Nanostructures Research GroupCenter for Solid State Electronics Research
Quantum corrected full-band Cellular Monte Carlo simulation of AlGaN/GaN HEMTs†
Shinya Yamakawa, Stephen Goodnick*Shela Aboud, and **Marco Saraniti
Department of Electrical Engineering, Arizona State University*Electrical Engineering Department, Worcester Polytechnic Institute
**Department of Electrical and Computer Engineering, Illinois Institute of TechnologyUSA
† This work has been supported by ONR, NSF, and HPTi.
Nanostructures Research GroupCenter for Solid State Electronics Research
Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for high-temperature, high-power and high-frequency device.– wide band gap, high saturation velocity– high electron density by spontaneous and piezoelectric polarization
effect
• Here the full-band Cellular Monte Carlo (CMC) approach is applied to HEMT modeling.
• The effect of the quantum corrections is examined based on the effective potential method.
Nanostructures Research GroupCenter for Solid State Electronics Research
Full-band transport model
Transport is based on the full electronic and lattice dynamical properties of Wurtzite GaN:
• Full-band structure• Full Phonon dispersion• Anisotropic deformation potential
scattering (Rigid pseudo-ion Model)
• Anisotropic polar optical phonon scattering (LO- and TO-like mode phonons)
• Crystal dislocation scattering• Ionized impurity scattering• Piezoelectric scattering
Nanostructures Research GroupCenter for Solid State Electronics Research
AlGaN/GaN hetero structure
AlGaN
GaN
PSP
PSP
PPE
+
2DEG
Tensilestrain
Ambacher et al., J. Appl. Phys. 87, 334 (2000)
P0
2DEG
AlGaNTensile strain
GaN
Fixed polarization charge is induced at the AlGaN/GaN interface
Ga-face (Ga-polarity)
( ) ( )
( ) ( ) ( )SP SP PE
P GaN P AlGaN
P GaN P AlGaN P AlGaN
PSP : Spontaneous polarizationPPE : Piezoelectric polarization (strain)
Nanostructures Research GroupCenter for Solid State Electronics Research
Effective potential approach
Quantization energy
Charge set-back
Effective potential approximation
Classical potential(from Poisson’s equation)
Smoothed Effective Potential
Effective potential takes into account the natural non-zero size of an electron wave packet in the quantized system.
This effective potential is related to the self-consistent Hartree potential obtained from Poisson’s equation.
2
200
1( ) ( )exp
22effV x V x d
aa
a0 : Gaussian smoothing parameter
depends onTemperatureConcentrationConfining potentialOther interactions
D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)
Nanostructures Research GroupCenter for Solid State Electronics Research
Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure
AlxGa1-xN Doped
GaN
15 nm
100 nm
Gate
AlxGa1-xN Spacer 5 nm
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)Al content x : 0.2 0.4
Schrödinger-Poisson (S-P) calculation
2 1
( ) ( )2 ( )
d deV z E z E
dz m z dz
( ) ( ) ( ) ( )
( ) D
d d dD z z V z P z
dz dz dz
e n z N
Al0.2Ga0.8N/GaN
F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)
Nanostructures Research GroupCenter for Solid State Electronics Research
Effective potential calculation
Quantum correction (QC) with effective potential
Self-consistent calculation :
The final effective potential shifts due to the polarization charge
• Solve Poisson equation with classical electron distribution
• Quantum correction with the effective potential method
• Calculate the electron density with the new potential (Fermi-Dirac statistics)
• Solve the Poisson equationRepeat untilconvergence
Al0.2Ga0.8N/GaN
Nanostructures Research GroupCenter for Solid State Electronics Research
Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial) Quantum correction (self-consistent)
a0 (Å) : Gaussian smoothing parameter
(Al0.2Ga0.8N/GaN)
Nanostructures Research GroupCenter for Solid State Electronics Research
Electron sheet density
0 100
5 1012
1 1013
1.5 1013
2 1013
1.0 2.0 3.0 4.0 5.0
1e17 - classical1e17 - SCHRED1e17 - Effective Potential1e18 - classical1e18 - SCHRED1e18 - Effective Potential
Inve
rsio
n ch
arge
den
sity
Ns [
cm-2
]
Gate voltage Vg [V]
(a)
Ns for Si MOSFET Ns for AlGaN/GaN HEMT
MOSFET with 6nm gate oxide.Substrate doping is 1017 and 1018 cm-3. MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49, 1019 (2002)
Al0.2Ga0.8N/GaN
Nanostructures Research GroupCenter for Solid State Electronics Research
Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN Al0.4Ga0.6N/GaN
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Gaussian smoothing parameter (a0) fitting
Nanostructures Research GroupCenter for Solid State Electronics Research
HEMT device simulation
1018cm-3 n-doped AlGaN (x=0.2) 15nm
UID AlGaN (x=0.2) 5nm
UID GaN channel 100nm
Gate
101
9cm
-3 n
-dop
ed
Sou
rce D
rain
100nm 100nm100nm
101
9cm
-3 n
-dop
ed
Simulated HEMT device
Electron distribution under the gate
Classical
Quantumcorrection
a0=6.4 Å
UID density : 1017 cm-3
Ec = 0.33 eVSchottky barrier B=1.2eV
Nanostructures Research GroupCenter for Solid State Electronics Research
Classical Effective potential
VG=0VVDS=6V
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ID_VDS, ID_VG
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Conclusion
• The effect of quantum corrections to the classical charge distribution at the AlGaN/GaN interface are examined. The self-consistent effective potential method gives good agreement with S-P solution.
• The best fit Gaussian parameters are obtained for different Al contents and gate biases.
• The effective potential method is coupled with a full-band CMC simulator for a GaN/AlGaN HEMT.
• The charge set-back from the interface is clearly observed. However, the overall current of the device is close to the classical solution due to the dominance of polarization charge.