CONTENTS

CONTENTS

Chapter 1: INTRODUCTION4

1.1. A retourn to investigations of germanium intrinsic point defects4

1.2.Motyvation and the scope5

Chapter 2: THEORETICAL BACKGROUND8

2.1.Single crystal growth process8

2.2. Semiconductor materials 10

2.2.1. The band structure10

2.2.2. Semiconductor type12

2.2.3. Energy levels in the band gap shallow and deep levels15

2.2.4. Recombination center16

2.3. Point defects17

2.3.1.Point defects generation19

2.3.1.1. Generation of equilibrium defects 20

a) Entalpy of formation20

b) Experimental determination of point defect properties22

2.3.1.2 Generation of excess defects 23

a) Irradiation23

b) Plastic deformation23

2.3.2. Diffusion24

2.4. Intrinsic point defect study method (literature review) 24

2.4.1. Quenching experiments24

2.4.1.1. Thermal conversion25

2.4.1.2. Participation of fast difusing dopants27

2.4.1.3. DLTS investigations29

Chapter 3: EXPERIMENTAL PART.31

3.1. Sample preparation31

3.2.1. Cutting31

3.2.2. Etching32

3.2. Quenching33

3.2.1. Rapid Thermal Annealing ( RTA)33

3.2.2. New Rapid Quenching apparatus (NRQa)34

3.2.2.1.Quenching baths35

3.3. Resistivitymeasurements 36

3.3.1. Four point probe36

3.3.2. Van der Pauw method37

3.3.2.1. Reproducibility of result39

3.4. Hall effect 40

3.5. Deep Level Transient Spectroscopy (DLTS)42

3.5.1. Basic idea of DLTS method44

3.5.2. DLTS limitations46

Chapter 4: RESULTS 47

4.1. Repeatatability of setups47

4.1.1. Rapid Thermal Annnealing (RTA)47

4.1.2. New Rapid Quenching apparatus (NRQa) 49

4.1.2.1. Quenching baths 49

a) Ethylene glycole49

b) Other50

4.2.Resistivity measurements53

4.2.1. Four point probe53

4.2.2. Van der Pauw technique53

4.2.2.1. After RTA53

4.2.2.2. After NRQa57

4.3. Hall effect63

4.3.1. Samples p-type (750 m)63

4.3.2. Samples n-type (750 m)63

4.4. DLT spectra66

4.4.1. After RTA66

4.4.1.1. Reproducibility of DLT spectrum67

4.4.2. After NRQa69

4.4.2.1. Reproducibility of DLT spectrum69

4.4.2.2. DLT spectrum mapping71

4.4.2.3. Investigation of Cu contamination73

Chapter 5: DISCUSSION75

5.1. Energy of formation of thermal defects75

5.1.1. Material76

5.1.2. Sample preparation procedure76

5.1.3. Setups76

5.1.3.1. Chamber contaminations76

5.1.3.2. Annealing time76

5.1.3.3. Cooling rate77

5.1.3.4. Resistivity measurements77

5.1.3.5. Arrhenius plot77

5.2. DLT spectrum78

Chapter 5: CONCLUSIONS 82

Refrences83

List of Tables85

List of Figures 86

1. INTRODUCTION1.1. A return to investigations of germanium intrinsic point defects

Evidence for the existence of an element that would be intermediate between silicon and tin was gained in 1886, when it was isolated from the silver sulfide mineral argyrodite. C. Winkel described this element (postulated previously by J. Newlands in 1864 and predicted by D. Mendeleev in 1871) and named it germanium in memory of his native country [1].

Ge and Si are closely together in the periodic table of the chemical elements and this is the reason why many properties of both elements are similar. Particular properties like those of the intrinsic point defects can, however, be quite different [2]. It is worth mentioning that defects in Si have been studied intensively for more than half a century, while for Ge research was strongly reduced at end of the 1960's. Germanium mineral resources are much more less abundant than those of Si. The overall cost, including minerals extraction, processing, pure semiconductor production, recycling etc., were one of the main reasons why silicon had won the competition as material of choice for electronic devices that time.

Nowadays its clear that the use of Si in high frequency and nano-electronic devices has its limits. Due to the much higher carrier mobility and compatible processing with reference to Si, a lot of industrial and academic research groups are reviewing and exploring Ge, its possibilities and limitations [3]. It is expected that Si can be effectively be replaced with Ge in more advanced and responsible devices as active layer [4]. Additionally, development of large diameter Ge wafers has progressed considerably in the last years. These favorable conditions stimulate growing interest in Ge.

Figure 1: Germanium wafers commercially available from Umicore ( range from 1 up to 12 inches [5])

1.2. Motivation and the scope of work

Germanium is an important semiconductor material used as an example in transistors, infrared optical devices, solar cells, such as substrate material for electronic devices. Presence of defects in material plays changes their properties such as conductivity, formation of precipitation, diffusion. Semiconductor materials are particularly very sensitive to the presence of defects, which can form one or more localized electronic states in the forbidden gap (shallow and deep levels can be introduced).

A large number of investigators have studied germanium, because for a successful industrial application, germanium layer should be free of detrimental lattice defects. In many cases defects are associated with diffusion and clustering of intrinsic point defects during crystal growth process. Some of the problems have been already resolved in the past and described in the literature. However, in many cases, there are still a lot open issues, because one of the critical issues in previous quenching experiments was fast diffusing atoms contamination like copper or nickel [6].

Nowadays, revision of previous as well as made new experiments and theoretical calculations/simulations can help to better understand the nature of the produced defects. This knowledge can be essential to controlling point defect formation and clustering behavior. Thus indirectly to quality of Ge material and also for advance device processing.

This master thesis focuses on the experimental evaluation of the formation energy of vacancy related defects based on quenching experiments. This can be done using resistivity measurements, because the resistivity depends on the carrier concentration and this is changed by the quenching experiment due to the formation of acceptors related to vacancy clustering. The formation energy can then be derived from an Arrhenius plot. In this study quenching experiments were performed using two quenching equipments, i.e. a Rapid Thermal Annealing (RTA) equipment as well as a New Rapid Quenching apparatus - NRQa that was built for this master thesis purpose. Also, different annealing times, quenching baths, sample types and thicknesses were chosen. Resistivity changes were investigated by the four point probe technique and by the van der Pauw method (at 300K). The carrier mobility in a magnetic field was measured using a Hall Effect. In the case of quenching experiments it is crucial to identify whether the change in resistivity is mainly caused by vacancy-related defects or if there is a considerable contribution due to metal contamination. This was studied by Deep Level Transient Spectroscopy (DLTS). The plan of the accurate work is schematically shown in Fig. 2.

(EXPERIMENTAL WORK Initial material)

(resistivity measurement) (p-type (750 m) n-type (750 m) p-type (2080 m) i-type * (2025 m)) (p-type (750 m) n-type (750 m) )

(etching procedure)

(quenching experiments) (NRQa) (RTA)

(Annealing for 5 minutes: 7500C, 8000C, 8500CQuenching in RTA by: radiation in constant N2 flow) (Annealing for : 10 minutes: 700 8500C 60 minutes: 7000C , 8500C Quenching by: droping in various bath's)

(Quenched material)

(resistivity measurements)

(Hall effect measurements)

(Schottky contacts)

( DLTS)

Figure 2: Plan of experimental work

2. THEORETICAL BACKGROUND2.1. Single crystal growth process

Polycrystalline materials consist of grains. The grain boundaries are defects and have significant effect on the physical and electrical properties of the material. Especially, in semiconductor materials multi-crystalline structure is of lower electrical quality. For that reason single crystals (no grain boundaries) are mainly used in microelectronic applications. When wafer cost becomes very important like in solar cells, multi-crystalline substrates are often preferred.

There are several single crystal growth methods such as Bridgman process, Verneuil process, but the Czochralski method is the most commonly used. Professor Jan Czochralski was a Polish outstanding metallurgist, crystallographer and chemist who is well known in the world as an inventor of this single crystal growth method [7]. Nowadays, this method is continuously improved and used not only for semiconductor materials such as silicon or germanium, but also for many other including lithium niobate, sapphire etc.

Briefly, in the Czochralski process, the crystal is pulled out of the melt by crystallization of the upper region of a melt meniscus. Highpurity semiconductor material is melted down in a crucible, for silicon usually made of quartz. In order to dope the crystal, impurity atoms are added to the molten phase. Afterwards, a seed crystal is dipped into the molten semiconductor, then rotated and pulled upwards, simultaneously. To extract a single crystal and to avoid unwanted instabilities (can provide change of the resistivity in some cases, especially in the central part of the crystal) the temperature gradients, speed of rotation and rate of pulling need to be restrictively controlled. However, despite this, the crystal often contains vacancy clusters. In some cases even the formation of larger agglomerates and dislocations during cooling of the crystal is possible. Larger vacancy clusters are visible as pits on the germanium wafer surface and have a similar geometry as the Crystal Originated Pits (COPs) observed on Si wafers. The COP can be modified and in some cases suppressed by hot zone design e.g. by an increase of cooling rate [8] or pulling rate [9].

Tweet [10] reported already half a century ago that presence and size of surface pits on Ge samples (Fig.3) depended on the thermal history of the crystal. During his experiments the pit density was reduced by an increase of their size. The observations were explained by a vacancy clustering mechanism, because the vacancy is the dominant intrinsic point defect in Ge.

Figure 3: Large smooth pits found upon etching sample of heat treated Ge. To be compared with typical terraced dislocation etch pit (arrow). Photograph x 40 [10]

Figure 4a) shows a schematical view of the different processes during Czochralski pulling of a crystal. At melt temperature both intrinsic point defects are present with their thermal equilibrium concentrations. It is assumed that after recombination with self-interstitials (I), a super saturation of vacancies (V) remains. This leads to the homogeneous nucleation of vacancy clusters at temperature Tn. After nucleation, further growth of the vacancy clusters is controlled by vacancy diffusion until depletion of the vacancy supersaturation [11].

a) b)

Figure 4: a) Schematic view of a Czochralski growing crystal. b) COPs observed on a Ge wafer [11]

Figure 4b) shows typical surface pits that can occasionally be observed on polished Ge wafer surfaces.

New research techniques such as computer simulation can help to make a prediction about the important impact of the cooling rate of the crystal (Fig. 5) on the density and the diameter of the voids.

Figure 5: Simulation of the void distribution, illustrating the important impact of the cooling rate of the crystal [11]

2.2. Semiconductor materials

2.2.1. The band structure

The main deference between conductors, semiconductors and insulators is their resistivity, which can be described by the electronic band structure. A semiconductor is a material as name suggests that has electrical conductivity between those of a conductor and an insulator. Basically, electrons in crystals are arranged in energy bands separated by energy gaps that are regions in energy for which no wavelike electron orbit exist. Thus the band structure of the material describes an electron energy that is allowed or forbidden for it. For insulators, no electrons can move in an electric field, because the allowed energy bands are either empty or filled. For metals as is shown in Fig.6, the energy bands are partly filled by electrons (10-90 %). For semiconductors and semi-metals, the energy bands are slightly empty or slightly filled. Origin of the energy gap is connected with the Bragg reflection condition

(1)

where k is the wavevector [12]. Its necessary to add that the intrinsic carrier concentration and intrinsic conductivity are controlled by

(2)

where Eg is the energy gap, kB Boltzmann constant and T temperature, and both will be decrease when the ratio of the band gap to temperature is large.

Figure 6: Schematic electron occupancy of allowed energy bands for an insulator, metal, semi-metal and semiconductor. The vertical extend of the boxes indicates the allowed energy regions; the shaded areas indicate the regions filled with electrons [12]

Figure 7: Plot of energy versus wave vector for an electron in a mono-atomic linear lattice constant a. The energy gap Eg shown is associated with the first Bragg reflection at k = /a; other gaps are found at n/a, for integral values of n [12]

2.2.2. Semiconductor types

Three cases ( i-type, p-type, n-type) of semiconductor types are shown in Fig.8. From left to right the simplified band diagram, including also changes in the density of states N(E), the Fermi-Dirac distribution function F(E), and the carrier concentrations are presented.

Figure 8: Schematic band diagram, density of states, Fermi-Dirac distribution, and the carrier concentration for I : intrinsic [(a) i-type] and for II: extrinsic [ (b) n-type, and (c) p-type] semiconductors at thermal equilibrium. Note that pn = ni2 all three cases [13]

Intrinsic semiconductor (i-type semiconductor, also called undoped )

In this material at 0 K the conductivity is 0, all states in the conduction band are vacant and all states in the valence band are filled (See Fig.6). At finite temperatures continuous thermal agitation exists, which results in excitation of electrons from the valence band to the conduction band and leaves an equal number of holes in the valence band, that is, n = p = ni , where ni is the intrinsic carrier density, n and p electron and hole concentration, respectively. This process is balanced by recombination of electrons in the conduction band with holes in the valence band. [13]. The Fermi level for an intrinsic semiconductor lies very close to the middle of the band gap. At high temperatures, the dominant process of carrier generation is thermal generation. The band gap of semiconductors decreases with increasing temperature. The smaller the band gap is, the higher the intrinsic carrier concentration will be, because ni increases with temperature (Fig.9a,b). This kind of material is appropriate for the study of point defect properties, because in this case, the conductivity is due mainly to thermal excitation and/or to crystal defects. It shall be deemed that in pure semiconductor any significant dopant species are present, so the number of charge carriers is depended on the properties of the material itself, instead of on the amount of impurities.

a) b)

Figure 9: a) Energy bandgaps of Ge, Si, and GaAs as a function of temperature. b) Intrinsic carrier densities of Ge, Si and GaAs as a function of reciprocal temperature [13]

Extrinsic semiconductor (doped)

In extrinsic semiconductor the number of holes in the valence band is not equal to electrons in the conductive band (n > p or n < p). Dopant atoms, which are added to an intrinsic semiconductor change the electron and hole carrier concentration of the semiconductor at thermal equilibrium and impurity (acceptor or donor) energy levels are introduced. In consequence, the higher the impurity concentration is, the lower the resistivity (Fig.10).

b) n-type semiconductor (n > p)

The concentration of electrons (majority carriers) is higher than holes (minority carriers). Due to doping with donor atoms, donor levels are introduced in the intrinsic semiconductor. The Fermi energy level lies closer to the conduction band than to the valence band and above the intrinsic Fermi energy level.

c) p-type semiconductor (p > n)

The concentration of holes (majority carriers) is higher than electrons (minority carriers). Due to doping with acceptor atoms, acceptor levels are introduced. The Fermi energy level lies closer to the valence band than to the conduction band and below the intrinsic Fermi energy level.

Figure 10: Resistivity versus impurity concentration for Ge, GaAs, and GaP at 300 K [13]

Germanium is a chemical element from group IV. The most common dopants for this group are donors from group V (As) and acceptors from group III (Ga) elements. Germanium crystallizes in the diamond structure, where each atom forms four covalent bonds, one with each of its nearest neighbors. If an impurity atom of valence five, such as arsenic is substitutional in the lattice, there will be four covalent bonds and one valence electron from the impurity, which will act as disturbance in the structure. If an impurity atom is trivalent, such as Ga, it is called an acceptor because it accept an electron from the valence band in order to complete the covalent bonds with the neighbor atoms, leaving holes in the band. As defined an acceptor level is negative if is filled by an electron and neutral if is empty. A donor level is positive if is empty and neutral if filled by an electron.

2.2.3. Energy levels in the band gap shallow and deep levels

Defects can form one or more localized electronic states in the forbidden gap of semiconductor. Deep or shallow energy levels in the band gap can be introduced by e.g. thermal treatment (vacancies related defects and/or levels connected with fast diffusing atoms) and by doping, respectively. Shallow levels are defined as energy levels less than 3kBT (0.075eV at room temperature) from the lower conduction band edge (The associated ionization energy can be approximately described by a modified hydrogen model.). In this case the impurity atoms only increase the electron concentration. Deep levels lie deeper than the corresponding hydrogenic state in the band. Electrons or holes from the shallow states which are related to doping impurities are easy to ionize, for instance at relatively low temperature. In this way free carriers for electrical conduction are produced. These carriers are trapped by deep states. Carrier mobility and lifetime are modified, because defect states act respectively as scattering and recombination centers. As is shown in Fig.11 it is possible to have many levels for a single impurity atom. For instance, copper in Ge has three acceptor levels in the bandgap. Copper is a troublesome contaminant in electrical measurements on thermal treated Ge. This fast diffusing atom can easily enter into the bulk during quenching experiments and introduces deep levels in the band gap. Simultaneously it can have an important influence on the interpretation of the effects of quenching on the electrical properties of the substrate and thus will also impact the vacancy properties derived from those experiments.

Figure 11: Measured ionization energies for various impurities in Ge. The levels below the gap center are measured from the top of the valence band and are acceptor levels unless indicated by D for donor level. The levels above the gap centers are measured from the bottom of conduction band level and are donor levels unless indicated by A for acceptor level. The band gap at 300 K is 0.66 eV [13]

2.2.4. Recombination centers

If carriers are generated in semiconductor, the thermal equilibrium condition is disturbed. For instance pn is not equal to ni2. In agreement with thermodynamic theory there needs to exist a process to re-establish the system equilibrium. There are band - to- band, single-level and multiple-level recombination processes depending on the number of levels in forbidden band gap. Let us assume that only one trapping energy level is present as is shown in Fig.12. Recombination can be described by: cn electron capture (1), en electron emission (2), cp hole capture (3), cv hole emission (4).

Figure 12: Recombination process. Single - level recombination. Ev ,Ec ,Et are the top of the valence band, the bottom of the conduction band and the trap energy levels, respectively [13]

According to Eg.3, the most effective recombination centers are those located near the middle of the bandgap (when Et Ei, = p = n). As is shown in Fig.11 many impurities have energy levels close to the middle of the bandgap they are efficient recombination centers. This plays a very important role in device applications, because the presence of impurities can efficiently reduce the minority - carriers lifetime. It must be emphasized that in some cases (i.e. switching-device application) a short life time is a desirable feature, but in other not.

(3)

where U is the recombination rate (cm-3/s), the capture cross section, th the carrier thermal velocity, Nt the trap energy level, p the hole concentration, n the electron concentration, ni the intrinsic carrier density, Ei the intrinsic Fermi level, Et the trap energy level, k-the Boltzmann constant and T the temperature.

2.3. Point defects

A point defect causes a perturbation in the periodicity of the crystal lattice. Various types of point defect can exist at the same time in one material (Fig.13). Additionally, when different types point defects are present many of point defect clusters can be created. For instance, the Frenkel pair (if a self-intersitial is close to a vacancy) or the divacancy (two vacancies on neighboring lattice sites).

Figure 13: Schematic representation of simple point defects: a) vacancy; b) self- interstitial; c) interstitial impurity; d) divacancy; e) substitutional impurity; f) vacancy substitutional impurity complex[14]

Neutral atomic imperfections - Types of point defects:

A. The vacancy

a) b)

Figure 14: a) vacancy , b) Frenkel pair [15]

Schottky defect

When a lattice atom leaves its regular lattice position and migrates to the surface direction a vacancy is formed (Fig.14a). When a high concentration of vacancies is formed, they will lead to a decrease in the density of the crystal. Vacancies can also be formed by in-diffusion from the surface to the interior of the crystal.

Frenkel pair

When an atom or ion obtains sufficient kinetic energy, it can leave its lattice site (a vacancy forms) and become an interstitial. Together with the associated vacancy it forms a Frenkel pair (Fig.14b).

A. An atom is in other position than in a regular lattice site ( interstitial)

extrinsic defect, an interstitial impurity (different nature as lattice atom)

intrinsic defect, the self-intersitial ( the same atom as lattice atom)

B. Foreign atom at regular lattice site (substitutional)

impurity at regular lattice position

anti-site atom

The atomic imperfections often occur in ionized form.

2.3.1. Point defects generation

As is shown in Fig.15, point defects can be classified as equilibrium and excess defects. The general opinion about the quenching induced defects in Ge is that they are related to vacancies, but some investigators have mentioned the possibility that the defect levels observed in quenched in germanium are also due to fast impurity contamination such as copper.

Figure 15: Classification of point defects with reference to generation method [15]

2.3.1.1. Generation of equilibrium defects

a) Enthalpy of formation

Defects can exist in equilibrium and non-equilibrium. Thermodynamic equilibrium is characterized by the minimum of a thermodynamic potential such as the Gibbs free energy i.e. systems at constant pressure and temperature. Shortly, when a system changes from a well-defined initial state to a well-defined final state, the Gibbs free energy G is equal to the work exchange.

The Gibbs free energy is defined as

(4)

which is the same as:

(5)

where:

U-the internal energy [ SI unit: J], p- pressure [SI unit: Pa], V-volume[SI unit: m3 ], T-the temperature[SI unit: K], S-the entropy[SI unit: J/K], H-the enthalpy[SI unit: J].

The presence of a defect in the material increases the enthalpy H and also decreases the entropy S (Fig.16).

Figure 16: Energy vs. defect concentration [15]

In statistical considerations, the change of free enthalpy during formation of, for instance, NV vacancies can be expressed by the Gibbs function Eq. (5) can be replaced by

(6)

where: (assumption: positive energy term can be compensated by gain of entropy) Nv correspond to vacancies, E0 vacancy formation energy and SV is complete entropy gain ( Entropy is a measure of the unavailability of a systems energy to do work.) defined by

(7)

where: kB is Boltzmann constant and G is the number of microstates corresponding to the observed thermodynamic macrostate. Probability G to form NV vacancies is Nat atoms equal to probability to choose NV atoms out of Nat atoms (numerator):

(8)

Using Eq. (7) and Stirling approximation (9)

(9)

one obtains

(10)

In thermal equilibrium:

(11)

(12)

in the lattice: NV 0. Eq.13 corresponds to the Arrhenius Equation which can be used, for example, to calculate the population of crystal vacancies. A number of investigators established that the density of quenchedin defects, in agreement with thermodynamic theory, is proportional to exp (-E0/kBT), where E0[eV] is the thermal defect formation energy and T[K] is the temperature before quenching, kB = 8,617 10-5 eV/K is the Boltzmann constant.

b) Experimental determination of point defect properties

One way to gain information on the intrinsic thermal defects is to quench the material from high temperature and to study physical properties sensitive to a change in defect concentration ex. free carrier concentration. The defects introduced by quenching induce indeed measurable changes.

The word quench refers to a rapid cooling. In material science, quenching is used to freeze in thermodynamically equilibrium. For instance, it can reduce crystallinity, because extremely rapid cooling can prevent the formation of all crystal structure, resulting in amorphous structure. In case of this manuscript, heat treatment and quenching Ge samples from different temperatures was applied to get thermally produced lattice defects. To freeze in as much as possible the thermal equilibrium at high temperature, a very high cooling rate is needed. Using a wide range of quenching temperatures allows to produce an Arrhenius plot from which the formation energy of the vacancy can be estimated. If Eq.13 is valid, the Arrhenius plot ( ln(NV) v.s 1 / T ) should be linear from which the pre-exponential (entropy ) and the activation energy (enthalpy) can be determined. Then, the slope E0 provides the formation enthalpy and the extrapolation of T-1 to zero the entropy term. Such experiments have been performed, resulting in E0 = 2.1 1.7 eV for Ge [14].

Such approach assumes:

all defects are electrically active (introduction of neutral defects does not modify carrier concentration)

there is no defect lost during the quenching process e.g. by out-diffusion, clustering or recombination (otherwise there is a considerable loss, the obtained enthalpy E0 might still be accurate, but the entropy surely not). This assumption is also valid if the loss is on independent of the temperature.

As was mentioned before, quenching experiments are difficult to perform in practice. Special care must be taken that fast diffusing impurities (such as copper in Ge) do not contaminate the sample (See 2.2.3).The interpretation of quenching data is therefore difficult and sometimes questionable (See Experimental Part). Vacancies and interstitials are mobile in germanium at studied quenching temperatures, thus the observed defects can e.g. be complexes and not single one. Additionally, the defects which are formed during quenching might not correspond to the dominant one but to the defects which have the largest ability to be trapped by impurities forming stable complexes.

2.3.1.2. Generation of excess defects

Irradiation

Ion implantation may be used to produce extended defect cascades. Also larger point defect clusters are generated under irradiaton. Using electrons up to several MeV, mostly Frenkel pairs are generated.

Plastic deformation

Depending on the temperature and other parameters, such as strain rate, point, linear and planar defects are generated by plastic deformation.

2.3.2. Diffusion

Defects more through the lattice as a result of thermal agitation. It is well accepted that in Ge, diffusion (mass transport by atomic motion) is dominated by vacancies.

Self- diffusion in Ge is the slowest diffusion process. There is strong evidence that in Ge this process is dominated by vacancies (radioactive tracer diffusion measurements [16] and Cu and Ni diffusion experiments in Ge crystals [17]). This provides direct evidence of the existence of an equilibrium concentration of intrinsic point defects. The activation energies associated with the diffusion coefficient measured in Ge range between 3.0 and 3.2 eV. The disagreement between self-diffusion and quenching results can be due to various mechanisms. The migration enthalpy is obtained from the study of the kinetics of annealing (from the change in defect concentration due to defect annihilation or association on various sinks). As the annealing process is thermally activated, the associated activation energy is the migration enthalpy. The study of the kinetics of the disappearance of the vacancies therefore provides information on the migration enthalpy of the vacancy.

2.4. Intrinsic point defect study method (literature review)

Thermal defects in Ge can be introduced in two ways: directly (quenching experiments) and indirectly (diffusion and participation of fast diffusing dopants such as Cu experiments [18]).

In the next paragraphs an overview is given of previously published experimental results with respect to the types of defects, the position of the energy levels, the activation energies for formation of thermal defects.

2.4.1. Quenching experiments

The main goal of quenching experiment was described already in 2.3.1.1.b. An example of a quenching set-up is schematically shown in Fig.17a. The set-up which was built in the frame of this master thesis, the New Rapid Quenching apparatus (NRQa) was based on this design.

After the initial preparation procedure (including careful surface cleaning to remove all metal contamination) it sample is placed in the furnace. Next, it is slowly heated in a controlled atmosphere (in case of Fig. 17A it was wet oxygen) and allowed to stabilize. The sample is quenched by dropping it in a quenching liquid, in the case of Fig. 17a this was ethylene glycol.

The concentration of quenched in defects increases exponentially with temperature in agreement with Eq.13 (See Fig.17b). The concentration is given by N = 1.85x1023 exp(-1.9eV/kT). Note that the error bars are quite large.

a) b)

Figure 17: a) Sketch of a set-up for quenching experiments. b) Number of quenched in vacancies per cm-3 as a function of quenching temperature (TQ) [18]

2.4.1.1. Thermal conversion

Thermal acceptor related defects are created in semiconductors by rapid cooling from temperatures higher than 6000C. Purde group [34] and Theuerer and Scaff [34], found that n-type germanium samples quenched from high temperature are converted to p-type material. Similar results obtained Samuelsson [19] (See Fig.18a). The observed modification in conductivity type is interpreted as an acceptor introduction and can be reversed by annealing at lower temperatures. After prolonged anneal at 400 0C, a total recovery is obtained, indicating that the out- diffusion/ annihilation of quenched- in thermal acceptors can be related to vacancies. Those experiments confirm presence of thermal acceptors. The concentration of vacancy related defects is higher if the heat treatment temperature before quenching is higher. Thermal conversion was archived (as Fuller and Struthers postulated [20]) when copper was present on the surface with .copper atoms diffusing into the sample. Further experiments were carried out to investigate the role of impurities in thermal conversion [21], [22]. Germanium specimens were covered by a number of alloys and metals and were heat treated for various lengths of time. Trousil [35] stated that not only copper atoms, but also vacancies act as acceptors. This illustrates that the mechanism of formation and annealing at thermal defects is quite complicated.

a) b)

Figure 18: a) Resistivity as a function of quenching temperature. X is a-sample with initial resistivity of 0.42 Ohmcm. O, is a sample with initial resistivity of 0.40 Ohmcm. b) Quenched- in acceptor density plotted against reciprocal quenching temperature. X is a sample with with donor density 3.3 x 1015 cm-3. o is a sample with donor density 3.5 x 1015 cm-3 [19]

Figure 19: The percentage of quenched- in acceptors not annealed plotted against annealing time in hours at 400 0C. X is a sample with initial resistivity 6.9 Ohmcm. O is a sample with initial resistivity 3.7 Ohmcm. The quenched- in acceptor density was about 1016 cm-3 in both samples [19]

2.4.1.2. Precipitation of fast diffusing dopants

As was mentioned earlier, impurities can introduce deep - level states in the band gap (See 2.2.3). In Ge, Cu atoms may be present in both interstitial and substitutional lattice positions [21]. Substitutional Cu atoms have the same order magnitude of diffusion activation energy as self-diffusion of Ge [22]. It is worth to note that thermal defects can have its origin inside of crystal (when substitutional Cu atoms moved to interstitial position) or can be formed during the Cu diffusion from the surface (dissociative mechanism [22] (Eq.14)). In the first case, contaminant atoms are very mobile, but in dissociative diffusion the migration rate of the vacancy is reduced by forming the relatively immobile substitutional Cu atoms. Substitutional Cu atoms are electrically active as acceptors, but interstitial atoms are not active at room temperature (interstitial Cu atoms act as deep donor level and they are stabile only above 700 0C [23]). Eq. 14 shows schematically the sequence of forming substitutional Cu.

(14)

where , Cus, and Cui are a Cu atom in substitutional and interstitial site, respectively, and V is vacancy.

Figure 20a shows that the solubility of Cu in Ge increases with the temperature. Fig. 20 b indicates that diffusion coefficient of fast diffusing atoms in Ge, such as Ni or Cu, is nearly independent of temperature. This shows that these atoms can penetrate into the bulk even at low temperatures. It is important to prevent samples from contamination to increase the accuracy of measurement of thermal defect energy, therefore formation in quenching experiments.

Figure 21 compares the solubility of thermal defects with that of Cu - atoms in Ge (obtained by Woodbuy and Tyler [25] ). According to Tweet [26] the solubility energy of Cus atoms in Ge is about 1.9 eV, in (400 700 0C) what is in agreement with Hiraki results [18]

a) b)

Figure 20: a) Solubility of contaminations in solid state (CBmax) in Si and Ge v.s T. Tm is melting temperature [6]. b) Diffusion coefficient Ds of contaminations in almost intrinsic state for Si and Ge v.s T [24]

Figure 21: The solubility of the thermal vacancy in Ge compared with that of substitutional Cu [18]

2.4.1.3. DLTS investigations

Substitutional copper introduces deep acceptor levels in the germanium band gap. Based on DLTS measurements, Kamiura [27] concluded that four copper-related hole traps [See Tab.1] exist in quenched germanium. The A(H1), B(H2), D(H4) traps exhibit the Poole-Frenkel effect. This mean that peak positions are shifted towards the low-temperature side by increasing the applied pulse voltage at a constant bias. This effect can be explained by the lowering of the activation energy for hole emission process under the attractive Coulomb potential of a negatively charged center, and therefore is an indication of the acceptor nature of these traps. [27]. The A(H1) trap was identified as single and B(H4) trap as double ionized acceptor levels of substitutional Cus [21]. Taking into consideration the magnitude of the hole capture cross section [See Tab.1] it can be concluded that the A(H1), B(H2) and D(H4) have a much larger cross section for hole capture than the C(H3). Additionally, the DLT peaks C(H3) and D(H4) overlap each other in spite of the considerable differences in their ionization energies. Therefore this suggests a donor character of the C(H3) trap, since the donor that is going to capture a hole is in a neutral charge state [27] [See Fig.22].

Table 1: Characteristics of hole traps observed by DLTS measurements. Level energies are with respect to the top of the valence band [31].

Trap

Energy level (eV)

Hole capture cross section (cm2)

A* (H1) B* (H2)

C* (H3) D* (H4)

0.04 0.09 0.23 0.33

(1-4) x 10-13 (1-2) x 10-13 (3-7) x 10-15 10-12 x 10-11

* New peak labels were made in case of adequate comparison with new obtained results (See 5.2).

Figure 22: DLTS spectra for a sample which was copper-diffused at 500 0C and then annealed at 280 0C for 60 min. Both reverse and pulse bias voltages are 1 V for the solid curve and 3 V for the dashed curve [27]

After annealing at 280 0C for 60 min (dashed curve in Fig.22), the B(H2) and C(H3) traps disappear and the densities of the A(H1) and D(H4) traps increase at the same time. In Fig.22 the A(H1) peak does not change by the annealing. In accordance with Kamiura [27] Annealing around 200 0C caused simultaneous annihilation of B(H2) and C(H3) traps with a correlated increase in Cus density by almost the same amount as the densities of annihilated B(H2) and C(H3) [27]. Study of the annealing kinetics by analyzing the resistivity changes according to Eq. 15 and the donor character of C(H3) trap point out that C(H3) arises from Cui and B(H2) from the Cui Cus pair.

(15)

3. EXPERIMENTS

3.1. Sample preparation

Quenching experiments were performed on monocrystalline, dislocation free germanium samples, prepared from a crystal pulled by Czochralski method. An overview of the investigated crystal samples is given in Tab.2.

3.1.1. Cutting

The samples were cut out out of the germanium wafer by scratching with a diamond and pressing included this cracking along the directions. Samples from thick germanium wafers, i.e. p-type (2080m), i-type (2025m)*, were cut out using a cutting device (Fig.23b).

Table 2: Investigated crystals specification

Material

Diameter

[mm]

Thickness

[m]

Sample dimensions [mm3]

Doping

Initial resistivity

[cm]

p-type

200

750

12x12x0.75

2.5x1014

17.93 0.65

5x5x0.75

n-type

200

750

15x15x0.75

0.25x1014

12.44 0.36

p-type

100

2080

10x10x2.08

5x1017

0.0128 0.0045

i-type*

100

2025

10x10x2.025

7x1014

5.08 0.09

* Company which produced this wafer labeled it as i-type. In fact it is p-type material (monocrystaline Ge was pulled after p+ crystal leading to residual doping). In undoped material the intrinsic carrier concentration at 300K is 2.4x1013 and the intrinsic resistivity is 47 cm.

a) b)

Figure 23: Sample preparation: a) Schematic examples of cleavage of thin wafers b) Cutting device used for thick wafers

3.1.2. Etching

The samples were carefully cleaned to remove contamination (fast diffusing atoms such as Cu, Ni which may diffuse into the bulk during quenching experiments and introduce deep levels in the band gap). At first, they were rinsed with high purity methanol (99.95%), then etched for 1 min in a solution of HF-HNO3 (1:3 ratio), rinsed with distilled water and immersed in methanol again. The etching process was slow and the solution changed color to yellowish.

Figure 24: Sample cleaning by etching

3.2. Quenching

Quenching experiments are difficult to perform in practice and the interpretation of the obtained data is complicated. Accuracy and uniformity of the annealing treatment temperature, and rate of quenching process are the key to proper measurements. To study vacancies or interstitials or both and to minimize the effects caused by chemical impurities such as Cu two approaches were used: Rapid Thermal Annealing (RTA) and New Rapid Quenching apparatus (NRQa).

3.2.1. Rapid Thermal Annealing (RTA)

After etching, the samples were held in high-purity proactive environment of high-purity methanol. For the rapid thermal annealing experiment, the samples were mounted in a silicon holder in the furnace chamber (Fig.25) and covered with a piece of silicon wafer. The following procedure was applied in heaters:

flushing the chamber with N2 (30s)

heating up to 700oC, 750 oC, 800 oC or 850 oC (20s)

annealing for 5 min

cooling in constant N2 flow - 2 min

a) b)

Figure 25: Rapid thermal annealing experiments: a) RTA - sample in a silicon holder, b) The annealing cycle

3.2.2. New Rapid Cooling apparatus (NRQa)

The cooling rate in RTA is rather low. This is the reason why a new quenching setup was made (Fig.27). After the etching procedure, the sample was placed in a quartz holder shown in Fig. 26, and a quartz tube inserted into which was tightly-closed.

Figure 26: Ge sample (5x5x0.75mm) in quartz holder, inside quartz tube with argon atmosphere

Figure 27: Schematic explanation of NRQa - New Rapid Quenching apparatus

The parts of the system within the dashed line in Fig. 27 are inside a horizontal furnace. Blue arrows show the direction and displacement of the sample placed on the quartz holder. Green arrows indicate the direction of gas flow. The experiments were made with reverse gas flow. However, it was found that the gas flow direction shown in Fig. 27 by the green arrows as offers better heat treatment condition. The temperature was controlled by PDI controller and was measured by thermocouple No. 1 and No. 2. The Ar flow was protectied the samples contaminants, and from oxidation temperature.

The following procedure was applied:

flushing the quartz tube with Ar (20 minutes) and waiting for an accurate temperature in furnace chamber

placement of the sample into the center of the furnace chamber

heating up the sample to 700oC, 750 oC, 800 oC or 850 oC and annealing (10 or 60 minutes)

cooling by dropping the sample into quenching bath

3.2.2.1. Quenching baths

To find the best quenching medium, tests with 6 liquids with different thermal conductivities were performed (See Tab.3). Experiments were carried out on monocrystalline, dislocation free germanium p-type samples with dimensions 5x5x0.75mm. The samples were heat treated for 10 minutes, at 850 0C. For the ethylene glycol bath, the sample dimensions were 12x12x0.75mm and 5x5x0.75mm.

Table 3: Thermal conductivies of at 25 0C the quenching liquids used here [32]

Substance

W/mK

Distilled water

0.58

Ethylene glycol

0.25

Methanol

0.21

Polyphenyl ether

0.14

Silicon oil

0.1

Liquid nitrogen

0.024

[1W/(m.K) = 1 W/(m0.C) = 0.85984 kcal/(h.m.0C) = 0.5779 Btu/ft.h.0F

3.3. Resistivity measurements

The four point probe technique and the van der Pauw method were applied to measure the sample resistivity before and after thermal treatment.

3.3.1. Four point probe technique

In order to investigate the uniformity of the germanium p-type (750m) wafer, resistivity measurements were carried using the four point probe technique [28] see Fig. 28 out only for initial wafer.

Figure 28: A schematic explanation (a) and photo (b) of the set up for four point probe measurements of conductivity

For probes resting on a semi-infinite medium, with current entering probe 1 and leaving probe 4, and assuming an equal spacing between the probes, the resistivity is given as:

(15)

The correction factor F depends on the sample geometry and can be divided into three components: F1, F2 and F3, which correct respectively, for: a) sample thickness, b) lateral dimensions and c) the position of the probe relative to the sample edges. These components have multiplicative character as described by the following expression:

(16)

In the measurements that were carried out, there was a non-conducting supportingwafer, the probe spacing s = 1.59 mm, sample thickness t = 0.75 mm and the distance to the edge was l.

The correction factors are given as follow:

(17)

(18)

(19)

Four point probe resistivity measurements were carried out on the p-Ge wafer along the radius. In each point, the measurements were performed three times, to eliminate the error connected with the differences in the applied force. Resistivity was measured at 15mm, 40mm and 70mm from the middle of the wafer and calculated from Eq. 15, using the correction factors from the Eq. 20, 21 and 22.

3.3.2. Van der Pauw metod

The van der Pauw method [28] was applied in order to measure the resistivity changes after heat treatment. One of the advantages of the van der Pauw technique is the small sample size compared with the size required for four-point probe measurements.

Figure 29: The sample configuration in the van der Pauw method

Ohmic contacts A, B, C, D were made along the periphery of the sample. The resistance RAB,CD is defined as RAB,CD = UCD/IAB where the current enters the sample through contact A and leaves through contact B; UCD = UC UD is the voltage difference between the contacts C and D. RBC,DA is defined in the similar way.

The resistivity can be calculated from:

(20)

where F is a function of the ratio Rr = RAB,CD/RBC,DA, satisfying the relation

(21)

The van der Pauw equations are based on the assumption of negligibly small contacts at on the sample periphery.

The measurements were carried before and after thermal treatment. The total carrier concentrations (Ntotal) were calculated using the following formula:

a) in the case of holes

(22) b) in the case of electrons

(23)

The electron and hole mobility at room temperature were assumed to be equal to the drift mobility for high purity germanium, e = 3900cm2/V s and h = 1900cm2/V s, respectively [28]. The concentration of carriers introduced by the quenching induced acceptors, increases exponentially with annealing temperature according to Eq.14 and is given as

(24)

where N(= NV) is the concentration of acceptors (holes) introduced by annealing in the temperature T; E0 [eV] is the energy of thermal defect formation and the prefactor is N0 ( =Nat) [ cm3]. The energy of formation of the thermal defects can be estimatedby plotting lnN vs. 1/ kB T, where kB = 8,617 10-5 eV/K is the Boltzmann constant.

For p-type samples the initial carrier concentration is subtracted from the concentration of carriers present in the material after annealing (N = Ntotal - Ninitial).

For n-type samples the doping concentration Ninitial was added to the concentration the carriers present in the material after annealing (N = Ntotal + Ninitial) in the case of sample which material had changed into p-type. In the case of the samples, which did not change to p-type, the initial (dopant) carrier concentration was subtracted from the total carrier concentration (N = Ninitial Ntotal)

3.3.2.1. Reproducibility of resistivity results

In order to check the reproducibility of the resistivity measurements (van der Pauw method) every sample (in NRQa). The currents of: 1,4 ; 1,2; 1; 0,7; 0,5;0,3;0,05 and 0,03 (mA) were applied in both directions.

Fig. 30 shows an example of obtained values for one specimen. It was observed that the last five values of resistivity remain in good agreement. The average of these values was calculated and used in the further analyses. In the case of RTA, resistivity was measured only for a current of 1 mA.

Figure 30: Dependence of resistivity on the current for sample i-type* Ge treated at 750 0C

3.4. Hall effect

The Hall effect measurement technique [28] has found wide applications in the characterization of semiconductor. This technique allows to determine the carrier concentration type, and Hall-mobility and the resistivity, in a relatively simple measurements that can also be performed as a function of temperature .

a) b)

Figure 31: Hall effect measurement. a) Schematic, b) Experimental setup

A magnetic field applied to a conductor, perpendicular to the current flow direction, produces an electric field perpendicular to both the magnetic field and the current (Fig. 31a). The Hall coefficient RH and the Hall mobility H, are obtained the van der Pauw configuration. By changing the current flow direction in a and without magnetic field it, the Hall voltage can be measured, from which the Hall coefficient RH can be derived using

(25)

where t is the sample thickness, VH the Hall voltage, B the magnetic field and I the current. Measurements were performed for B= 0.2 T and 0.3 T , and average value was calculated.

The Hall mobility H is defined as

(26)

where is the resistivity (obtained from a resistivity measurements). The Hall mobility is not identical to the conductivity mobility. The differences can be quite significant especially for the current due to motion of holes. Therefore in order to calculate the carrier concentration, the Eq. 22, 23 must be corrected for the Hall scattering-factor (r). This lead to the following formula:

(27)

(28)

where p is the total concentration of holes and n the total concentration of electrons. RH is the Hall coefficient and e the elementary charge of 1.61019C.

The Hall mobility depends on the temperature and carrier concentration as is shown in a Fig.32a and Fig.32b. In case of the experiments carried out on p-type semiconductor the Hall mobility was calculated from the Eq.26 with the resistivity values obtained by the van der Pauw technique. The Hall mobility H for the as-received sample is differing from the ideal drift mobility h = 1900 cm2/Vs by the factor r. Therefore, this r factor was assumed to be the same for the annealed samples and the apparent conductivity motilities were calculated from the following equation:

(29)

a) b)

Figure 32: Literature examples of (a) Hall mobility/conductivity as a function of temperature [29]and (b) the concentration dependence of the Hall mobility at room temperature [30]

3.5. Deep Level Transient Spectroscopy (DLTS)

The effects metallic atoms in germanium have been investigated intensively between 1952 1965 using Hall Effect and photoelectric measurements. Deep-Level Transient Spectroscopy (DLTS) and Photo Thermal Ionization Spectroscopy (PTIS) were later use for more detailed studies of metal atoms related defects in Ge during the 1980s and early 90s.

Deep-level transient spectroscopy (DLTS) is a powerful method to characterize traps in semiconductors. In the case of quenching experiments, it is crucial to identify whether the change in resistivity is caused by vacancy-related defect levels or by metal contamination. The DLTS technique is based on junction capacitance measurements. It requires the presence of a carrier depleted layers and therefore samples with Schottky barriers or p-n junctions.

In this master thesis, Schottky barriers were used. The barrier contacts were developed on the surface, of the samples etched for 1s in a solution of HF:HNO3 (1:3 ratio) and on as-cleaned.The layer of indium was evaporated on one side Fig.33a) and indium-gallium contact put on the opposite side, see Fig.33b). The sample was placed for measurements into the cryostat. The measurement was carried out over a range of temperatures, for example from 6 K up to 185 K ( in , where the liquid helium was the cooling medium.

a) b)

Figure 33:Stages DLT sample preparation: a) the layer of indium on the sample, b) DLT holder

a) b)

Figure 34: Sputtering device (a) and DLTS equipment (b) used in the present study

By applying a bias pulse in the depletion of Schottky barrier and analyzing the capacitance transient associated with the return to equilibrium conditions over a range of temperatures the spectrum of traps present in the material can be obtained. The peak positions are determined by the thermal emission of the respective traps and the peak heights are proportional to the trap concentration. The sign of each peak indicates whether it is due to a minority or a majority carriers. This technique can be used to measure the thermal emission rate, activation energy, concentration depth profile and to estimate capture rate of each trap.

3.5.1. Basic principles of the DLTS method

In order to explain DLTS, the pulsed bias capacitance transients should be first considered. A reverse biased pulse applied into Schottky diode changes metal-semiconductor interface and as a consequence the occupation of deep energy levels (See Fig.35). If the reverse bias decreases, the width of depletion region also decreases. When the investigated level is below EF if is fully filled. When the reverse bias increases again, the investigated level is above EF and emission of the trapped carriers to the original state takes place In the transition region (y < x < w) the equilibrium occupation of defect states exists due to generation-recombination processes. The neutral region (x > w) charge of the ionized dopants is canceled by the presence of mobile carriers. When x < y, the observed region is totally depleted of mobile carriers (occupation is controlled through emission processes) [31].

Figure 35: Structure of a metal n-type semiconductor junction under reverse bias with one deep trap: VB is the junction barrier height: VR is the applied reverse bias, EC is the energy position of the conduction band edge, ED is the shallow donor level, EF is the Fermi level, ET is the trap level, y is the point at which EF and ET intersect, and W is the edge of the depletion region: the boundary conditions are V (0) and V (W) = VB +VR. [31]

Minority and majority carrier traps can be defined in the depletion region in terms of the thermal emission. In the case of minority carriers traps, thermal emission is much lower than the corresponding rate for majority carriers (emin >> emaj). The opposite is for majority carrier traps (emaj >> emin). It should be noted that an electron trap is a minority carrier trap in p-type material and majority carrier trap in n-type material.

Figure 36: Definition of the terms majority carrier trap and minority carrier trap(vertical columns) and electron trap and hole trap (horizontal rows) (the relative magnitudes of the carrier emission rates en and ep are indicated by the width of the arrows [31])

The rate window concept is an essential part in DLTS measurement. It is necessary to set an emission rate window such that the measurement apparatus only responds when it sees a transient with a rate within this window. If the emission rate of a trap is varied by varying the sample temperature, the instrument will show a response peak at the temperature where the trap emission rate is within the window[31].

a) b)

Figure 37: a) Schematic illustration of the basic principle of the DLTS method, namely, the rate window concept: The lower part of the figure is a typical activation energy plot for the case of two traps. The upper part of figure shows the resulting response of figure shows the resulting response of a capacitance transient measurement apparatus equipped with a rate window; b) Definition of the rate window by a double boxcar. The left hand side presents capacitance transient at various temperatures, and the right-side is the corresponding DLTS signal whereby the signal is defined by the difference between the capacitance at time t1 and t2 as a function of temperature [31]

3.5.2. DLTS limitations

DLTS technique has also some limitations. The most serious one is difficults in preparing a good device, for which basic principles (par 3.5.1) are applicable.The second one is heavy doping. Capacitance spectroscopy is essentially a boot-strap technique where the minimum detectable defect concentration is always some fraction (typically 10-4) of the shallow level doping. Thus, for example in material with shallow level concentration of 1014 cm-3, one has a defect detectability limit of 1010 cm-3. With material doped to 1018 cm-3, on the other hand, one cannot see defect less than 1014 cm-3 in concentration. Heavy doping also creates large electric fields in the depletion layer which may influence the results.[31].

4. RESULTS

4.1. Repeatability of setups

4.1.1. Rapid Thermal Annealing (RTA)

Samples p-type (750 m) - the cooling rate was estimated by calculating the temperature slope for every 100oC as plotted for samples annealed at 750oC, 800oC and 850oC in Fig.38. The cooling rate estimated in this way was in the range 20-25oC/s between 850oC and 600oC and 4 - 15oC/s in lower temperatures (500 - 300oC). Higher cooling rates were intended to be applied for p12-850 oC (flow rate 15 instead of 10 - in arbitrary units). However, the cooling temperature profile was not changed significantly.

Figure 38: Cooling profiles for samples annealed in 850oC, 800oC and 750oC, respectively

For samples n-type (750 m)- the cooling rate was estimated in the same way, as plotted for samples annealed at 750oC and 800oC in Fig. 39. At high temperatures it reached values in the range 20 - 25oC/s and at lower temperatures 4 10 oC/s. For each temperature two runs of RTA were carried out. In the first, only one sample was annealed, and in second three were placed in a holder and annealed together. There were no significant differences observed between cooling for different batches. However, in the second case the cooling rate is slightly lower, as shown on Fig. 40. This small difference had already strong influence on the results, because the sample which cooled down slightly faster changed in type already after annealing at 750oC while the ones annealed in the second run, remained n-type, as will be shown later. The purpose of annealing 3 samples at the same time (in one batch) was to check or not the scatter of the results is a due to the differences in cooling rate. It occurred that the samples annealed in the same batch had various concentrations of thermally induced carriers, so the cooling rate was not the only factor that contributed to the high scatter of the measured values.

Figure 39: Differences in cooling for various batches

Figure 40: Approximate coolings as a function of temperature

.

4.1.2. New Rapid Quenching apparatus (NRQa)

To check reproducibility of the quenching setup, tests with and without samples were carried out. The total heating process was 10 minutes. The temperature was measured by two thermocouples. Average for two runs are shown in Fig. 41. Temperature differences are noticeable till 2 minutes after start of heating procedure.

Figure 41: The setup temperature as a function of time with and without sample, measured by two thermocouples,(a p-type 750m) sample

4.1.2.1. Quenching baths

a) Ethylene glycol

This fluid was used in the past [32]. Unfortunately, in the present study first tests showed that quenching of p-type samples (10x10x0.75mm) in ethylene glycol resulted in their disintegrator (Fig.42). To prevent that situation in next tests a smaller size of samples (5x5x0.75mm) were used and a glass wool pad was used to protected them from shock on hitting the ethylene glycol bath.

Figure 42: Ge p-type sample (10x10x0.75mm) after quenching in ethylene glycol

Unfortunately, significant resistivity differences were observed for samples heated at the same temperature. This can be explained by the fact that samples were dropped to in a different spot in the container liquid. For instance, the sample dropped on glass wool (Fig.43) or in the ethylene glycol are expected to be exposed to a quite different quenching history and thus also different final resistivity.

Figure 43: Ge p-type sample (5x5x0.75mm) after quenching in ethylene glycol lies on glass wool pad

b) Other

Samples quenched in distilled water and ethylene glycol also disintegrated in small pieces. To as sure of the reproducibility of result obtained for ethylene glycol (See 4.1.2 a), additional tests were made with another shape of container. The sample broke again and it was decided not to use this quenching liquid. In all other cases lower resistivity than the was measured. The results obtained [Tab.4] are in good agreement with thermal conductivity date (See Tab.3, Fig.44). The results Table 3 give evidence that distilled water and ethylene glycol have the highest thermal conductivity. However, in these liquids leads to a destruction of the samples. The lowest resistivity was reached for samples quenched in methanol and the highest for samples quenched in liquid nitrogen.

Table 4: Resistivity data for p-type (5x5x0.75mm) germanium after quenching from 850 0C, quenched in different cooling fluids

Resistivity values for different cooling mediums [cm]

850 0C

(distilled water)

850 0C

(ethylene glycol)

850 0C

(methanol)*

850 0C

(SANTOVAC 5 oil)

850 0C

(silicon oil)

850 0C

(liq.nitrogen)

p-32-4 **

p-32-1 **

p-32 1.37

p-34-3 1.47

p-34-4 1.65

p-35-1 1.47

p-35- 2 1.67

p-141-1 3.34

p-142-2 3.40

p-142-4 2.87

p-150-1 2.68

p-150-2 3.14

p-143-3 4.52

p-143-4 4.68

Average -----

St.Dev. -----

-----

-----

1.37

-----

1.57

0.11

3.09

0.31

4.6

0.11

* flammable: dangerous

** samples broken

Figure 44: Resistivity data for p-type (5x5x0.75mm) germanium after quenching in different fluids

Due to the flammability of methanol, it was decided not to use it for further quenching experiments. Further experiments were carried out in SANTOVAC 5 oil . The results obtained revealed, however, that despite lower thermal conductivity, the best bath was silicon oil. The use of resulted in high scatter the results (See Fig.45).

First measurements in this series of experiments, performed for 700 and 850 0C seemed to be very promising. However, additional tests in 750-825 0C gave very questionable results. Experiments were performed a second time with fresh SANTOVAC 5 oil and the scattering was confirmed. Especially for 795 0C a large variation was noticed. The cause of this scattering is difficult to explain. However, it is clear that the SANTOVAC 5 color was changing (Fig.46) during quenching experiments, which indicates changes in the oil properties and might be the reason of the large scatter of date.

Figure 45: Dependence of resistivity results for p-type (5x5x0.75mm) germanium quenched in SANTOVAC 5 oil (polyphenol ether)

Figure 46: Color change of SANTOVAC 5 oil: A - after two weeks, B - fresh oil

4.2. Resistivity measurements

4.2.1. Four point probe tests

Four point probe resistivity measurements were carried out on the p-type (750 m) germanium wafer along its radius. In each point, the measurements were repeated three times, to eliminate the error connected with the differences in the force applied to connect which pressed the probes to the sample surface. Resistivity was calculated for measured 15, 40 and 70mm from the middle of the wafer and using from the Eq. 15, and the correction factors from the Eq. 17, 18 and 19. The obtained values were respectively 19.46, 19.11 and 19.27 cm. Based on this, it can be stated, that the initial resistivity of the wafer is uniform and was estimated at = 19.3 0.2 cm.

4.2.2. Van der Pauw method

4.2.2.1. After RTA

Samples p-type (10x10x0.75mm) - the measurements were performed right after annealing and repeated after different time intervals in order to detect any changes with time. It was observed that the resistivity decreases with the annealing temperature due to higher number of acceptors being quenched (Fig45). This drop in resistivity is predicted by the theory (Fig. 9a) and confirmed by the previous experiments Fig. 17b. The quenched samples remain stable with time (Fig.48) within the measurement error (3%).

Table 5: Resistivity data for p type (10 x10 x0.75mm) germanium before and after annealing

Resistivity changes with anneal temperature [cm]

Initial

750 0C

800 0C

850 0C

p02 17.90

p09 17.67

p28 17.86

p29 18.02

p03 7.74

p10 9.67

p13 7.48

p25 6.51

p04 3.86

p11 5.46

p14 3.95

p26 4.21

p05 2.59

p12 2.65

p15 2.98

p27 2.25

Average 17.86

St.Dev. 0.14

7.85

1.32

4.37

0.74

2.87 0.30

Figure 47: Scattering of the results for p-type samples (10x10x0.75mm) annealed at 750, 800 and 850oC for 5 minutes

Figure 48: Resistivity changes with time for p-type samples (10x10x0.75mm) annealed at 750, 800 and 850oC for 5 minutes

Fig.49 shows the dependence of thermally induced carrier concentration on the annealing temperature for p-type (10x10x0.75mm ). The obtained value of energy of thermal defect formation E0 is 1.38 0.17 eV and the prefactor is N0 = 1.521021 cm3. This formation energy is much lower than the 2eV obtained by Letaw [6] .

Figure 49: Dependence of thermally induced carrier concentration on the annealing temperature for p-type (10x10x0.75mm) after a 5 minute anneal

Samples n - type (12x12x0.75mm) - the experimental results are listed in Table 6. The resistivity of the n-type sample increases with the annealing temperature for the reasons explained earlier.

Table 6: Resistivity measurements for n-type (12x12x0.75mm) germanium before and after an-nealing

Resistivity changes with anneal temperature [cm]

Initial

700 0C

750 0C

800 0C

850 0C

n24 11.87

n29 12.01

n34 12.23

n24 15.83

n32 13.18

n47 15.27

n30 7.06

n23 15.53

n33 12.46

n48 13.18

n29 2.56

n26 2.92

n34 3.23

n49 3.91

n28 1.77

n27 1.80

n35 1.55

n50 3.08

Average 12.04

St.Dev. 0.18

14.76

1.40

12.06

3.58

3.16

0.33

2.05

0.14

The samples annealed at 750 and 800oC exhibit behaviors similar to the intrinsic material. The concentration of dopant is compensated by the generated carriers. The resistivity drops down, due to increasing number of acceptors formed. Some samples annealed at 750oC did not change their semiconductivity type. Their resistivity did not differ from the initial resistivity (and was lower than for the sample annealed at 700oC). This samples therefore they were not analyzed in calculating of the defect formation energy. Only the sample which changed to p-type were taken into consideration. The obtained value of thermal energy defect formation E0 is 2.29 0.29 eV and the prefactor N0 = 4.461025 cm3. This formation energy is much closer to previously published values.

Figure 50: Resistivity as a function of quenching temperature

Figure 51: Dependence of carrier concentration on the annealing temperature.

4.2.2.2. After NRQa

a) Samples p-type (5x5x0.75mm)

First experiments with silicon oil bath were made with a gas flow opposite to the one indicated in Fig. 27. The results are listed in Table 7. A decrease in resistivity is observed, as expected. However, the obtained energy of thermal defect formation is too low (E0 = 0.78 0.17 eV with prefactor N0 = 2.76 1018 cm3). This suggests that the cooling rate in this configuration was higher than in RTA.

Table 7: Results of the resistivity measurements for p-type (5x5x0.75mm) germanium after annealing for 10 minutes and quenching in silicon oil

Resistivity changes with anneal temperature [cm]

Initial

750 0C

800 0C

850 0C

p02 17.90

p09 17.67

p28 17.86

p29 18.02

p-154-3 5.16

p-145-4 6.14

p- 145-3 5.56

p-153-1 4.03

p-150-3 4.35

p-150-3 4.50

p-141-1 3.34

p-142-2 3.40

p-142-4 2.87

p-150-1 2.68

p-150-2 3.14

Average 17.86

St.Dev. 0.14

5.62

0.49

4.30

0.24

3.09

0.30

Figure 52: Resistivity values for samples p-type (5x5x0.75mm) annealed at 750, 800, and 850 0C for 10 minutes, and quenched in silicon oil

Figure 53: Dependence of thermally induced carriers concentration on the treatment temperature for p-type (5x5x0.75mm) germanium samples annealed for 10 minutes and quenched in silicon oil

To improve cooling rate, gas flow direction was changed to the one indicated in Fig.27. The obtained resistivities obtained afterthat are given in Tab.8 and shown in Fig.54. The energy of thermal defect formation is estimated at E0 = 1.53 0.14 eV and the prefactor is N0 = 4.13 1022 cm3. For this configuration, the cooling rate was higher, because the holder was drown out in the same direction as gas flow. In the consequence, E0 is higher than in the previous case.

Table 8: The results of the Resistivity measurements for p-type (750 m) germanium after treatment, quenched in silicon oil

Resistivity changes with anneal temperature [cm]

Initial

700 0C

725 0C

750 0C

775 0C

800 0C

850 0C

p08 18.83

p09 17.27

p28 17.82

p29 17.81

p190-2 6.46

p190-3 4.8

p190-8 6.67

p162-1 3.78

p-162-3 3.78

p-190-4 3.1

p168-3 2.1

p168-2 3.22

p190-9 3.27

p170-1 1.72

p170-3 1.29

p163-1 2.04

p167-2 1.67

p168-1 0.84

p190-6 0.78

p167-3 0.54

p141-3 0.76

p167-4 0.66

Aver. 17.93

St.Dev. 0.65

5.98 1.03

3.55 0.39

2.86

0.66

1.68

0.38

1.1

0.5

0.65

0.11

Figure 54: Dependence of thermally induced carrier concentration on the temperature for p-type (750m) germanium samples annealed for 10 minutes and quenched in silicon oil

The resistivity data for p-type (750 m) samples treated for 10 minutes at 700, 725, 750, 775, 800 0C and quenched in silicon oil, are given in Figure 55.

The estimates of n resistivity for samples treated at 8500C were not taken into account in the Arrhenius plot (like Samuelsson et al did ). The estimated activation energy was E0 = 1.74 0.33 eV with prefactor is N0 = 4.521023 cm3 (Fig.55).

Hall Effect was also used for p-typ (750m) germanium samples (thermal treatment for 10 minutes) to determine concentration and activation energy for thermal defects. The value E0 = 1.97 0.21 eV and N0= 9.051024 cm3 were obtained. Carrier concentration was calculated from Hall Effect assuming a scattering factor of 1.5 (Fig.55).

The carrier concentration from Hall Effect was plotted together with average values of carrier concentration obtained by van der Pauw method are plotted in Fig. 55.

Figure 55: Concentration of thermally introduced carriers vs. reciprocal temperature for p-type (750m) germanium samples treated for 10 minutes (carriers concentration for both Hall Effect and Van der Pauw technique obtained)

b) Samples p - type (10x10x2.08mm)

Resistivity values were estimated for the current: 60; 50; 40; 30; 20; 10 (mA) in both current directions. Obtained values (Tab.9 and Fig. 56) show that material is highly doped. According to the literature, the thermal treatment of high doped material results in defect concentrations remaining well below the dopant concentration.In the consequence, no resistivity change is observed, even for the highest anneal temperatures. However, to much a surprising the resistivity of examined samples insignificantly increases after quenching.

Table 9: The results of resistivity measurements for p-type (2080 m) germanium

Resistivity changes with anneal temperature [cm]

initial

700 0C

850 0C

p-300-1 0.0103

p-300-2 0.0188

p- 300-6 0.0106

p-300-2 0.0341

p-300-4 0.0260

p-300-1 0.2540

p-300-5

0.0107

p-300-6

0.0108

p-300-7

0.0108

Average 0.0128

St.Dev. 0.0045

0.1047

0.1294

0.0108

0.0001

Figure 56: Resistivity values for samples p- type (2080 m) in initial state and annealed at 700 and 850 0C, quenched in silicon oil

Samples i- type (10x10x2.025mm)*

Annealing of this samples were preformed for 10 and 60 minutes (Tab.10) to see possible resistivity change due to prolonged annealing. It was observed that the resistivity of samples treated for 60 minutes is lower than that of samples annealed for 10 minutes (Fig.57). As a consequence, thermal defect concentration and the observed defect formation energy are different ( see Fig. 58).

Table 10: The results of resistivity measurements for i-type (2025m) germanium before and after quenching in silicon oil

Resistivity changes with temperature [cm]

Time

Initial

700 0C

750 0C

800 0C

850 0C

10 min

300 K

i-303-1 5.01

i-303-5 5.14

i-303-18 4.2

i-303-13

3.64

i-303-19 2.84

i-303-12 2.0

i-303-11 2.2

i-303-10 2.35

Average

5.08

St.Div.

0.09

2.18

0.17

60 min

300 K

5.01

i-303-23 4.17

i-303-22

2.6

----

i-303-21 1.07

The formation energy obtained for 10 minute anneals is E0 = 1.17 0.03 eV with prefactor N0 = 1.641020 cm3 while for 60 minutes E0 = 1.74 0.31 eV and N0 = 1.731023 cm3.

Figure 57: Resistivity data for i-type (2025m) germanium after annealing for 10 and 60 minutes and quenching in silicon oil

Figure 58: Dependence of thermally induced carriers concentration on the treatment temperature for i - type (2025 m)* for germanium samples anneald for 10 and 60 minutes

4.3. Hall Effect

4.3.1. Samples p-type (750 m)

The Hall mobility H for the samples prior to their annealing is different by a factor r1 = 1.56 (in case RTA) and r2 = 1.53 ( in case NRQa) from the ideal drift mobility h = 1900 cm2/Vs. These r1 and r2 factors were assumed to be constant for other samples in every batch and the apparent conductivity mobilities were calculated from Eq.29 ( See Tab.11 and Tab.12).

Table 11: The initial resistivity, Hall coefficient RH, total carrier concentration Ntotal , Hall mobility H, Hall mobility*(a factor) H * and total carrier concentrations Ntotal for p-type germanium before and after thermal treatment in RTA

[cm]

RH [m3/C]

Ntotal [cm-3]

H [cm2 /Vs]

H * [cm2 /Vs]

Initial

17.86 0.14

0.053 0.003

1.18 1014 9.36 1011

2970 170

1900 110

750 0C

7.85 1.32

0.019 0.003

5.00 1014 6.77 1013

2420 380

1550 250

800 0C

4.37 0.74

0.008 0.001

1.14 1015 1.13 1014

1830 230

1170 150

850 0C

2.87 0.30

0.006 0.001

1.69 1015 1.19 1014

2090 350

1340 220

Table 12: The results of the measurements of the resistivity, total carrier concentration Ntotal , Hall mobility H, Hall mobility*(a factor) H * and total carrier concentrations Ntotal for p-type (750m) germanium before and after thermal treatment in NRQa

[cm]

RH [m3/C]

Ntotal [cm-3]

H [cm2 /Vs]

H * [cm2 /Vs]

Initial

17.20

0.050

1.23 1014

2910

1900

700 0C

4.71

0.013

4.66 1014

2800

1830

750 0C

3.32

0.007

8.92 1014

2110

1380

775 0C

1.31

0,003

1.86 1015

2290

1500

8000C

0.8

0,002

2.82 1015

2500

1630

The dependence of Hall mobility on the carrier concentration for samples treated in RTA and NRQa is shown in Fig. 59. It was found that for both setups the tendency is similar. The mobility drops to a minimum at around 1x1015 cm2 of the total concentration and afterwards increases again. Three conclusions are still possible: 1. scattering factor changes. 2. Drift mobility changes 3. Both.

Figure 59: The Hall mobility*(a factor) H * dependence on the carrier concentration

Figure 60: The Hall mobility*(a factor) H * dependence on the annealing temperature

4.3.2. Samples n-type (750 m)

In the initial state, the majority carriers were electrons and by heating and quenching, acceptors are introduced. For each annealing temperature, there was specific number of acceptors introduced to the sample. This resulted in a change of the sign of a Hall coefficient at the certain annealing temperature, for which sufficiently large number of holes was introduced to compensate the dopant concentration. The obtained results are not conclusive for samples annealed in 800oC, because of the accuracy of the measurements.

Table 13: The results of measurement of resistivity, Hall coefficient RH, Hall mobility H, for n-type (750 m) germanium before after annealing

[cm]

RH [m3/C]

H [cm2 /Vs]

Initial

12.04 0.18

-0.0484 0.0035

4020 310

700 0C

14.76 1.4

- 0.0494 0.0078

3350 420

750 0C

p750 0C

12.06 3.58

-0.0345 0.0033

0.0132

2420 382 1870

800 0C

p800 0C

3.16 0.33

-0.00002 0.0002

0.00158

60 30 620

p-> 850 0C

2.05 0.14

0.0003 0.0002

110 50

Fig. 61 shows the dependence of carrier mobility on the annealing temperature. For non heat-treated samples, the mobility measured at room temperature does not differ from the drift mobility for high purity germanium e = 3900cm2/Vs [13]. The possible reason of very low mobilities of the samples after annealed at high temperatures changed to p-type is that their non uniform. As was mentioned in paragraph 2.2.3, scatter at impurities can influence the mobility.

Figure 61: Hall mobility of carriers for different annealing temperatures

4.4. Deep Level Transient Spectroscopy (DLTS)

4.4.1. After RTA

During the measurements, the filling pulses of 2 ms and bias -1 V to -0.01 V were applied. The emission window was 5.12 ms. The measurements was carried out at the temperature range from 6 K up to 185 K. The DLTS study of the sample annealed at 750oC proves the presence of copper. Besides the copper related energy levels (peak H4 - 0.314eV and peak H2-0.04eV) there are two other acceptor levels (peak H1- 0.028eV and peak H3-0.128eV) (Fig.60). The concentration on those exceeds twice the concentration for copper.

Table 14: The temperature positions, activation energies, emission rates, trap concentrations and corresponding capture cross-sections obtained in DLT measurement for samples after RTA

Peak label

T [K]

ET [eV]

KT [s-1K-2]

NT [cm-3]

pa [cm2 ]

H1

18.8

0.028

2.39 107

2.04 1013

4.04 10 -14

H2

23.2

0.040

1.31 108

1.14 1013

1.48 10 -13

H3

80.3

0.128

3.47 106

0.94 1013

4.24 10 -15

H4

144.8

0.314

8.24 108

0.91 1013

1.12 10 -13

H1a

18.7

0.027

---

---

---

4.4.1.1. Reproducibility of DLT spectrum

A second DLTS test was carried out to investigate reproducibility of the results. The obtained peak position and energy H1a shown in Fig. 63 correspond to peak H1 in Fig. 62 suggesting a good reproducibility.

Figure 62: DLT spectrum for p-type (750 m) germanium sample treated at 750oC (RTA)

Figure 63: DLT spectrum for p-type (750 m) germanium sample treated at 850oC (RTA)

Figure 64: Arrhenius diagram for energy levels found in a p-type (750 m) germanium sample treated for 5 min at 7500C (in RTA)

The capacitance drop with decreasing temperature is showing in Fig. 65.

Figure 65: Capacitance dependence on the temperature for sample treated at 750 0C (RTA)

4.4.2. After NRQa

Measurements were carried out in the temperature range from 8 K up to 266 K, while the liquid helium used as the cooling medium. The filling pulses of 2.415 ms and bias -2V to -0.5V were applied. The emission window was 5.12 ms. Only three peaks were observed.

Table 15: The obtained temperature positions, activation energies, emission rates for sample after NRQa

Peak label

T [K]

ET [eV]

KT [s-1K-2]

H1

17.2

0.0198

54361.9

H4

142.9

0.2587

1.62 107

H5

44.6

0.0695

1.14 107

4.4.2.1. Reproducibility of DLT spectrum

Also DLT spectrum was obtained for sample p-166-2 ( treated for 10 minutes at 825 0C, quenched in Santovac 5 oil) and plotted together with data for sample p-type (p-190-8). Etching changes thickness of specimen for p-type (p-190-8) from 740 m to 600 m. This gives a lower value of resistivity (from 6.67cm to 5.67 cm). The magnitude of these two spectra show repetitive nature (Fig. 67).

Figure 66: Comparison of DLT spectra for p-type (750 m) (p-190-8) germanium samples annealed for 10 minutes at 700 0C, quenched in silicon oil and sample p-166-2 for 10 minutes at 825 0C, quenched in Santovac 5 oil

Figure 67: Magnification of the date in Fig. 66

Figure 68: Arrhenius diagram for energy levels found in a p-type (750 m) germanium sample treated for 10min at 700 0C, quenched in silicon oil

4.4.2.2. DLT spectrum- peaks mapping

Identification of