enhancements to tcad tools for advanced iii-v semiconductor
TRANSCRIPT
© 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
© 2015 Synopsys, Inc. All rights reserved. 2
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
© 2015 Synopsys, Inc. All rights reserved. 3
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.
© 2015 Synopsys, Inc. All rights reserved. 4
• 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)
© 2015 Synopsys, Inc. All rights reserved. 5
• Ga-mole fraction
• Film thickness or nano wire size/shape
• Doping
• Stress components
• Inversion layer area density
• Gate stack properties
Material database for Sentaurus QDD
device simulation (dependencies)
© 2015 Synopsys, Inc. All rights reserved. 6
Material database for Sentaurus QDD
device simulation (extraction)
QDD material database
Measurements
“High-level” Reference tools (Sband, SMC, …)
Validation on III-V Devices
Small parameter
space
Large parameter
space
© 2015 Synopsys, Inc. All rights reserved. 7
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)
© 2015 Synopsys, Inc. All rights reserved. 8
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
© 2015 Synopsys, Inc. All rights reserved. 9
• 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
© 2015 Synopsys, Inc. All rights reserved. 10
• 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)
© 2015 Synopsys, Inc. All rights reserved. 11
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.
© 2015 Synopsys, Inc. All rights reserved. 12
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.
© 2015 Synopsys, Inc. All rights reserved. 13
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)
© 2015 Synopsys, Inc. All rights reserved. 14
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
© 2015 Synopsys, Inc. All rights reserved. 15
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)
© 2015 Synopsys, Inc. All rights reserved. 16
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.
© 2015 Synopsys, Inc. All rights reserved. 17
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
© 2015 Synopsys, Inc. All rights reserved. 18
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
© 2015 Synopsys, Inc. All rights reserved. 19
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.
© 2015 Synopsys, Inc. All rights reserved. 20
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.
© 2015 Synopsys, Inc. All rights reserved. 21
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.
© 2015 Synopsys, Inc. All rights reserved. 22
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
© 2015 Synopsys, Inc. All rights reserved. 23
nMOS DoubleGate (110) – 10nm:
In0.53Ga0.47As (wf=4.9)
Ninv (linear) vs. Vgate Ninv (log) vs. Vgate: below Vth
Extraction of quantization parameters
© 2015 Synopsys, Inc. All rights reserved. 24
Carrier profile (at 1.0V) Capacitance vs. Vgate
Min. rms(Ninv)=15.13%
Min. rms(Ninv)=7.10%
Min. rms(Ninv)=15.16%
Min. rms(Ninv)=13.65%
nMOS DoubleGate (110) – 10nm:
In0.53Ga0.47As (wf=4.9)
Extraction of quantization parameters
© 2015 Synopsys, Inc. All rights reserved. 25
Carrier profile (at 1.0V) Ninv vs. Vgate
Min. rms(Ninv)=3.71%
Min. rms(Ninv)=0.21%
(Schrödinger) nMOS DoubleGate (110) – 20nm:
In0.53Ga0.47As (wf=4.9)
Extraction of quantization parameters
© 2015 Synopsys, Inc. All rights reserved. 26
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
Extraction of quantization parameters
© 2015 Synopsys, Inc. All rights reserved. 27
Sband-Schro
Classical
rms(Ninv)>700k% DG (γ=1.24)
rms(Ninv)>3k%
DG/MV(γ=1.61)
rms(Ninv)>718%
Extraction of quantization parameters
eDensity in 2D Fin (5nmx20nm) at Vg=0.35V