GaN and GaN/AlGaN HeterostructureProperties Investigation and Simulations

Ziyang (Christian) XiaoNeil Goldsman

University of Maryland

OUTLINE

1. GaN (bulk)

1.1 Crystal Structure

1.2 Band Structure Calculation

1.3 Monte Carlo Simulation

2. GaN/AlGaN

2.1 Heterostructure and 2D Electron Gas (2DEG) Formation

2.2 2DEG Potential Well Modeling and 2D Monte Carlo Simulation

01/13

1.1 GaN Lattice Structure

• Crystal structure: • Wurtzite

• Lattice constant: • a = 3.186Å• c = 5.186Å

• Unit lattice vector:• 𝑎𝑎1 = 𝑎𝑎 1,0,0

• 𝑎𝑎2 = 𝑎𝑎 12

, 32

, 0

• 𝑎𝑎3 = 𝑐𝑐 0,0,1

Figure: Primitive unit cell and hexagonal conventional unit cell of GaN

02/13

𝒂𝒂𝟏𝟏𝒂𝒂𝟐𝟐

𝒂𝒂𝟑𝟑

1.1 GaN Reciprocal Lattice

The reciprocal lattice of a Wurtzitecrystal is also a hexagonal lattice, with:

Reciprocal lattice unit vector:𝑏𝑏1 = 2𝜋𝜋

𝑎𝑎1, 1

3, 0

𝑏𝑏2 = 2𝜋𝜋𝑎𝑎

0, 23

, 0

𝑏𝑏3 = 2𝜋𝜋𝑐𝑐

0,0,1High symmetry point:

Figure: The reciprocal lattice of a Wurtzite crystal with labeled high symmetry point

03/13

1.2 Band Structure Calculation

Method: Empirical Pseudopotential Method (EPM)• Due to the periodicity of the lattice, the Schrodinger Equation is expressed in an algebra

matrix equation:

ℏ2 𝑘𝑘 + 𝐺2

2𝑚𝑚𝑈𝑈 𝐺 +

𝐺`

𝑉𝑉 𝐺 − 𝐺 ` 𝑈𝑈 𝐺` = 𝐸𝐸 𝑈𝑈 𝐺

• Where:E is the allowed electron energy states

𝐺 is the reciprocal lattice vectors𝑈𝑈 𝐺 is the Fourier transformation constant for Bloch functions

𝑉𝑉 𝐺 is the Fourier transformation constant for V(r)

𝑉𝑉 𝐺 =1ΩΩ

𝑑𝑑𝑟𝑟 𝑉𝑉 𝑟𝑟 𝑒𝑒−𝑖𝑖𝐺𝑟𝑟

V(r) is the periodic lattice atomic potential04/13

1.2 Band Structure Calculation

EPM Experiment

Eg(Γ1-Γ6) 3.46eV 3.5eV[1]3.33-3.35eV[4]

𝑚𝑚∗ /𝑚𝑚0 0.165 0.20 ± 0.02[2]

Eg(Γ3-Γ5) 6.12eV 5.3eV[3]

Eg(𝑀𝑀3-𝑀𝑀4) 7.6eV 7.0-7.1eV[3]

[1] B. Monemar, Phys. Rev. B, 1973[2] A. S. Barker Jr. et al, Physical Review B, 1974[3] S. Bloom et al, physica status solidi, 1974[4] A. M. El-Naggar, J Mater Sci: Mater Electron, 2012

Band Structure for Mobility and Transport Properties including Velocity Overshoot

05/13

𝑨𝑨 𝑳𝑳 𝑴𝑴 𝜞𝜞 𝑨𝑨 𝑯𝑯 𝑲𝑲 𝜞𝜞Figure: Calculated band structures and Density of States using EPM

Ener

gy (e

V)

U1

6

5

3

4

3

1.2 Band Structure Calculation

Figure: 3D Band Structure(Left) and contour(Right) of the band structure of the top-most valence band and bottom-most conduction band along Plane A

(a)

(b)

Plane A

Bottom mostConduction Band

Top most Valence Band

ΓM K

Energy: eV8

7

6

5

4

-0.5

-1

-1.5

-2

-2.5

Bandgap

Energy: eV

8

6

4

2

0

-4

-2

Γ KM

06/13

𝒌𝒌𝒙𝒙 𝒌𝒌𝒚𝒚

1.3 GaN Bulk Monte Carlo Simulation

• Use Band Structure for MC.

• The whole electrical field range

simulation reveals:

1. A peak velocity of 2.83 × 107 cm/s at

150kV/cm

2. A saturation velocity beyond 250kV/cm at

about 2.2~2.3 × 107 cm/s

3. Low field mobility (ie. the slope of the

curve at low electrical field range)

changes with the impurity concentration

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

3.00E+07

0 100 200 300 400 500

Drift

vel

ocity

(cm

/s)

Electrical Field (kV/cm)

Bulk MC simulation

Figure: Whole electrical field range simulation of drift velocity with purity concentration at 1017𝑐𝑐𝑚𝑚−3

07/13

1.3 GaN bulk MC simulation

Bulk low field mobility vs. Impurity concentration extracted from MC simulation. The experimental data sets Data.1∼4 are mobility values taken from references [1],[2],[3],[4]

1. Simulation results are generally higher than the experimental data probably due to lack of consideration of other possible scattering types

2. The simulation results agree with the general trend laid by the experimental data.

0

100

200

300

400

500

600

700

800

1E+17 1E+18

Mob

ility

(cm

^2/V

s)

Impurity Conc. (cm^-3)

Bulk GaN mobility vs. Impurity concentration

Monte CarloData. 1Data.2Data.3Data.4

[1] M. Asif Khan et al, Appl. Phys. Lett. ,1995[2] H. Tang et al, Appl. Phys. Lett. ,1999 [3] J. M. Redwing et al, Appl. Phys. Lett. ,1996[4] R. P. Tompkins et al, Army Research Lab, 2015

08/13

OUTLINE

1. GaN

1.1 Crystal Structure

1.2 Band Structure Calculation

1.3 Monte Carlo Simulation

2. GaN/AlGaN

2.1 Heterostructure and 2D Electron Gas (2DEG) Formation

2.2 2DEG Potential Well Modeling and 2D Monte Carlo Simulation

2.1 GaN/AlGaN HEMT:2D-Electron Gas (2DEG) Transport

1. GaN/AlGaNheterostructure is the center of the device.

2. A 2DEG is formed at the interface without doping in either AlGaN or GaNlayer or bias

Buffer Layers/ Transition Layers/ Substrate

GaN un-doped

AlGaNS contact D contact

Gate

Figure: General device structure of a GaN/AlGaN based HEMT

2DEG Channel

09/13

2.1 Formation of 2DEG

Band-Bending

Electron transport

-

AlGaN

GaN

𝑃𝑃𝑆𝑆𝑆𝑆 + 𝑃𝑃𝑆𝑆𝑃𝑃 𝑃𝑃𝑆𝑆𝑆𝑆

++++++

------

---

+++

Reaching critical thickness

𝐸𝐸𝐹𝐹

AlGaN

GaN

𝐸𝐸𝐹𝐹

AlGaN

GaN

𝐸𝐸𝐹𝐹

AlGaN

GaN

Surface Donor”full”

Surface Donor”half empty”

2DEG

10/13

2D potential quantum well

2.2 2DEG potential well modeling

(a)

Ener

gy (e

V)

Distance(um)

Picked subbands:3 subbands

(b)

Distance(um)

Picked subbands:2 subbands

Figure: the approximated wave function Ψ 2 for a triangular potential well with illustrated potential well. The potential well parameters are list on the side

E_th Slope

Case (a) 0.45eV 0.2eV/3.5nm

Case (b) 0.75eV 0.52eV/4.5nm

1. The wave function is calculated from the infinite triangular potential well.

2. The selected subbands are determined by 𝐸𝐸𝑡𝑡𝑡.

3. For 2D scattering (electron energy below 𝐸𝐸𝑡𝑡𝑡), the included scattering types are: acoustic scattering and polar optical scattering

11/13

2.2 2DEG Monte Carlo simulation

Figure: (a)Mean drift electron velocity vs. Electrical field. (b) collections of experimental data for 2DEG mobility and the results of 2D MC simulation from this work. The experimental data sets Data.1∼8 are mobility values taken from references [5],[6],[7],[8],[9],[10],[11],[12]

0.0E+0

5.0E+6

1.0E+7

1.5E+7

2.0E+7

2.5E+7

3.0E+7

0 100 200 300 400 500

Mea

n ve

loci

ty (c

m/s

)

E field(kV/cm)

Mean velocity

Case(a)

Case(b)

3D

(a)

0

500

1000

1500

2000

2500

0.00E+00 2.00E+13 4.00E+13

Mob

ility

(cm

^2/V

s)Electron Sheet Density (cm^-2)

2DEG mobility vs. electron concentration

Data.1Data.2Data.3Data.4Data.5Data.6Data.7Data.8Case(a)Case(b)

(b)

[5] R. Gaska et al. Appl. Phys. Lett., 1998 [6] Y.-F. Wu et al, Appl. Phys. Lett. ,1996 [7] J. M. Redwing et al, Appl. Phys. Lett. ,1996[8] F. Recht et al, IEEE Electron Device Letters, 2006 [9] H. Tang, Appl. Phys. Lett., 1999[10] R. P. Tompkins et al, Army Research Lab, 2015[11] S. Acar et al, Thin Solid Films, 2007[12] O. Katz et al, IEEE Transactions on Electron Devices, 2003

12/13

1. GaN band structure calculation gives good agreement with experimental data

and/or first principle calculations.

2. GaN bulk Monte Carlo Simulation gives agreeable results comparing to

experimental data with a positive offset indicating needs to include more

scattering mechanisms

3. 2D Electron Gas Monte Carlo simulation gives results within the range of the

experimental data collections

4. Bulk GaN Mobility ranges from 500 to 750 𝑐𝑐𝑚𝑚2/𝑉𝑉𝑉𝑉 in our simulation, while 2DEG

mobility is around 1500 - 1700 𝑐𝑐𝑚𝑚2/𝑉𝑉𝑉𝑉.

Conclusion

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Thank you!Any questions?

• The strong true potential of the ions is replaced by a weaker potential valid for the valence electrons.

• It approaches the unscreened Coulomb potential at large values of r.

• The parameters will be adjusted until good convergence achieves between calculation results and experimental data.

-Z/r

Back-up: Pseudopotential

Back-up: Heterostructure

Relaxed GaN substrate

AlGaN film under tensile strain

𝑃𝑃 𝑆𝑆𝑃𝑃

-+

Figure: the spontaneous polarization of bulk GaN(AlGaN) is due to the lack of symmetry along the [0001] direction

Figure: Due to the lattice mismatch between AlGaN film and GaN substrate, the film is under biaxial tensile strain, which results in piezoelectric polarization

Cation

Anion

[000

1]

[000-1]

Ga-face

N-face

Back-up. heterostructure Poisson solver

Parameter inputs:

x = 0.2 for 𝐴𝐴𝐴𝐴𝑥𝑥𝐺𝐺𝑎𝑎1−𝑥𝑥𝑁𝑁

𝑁𝑁𝐷𝐷−𝐺𝐺𝑎𝑎𝐺𝐺 = 1017𝑐𝑐𝑚𝑚−3

𝐸𝐸𝐹𝐹−𝐴𝐴𝐴𝐴𝐺𝐺𝑎𝑎𝐺𝐺 =𝐸𝐸𝑔𝑔−𝐴𝐴𝐴𝐴𝐺𝐺𝑎𝑎𝐺𝐺

2

𝜎𝜎𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑟𝑟𝑖𝑖𝑎𝑎𝑐𝑐𝑖𝑖 = 1013𝑐𝑐𝑚𝑚−2

𝑤𝑤𝜎𝜎 = 0.02𝑛𝑛𝑚𝑚

Note: this is a test run for the solver, the specific parameters for the structure differ from case to case