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

Nanostructures Research GroupCenter for Solid State Electronics Research

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

Nanostructures Research GroupCenter for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research GroupCenter for Solid State Electronics Research

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.