Device and Monte Carlo Simulation of

GaN material and devices

Presenter: Ziyang Xiao

Advisor: Prof. Neil Goldsman

University of Maryland

OUTLINE - GaN

Introduction and Background

Device Simulation (Lateral vs Vertical)

Monte Carlo Simulation for bulk GaN and 2DEG Electron Transport

2/23

GaN Application Advantages

Superior Material Properties

Large Bandgap

High saturation velocity

High carrier density and high electron

mobility

Technical Advantages

Improved transient characteristics and

switching speed

Power System Reduction in system volume and weight

High Frequency RF power

3/23

GaN Electron Transport

n+ GaN Drain

UID GaN

AlGaNS contact S contact

Gate

Figure: Sketch of Current Aperture Vertical Electron Transistor (CAVET)

p-GaN (CBL) p-GaN (CBL)Aperture

n- GaN Drift Region

D contact

4/23

OUTLINE - GaN

Introduction and Background

Device Simulation (Lateral vs Vertical)

Monte Carlo Simulation for bulk GaN and 2DEG Electron Transport

5/23

Lateral vs. Vertical

n+ GaN Drain

UID GaN

AlGaNS contact S contact

Gate

Figure: Sketch of Current Aperture Vertical Electron Transistor (CAVET)

p-GaN (CBL) p-GaN (CBL)Aperture

n- GaN Drift Region

D contact

𝑰

𝑰

6/23

Lateral vs. Vertical

Lateral:

• Low parasitic capacitance thus low conduction loss and low switching losses

• Relatively simpler fabrication process

• Easier to obtain bi-directional switch.

• Increase of breakdown voltage increases the chip sizes

• Current flows near the device surface. Thus current collapse phenomenon and increase dynamic on-resistance is more serious

Vertical:

• Require high quality native substrate (GaNsubstrate)

• More complex fabrication process

• The increase of breakdown results in the increase of the thickness of the device, thus expecting to achieve a higher power density.

• Current flows through the bulk region away from the surface, expecting to have less current collapse.

7/23

Simulated Devices (Lateral)

Sou

rce D

rain

AlGaN

𝒏 − 𝒕𝒚𝒑𝒆: 𝟏𝟎𝟏𝟓𝒄𝒎−𝟑

GaN

𝒏 − 𝒕𝒚𝒑𝒆: 𝟏𝟎𝟏𝟓𝒄𝒎−𝟑

𝒑 − 𝒕𝒚𝒑𝒆: 𝟏𝟎𝟏𝟓𝒄𝒎−𝟑

+++++++++++++++++++++

Gate

8/23

Gate Sweep (Lateral)

Figure: Drain current with gate sweeping of the simulated lateral device. 𝑉𝑑 = 0.02𝑉, 𝑉𝑠 = 0𝑉.

Figure: Sheet electron density at the interface vs. applied gate voltage. 𝑉𝑑 = 0𝑉, 𝑉𝑠 = 0𝑉.

𝑉𝑔(𝑉)

𝐼 𝑑(𝐴

)

𝑉𝑔(𝑉)

9/23

IV characters (lateral)

Figure: I-V character curve of simulated lateral device

𝑉𝑔 = 0,−2,−4,−6,−8,−10𝑉

Figure: Zoom in on the I-V character curve in the 0-10V range

𝑉𝑔 = 0,−2,−4,−6,−8,−10𝑉

𝑉𝑑𝑠(𝑉)

𝐼 𝑑(𝐴

)

𝐼 𝑑(𝐴

)

𝑉𝑑𝑠(𝑉)

10/23

Electron Concentration

Figure: Animation of how electron concentration changes w.r.t. changing drain voltage at Vg = 0V

Figure: Animation of how electron concentration changes w.r.t. changing drain voltage at Vg = -6V

11/23

Simulated Devices (Vertical)

𝒏 − 𝑮𝒂𝑵:𝟐 × 𝟏𝟎𝟏𝟔𝒄𝒎−𝟑

𝒏 − 𝑮𝒂𝑵:𝟐 × 𝟏𝟎𝟏𝟔𝒄𝒎−𝟑

𝒑 − 𝑮𝒂𝑵:𝟓 × 𝟏𝟎𝟏𝟕𝒄𝒎−𝟑

𝑪𝑩𝑳

𝒑 − 𝑮𝒂𝑵:𝟓 × 𝟏𝟎𝟏𝟕𝒄𝒎−𝟑

𝑪𝑩𝑳

Source Source

Gate

𝒏 − 𝑨𝒍𝑮𝒂𝑵: 𝟏 × 𝟏𝟎𝟏𝟓𝒄𝒎−𝟑

𝒏 − 𝑮𝒂𝑵: 𝟏 × 𝟏𝟎𝟏𝟓𝒄𝒎−𝟑

12/23

Gate Sweep (Vertical vs. Lateral)

Figure: Sheet electron density comparison( between lateral and vertical device) at the interface vs. applied gate voltage. 𝑉𝑑 = 0𝑉, 𝑉𝑠 = 0𝑉.

Figure: Drain current comparison( between lateral and vertical device) with gate sweeping of the simulated lateral device. 𝑉𝑑 = 0.02𝑉, 𝑉𝑠 = 0𝑉.

𝑉𝑔(𝑉) 𝑉𝑔(𝑉)

𝐼 𝑑(𝐴

)

13/23

IV character (Vertical)

𝑉𝑔 = 0𝑉

𝑉𝑔 = 3𝑉

𝑉𝑔 = 4𝑉

𝑉𝑔 = 5𝑉

𝑉𝑔 = 6𝑉

Figure: I-V character of the simulated vertical device Figure: I-V character of the simulated lateral device

𝑉𝑔 = 0𝑉

𝑉𝑔 = 2𝑉

𝑉𝑔 = 4𝑉

𝑉𝑔 = 6𝑉𝑉𝑔 = 8,10𝑉

𝑉𝑑𝑠(𝑉)

𝐼 𝑑(𝐴

)

𝑉𝑑𝑠(𝑉)

𝐼 𝑑(𝐴

)14/23

Electron Concentration (Vertical)

Figure: Animation of how electron concentration w.r.t. changing drain voltage at Vg = 0V

Figure: Animation of how electron concentration w.r.t. changing drain voltage at Vg = -6V

15/23

OUTLINE - GaN

Introduction and Background

Device Simulation (Lateral vs Vertical)

Monte Carlo Simulation for bulk GaN and 2DEG Electron Transport

16/23

Bulk GaN Monte Carlo Simulation

• The GaN bulk Monte Carlo is based on a three-valley model (Γ1 valley, Γ3 valley and U valley), among which Γ1 valley handles mostly low electrical field scattering events, while the Γ3 valley and U valley will participate in the high field scattering.

Figure: EPM calculated conduction band structure with illustration of included valleys for Monte Carlo simulation

𝐴 𝐿 𝑀 Γ 𝐴

Ener

gy (

eV)

Γ1

Γ3𝑈

Three-valley model parameters

Valley OffsetEffective

massNonparabolicity

Γ1 0 eV 0.2𝑚0 0.189 𝑒𝑉−1

Γ3 1.9 eV 𝑚0 0.065 𝑒𝑉−1

𝑈(𝐿 − 𝑀) 2.1 eV 𝑚0 0.029 𝑒𝑉−1

• The included scattering types are: acoustic phonon scattering, piezoelectric scattering, impurity scattering, polar optical scattering, inter-valley scattering.

17/23

MC Results (Velocity and Valley Occupancy)

Figure: Valley occupation vs. electric field (full range: 0 –450 kV/cm) with impurity concentration of 1017 𝑐𝑚−3. The insert is part of the conduction band structure of GaN and the approximated three valley model used in the simulation

𝐴 𝐿 𝑀 Γ 𝐴

Ener

gy (

eV)

Γ1

Γ3

𝑈

Figure: Average drift velocity vs. electric field (full range: 0 -450kV/cm) with impurity concentration of 1017𝑐𝑚−3. The inserts are the distribution of the drift velocity at selected electrical field.

18/23

MC Results (Mobility)

Figure: 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] and [4], respectively.

Reference:

[1] Rode el ta. 1995, Applied Physics Letters 66

[2] Tompkins el ta. 2015, ARL-TR-7209

[3] Tang el ta. 1999, Applied Physics Letters 74

[4] Redwing el ta. 1996, Applied Physics Letters 69

Exp. Data

This Work

19/23

2DEG Monte Carlo Simulation

Figure: The approximated wave function Ψ 2 for two triangular potential wells. The Potential well is also shown together with the wavefunctions. The parameters are the two potential wells are: (a) 𝐹𝑖𝑛𝑡=0.057V/nm, 𝐸𝑡=0.45eV; (b) 𝐹𝑖𝑛𝑡=0.116V/nm, 𝐸𝑡=0.75eV.

1. 𝐹𝑖𝑛𝑡 determines where the subbands are located inside the potential well;

𝐸𝑛 =ћ2

2𝑚∗

13 3𝜋

2

𝑞𝐹𝑖𝑛𝑡

𝑛 −14

23

φ𝑛 𝑧 = 𝐴 ∙ 𝐴𝑖

2𝑚∗𝑞𝐹𝑖𝑛𝑡

ћ2

13

𝑧 −𝐸𝑛

𝑞𝐹𝑖𝑛𝑡

1. 𝐸𝑡 determines how many subbands are included in the 2D Monte Carlo simulation

2. If the electron energy is below 𝐸𝑡, it will be considered under 2D scattering.

3. If the electron energy is above 𝐸𝑡, it is regarded as being in 3D scattering realm.

𝐸𝑡

20/23

2D MC Results (Drift Velocity)

Figure: (Left) Average drift velocity vs. full range electrical field; (Right) Zoom-in onto the low electrical field range of the left graph. Curves labeled "Case(a)" and "Case(b)" are 2D Monte Carlo simulation results with potential well parameters listed in the table on the right. Curve labeled "3D" is the bulk Monte Carlo simulation result with impurity concentration of 1017𝑐𝑚−3.

𝐸𝑡(𝐞𝐕) 𝐹𝑖𝑛𝑡(𝑽/𝒏𝒎)

Case(a) 0.45 0.057

Case(b) 0.75 0.115

Table: Parameters for triangular potential wells labeled Case(a) and Case(b) in the figure on the left implemented in 2D Monte Carlo simulation

21/23

2D MC Results (Mobility)

Figure: 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 [1]-[8], respectively.

Reference:[1] Gaska el ta. 1998, Applied Physics Letters 72[2] Wu el ta. 1996, Applied Physics Letters 69[3] Redwing el ta. 1996, Applied Physics Letters 69[4] Recht el ta. 2006, IEEE Electron Device Letters 27, 205–207[5] Tang el ta. 1999, Applied Physics Letters 74[6] Tompkins el ta. 2015, ARL-TR-7209[7] Acar el ta. 2008, Thin Solid Films 516, 2041 –2044[8] Katz el ta. 2003, IEEE Transactions on Electron Devices 50, 2002–2008

Exp. Data

This work

22/23

Conclusion

1. Both lateral and vertical devices simulated are normally-ON devices due to the presents

of the polarization induced charges at the interface.

2. The conductivity of the both vertical and lateral devices are mainly dominated by the

channel of 2DEG at the interface of GaN/AlGaN.

3. Pinch-off in lateral device happens under the gate edge near the drain side, while in

vertical device, the pinch-off happens in the aperture region.

4. More scattering mechanisms needs to be included to account for the discrepancies for

bulk MC simulation while not for 2DEG MC simulation.

23/23

Thank you!Any Questions?

Backup Slides

Figure: Average electron energy vs. electric field (full range: 0 – 450 kV/cm) with impurity concentration of 1017𝑐𝑚−3. The inserts are the distribution of the electron energy at selected electric field

25/23

2D MC Analysis

1. 2DEG shows higher mobility that 3D bulk

• Possibly because of the absence of impurity

scattering

• The quantized energy levels possibly lower

the crossover between the original state and

possible final states to be scattered into:

𝑆𝑘→𝑘′ = 𝐴 𝑘|∆𝑉| 𝑘′

2. 2DEG mobility differs from one another with

different quantum well structure (i.e. different

𝐹𝑖𝑛𝑡 and 𝐸𝑡)

• Future work is needed to reveal the

relationship between the mobility and the

quantum well structural parameter

Electron Energy (eV) Electron Energy (eV) Electron Energy (eV)

Scat

teri

ng

rate

(s^

-1)

Scat

teri

ng

rate

(s^

-1)

Scat

teri

ng

rate

(s^

-1)

(a) (b) (c) Aco

ustic

Polar O

ptical

Emissio

nPo

lar Op

ticalA

bso

rptio

n

Figure: Scattering rate comparison between 3D scattering (blue) and 2D scattering (Orange) with electrons starting from 1st subband (a), 2nd subband (b) and 3rd

subband, respectively. The structural parameter for the calculation is from Case(a) mentioned in the previous slide

26/23