enhancements to tcad tools for advanced iii-v semiconductor

© 2015 Synopsys, Inc. All rights reserved. 1

Enhancements to TCAD tools for advanced

III-V semiconductor devices: Material

Parameter Database and Model Pre-Calibration

for QDD Simulation

Axel Erlebach and Helen Lee

26.1.2015


Content

• Material database and model frame for Sentaurus QDD device

simulation

- Model frame

- Extraction methodology

- Results

• Extraction of parameters from measurements

• Extraction of parameters from reference tools

• Validation


Model frame for Sentaurus Device QDD

device simulation

Drift-diffusion transport model with quantum correction (density gradient

or MLDA)

Inclusion of ballistic resistance for short channels.

Ratio between mobility and diffusivity from MC – Einstein relation not valid.

High-field saturation model with increased saturation velocity for velocity

overshoot calibrated to MC.

Material database for the model parameters.

Model for unstrained mobility considering confinement effects in thin layers

and small structures

Multi-valley subband models for stress induced mobility enhancement.


• Permittivity

• Heat capacitance

• Thermal conductivity

• Band gap and electron affinity

• Band gap narrowing

• Density of states

• Quantization

• Doping dependent bulk mobility

• Inversion layer mobility and mobility in thin films

• Stress dependence

• Band structure properties

Material database for Sentaurus QDD

device simulation (parameters)


• Ga-mole fraction

• Film thickness or nano wire size/shape

• Doping

• Stress components

• Inversion layer area density

• Gate stack properties


device simulation (dependencies)



device simulation (extraction)

QDD material database

Measurements

“High-level” Reference tools (Sband, SMC, …)

Validation on III-V Devices

Small parameter

space

Large parameter

space


Thermal Conductivity for In1-xGaxAs

• Random distribution of Ga and In atoms in the sub-lattice sites

Kappa for In1-xGaxAs alloys are smaller than InAs & GaAs binary

• Tabulated kappa values in J-release MaterialDB are determined based on

experimental data.

Ref:

1) S. Adachi, JAP (2007)

2) M. S. Abrahams, J. Phys. Chem. Solids (1959)

3) D. G. Arasly, Sov. Phys. Semicond. (1990)


Bandgap for In1-xGaxAs

Ref:

1) I. Vurgaftman, JAP (2001)

2) R. E. Nahory, JAP (1975)

3) K. Kim, APL (2002)

4) D. K. Gaskill, APL (1990) At 300K

• 0K-bandgap in I-release MaterialDB

Bowing interpolation: Eg0(x)=0.417+0.625x+0.477x2

• Temperature-related Varshni parameters in J-release MaterialDB

Linear interpolation

at 300K


• A linear interpolation scheme is used for electron effective mass.

The tabulated values of density of states at 300K (Nc300) in J-release

MaterialDB are derived from

Nc300 for In1-xGaxAs

𝑁𝑐 300 = 2.5094𝐸19𝑚𝑒

𝑚0

3 2


• A bowing interpolation is proposed for each Luttinger parameter (𝛾1, 𝛾2, 𝛾3)

• The overall hole effective mass is composed of heavy hole and light hole.

• The density of states at 300K (Nc300) in J-release

MaterialDB is derived from

Nv300 for In1-xGaxAs

𝑁𝑣 300𝐾 = 2.5094𝐸19𝑚𝑝

𝑚0

3 2

𝑚𝑝 = 𝑚𝑙ℎ∗ 3 2

+𝑚ℎℎ∗ 3 2

2 3

Ref:

1) I.Vurgaftman, JAP (2001)

2) K. Alavi, PRB (1980)

3) R. J. Warburton, SST (1991)

4) N. J. Traynor, PRB (1997)


BGN (Jain-Roulston) for p- & n-GaAs

• For p-GaAs, original Jain-Roulston model parameters give a good approximation of

BGN to experimental data.

• For n-GaAs, coefficients in Jain-Roulston model are determined through curve fitting.

Linear interpolation of the

model parameters between

GaAs and InAs.


BGN (Jain-Roulston) for p- & n-InAs

• For p-InAs original Jain-Roulston model parameters are used to determine coefficients,

but there is no experimental data found to justify it.

• For n-InAs, coefficients in Jain-Roulston model are determined through curve fitting. Limit

of BGN shall be defined as higher doping might change drastically the band structure.

Linear interpolation of the

model parameters between

GaAs and InAs.


Bulk mobility for GaAs

Electron mobility for GaAs Hole mobility for GaAs

Ref: M. Sotoodeh et al., “Empirical low-field mobility model for III-V compounds applicable in device

simulation codes,” JAP 87, pp. 2890 (2000)


Bulk mobility for In1-xGaxAs (electrons)

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

0 0.2 0.4 0.6 0.8 1

Ele

ctr

on

mo

bil

ity (

cm

2/V

s)

x-Ga

Experimental data

Interpolation in MaterialDB Two-sectional linear interpolation

for InGaAs


Hole mobility for In0.53Ga0.47As

Bulk mobility for In0.53Ga0.47As

Electron mobility for In0.53Ga0.47As

Ref: M. Sotoodeh et al., “Empirical low-field mobility model for III-V compounds applicable in device

simulation codes,” JAP 87, pp. 2890 (2000)


Inversion layer mobility for In0.53Ga0.47As

Interface charges

influence the mobility

roll-off.

Sband and Sdevice

results are without

interface charge to allow

calibration of doping

dependence.


e_gamma and h_gamma are calibrated for DG+MV model with rms-Ninv errors smaller than 4% and 3%, respectively, over the whole mole fraction range

No dependence of e_gamma on sidewall orientations is observed for n-bulk configuration

n-Bulk

p-Bulk

Quantization parameters for In0.53Ga0.47As


No dependence of e_gamma on sidewall orientations is observed for n-double-gate configurations with 10nm and 20nm thickness

n-DG

p-DG

n-DG

p-DG

Quantization parameters for In0.53Ga0.47As


Extraction of parameters from

measurements

• Inversion layer mobility

Traps – Fermi level pinning

Charged traps – Coulomb scattering

Strong dependence on process conditions for

surface roughness mobility degradation

• Bulk mobility

Only limited number of measurements.

• Band structure parameters

Only limited number of measurements.


Extraction of parameters from reference

tools

• To fill the gap between measurements available and

measurements needed and to increase the parameter

space “high-level” reference tools are used.

Sband for low field mobility extraction and quantization.

SMC for high field mobility extraction.


Extraction of quantization parameters

1. Investigated quantization models include density gradient model

(DG), density gradient + multivalley models (DG/MV), and MLDA

model.

For In1-xGaxAs materials, the electron occupancy in other

valleys (i.e. L-valley) should be considered as well at high

gate voltage.

2. Use 1D Schrödinger equation in Sband as reference tool to obtain

the carrier density distribution in inversion layer.

3. Employ the quantization model in Sdevice and adjust the fitting

factors in order to minimize the root-mean-square error of total

inversion charge within investigation voltage range compared to

SE.

4. Classical solutions from Sband and Sdevice tools are compared to

ensure correct material parameter inputs.


InGaAs structures

Oxide: 0.6nm 1 µm-InGaAs

Doping=-1e15

V(bottom)=0V

V(gate)=1V

HfO2: 1.4nm

InGaAs

n-MOS bulk n-MOS double gate

Oxide: 0.6nm

InGaAs thin layer

Doping= -2e17 Thickness

(5-20nm)

HfO2: 1.4nm

Oxide: 0.6nm

HfO2: 1.4nm

V(gate)=1V

V(gate)=1V


nMOS DoubleGate (110) – 10nm:

In0.53Ga0.47As (wf=4.9)

Ninv (linear) vs. Vgate Ninv (log) vs. Vgate: below Vth



Carrier profile (at 1.0V) Capacitance vs. Vgate

Min. rms(Ninv)=15.13%




nMOS DoubleGate (110) – 10nm:

In0.53Ga0.47As (wf=4.9)



Carrier profile (at 1.0V) Ninv vs. Vgate



(Schrödinger) nMOS DoubleGate (110) – 20nm:

In0.53Ga0.47As (wf=4.9)



Sband-Schro. Classical

rms(Ninv)~148% DG (γ=1.24)

rms(Ninv)~18.8%

DG/MV (γ=1.61)

rms(Ninv)~3.6%

eDensity in 2D Fin (20nmx20nm) at Vg=0.35V



Sband-Schro

Classical

rms(Ninv)>700k% DG (γ=1.24)

rms(Ninv)>3k%

DG/MV(γ=1.61)

rms(Ninv)>718%


eDensity in 2D Fin (5nmx20nm) at Vg=0.35V

enhancements to tcad tools for advanced iii-v semiconductor

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