Slide 1

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 2

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 3

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 4

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 5

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 6

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 7

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 8

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 9

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 10

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 11

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 12

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 13

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 14

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research


Slide 15

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 Technology
USA
†

This work has been supported by ONR, NSF, and HPTi.

Nanostructures Research Group

Center for Solid State Electronics Research

Motivation and Approach
• AlGaN/GaN HEMT is the attractive candidate for hightemperature, 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 Group

Center 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 Group

Center for Solid State Electronics Research

AlGaN/GaN hetero structure
Ga-face (Ga-polarity)
Tensile
strain

PSP

PPE

+

AlGaN

2DEG

PSP

2DEG

PSP : Spontaneous polarization
PPE : Piezoelectric polarization (strain)
P0

Fixed polarization charge is induced
at the AlGaN/GaN interface
  P ( G aN )  P ( A lG aN )

AlGaN

 PSP ( G aN )   PSP ( A lG aN )  PP E ( A lG aN ) 
Nanostructures Research Group

Center for Solid State Electronics Research

GaN

GaN

Tensile strain

Ambacher et al., J. Appl. Phys. 87, 334 (2000)

Effective potential approach
Smoothed Effective Potential
Classical potential
(from
Poisson’s equation)
Effective potential
approximation

This effective potential is related
to the self-consistent Hartree
potential obtained from Poisson’s
equation.

Quantization energy
Charge set-back

V eff ( x ) 





V
(
x


)
exp


2

2  a 0 
 2 a0
1

2


 d


D.K. Ferry, Superlattices and Microstructures 28, 419 (2000)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential takes into
account the natural non-zero size
of an electron wave packet in the
quantized system.

a0 : Gaussian smoothing parameter

depends on
 Temperature
 Concentration
 Confining potential
 Other interactions

Schrödinger-Poisson calculation
Calculated AlGaN/GaN structure

Schrödinger-Poisson (S-P) calculation
d  1 d 

    eV ( z )   E ( z )   E 
2 dz  m ( z ) dz 
2



Gate
AlxGa1-xN Doped
AlxGa1-xN Spacer

15 nm
5 nm

d
dz

D(z) 

d 
d

V (z)  P(z)
  ( z )
dz 
dz


 e  n( z )  N D 


GaN

100 nm

Al0.2Ga0.8N/GaN
Modulation doping : 1018 cm-3
Unintentional doping : 1017 cm-3
(for AlGaN and GaN)
Al content x : 0.2  0.4

F. Sacconi et al., IEEE Trans. Electron Devices 48, 450 (2001)

Nanostructures Research Group

Center for Solid State Electronics Research

Effective potential calculation
Quantum correction (QC)
with effective potential
Self-consistent calculation :
•

Solve Poisson equation with
classical electron distribution
• Quantum correction with the
effective potential method
• Calculate the electron density
with the new potential (FermiDirac statistics)
• Solve the Poisson equation
Repeat until
convergence

Al0.2Ga0.8N/GaN

The final effective potential shifts due to the polarization charge
Nanostructures Research Group

Center for Solid State Electronics Research

Electron distribution
Electron distribution for S-P, classical and quantum correction
Quantum correction (initial)

Nanostructures Research Group

Center for Solid State Electronics Research

(Al0.2Ga0.8N/GaN)

Quantum correction (self-consistent)

a0 (Å) : Gaussian smoothing parameter

Electron sheet density

2 10

Inversion charge density N

1.5 10

Ns for AlGaN/GaN HEMT

13

13

1 10

13

5 10

12

0 10

(a)

1e17 - classical
1e17 - SCHRED
1e17 - Effective Potential
1e18 - classical
1e18 - SCHRED
1e18 - Effective Potential

s

-2

[cm ]

Ns for Si MOSFET

Al0.2Ga0.8N/GaN

0

1.0

2.0

3.0

4.0

5.0

Gate voltage V [V]
g

MOSFET with 6nm gate oxide.
Substrate doping is 1017 and 1018 cm-3.
Nanostructures Research Group

Center for Solid State Electronics Research

MOSFET data:
I. Knezevic et al., IEEE Trans. Electron Devices 49,
1019 (2002)

Comparison of electron distribution with S-P
Al0.2Ga0.8N/GaN

Nanostructures Research Group

Center for Solid State Electronics Research

Al0.4Ga0.6N/GaN

Gaussian smoothing parameter (a0) fitting

Nanostructures Research Group

Center for Solid State Electronics Research

HEMT device simulation
Electron distribution under the gate
Simulated HEMT device
100nm

100nm

Classical

100nm

n -d o p e d A lG a N (x= 0 .2 ) 1 5 n m

U ID A lG a N (x= 0 .2 ) 5 n m

-3
19

10 cm

U ID G a N c h a n n e l 1 0 0 n m

19

10 cm

n -d o p e d

-3

-3

n -d o p e d

18

10 cm

D ra in

S o u rc e

G a te

1017

cm-3

UID density :
Ec = 0.33 eV
Schottky barrier B=1.2eV

Nanostructures Research Group

Center for Solid State Electronics Research

Quantum
correction
a0=6.4 Å

Effective potential

Classical
VG=0V
VDS=6V

Nanostructures Research Group

Center for Solid State Electronics Research

ID_VDS, ID_VG

Nanostructures Research Group

Center 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.

Nanostructures Research Group

Center for Solid State Electronics Research