of an impurity band when neighboring Bohr orbitals overlap;

• The tailing of the edge of the conduction and valence bands due to the sta-tistical variation of the local doping concentration;

• The interactions among electrons, holes, and ionized impurities that alter theband structure from that in intrinsic and lowly doped material.

The overall effect of these phenomena is what has become to be called apparentbandgap narrowing, or simply bandgap narrowing. This effect is significant in BJTsbecause of the presence of the heavily doped emitter. The result is that the pnproduct in this region has to modified [60]:

pe0ne0 = n2i0exp∆Ege

KT(2.38)

where ∆Ege = Eg0−Ege is the apparent bandgap narrowing, and n2i0 is the intrinsiccarrier concentration for a lightly doped semiconductor.

The apparent bandgap narrowing can also be described by an effective dopingconcentration in the emitter Ndeff , as suggested in Eq. 2.39. It is clear thatthe bandgap narrowing reduces the effective doping concentration in the emitter;consequently the emitter efficiency decreases [60].

Ndeff = Ndeexp− ∆Ege

KT(2.39)

In SiC, the band edge displacement and the bandgap narrowing have been mod-eled by Lindefelt [61]. In this study, the bandgap considered is the gap betweenthe bottom of the conduction band and the top of the valence band; this gap isrelevant to determine the intrinsic carrier concentration and appears in the currentequations Eq. 2.2 and Eq. 2.3. The interactions included, in the case of n-typedopants, are between:

• A conduction band electron and the gas of conduction band electrons intro-duced by the doping;

• A conduction band electron and the ionized donor ions;

• A hole (minority carrier) with the gas of conduction band electrons;

• A hole and the ionized donors.


The first two interactions affect the conduction band edge, whereas the latter twoshift the valence band edge. The hole-hole interaction is neglected because of theirlow concentration in highly n-doped semiconductors. The total band edge displace-ment can be expressed according to Eq. 2.40 and Eq. 2.41 [61].

∆Ec = Anc

(

N+D

1018

)1/3

+Bnc

(

N+D

1018

)1/2

=

= −1.50× 10−2

(

N+D

1018

)1/3

+−2.93× 10−3

(

N+D

1018

)1/2

, (2.40)

∆Ec = Anv

(

N+D

1018

)1/4

+Bnv

(

N+D

1018

)1/2

=

= −1.90× 10−2

(

N+D

1018

)1/3

+−8.74× 10−3

(

N+D

1018

)1/2

. (2.41)

2.9 Limitations of Physical Models

The main concern about physical models for SiC is related to the highly-dopedemitter. Although the doping concentration is high enough that the Fermi levellies at an energy smaller than 3kT below the conduction band (see Fig. 2.4),and hence the dopants should be considered completely ionized, this is not seenfrom the sheet resistance extrapolated from TLM measurements, as demonstratedin Fig. 2.5. Since the sheet resistance shows a rather constant behavior for awide temperature range, it can be deduced that the ionization of the dopants andthe reduction of the mobility oppose each other. However, simulations show a

0.4 0.8 3.0 3.1 3.21015

1016

1017

1018

1019

3kT

EF

Ev Ec

n

Car

rier C

once

ntra

tion

[cm

-3]

Fermi Energy [eV]

p + ND+

Figure 2.4: Graphical method to determine the Fermi energy level. The doping con-centration is 1 × 1019 cm−3, the ionization energy is 65 meV, and the temperatureis 300 K (After Shockley [62].)

2.9. LIMITATIONS OF PHYSICAL MODELS 25

20 40 60 80 100 120 140 160 180 20040

60

80

100

120

140

160

Measurement Simulation

E

mitt

er S

heet

Res

ista

nce

[/s

q]

Temperature [oC]

Figure 2.5: Comparison between simulated and measured sheet resistance as func-tion of the temperature in the emitter region.

monotonous trend for the sheet resistance suggesting that the reduction of themobility is predominant over the incomplete ionization model. As consequence ofthis disagreement, the incomplete ionization model might be questionable since itneglects to consider the Mott transition.

Recent works have shown that this transition is also crucial when modeling theincomplete ionization in silicon [63, 64]. This is because, around this transition, thecommon assumption of completely ionized dopants is weak; in [63], it is shown thataround the Mott transition only around 75% of the dopants are ionized, and thatthe complete ionization is obtained only at a considerably higher dopant density.

The uncertainty about the incomplete ionization model leads to uncertaintyabout the bandgap narrowing, since it depends on the ionized donors; consequently,the pn product in the emitter might be inaccurate.

A better agreement is obtained in the base region, as illustrated in Fig. 2.6.

20 40 60 80 100 120 140 160 180 20020

25

30

35

40 Simulation Measurement

Bas

e S

heet

Res

ista

nce

[k/s

q]

Temperature [oC]

Figure 2.6: Comparison between the simulated and measured sheet resistance asfunction of temperature in the base region.


The negative temperature dependence of the mobility and the incomplete ionizationmodel properly predict the reduction of the sheet resistance with temperature.However, it is worth to notice that, due the limited temperature range investigated,and the availability of only one doping for the base region, these two models mightbe weak at higher temperature or with higher doping concentration.

Chapter 3

Simulation and Characterization of

SiC BJTs

In this chapter, simulations and measurements of SiC BJTs are compared. Adetailed investigation of the three main aspects, i.e., breakdown voltage (BV), cur-rent gain (β) and on-resistance (RON ) is presented. In addition, a brief overviewof switching waveforms is shown. Finally, an investigation of long-term stability ispresented.

3.1 Breakdown Characteristic

In order to exploit the low specific on-resistance of SiC devices, an efficient junctiontermination extension (JTE) has to be designed to obtain a BV close to ideal.The ideal value is provided by the analysis of a parallel-plane diode (section 1.2);however, in an actual device, the BV is strongly reduced by the presence of electricfield crowding at the edges of the device. Therefore, edge terminations are requiredto alleviate this crowding.

The two main termination techniques in SiC technology are implanted andetched JTE [65, 66, 67, 68]. In both methods, the key step is to achieve an ac-curate dose in the JTE region so this region becomes completely depleted at theBV, and then acts as a high resistive layer reducing the electric field at the outeredge.

In paper I, an etched JTE has been chosen to achieve an efficient termination.This study has been performed on SiC PiN diodes due to their fabrication simplicity.The cross-sectional view of the fabricated devices is illustrated in Fig. 3.1. Thesediodes have been fabricated on a 3-in 8o off-axis 4H-SiC substrate. The drift layeris 29 µm thick and has a nitrogen concentration of 2.2 × 1015 cm−3, whereas theanode layer is 2.1 µm thick and has an aluminum concentration of 5 × 1017 cm−3.However, when etched JTE is chosen as termination technology, it is very importantto determine the Al profile in the anode layer by means of SIMS. The insert in Fig.

27

28 CHAPTER 3. SIMULATION AND CHARACTERIZATION OF SIC BJTS

Figure 3.1: Cross-sectional view of the fabricated device. (Insert) Aluminum profileas measured with SIMS.

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.21.0

1.5

2.0

2.5

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3.5

4.0

4.5

5.0

Bre

akdo

wn

Vol

tage

[ x

106 V

]

Dose [cm-2]

Measurement Konstantinov Hatakeyama

upper bound

Figure 3.2: Comparison between simulated and measured breakdown voltage asfunction of the JTE dose.

3.1 indicates that this profile is not constant, but shows a significant concentrationreduction towards the drift layer.

The simulated and measured BV are summarized and compared in Fig. 3.2.It can be seen that, when a single JTE is implemented, there is an optimum doseof around 1.2 × 1013 cm−2 with which it is possible to reach a breakdown voltageof around 4 kV; this optimum dose is also confirmed by simulation when isotropiccoefficients by Konstantinov et al. [8] are chosen. However, when anisotropiccoefficients are selected [12], the optimum dose is around 0.9 × 1013 cm−2, and asignificant reduction is present at higher doses.

3.1. BREAKDOWN CHARACTERISTIC 29

1.20 1.25 1.30 1.35 1.40 1.45 1.501.5

2.0

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Bre

akdo

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Vol

tage

[ x

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]

Dose [cm-2]

Measurement (S-JTE) Konstantinov (S-JTE) Hatakeyama (S-JTE) Measurement (D-JTE) Konstantinov (D-JTE) Hatakeyama (D-JTE)

upper bound

0.9

Figure 3.3: Comparison between simulated end measured breakdown voltage asfunction of the JTE1 dose. The symbols connected with lines indicate the resultsfrom Fig. 3.2, whereas the symbols at 1.5 × 1013 cm−2 are for the two-zone JTE.

However, both the simulations and measurements indicate that the range aroundthe optimum dose is considerably narrow and the BV suffers of a large reduction ifthe dose is either lower or higher. To alleviate this limitation, a double JTE can beimplemented; in fact, the simulated and measured results demonstrate that a widerrange is obtained (see Fig. 3.3), and a breakdown voltage of 4.3 kV is achievedwhen the dose in the JTE1 is around 1.5 × 1013 cm−2, and the dose in JTE2 is 1× 1013 cm−2 (half-filled square in Fig. 3.3). This represents a large improvementcompared with the value of around 2.5 kV obtained with a single JTE. Moreover,the measurements suggest that the breakdown voltage is less sensitive to JTE2dose variations (not shown in Fig. 3.3). In simulations, three different JTE2 doseshave been chosen, that is, 0.9, 1 and 1.1 × 1013 cm−2. The isotropic coefficientssimulate values close to 4.3 kV for the three JTE2 dose (half-filled circles in Fig.3.3), whereas anisotropic coefficients show significant variations with JTE2 dosevariations, and only the JTE2 dose of 0.9 × 1013 cm−2 gives a value close to themeasured one (half-filled triangles in Fig. 3.3).

From the simulations, it can be concluded that the isotropic simulations givea good agreement with the measurements; therefore, they could be chosen whendesigning JTE terminations. On the other hand, the anisotropic simulations are indisagreement with the measurements in the high-dose range; therefore, more inves-tigation investigation is needed. As a matter of fact, the measurements demonstratethat, due to the wider range, a double JTE may be less sensitive to process varia-tions. It is also worth to notice that the implementation of a double JTE does notincrease the total length of the JTE region since, in this study, the total length hasbeen maintained constant.

The analysis of the electric field distribution for different doses is summarized


(a) Single JTE (Low dose.) (b) Single JTE (High dose.)

(c) Single JTE.

Figure 3.4: (b) and (a) Optical luminescence images at the breakdown for doses of5 × 1012 and 2.2 × 1013 cm−2, respectively. (c) Electric field distribution for thesingle JTE at the breakdown. The high, optimum and low doses are 2.2, 1.2 and0.5 × 1013 cm−2, respectively.

in Fig. 3.4 where the optical luminescence images at the breakdown and the elec-tric field distribution extrapolated from the simulations are compared. Fig. 3.4aindicates that, when the JTE dose is higher than the optimum value, the peakof the electric field is located at the outer edge of the JTE, as confirmed by theelectric field distribution in Fig. 3.4c. In contrast, when the JTE dose is lowerthan the optimum value, this peak is located at the inner edge, as indicated in Fig.3.4b and confirmed in Fig. 3.4c. It is worth to notice that the luminescence islocated at one single spot suggesting that the breakdown is initiated by a surfaceimperfection. Therefore, it is important that the maximum of the electric field isdistributed inside the device. This is shown in Fig. 3.4c where it can be seen that,when the JTE is close to the optimum, the electric field presents a more uniformdistribution along the JTE length; therefore, no bright spot can be detected at theedges.

3.2. CURRENT GAIN 31

Figure 3.5: Comparison of the electric field distribution between single and doubleJTE at 2.4 kV. For the single JTE, the dose is 1.5 × 1013 cm−2, whereas, for thedouble JTE, the JTE1 dose is 1.5 × 1013 cm−2, while the JTE2 dose is 1 × 1013

cm−2.

Fig. 3.5 shows that it is possible to avoid the large peak observed with the singleJTE adding the second JTE2. The electric field distribution has been extrapolatedat a dose of 1.5 × 1013 cm−2. This confirms that the additional JTE2 reduces theelectric field at the outer edge, and then higher breakdown can be obtained.

It is worth to mention that, as already suggested by the optical luminescenceimages, material quality is crucial to obtain high breakdown voltage. Studies onpn and Schottky diodes have reported that defects introduced during the epitaxialgrowth can affect the BV. These defects can be carrots [69, 70], polytype inclusion[69] or pits [71].

In this section, simulations and measurements demonstrate that a two-zoneetched JTE can be an efficient termination to avoid the electric field crowding; infact, a BV of 4.3 kV, which is close to the ideal value of 4.5 kV, can be obtained. TheJTE design has a dose of around 1.5 × 1013 cm−2 in the JTE1, whereas the dosein JTE2 is 1 × 1013 cm−2. Moreover, the simulations with the impact ionizationcoefficients extrapolated by Konstantinov et al. [8] demonstrate a good agreementwith the measured BV.

3.2 Current Gain

Since the BJT is a current-controlled device, it is crucial to have high currentgain in order to reduce the power required by the drive circuit. Several studieshave concentrated on increasing the current gain β of SiC BJTs by optimizingthe emitter-base geometry [72], by improving the epitaxial growth [72, 73], and byimproving the surface passivation layer [74, 75, 76]. Moreover, a new 4H-SiC BJTwith suppressed surface recombination structure has been proposed [77].


Figure 3.6: Cross-sectional view of the fabricated device

A cross sectional view of the fabricated BJTs, which have been characterizedand modeled, is provided in Fig. 3.6. The devices are grown on a 2-in 8 off-axis 4H-SiC substrate. A complete description of the fabrication process has beenpresented in [78]. The emitter consist of a N+ epilayer 1.33 µm thick with a dopingconcentration of 1 × 1019 cm−3 and a capping layer of 200 nm doped to 4 × 1019

cm−3 to obtain a very low specific contact resistivity (ρc). The base epilayer is730 nm with a linearly graded aluminum (Al) doping with a peak concentration of3.5 × 1017 cm−3 at the emitter interface. In simulations, the base doping profilehas been approximated with a concentration of 3 × 1017 cm−3, but maintainingthe same Gummel number. The drift N- epilayer was designed 20 µm thick witha doping concentration of 3 × 1015 cm−3. However, C-V measurements on thebase-collector diode of large area BJTs have determined an actual collector dopingconcentration of 1 × 1015 cm−3.

In this section, the temperature behavior and the influence of the base-emittergeometry are investigated. A particular attention is placed on the BJT character-istics at high current density. The aim is to highlight the limiting factors for thecurrent gain in order to optimize the BJT design. Although it is desired to design adevice as small as possible conducting a high current density at elevated tempera-ture, the reduction of the current gain limits the device to meet these requirements.In particular, the internal forward biasing of the base-collector junction causes thisreduction at high temperature and when a narrow emitter width is designed. Con-cerning the base-emitter distance, which is the distance between the base contactand the emitter sidewall, an increase in the base current is observed due to thediffusion of the electron injected from the emitter towards the base contact.


3.2.1 Influence of the temperature

In paper II, a model to describe the temperature behavior of the current gain isdeveloped; moreover, the results are compared with measurements. The summaryof the physical models and parameters that lead to the best agreement with themeasurements is:

• Surface recombination modeled using one single energy level at 1 eV abovethe valence band (donor-like), a capture cross section of 1 × 10−15 cm2, anda trap concentration of 2 × 1012 cm−2.

• SRH recombination with τmax,n,p = 50 ns.

• Auger recombination.

• Incomplete ionization with ionization energies for nitrogen and aluminum of0.065 and 0.210 eV respectively.

• Bandgap narrowing, at room tempearature, of 60 meV in the emitter (20 meVfor the conduction band and 40 meV for the valence), and of 80 meV in thecapping layer (30 and 50 meV).

• Fermi-Dirac (F-D) statistics.

The measurements have been performed on a single-finger transistor with anemitter width of 20 µm and a length of 500 µm. The total active area is 0.045mm2, and the current density of 100 A/cm2 is reached when the simulated currentis 45 mA.

The model demonstrates a good agreement with the measurements at threedifferent temperatures (see Fig. 3.7a). Moreover, the simulations satisfactorily fit

10-6 10-5 10-4 10-3 10-2 10-10

10

20

30

40

50

60

150 oC

100 oC

measurement simulation

Cur

rent

Gai

n

Collector Current [A]

VCB = 0 V

27 oC

(a) Current gain versus collector current.

2.3 2.4 2.5 2.6 2.7 2.8 2.910-8

10-6

10-4

10-2

Cur

rent

[A]

Base-Emitter Voltage [V]

measurement simulation

(b) I-V characteristic of the base-emitter diodeat room temperature.

Figure 3.7: Comparison between simulated and measured characteristics.


10-5 10-4 10-3 10-2 10-10

20

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60

80

100

120

140

Cur

rent

Gai

n


VCB = 0 V

measurement

5 x 1011 cm-2 - 200 ns

Figure 3.8: Influence of the the interface trap concentration and bulk carrier lifetimeon the maximum current gain

the measurements both at low and high collector current. At low collector current,the bulk carrier lifetime and the interface traps adequately model the recombinationcurrent; this can also be seen from the ideality factor of the base emitter diode (seeFig. 3.7b). At high collector current, the carrier lifetime, the interface traps, andthe incomplete ionization with the consequent bandgap narrowing in the emittersatisfactorily model the emitter efficiency and the base transport factor. Moreover,the model demonstrates a good agreement in the reduction of the current gain andknee current when the temperature increases.

1.5 2.0 2.5 3.0 3.5 4.01013

1014

1015

1016

1017

high injection

base

Con

cent

ratio

n [c

m-3]

Distance [ m]

Electron Hole

collector

forward biasing

donor

ionized acceptor

(a) 27C

1.5 2.0 2.5 3.0 3.5 4.01013

1014

1015

1016

1017

Con

cent

ratio

n [c

m-3]

Distance [ m]

Electron Hole

alleviatedhigh injection

forward biasing

base collector

donor

ionized acceptor

(b) 150C

Figure 3.9: Carrier and doping concentration along the cross section AA’ (see Fig.3.6) when the maximum current gain is reached. The simulated bias conditions are(a) VBE = 3.0V and VCB = 0V , and (b) VBE = 2.75V and VCB = 0V .


In good agreement with measurements, it is possible to investigate the influenceof the surface and bulk recombination on the current gain. As can be seen in Fig.3.8, a βmax of around 140 could be obtained with a trap concentration of 5 × 1011

cm−2 and τmax,n,p = 200 ns. This confirms that the surface passivation and thematerial quality are limiting factors for improving the current gain. In addition, itis worth to notice that the β improves also at low collector current. This is due tothe lower trap concentration rather than the longer bulk carrier lifetime.

The carrier concentration along the cross section AA’ (see Fig. 3.6) has beeninvestigated to explain the cause of the current gain drop at high collector current.Fig. 3.9a indicates that high injection in the base and internal forward biasing ofthe base-collector junction occur simultaneously. The high injection is mainly dueto the low concentration of ionized acceptors; this decreases the emitter efficiency.On the other hand, the base-collector junction is forward biased because of theinternal voltage drop that occurs across the lowly doped collector region, and theBJT enters into the quasi-saturation region. However, at 150C (see Fig. 3.9b),the high injection is alleviated because of the higher concentration of the ionizedacceptors, but the internal forward biasing is still present.

The internal forward biasing of the base-collector junction, together with thenegative temperature dependence of the mobility, is also the cause of the reductionof the knee current when temperature increases. The lower mobility increases thecollector resistance, and then the internal voltage drop across the drift layer for afixed collector current. This is evident from Fig. 3.10a in which the current gainwith two different biasing VCB is compared. As can be seen, applying a VCB =10 V alleviates the internal forward biasing; therefore, the reduction of the currentgain and of the knee current is moved at higher current. It is also worth to noticethat, when VCB = 0 V, a very sharp reduction in the current gain is present at very

10-3 10-2 10-10

10

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150 oC

100 oC

Cur

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VCB = 10 V VCB = 0 V 27 oC

(a) Current gain

10-3 10-2 10-1

10-4

10-3

10-2

increasing T

Bas

e C

urre

nt [A

]


VCB = 10 V VCB = 0 V

increasing T

(b) Base current

Figure 3.10: Comparison between electrical characteristic with VCB = 0 V andVCB = 10 V.


high current, and this phenomenon is more evident at high temperatures. FromFig. 3.10a, this very sharp reduction can be extrapolated to occur at a collectorcurrent of around 60 mA at room temperature, and this collector current decreasesto around 30 mA at 150 oC. As suggested in Fig. 3.10b, the sharp reduction in thecurrent gain is due to the large increase of the base current. This phenomenon isdiscussed in section 3.3.

3.2.2 Influence of the emitter-base geometry

In paper III, the model has been used to investigate the influence of the base-emittergeometry on the current gain. The simulated and measured βmax as function of thegeometrical dimension WE and WP are summarized in Fig. 3.11. The devices withdifferent WE has a constant WP = 7 µm, whereas the devices with different WP

has a constant WE = 20 µm. Fig. 3.11a reveals that, when the emitter is reducedbelow 30 µm, the current gain shows a reduction. On the other hand, for wideremitter, the current gain saturates to its highest value. The saturation behavioris due to the high sheet resistance of the base layer, which, in turn, causes thedepolarization of the base-emitter junction. This depolarization is also the causeof the so-called emitter crowding, which is the tendency of the collector current toflow through the emitter region closer to the emitter edge. The same saturationbehavior is present when the distance WP is varied, as illustrated in Fig. 3.11b.When WP is smaller than 4 µm, the current gain decreases, whereas, when thisdistance is larger, the current gain saturates to its highest value.

5 10 15 20 25 30 35 40 4538404244464850525456

Max

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Emitter Width [ m]

Simulation Measurement

(a)

2 3 4 540

42

44

46

48

50

52

54

Max

imum

Cur

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Gai

n

Emitter-Base Distance [ m ]


(b)

Figure 3.11: Maximum current gain with VCB = 0 V at room temperature (a)for different emitter widths WE (WP = 7 µm) and (b) for different emitter-basedistances WP (WE = 20 µm). Simulated and measured values are compared.


Emitter width

The reduction of the current gain when WE is reduced is due to two mechanisms:higher bulk recombination in the emitter region, and earlier internal forward biasingof the base-collector junction. Nevertheless, the latter mechanism is predominant.As can be seen in Fig. 3.12a, narrower emitter also leads to a lower knee current.This is because the narrower emitter constrains the collector current to flow througha smaller area. Therefore, the 8µm-BJT enters in the quasi-saturation region atlower collector current, i.e., at around 30 mA, whereas the 40µm-BJT enters in thisregion at around 70 mA. This explanation is confirmed by analyzing the hole con-centration when the 8µm-BJT reaches its maximum current gain (see Fig. 3.12b).For the 8µm-BJT, the hole concentration is larger than the donor concentration inthe drift region, whereas for the 40µm-BJT is still around four orders of magnitudelower than the collector doping.

If the base-collector junction is biased to avoid its forward biasing, the differencein βmax between the 40µm-BJT and the 8µm-BJT becomes smaller (see Fig. 3.13),and the main acting mechanism is now the recombination in the emitter region.This recombination is extrapolated along the cross section CC’ when the βmax forthe 8µm-device is reached, i.e., at a collector current of 100 mA, and is illustratedin Fig. 3.14a. The bias conditions are VBE = 3.37 V for the 8µm-device, whereasVBE = 3.33 V for the 40µm-device, and VCB = 15 V is for both the devices. It canseen that the bulk recombination is largely due to SRH recombination; moreover,the surface recombination, which is due to interface traps, plays an important role.The integrals of the total recombinations over the emitter width are 1.46 × 1020

and 1.75 × 1020 cm−1s−1 for the 40µm- and 8µm-devices respectively. However,it can be seen that the SRH recombination increases when the emitter width WE

is reduced, while the surface recombination remains constant. Therefore, it can

10-3 10-2 10-110

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60WE = 40 m

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WE = 8 m

(a) Current gain versus collector current.

0 5 10 15 20 25109

1011

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cent

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n [c

m-3]

Distance [ m]

Donor

WE = 8 m

(b) Hole and donor concentrations along thecross-section BB’ (see Fig. 3.6) at IC = 30 mA.

Figure 3.12: Influence of the emitter width on the knee current with VCB = 0V .


0.04 0.08 0.12 0.16 0.20 0.241520253035404550556065

VCB = 15 V

Cur

rent

Gai

n


WE = 40 m WE = 8 m

VCB = 0 V

Figure 3.13: Simulated current gain as function of collector current.

be concluded that the base current is dominated by bulk recombination instead ofsurface recombination. This is confirmed by the analysis of the base current fordifferent emitter widths, as illustrated in Fig. 3.14b. The base current is dividedby the total emitter periphery length (2 LE) and is plotted as function of the base-emitter voltage. Since the base current demonstrates variations with the emitterwidth, it can be concluded that IB is proportional to the emitter area and not tothe total emitter periphery length.

0 2 4 6 8 10 12 14 16 18 20 22

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1025

1027

WE = 40 m

Rec

ombi

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-1]

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Total SRH Auger

WE = 8 m

surface recombination

(a) Recombination in the emitter region.

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e C

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nt [A

/cm

]


40 m 20 m 8 m

increasing WE

(b) Base current.

Figure 3.14: Influence of the emitter width on the current gain. (a) shows therecombination in the emitter region along the cross section CC’ (see Fig. 3.6),whereas (b) shows the measured IB / (2 LE) as function of VBE with LE = 500µm.


Base-emitter distance

The measured and simulated Gummel plot with VCB = 15 V is compared in Fig.3.15. This biasing condition is chosen to avoid the internal forward biasing of thebase-collector junction, and then to avoid an additional component for the basecurrent due to the hole injected in the collector. As can be seen, at low biasconditions, the 2µm-device shows a larger current gain than that for the 5µm-device. This is due to the smaller recombination area between the base region andthe passivation layer. It is also worth to notice that, for the 2µm-device, both baseand collector currents are larger that those for the 5µm-device due to the moreuniform biasing of the base-emitter junction. However, at high bias condition, thecurrent gain for the 2µm-device begins reducing and becomes smaller than that forthe 5µm-device. This reduction can also be seen from the current gain as functionof the collector current in Fig. 3.16, and it is caused by the additional diffusioncurrent introduced by the presence of the base contact closer to the emitter mesa.

The influence of the base contact is confirmed by simulations, as illustrated inFig. 3.17a. The electron current density has been extrapolated along the cross-section DD’ at a collector current of 100 mA. The bias conditions are VBE = 3.20V for the 5µm-device, and VBE = 3.03 V for the 2µm-device. However, only thevertical component, which is normal to the base contact, has been selected. Thiscomponent represents the amount of electrons that recombines at the base contactthus increasing the base current. Fig. 3.17a suggests that, for the 2µm-device, theelectron current is several order of magnitude larger than that for the 5µm-device.The direction of this component is confirmed by electron distribution extrapolatedalong the cross-section EE’ (see Fig. 3.17b). This cross-section is placed close to thecontact edge and is perpendicular to the cross-section DD’. Fig. 3.17b also suggeststhat, at the same collector current, the electron concentration for the 2µm-device

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.010-7

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IB

Cur

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[A]


WP = 5 m WP = 2 m

IC

0

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(a) Measurement

2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.410-7

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(b) Simulation

Figure 3.15: Comparison between measured and simulated Gummel plot with VCB

= 15 V. The thick arrows indicate when the current gain begins to reduce.


10-3 10-2 10-120

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70

Cur

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Gai

n


Simulation 5 m Simulation 2 m Measurement 5 m Measurement 2 m

Figure 3.16: Comparison between measured and simulated current gain for the5µm- and 2µm-device with VCB = 15 V.

is several orders of magnitude larger compared with the electron concentration forthe 5µm-device. This larger amount of electrons increases the base current thusreducing the current gain.

10 11 12 13 14 15 16 1710-8

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ensi

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' [A

/cm

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EmitterEdge

Base Contact2 m-device

Base Contact5 m-device

(a) Electron current

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3109

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Ele

ctro

n C

once

ntra

tion

[cm

-3]

Distance [ m]

5 m 2 m

Base ContactBase-CollectorJunction

(b) Electron concentration

Figure 3.17: (a) Electron current density (component normal to the base contact)along the cross-section DD’. (b) Electron concentration along the cross-section EE’.The bias conditions are VBE = 3.20 V for the 5µm-device, and VBE = 3.03 V forthe 2µm-device, while IC = 100 mA is for both devices.

3.3. ON-RESISTANCE 41

3.3 ON-resistance

As demonstrated in Eq. 1.3, the unipolar on-resistance (Runi) strongly increasesas the designed BV increases. Moreover, due to the negative temperature depen-dence of the mobility, the Runi strongly increases with temperature. Although thisis convenient for paralleling BJTs, large on-resistance (RON ) can lead to signif-icant power dissipation during the on-state. In addition, most of the SiC BJTshave demonstrated an RON larger than the Runi value [79, 80], and absence ofconductivity modulation.

In order to reduce the power dissipation during the on-state, it is desired tohave a BJT with a very low forward voltage drop (VDROP ). In this section it isshown that it it is difficult to meet this requirement if the device has to conduct ahigh current density because of the large base current needed to maintain the BJTin this operating condition.

In paper IV, the limiting factors for improving the RON are investigated. Thesimulated and measured output characteristics are compared at both room and hightemperature. The measurements have been performed on multi-finger BJTs with anactive area of 0.04 mm2 (excluding contact pads). The insert in Fig. 3.18 illustratesa microscopic image of the device. This type of structure is sufficiently large to allowthe current spreading to be neglected outside the active area. The simulations havebeen performed according to the physical model presented in papers II and III.

The simulated and measured output characteristics at room temperature arecompared in Fig. 3.19. The results are compared for three different base currents,that is, 1.5, 2 and 8 mA. In addition, the simulated output characteristics at higherbase currents, i.e., 30 and 500 mA, are presented. On the other hand, in Fig. 3.20,

Figure 3.18: Cross-sectional view of the fabricated device. (insert) Microscopicimage of the fabricated device. The dotted area is the active area of 0.04 mm2.


0 1 2 3 4 50

20

40

60

80

100

120

0,5 A

30 mA

8 mA 2 mA

Col

lect

or C

urre

nt [m

A]

Collector-Emitter Voltage [V]


IB = 1,5 mA

200 W/cm2

Figure 3.19: Comparison between measured and simulated output characteristicsat 27C. Simulated characteristics at high base currents are also provided.

the simulated and measured output characteristics are compared at 27, 100 and150 C with a fixed base current of 2 mA. A good agreement is obtained suggestingthat the simulations satisfactorily model the actual device. The simulations and themeasurements indicate that conductivity modulation is absent, and the BJT acts asa unipolar device. In other words, the collector current curves for the different basecurrents overlap in the saturation region. This is confirmed by the RON extractedat different temperatures. Table 3.1 demonstrates that on-resistance (RON ) showsthe same positive temperature dependence of the Runi. This negative dependenceis due to the reduction of the mobility when the temperature increases.

0 1 2 3 4 50

20

40

60

80

100

120

150 oC

100 oC

Col

lect

or C

urre

nt [A

]


Measurement Simulation 27 oC

Figure 3.20: Comparison between measured and simulated output characteristicsat different temperatures with IB = 2mA.

3.3. ON-RESISTANCE 43

Table 3.1: Summary of the extrapolated RON and Runi.

Temperature [C] 27 100 150

Measured RON [mΩ cm2] 12 20 26Simulated RON [mΩ cm2] 12 19 25Unipolar Value [mΩ cm2] 11 18 23

High-blocking-voltage BJTs dissipate elevated power when they operate in theconduction mode because of the large RON . Therefore, conductivity modulationis needed to decrease the RON below the Runi. However, as can be seen in Fig.3.19, if the BJT has to conduct a current density of 200 A/cm2 (IC = 80 mA) witha maximum forward voltage drop (VDROP ) of 1 V, then a power dissipation limitof 200 W/cm2, the forced current gain (βFORCED) is only 0.15 (IB = 500 mA).The βFORCED is defined as the current gain when the BJT operates in the quasi-saturation region. On the other hand, if the current density is 150 A/cm2 (IC = 60mA) with the same power dissipation limit (IB = 30mA) the βFORCED is aroundtwo. However, these very low values can hinder the use of high-blocking-voltageBJTs in practical applications. In addition, Fig. 3.21 suggests that the processquality has little influence on the βFORCED improvement; therefore, it is difficult toachieve reasonable performance only by improving the process conditions. However,it can be seen that bulk carrier lifetime has more impact compared with the interfacetraps. When the bulk carrier lifetime increases from 50 ns to 200 ns, the forcedcurrent gain improves from 0.15 to around one. The main reason for these verylow values is the internal forward biasing of the base-collector junction. In thissituation, the extrinsic base region of the BJT has a similar carrier distribution asa forward-biased pn diode. Therefore, there is a large injection of electrons from thecollector into the extrinsic base. Since the base region is very thin, these electronsreach the base contact; consequently, the base current increases to supply their

50100

150200

510

15200

0.20.40.60.8

11.2

Lifetime [ns]Trap Conc. [×1011cm−2]

β FO

RC

ED

Figure 3.21: Response surface for the βFORCED at JC = 200A/cm2 and VCE = 1Vas function of the interface traps and bulk carrier lifetime.


recombination. This is the reason of the sharp reduction of the current gain and ofthe sharp increase of the base current observed in Fig. 3.10.

3.4 Design Improvement

According to the analysis in sections 3.2 and 3.3, it can be concluded that the BJTdesign has to be improved if a low VDROP , a high current density and a largerβFORCED are desired. In this section, it is shown that increasing the extrinsic-basedoping allow meeting these requirements; in addition, the maximum current gain isimproved. Furthermore, the simulated BJT demonstrates that the strong positivetemperature dependence of the RON , observed when the device acts as a unipolardevice (see Fig. 3.20), is alleviated.

The proposed design is illustrated in Fig. 3.22, and it suggests to increase theextrinsic base doping in order to:

• Reduce the diffusion of the electrons, injected from the emitter, towards thebase contact.

• Reduce the injection of electrons from the collector into the extrinsic base.

Ion implantation [81, 82], epitaxial regrowth [83], and selective epitaxial growth[84, 85] have been successfully demonstrated in SiC technology, and they couldbe used for this purpose. However, it should be mentioned the fabrication of theproposed design can be technologically challenging because the ion implantationcan introduce defects, whereas the isolation between the base and the emitter canbe the main issue in the epitaxial regrowth and selective epitaxial growth.

Figure 3.22: Cross-sectional view of the proposed new design with increased extrin-sic base doping concentration.

3.4. DESIGN IMPROVEMENT 45

10-3 10-2 10-120

30

40

50

60

70

Cur

rent

Gai

n


Proposed Design Actual Design

Figure 3.23: Current gain as function of the collector current. The actual design isillustrated in Fig. 3.6, whereas the proposed design in Fig. 3.22 with an extrinsicbase doping equal to 5 × 1018 cm−3. Both the designs have WP = 2µm.

The simulated current gain as function of collector current with VCB = 15 V isillustrated in Fig. 3.23. It can be seen that a larger β is obtained with the proposeddesign. The actual design is illustrated in Fig. 3.6, whereas the proposed design inFig. 3.22 with an extrinsic base doping of 5 × 1018 cm−3; however, both the designshave WP = 2µm, WE = 20µm and an active area of 0.045 mm2. It is worth tonotice that WP = 2µm, together with higher doping, results in an improved biasingof the base-emitter junction. This can be deduced when the electron current densitytowards the base contact is extrapolated along the cross-section DD’ at IC = 100mA. In fact, the bias conditions for the base-emitter diode are VBE = 3.03 V for theactual design, and VBE = 2.92 V for the proposed design. As seen in Fig. 3.24a, thehigher doping reduces the electron current density towards the base contact. Thisreduction is caused by the shift of the conduction band, which induces a barrier forthe electrons, as illustrated in Fig. 3.24b, and also by the reduction of the lateraldiffusion length.

The output characteristic of the proposed design is illustrated in Fig. 3.25. Thedimensions are WE = 20 µm, WP = 2 µm, a base contact width of 14 µm, and anactive area of 4 mm2. This device has been simulated with a carrier lifetime of 200ns and a trap concentration of 5 × 1011 cm−2 in order to compare its βFORCED

with the highest βFORCED of around one simulated for the actual device (see Fig.3.21). The simulated βFORCED at room temperature is around 8; this representsa large improvement compared with that for the actual design.

As already mentioned, the reason of the very low βFORCED for the actual designis the large injection of electrons from the collector into the extrinsic base. Incontrast, increasing the doping of this region alleviates this injection, thus stronglyreducing the base current to maintain the BJT in the quasi-saturation region. The


10 11 12 13 1410-6

10-4

10-2

100

102

104

Ele

ctro

n C

urre

nt D

ensi

ty N

orm

al to

DD

' [A

/cm

2 ]

Distance [ m]

Actual Proposed

Emitter Edge Base Contact

(a) Electron current.

9 10 11-0.2

-0.1

0.0

0.1

2.9

3.0

3.1

3.2

Valence Band

Ene

rgy

[eV

]

Distance [ m]

Conduction Band

(b) Conduction and valence band for the pro-posed design.

Figure 3.24: Influence of the increased extrinsic base doping along the cross-sectionDD’. The bias conditions are VBE = 3.03 V for the actual design, and VBE = 2.92V for the proposed design.

reduction of the electrons injected into the extrinsic base is illustrated in Fig. 3.26,where the electron and hole concentrations along the cross section FF’ (see Fig. 3.22and Fig. 3.18) are provided. The bias conditions are VBE = 3.14 V for the actualdesign and VBE = 2.95 V for the proposed design, while VCE = 1 V and IC = 80mA are for both the devices. It is possible to see that the electron concentration forthe proposed design is lower than the electron concentration of the actual design;therefore, the base current is strongly reduced.

0 1 2 3 4 50

20

40

60

80

100

120

200 A/cm2

10 mA

27 oC 100 oC 150 oCC

olle

ctor

Cur

rent

[mA

]

Collector Voltage [V]

IB = 1 mA

Figure 3.25: Simulated output characteristic for the proposed design illustrated inFig. 3.25 with an extrinsic base doping equal to 5× 1018cm−3 and WP = 2µm.

3.5. SWITCHING PERFORMANCE 47

0.0 0.1 0.2 0.3 0.4 0.5 0.61014

1015

1016

1017

1018

Con

cent

ratio

n [c

m-3]

Distance [ m]

Actual Proposed

hole

electron

Figure 3.26: Electron and ionized acceptor concentrations along the cross sectionFF’ (see Fig. 3.22 and Fig. 3.18). The bias conditions are VBE = 3.14 V for theactual design and VBE = 2.95 V for the proposed design.

In addition, in Fig. 3.25, it can be seen that conductivity modulation is presentbecause the curves at the two different base currents are separated. With a basecurrent of 1 mA, the BJT acts as a unipolar device; however, when the base currentincreases to 10 mA, the saturation and quasi-saturation regions appear. Moreover,with this base current, when the temperature is increased, the VDROP to maintaina collector current of 80 mA increases less abruptly than when the BJT acts as aunipolar device. This is due to the positive temperature dependence of the holediffusion length Lp (see Eq. 3.1) [86].

Lp =√

Dpτp =

√

kBT

qµpτp ∝ (T 1T−2.15T 1.72)0.5 ∝ T 0.285 . (3.1)

In Eq. 3.1, Dp is the diffusion coefficient expanded according to the Einsteinequation with -2.15 as temperature coefficient for the hole mobility µp, and τp is thebulk carrier lifetime with 1.72 as temperature coefficient. When the temperatureincreases, the modulated part of the collector region expands while the unmodulatedpart increases its resistance. The two mechanisms oppose each other, but thenegative temperature dependence of the mobility is predominant.

3.5 Switching Performance

Switching characteristics have been measured on large area BJTs with an activearea of 3 mm2. A detailed description of the SiC BJT characteristic and fabricationis provided in [5]. The schematic of the test circuit for the switching measurementsis illustrated in Fig. 3.27. The passive network is composed of a small resistor (2 Ω)


Figure 3.27: Schematic of the test circuit for switching measurements.

in series with a capacitor (47 nF) for a high dynamic base current during turn-onand turn-off, and of a resistor (47 Ω) for biasing the BJT during the on-state. Thelarge inductor, connected in parallel with the diode, can be assumed to provide astable current; therefore, in simulation, this is replaced with a current generator.In the actual circuit, a 1200 V Schottky diode is used; however, a pn diode is usedin simulations.

The comparison between the measured and simulated static characteristics oflarge (3 mm2) and small area (8 × 10−3 mm2) are summarized in Fig. 3.28;Fig. 3.28a compares the output characteristic at room temperature for the large

0 1 2 3 4 50

2

4

6

8

10

12300 mA

IB = 160 mA

Measurement SimulationC

olle

ctor

Cur

rent

[A]


180 mA

(a) Output characteristic.

10-5 10-4 10-3 10-2 10-10

10

20

30

40

50

60


Cur

rent

Gai

n


(b) Current gain.

Figure 3.28: Comparison between measured and simulated static characteristics for(a) large area and (b) small area BJT.

3.5. SWITCHING PERFORMANCE 49

0 20 40 60 80 100 120 140 160 180 200-500

50100150200250300350400

Col

lect

or V

olta

ge [V

]

Time [ns]

(a) Collector Voltage.

0 20 40 60 80 100 120 140 160 180 200024681012141618

Col

lect

or C

urre

nt [A

]

Time [ns]


(b) Collector Current.

Figure 3.29: Comparison between measured and simulated turn-on waveforms forthe large area BJT.

area BJT, whereas Fig. 3.28bcompares the current gain as function of collectorcurrent for the small area BJT. The disagreement present between the measuredand simulated output characteristic may be due to unequal biasing of the base-emitter junction caused by problems in the metalization on the large area BJT.However, a better agreement is obtained with a small area BJT.

The measured BJT has been switched from VCE = 400 V to IC = 10 A (turn-on), and vice versa (turn-off). The input voltage of 20 V with the resistor of 47Ω (see Fig. 3.27) provides a base current of around 300 mA that is sufficient todrive a collector current of 10 A while the BJT in saturation (see Fig. 3.28a). The

0 20 40 60 80 100 120 140 160 180 2000

100

200

300

400

500

Measurement SimulationC

olle

ctor

Vol

tage

[V]

Time [ns]

(a) Collector Voltage.

0 20 40 60 80 100 120 140 160 180 200-2

0

2

4

6

8

10


Col

lect

or C

urre

nt [A

]

Time [ns]

(b) Collector Current.

Figure 3.30: Comparison between measured and simulated turn-off waveforms forthe large area BJT.


0 20 40 60 80 100 120 140 160 180 2000

1

2

3

4

5

6

Bas

e-E

mitt

er V

olta

ge [V

]

Time [ns]

012345678

Bas

e C

urre

nt [A

]

(a) Turn-on.

0 20 40 60 80 100 120 140 160 180 200-30

-25

-20

-15

-10

-5

0

5

Bas

e-E

mitt

er V

olta

ge [V

]

Time [ns]

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Bas

e C

urre

nt [A

]

(b) Turn-off.

Figure 3.31: Base voltage and current during turn-on and turn-off for the large areaBJT.

measured and simulated switching characteristics are summarized in Fig. 3.29 andFig. 3.30. As already reported in [5], a turn-on of 18 ns and turn-off of 10 ns isobtained. In addition, Fig. 3.31 illustrates the base voltage and current duringturn-on and turn-off.

As suggested in Fig. 3.31a, the RC network in the base drive circuit providesa high-dynamic response for the base voltage and current. Therefore, the base-emitter junction rapidly becomes forward biased, and the collector current canbegin raising already after 20 ns. The rate depends on the inductor connectedto the collector terminal; this inductor causes also the small drop in the collectorvoltage. The collector current presents a peak at around 40 ns due to chargesinjected from the diode. At this point, the diode can start supporting the voltageacross its depletion layer; as a result, the collector voltage drops and reaches itssteady-state value rapidly due to the absence of conductivity modulation. The largepeak in the base current observed after 40 ns is due the oscillations in the base-emitter voltage due to the parasitic inductors at each terminal. These oscillationforward bias the base-collector junction causing a large injection of holes into thecollector region. However, after this peak, the base voltage and current reach theirsteady-state conditions.

As already mentioned, conductivity modulation is absent in the BJT when it isin its on-state. Therefore, during turn-off, the long storage time observed in siliconBJTs is avoided, and the short delay between when the base current is reversedand the collector current begins raising is only due to the removal of charges in thebase region. Moreover, the absence of conductivity modulation avoids the currenttail observed in silicon bipolar devices. Consequently, it can be concluded that,when the SiC BJT acts as a unipolar device, the switching frequency can be largercompared with silicon bipolar devices.

3.6. LONG-TERM STABILITY 51

3.6 Long-term Stability

The long-term stability of SiC BJTs is still one of the main issues to be solvedbefore these devices can be commercially available. The degradation of the BJTcharacteristics is mainly due to electrical stress and operation in presence of radia-tion. The degradation due to electrical stress appears during the normal operationof the BJT, and it can be divided in two two types: bipolar degradation and cur-rent gain degradation. The first type produces a device failure because both theon-resistance and the current gain are strongly affected; the second type, instead,degrades only the current gain, and it seems less problematic. On the other hand,the degradation due to radiation is present when the device operates in applicationssuch as aviation and space exploration. Silicon carbide is believed to be more resis-tant than silicon due to its larger bandgap, i.e., less generation of electron-hole pairsdue to ionization, and larger displacement energies, i.e. fewer vacancy-interstitialsdue to nuclear stopping.

3.6.1 Bipolar degradation

Under forward bias stress at high current density, SiC BJTs can suffer from degra-dation of the on-resistance (RON ) if high basal plane dislocation (BPD) densityis present. It is widely believed that stacking faults (SFs) are created by the re-combination of electron-hole pairs at the BPDs, which acts as a nucleation site.When the BJT operates in the quasi-saturation or saturation region, the base andthe collector regions are flooded with electron-hole pairs, and their recombinationconvert the BPDs into SFs. These SFs degrade both the current gain (β) and theon-resistance (RON ). The β is degraded because these SFs reduce the carrier life-time, whereas the RON because they act as carrier traps in the collector introducing

0 2 4 6 80

20

40

60

80

100

lower increased RON

2 mA

1.5 mA

Col

lect

or C

urre

nt [m

A]


unstressed 30 hours

IB = 1 mA

(a) Output characteristic.

10-4 10-3 10-2 10-10

10

20

30

40

50

reduction ofthe knee current

Cur

rent

Gai

n


unstressed 30 hours

VCB = 0 V

(b) Current gain versus collector current.

Figure 3.32: Comparison between the electrical characteristics after 30 hours ofstress for a BJT with an active area of 0.04 mm2.


(a) Unstressed. (b) After stress.

Figure 3.33: Stacking fault formation in a single finger BJT.

local high-resistive layer [87]. It is easy to detect SF formation from electrical mea-surements (see Fig. 3.32). The BJT has an active area of 0.04 mm2 and has beenstressed by forcing a constant base-emitter current with open collector. After 30hours, the output characteristic presents an increased RON and a reduced β (seeFig. 3.32a); in addition, the knee current is also strongly reduced (see Fig. 3.32b).The reduction of the knee current is because the high-resistive layer in the collectorforward biases the base-collector junction at lower collector current compared withthe unstressed device.

The SF formation can also be detected by analyzing the electrolumiscence im-ages at 450 nm, as can be seen in Fig. 3.33.

The BPDs and their consequent conversion into SFs is one of the main issue forbipolar devices. Although it has been reported that, at the start of the epitaxialgrowth for a 4o off-axis, around 90% of the BPDs convert into threading edgedislocations (TEDs), which result to be innocuous for bipolar devices, many studieshave investigated methods to enhance this conversion during the epitaxial growth.The main methods consist in:

• Using etching process to modify the surface morphology of the substrate [88,89];

• Growing the epi-layer on a substrate with lower angle [90];

• Growing the epi-layer with higher C/Si ratio [91].

3.6.2 Current gain degradation

When the BPDs density is very low, the SFs formation, and then the bipolardegradation, can be suppressed. However, the BJTs can still suffer from current


gain degradation, but with no significant drift of the on-resistance. Unlike thebipolar degradation, the reason for this type of degradation is still unclear, andthere are few studies investigating this issue [92, 93, 94].

In [92], this type of degradation is attributed to three different phenomena:

I Increase of the interface trap density along the SiC/SiO2 interface, which, inturn, leads to an increased surface recombination;

II Degradation of the base-emitter region caused by recombination enhanced de-fect reactions (REDR) [95, 96];

III Small size stacking faults in the base-emitter region.

In paper V, the current gain degradation has been investigated. The BJTstructure consists of an emitter doped to 6 × 1018 cm−3 and 1.35 µm thick, abase doped to 4.3 × 1017 cm−3 and 650 nm thick, and a collector doped to 3 ×1015 cm−3 and 25 µm thick. A complete description of the fabrication process hasbeen presented in [5]. In order to investigate the degradation of the base region,a transistor with an emitter width of 20 µm and an active area of 1.6 × 10−3

mm2 (excluding contact pads) has been chosen. This device has been stressed bya base-emitter current, with open collector, of 80 mA for 10 hours.

The following characteristics have been compared before and after stress:

• Gummel plot at 27 oC with VCB = 5 V. This biasing is to avoid forwardbiasing the base-collector junction.

• Difference in the base current, extrapolated from the Gummel plot, whenmeasured with VCE = 5 and 150 V. The high voltage is to increase the

2.50 2.55 2.60 2.65 2.7010-7

10-6

10-5

10-4

IB

IB

VCE = 5 V VCE = 150 V

Cur

rent

[A]


IC

2.62 2.63 2.64

Figure 3.34: Gummel plot illustrating the effect of the application of a VCE = 150V.


2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.410-7

10-6

10-5

10-4

10-3

10-2

10-1

VCB = 5V

IC

Cur

rent

[A]


unstressed 10 hours

IB

0

10

20

30

40

50

60

Cur

rent

gai

n

(a)

10-6 10-5 10-4 10-3 10-2 10-10

10

20

30

40

50

60

Cur

rent

Gai

n


unstressed 10 hours

(b)

Figure 3.35: Comparison between electrical characteristics before and after 10 hoursof stress. The Gummel plot has been measured at 27 oC and with VCB = 5 V.

depletion region onto the base region, and then have a narrower electricalbase. This characterization has been performed at 16, 27 and 39 oC.

• Base-emitter current in the low voltage range when the base-emitter diode,with open collector, is characterized. This characterization has also beenperformed at 16, 27 and 39 oC.

These characterizations are to detect the increase of recombination in the deviceafter the stress. However, the second measurement is to distinguish whether therecombination is in the bulk region of the base. In [60], it is suggested that, tovary this recombination current, reverse biasing the base-collector junction can beapplied to reduce the electrical base width of the BJT. This reverse biasing producesa reduction of the base current and an increase of the collector current, as can beseen in Fig. 3.34. Although most of the depletion region is in the collector region, adepletion region in the base of around 15 nm, when VCB = 5 V, and 60 nm, whenVCB = 150 V, can be obtained.

The reduction of the current gain β is shown in Fig. 3.35. The Gummel plotfor the unstressed device is compared with the characterization after 10 hours ofelectrical stress. It can be seen from Fig. 3.35a that, after stress, a significantreduction of the collector current is present; this leads to a reduction of the currentgain from 55 to approximately 45. In addition, from Fig. 3.35b, it can be concludedthat no bipolar degradation is present because no strong reduction of the kneecurrent is detected (compare with Fig. 3.32b).

The difference between the base current measured with VCE =5 V and withVCE = 150 V is provided in Fig. 3.36. It can be seen that, after stress, thisdifference is larger than the difference measured before stress. This suggests that thedegradation of the lifetime in the base region might be the cause for the degradation


2.65 2.70 2.75 2.8010-8

10-7

10-6

n = 1

15 oC

I B,5V

- I B,

150V

[A]


unstressed 10 hours39 oC

27 oC

n = 2

Figure 3.36: The differences of the base currents extrapolated from the Gummelplot. These differences has been calculated between the measurements with VCE

= 5 V and the measurement with VCE = 150 V.

of the current gain. The recombination current in the base is described by Eq. 3.2,

IrB =qADnBnB0√

DnBτnBsinh(

WB/√DnBτnB

)

(

coshWB√DnBτnB

− 1

)

expqVBE

KT, (3.2)

where A is the area, DnB is the diffusion constant for the electrons, nB0 is theelectron concentration at equilibrium, τnB is the lifetime for the electrons, and WB

is the base thickness [60]. This equation predicts a positive temperature dependenceand an ideality factor equal to one. The temperature dependence is confirmed bymeasurements in Fig. 3.36, but an ideality factor larger than one is extrapolated.The value of around 1.5 suggests that the degradation of the lifetime in the baseregion might be only one of the causes for the degradation of the current gain.

The characteristic of the base-emitter diode is illustrated in Fig. 3.37. Anappreciable difference can be detected in the very low current region (below 0.1nA), comparing the pre-stress and after-stress condition; moreover, this differenceis present for the three temperatures. This suggests that the recombination currentin the base-emitter depletion region increases after stress. However, the analysisof the additional recombination current, which is induced by the electrical stress,indicates that this component has an ideality factor larger than two (around 2.2), asillustrated in 3.38. Although, theoretical calculations of the recombination currentfor the case of strong recombination show that the ideality factor is equal to two,practical and theoretical studies indicate that this value should lie between one andtwo, depending on the physical properties of the traps [97]. However, values largerthan two have been reported in silicon BJTs. In fact, in [98], it has been shown thatthe ideality factor changes depending on the surface potential and values larger thantwo are obtained when the interface is depleted. Therefore, it might be that the


electrical stress affects the passivation layer inducing charges in the oxide, which,in turn, affect the surface potential.

1.8 2.0 2.2 2.4 2.6 2.810-13

10-11

10-9

10-7

10-5

10-3

15 oC

27 oC

Bas

e cu

rren

t [A

]


unstressed 10 hours

39 oC

1.8 1.9 2.0 2.110-13

10-12

10-11

10-10

Figure 3.37: Base-emitter diode characteristic before and after 10 hours of stress.(Inset) Enlargement of the very low current region (below 0.1 nA)

1.8 1.9 2.0 2.1 2.210-13

10-12

10-11

10-10

n > 2

I reco

mbi

natio

n [A]


39 oC 27 oC 15 oC

n = 2

Figure 3.38: Recombination current for the three different temperatures. The re-combination current is the difference between the base current after stress andbefore stress.

3.6.3 Radiation hardness

In paper VI, the impact of ionizing radiations on the passivation layer betweenbase and emitter has been investigated by implanting helium He (α-particles) atthe SiO2/SiC interface. Since the passivation layer is 2 µm thick, SRIM simulation


Figure 3.39: Schematic of the experiment.

suggests that an energy of 600 kV is required for the He atoms to stop at thisinterface. The ion fluences chosen for the implantation are 1 × 1012, 1 × 1013, 1× 1014, 1 × 1015, 5 × 1015 and 1 × 1016 cm−2. A schematic of this experiment isillustrated in Fig. 3.39. The cross-sectional view of the fabricated device is insteadillustrated in Fig. 3.6, whereas a complete description of the fabrication processis presented in [78]; in addition, the physical models and parameters used for theelectrical simulations are provided in Paper II.

The SRIM simulation suggests that the implantation process introduces positive

2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.30.0

0.2

0.4

0.6

0.8

1.0

1.2

+ 1 x 1012 cm-2

+ 7 x 1011 cm-2

/ M

AX


no charge

+ 5 x 1011 cm-2

(a) Simulation

2.50 2.75 3.00 3.25 3.50

0.2

0.4

0.6

0.8

1.0

1.2

max

Base-emitter voltage [V]

Unimplanted 1x1015 cm-2

5x1015 cm-2

1x1016 cm-2

(b) Measurement

Figure 3.40: Comparison of the normalized current gain versus base-emitter voltage(a) for different positive charge concentrations and (b) for different fluences. Thecurrent gain is normalized to the current gain at VBE = 3 V.


2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.310-10

10-9

10-8

10-7

10-6

10-5

10-4

IB

Cur

rent

[A/

m]

Base-emitter voltage [V]

no charge + 5 x 1011 cm-2

+ 7 x 1011 cm-2

+ 1 x 1012 cm-2

IC

(a) Simulation.

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

10-6

10-5

10-4

10-3

10-2

10-1

5 x 1015 cm-2

Before radiation After radiation

Base

Cur

rent

[A]


Collector

2.5 2.6

Unimplanted 1x1016cm-2

increasingdose

(b) Measurement.

Figure 3.41: Comparison of the Gummel plot (a) for different positive charge con-centrations and (b) for different fluences.

fixed charge in the oxide because the electronic stopping is predominant comparedwith nuclear stopping. The effect of this positive fixed charge on the electricalperformance has been simulated, and the result compared with measurements. Fig.3.40 compares the simulated and the measured current gain as function of the base-emitter voltage. The simulations show that, with a positive charge concentrationof 5 × 1011 cm−2, a larger gain is obtained compared with the situation with nocharge. However, with higher concentrations, the current gain drops abruptly. Onthe other hand, in measurement, the increase of the current gain is absent, and thecurrent gain is strongly reduced already at the lowest fluence of 1 × 1014 cm−2 (notshown).

The analysis of the simulated and measured Gummel plot (see Fig. 3.41) in-dicate that the degradation of the current gain is mainly due to the increase ofthe base current; this increase is directly dependent on the positive charge con-centration in simulation (see Fig. 3.41a), and on the fluence in measurement (seeFig. 3.41b). An increase in the collector current is also observed, but this does notprevail over the increase of the base current since the current gain degrades.

Electron concentration and total recombination have been extrapolated alongthe cross section AA’ (see Fig. 3.39) at VBE = 2.9 V, and are illustrated in Fig.3.42. The explanation for higher current gain is in Fig. 3.42a; it can be seen thatthe total recombination decreases when the positive charge increases. However,when the charge concentration increases to 1 × 1012 cm−2, although the surfacerecombination decreases, the electron concentration becomes larger than the ionizedacceptor concentration (see Fig. 3.42a). This situation creates an effective n-typeinversion layer between the emitter region and the base contact. As a result, thebase current largely increases. This phenomenon has been previously observed insilicon BJTs. The increase in the collector current has been explained by the fact


10.0 10.5 11.0 11.5 12.0 12.5 13.01013

1014

1015

1016

1017

1018

1019

ionized acceptor

Ele

ctro

n C

once

ntra

tion

[cm

-3]

Distance [ m]

(a)

10.0 10.5 11.0 11.5 12.0 12.5 13.01022

1023

1024

1025

1026

1027

1028

Rec

ombi

natio

n [c

m-3 s

-1]

Distance [ m]

no charge + 5 x 1011

+ 7 x 1011

+ 1 x 1012

(b)

Figure 3.42: (a) Electron concentration and (b) total recombination extrapolatedalong the cross section AA’ in Fig 3.39

that the inversion layer is connected to the emitter region, and this acts as anextended emitter region [99].

As a result, it may be concluded that the ionization in the oxide during theimplantation process creates positive charge, and this degrades the current gain.However, according to the SRIM simulation, structural damage might be created atthe interface between SiO2 and SiC. The effect of this damage has been simulated byadding a high-resistive layer with reduced lifetime underneath the passivation layer.These device simulations show that the additional layer can model the increase ofthe base current, but not the increase of the collector current, which instead de-creases in the simulation. However, some combinations of positive charge and ahigh-resistive layer at the interface could explain the experimental data. Neverthe-less, since it is very arduous to quantify the amount of positive charge introducedand the extent of the damage, this device simulation is not shown.

Chapter 4

SiC diodes

The possibility to develop high-voltage SiC device can have a great impact onhigh power utility applications such as solid-state transformers. These new systemshave the potential to be the key-point in smart grid in which many sources of greenenergy, such as wind and solar, are included. For these high-voltage applications,SiC JFETs [100], MOSFETs [101], BJTs [102], GTO thyristors [103], IGBTs [104]and diodes [105] are being developed. In this section, simulations of a 10 kV diodeare presented.

4.1 Design of a 10 kV PiN diode

The design of a PiN diode consists in two main parts, reverse characteristic andforward characteristic. The reverse characteristic is due to doping and thickness ofdrift layer, and termination technology. The aim of this work is also to demonstratethe achievement of conductivity modulation in the drift region by means of lifetimeenhancement implanting carbon atoms in the lattice followed by high temperatureannealing [39].

4.1.1 Reverse characteristic

In order to have the designed breakdown (BV) with the lowest on-resistance (RON ),a punch-through (PT) design can be implemented. In this design, the drift layeris designed in order to have an electric field at the drift/substrate junction of onethird compared with the electric field at the pn junction (see Fig. 4.1). The

61

62 CHAPTER 4. SIC DIODES

Figure 4.1: Electric field distribution at the breakdown in a PiN diode.

characteristics of the drift layer are calculated according to Eq. 4.1 - 4.3.

topt =3

2

BVCBO

EC(4.1)

Rdrift,opt =27

8

BV 2CBO

µǫSE3C

(4.2)

NDopt =topt

1.6× 10−19µRdrift,opt; (4.3)

In order to have some margin on the breakdown voltage, the diode is designedto block 13 kV. In this situuation, the optimum drift doping and thickness are:

• doping = 7× 1014cm−3

• thickness = 100 µm.

Implanted Junction Termination Extension (JTE) has been chosen as termi-nation technology, and the total JTE length is around 1 mm. Simulations havebeen performed using the isotropic coefficients by Konstantinov [8] . The aim ofthis simulation study is to find the optimum design, and analyze the effect of pro-cess variations on the breakdown voltage. The variation parameters are mainlythe number of JTE regions and their doses. Three, four and five JTE have beensimulated; in order to simplify this analysis, a box profile with a fixed thickness(130 nm) and different doping values has been used to vary the JTE dose. Theprocess steps for the 3-JTE design are illustrated in Fig. 4.2.

The results are summarized in Fig. 4.3. It is possible to see that with the3-zone JTE there is a large drop in the breakdown voltage when the dose in themiddle region is higher than 0.9 × 1013cm−2, which represents the optimum dose.

4.1. DESIGN OF A 10 KV PIN DIODE 63

Figure 4.2: Process steps for the 3-JTE design.

This is caused by the high electric field peak at the outer edge, as illustrated inFig. 4.4a. When the dose is equal to the optimum, the Critical Electric Field (EC)at the outer edge is reduced and a more uniform distribution is obtained. Thisis because, when the optimum dose is present, the JTE is completely depletedat the breakdown voltage and it acts as a high-resistive layer. Consequently, theelectrostatic potential strongly decreases along the JTE, and then the voltage dropacross the pn junction at the outer edge is reduced.

Assisting the 3-JTE design with an additional JTE region with low doping (0.5× 1013 cm−2), i.e., implementing a 4-zone JTE, it is possible to have a wider rangewith breakdown voltages close to the ideal value. Fig. 4.4b suggests that theadditional JTE region with low doping reduces the electric field at the outer edgeand helps to produce an uniform distribution. Therefore, it can be concluded thatthe 4-JTE design can give the same electric field distribution as in the optimumcase although the design is not optimized.

However, as seen in Fig. 4.3, a slight reduction is observed when the dose inthe middle JTE is lower then the optimum. This reduction can be avoided byadding a further JTE region with high dose (1.3 × 1013 cm−2). In this case, a widerange, which spans from 0.7 to 1.1 × 1013 cm−2, could be obtained. It worth tohighlight that the larger number of JTE is implemented the wider range is obtained,but, this introduces complexity in the process leading to practical challenges whenfabricating high voltage devices.

The large reduction observed for the 3-JTE design when the dose in the middleregion is larger than the optimum is dependent on implantation profile at cornerof the outer edge. In order to investigate this dependence, implanted aluminum


0.7 0.8 0.9 1.0 1.1 1.26

7

8

9

10

11

12

13

3 JTE 4 JTE 5 JTEB

reak

dow

n V

olta

ge [k

V]

Dose [cm-2]

Figure 4.3: Simulated breakdown with different numbers of JTE. The dose on thex-axis is the dose in the middle JTE for the 3- and 5-JTE designs, whereas it is thesecond JTE from the p layer for the 4-JTE design.

0 200 400 600 800 10000.0

0.5

1.0

1.5

2.0

2.5

Ele

ctric

Fie

ld [

x 10

6 V/c

m]

Distance [ m]

low optimum

(a) Low - Optimum

0 200 400 600 800 10000.0

0.5

1.0

1.5

2.0

2.5

Ele

ctric

Fie

ld [

x 10

6 V/c

m]

Distance [ m]

3 JTE 4 JTE

(b) 3 JTE - 4 JTE

Figure 4.4: Comparison of the electric field distribution at the breakdown.

profiles at two different energies, i.e., 30 and 300 kV, have been simulated accordingto [106]; the results are illustrated in Fig. 4.5a. As expected, higher energy resultsin a deeper peak position with a wider distribution, whereas the energy of 30 kVleads to a shallower peak very close to the surface and a narrower distribution.Concerning the lateral profile, a Gaussian profile with a lateral distribution equalto 0.7 of the vertical one has been assumed. The results of this investigation areillustrated in Fig. 4.5. It can be seen that, when the design with 30 kV reaches itsbreakdown, around 7000 V, the design with 300 kV, which presents a BV of around11 kV, shows a lower electric field. Moreover, the maximum electric field is locateddeeper in the SiC. This can prevent an earlier breakdown in practical applications


due to any surface defect.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91014

1015

1016

1017

1018

1019

peak position = 50 nmwidth = 10 nm

Alu

min

um C

once

ntra

tion

[cm

-3]

Distance [ m]

300 kV 30 kV

peak position = 300 nmwidth = 100 nm

(a) Aluminum profile.

(b) 30 keV. (c) 300 keV.

Figure 4.5: (a) Aluminum profile. Electric field distribution at 7000 V for (b) 30kV profile, and (c) 300 kV profile.

4.1.2 Forward characteristic

The influence of carrier lifetime on the forward voltage drop at a current densityJC = 100 A/cm2 has been simulated. The anode layer is 1.5 µm thick and dopedat 5 × 1018 cm−3; the capping layer is doped at 1 × 1019 cm−3 in order to havevery low contact resistivity ρc.

It is very important to improve the lifetime of this class of devices because, asindicated in Fig. 4.6, the forward voltage drop (VDROP ) across of the drift layer,when it acts as a unipolar layer, is as large as around 9.5 V; moreover, it has astrong positive temperature dependence. However, a bulk carrier lifetime of 100ns in the lowly doped region can already reduce the VDROP by inducing partially


20 40 60 80 100 120 1403.0

3.2

8

12

16

20

VD

RO

P @10

0 A

/cm

2 [V]

Temperature [oC]

unipolar

100 ns

500 ns

1 s

Figure 4.6: Forward voltage drop at a current density of 100 A/cm2 as function oftemperature.

conductivity modulation (see Fig. 4.7). In this case, the VDROP also shows aless strong positive temperature dependence; in fact, the VDROP is around 5 V atroom temperature, and it increases to around 7.5 V at 150 C. On the contrary, abulk carrier lifetime of 1 µs can induce conductivity modulation in the entire driftregion with a very large carrier concentration (see Fig. 4.7). This further decreasesthe VDROP to around 3.1 V; in addition, this value shows a moderate negativetemperature dependence.

The highly-doped anode layer is to obtain a high anode efficiency, thus inducingconductivity modulation at low current density. The forward voltage drop at 100A/cm2 has been investigated as function of the doping and thickness of the anode

0 10 20 30 40 50 60 70 80 90 1001101013

1014

1015

1016

1017

1018

1 s

electron hole

100ns

Con

cent

ratio

n [c

m-3]

Distance [ m]

donor

Figure 4.7: Carrier concentration at a current density of 100 A/cm2.


layer. The simulation results are summarized in Fig. 4.8; it is suggested that, asexpected, the carrier lifetime plays an important role; however, the anode dopingis also important even when the carrier lifetime is as high as 1 µs. On the otherhand, the anode thickness is less important especially with long carrier lifetime.

1 1053.0

3.5

4.0

4.5

5.0

5.5

6.0

1 s500 ns

VD

RO

P at 1

00 A

/cm

2

Anode Doping Concentration [x 1018 cm-3]

2 m 4 m

100 ns

1 x 1018 shows a valuelarger than 6 V

Figure 4.8: Forward voltage drop at a current density of 100 A/cm2 as function ofdoping and thickness of the anode layer.

Chapter 5

Conclusions and Future Outlook

In this thesis, the different characteristics of 4H-SiC BJTs, such as breakdownvoltage (BV), current gain (β), on-resistance (RON ), and briefly switching havebeen simulated; in addition, the results have been compared with measurements inorder to validate the model. If an accurate model is developed, simulation can bevery useful to understand the BJT characteristics, investigate their limiting factors,and finally improve their performance.

In order to improve the BV, an efficient termination has been implemented onSiC PiN diodes; an efficient termination requires an optimum dose in the JTE re-gion in order to have this region completely depleted at breakdown thus reducingthe electric field crowding at the outer edge of the device. The comparison of simu-lated and measured BV as function of the JTE dose suggests that an optimum doseof around 1.2 × 1013 cm−2 is required to obtain a BV of around 4 kV. However,the range around the optimum is very narrow, and a large reduction in the BVis observed when the JTE dose is either lower or higher than the optimum. Thesimulations suggest that it is possible to expand this range implementing a two-zone JTE. This is also confirmed by the measurements since the fabricated devicesdemonstrate a BV of around 4.3 kV when the dose in the JTE1 is around 1.5 ×1013 cm−2 and the dose in the JTE2 is around 1 × 1013 cm−2. In addition, the sim-ulations and measurements demonstrate a good agreement between the simulatedelectric field distribution inside the device and the optical luminescence measuredat breakdown.

In order to reduce the power consumption of the driver circuit, it is required toimprove the β. In this thesis, an accurate modeling to describe the current gainbehavior has been presented, and the simulations have been compared with mea-surements in order to validate this model. A good agreement has been obtained,and the influence of temperature and base-emitter geometry can be satisfactorilydescribed. The simulations suggest that bulk carrier lifetime and surface recombi-nation are the limiting factors for improving the BJT current gain. If an interfacetrap concentration of 5 × 1011 cm−2 and a bulk carrier lifetime of 200 ns is chosen,

69

70 CHAPTER 5. CONCLUSIONS AND FUTURE OUTLOOK

a current gain of around 140 is simulated. In addition, the simulations indicatethat, when operating at a high current level, the internal forward biasing of thebase-collector diode causes the current gain to drop. This phenomenon also causesthe reduction of the knee current, and it is more pronounced at elevated tempera-tures. In addition, the simulations and measurements show that an emitter widthof around 20 µm is required to avoid a reduction in the current gain. This is becausea narrower emitter causes an earlier internal forward biasing of the base-collectorjunction and higher recombination in the emitter; however, the first mechanism ispredominant. Furthermore, the simulations and measurements show that the spac-ing between the base contact and the emitter sidewall is important. If this spacingis lower than 4 µm is present a significant diffusion of electrons, injected from theemitter, towards the base contact. This increases the base current; therefore; thecurrent gain decreases.

In order to reduce the power losses during the on-state, low RON is required.When a high-voltage BJT with a lowly doped collector is designed, conductivitymodulation is needed to reduce the forward voltage drop. However, the forced cur-rent gain is strongly reduced, especially if a high current density is desired, becauseof the large injection of electrons from the collector into the extrinsic base. Theelectrons diffuse towards the base contact and increase the base current. The simu-lations suggest that, increasing the extrinsic base doping can alleviate this diffusion.Moreover, this design can allow placing the base contact closer to the emitter side-wall with no reduction in the current gain. This is because the diffusion of theelectrons, injected from the emitter, towards the base contact can be alleviated.

The comparison of simulated and measured switching performance show that,when the device acts as a unipolar device, i.e., no conductivity modulation ispresent, the transient is fast and a turn-on of around 18 ns and turn-off of around10 ns can be obtained. The key point is to have a high-dynamic base current torapidly charge and discharge the base capacitance.

The investigation of current gain degradation due to electrical stress shows thata strong reduction (around 20%) occurs after 10 hours. The analysis of the Gummelplot suggests that the reduction of the carrier lifetime in the base-emitter regionmight be one of the causes; however, since the recombination current in the base-emitter depletion region shows an ideality factor larger than two, the passivationlayer might also be affected.

In addition, the degradation due to ionizing radiations is investigated. Thesimulations suggests that the creation of positive charges in the silicon oxide canincrease the base current thus reducing the current gain. The increase of the basecurrent is also seen in measurements. The analysis of the electron concentrationinside the device suggests that the positive charge can create an effective n-typeinversion layer between the emitter region and the base contact.

Finally, some considerations about future work:

• Deeper understanding of the high-doping effects in the emitter to obtain anaccurate modeling for the pn product and mobility in this region.

71

• Further investigation of the anisotropic behavior of the impact ionizationcoefficients.

• Simulation and characterization of SiC BJTs at higher temperatures. In thisthesis, BJTs have been simulated and characterized at up to 150 oC; however,due to the thermal properties of SiC, higher temperature operation can beobtained.

• Modeling of the switching performance when conductivity modulation ispresent in the collector.

• Further investigation of the current gain degradation. Concerning degra-dation due to electrical stress, it is important to discriminate whether thepassivation layer is involved. Concerning the degradation due to harsh envi-ronment, replacement of SiO2 with Al2O3 (high-k) could be a proper solutionto avoid this degradation [107].

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