Modeling of SiC & GaN:Interfaces, Transport & Devices

University of MarylandNeil Goldsman

Ziyang Xiao, Chris DarmodyDev Ettisserry & Akin Akturk

Army Research LabAivars Lelis, Dan Habersat & Ron Green

Outline1. Neil Goldsman

a) Summary of Key Earlier Resultsb) SiC vs. GaN

2. Chris Darmodya) Device Simulation of SiC Trench MOSFETs

3. Ziyang Xiaoa) GaN: Band Structure & Monte Carlo Transportb) AlGaN: 2D Electron Gas, Energy Bands & Monte Carlo

4. Neil Goldsmana) Oxide Reliability & Oxygen Vacancies

Modeling of SiC & GaN:Interfaces, Transport & Devices

SiC & GaN Device Virtual Fab, Design and Analysis Platform

Process & Fabrication Modeling

(Device Structure &Defect Generation)

Device Modeling(I-V & Performance)

Monte Carlo: (Transport)

Density Functional Theory

(Defects)

Σ

CoolSPICECircuit Design

Device Meet Specs?YES

NO

EXPERI

MEN

T

Summary of Key Results:Transition Region & Atomic Origin of Defects

• Reliability: Threshold Instabilities• Due to Oxide Vacancies and Carboxyl Substitutions in SiO2 side of Trans.

Region (TR)

• Interface States: Mobility Degradation at Low Vgs. • Due to atomic defects in SiC side TR.

• Surface roughness: Mobility Degradation at Low Vgs• Transition Region: Mobility Degradation due to Disruptions in

Bloch Functions and Increased Density of States.• Non-Stoichiometric Substitutions and Interstitials in SiC side of Interface• Oxygen substituting for Carbon and Carbon Interstitials identified and key

Non-Stochiometric Structures in TR.

Interpretation of the Interface from Device and DFT Simulations and Experiment

Summary of Key Results: Passivation

• Nitrogen: • Passivates Carboxyl Defects in Oxide• Passivates E’ centers in Oxide• Passivates carbon interstitials• But too much N generates more (+) charge & more states

near CB.• Gives rise to counter doping layer at interface

• Improves field effect mobility mainly due to counter doping.

SiC and GaN

SiC GaN Si

Mobility Low High Medium

Voltage High Medium Low

OperatingTemperature

High High Low

ThermalConductivity

High Medium Medium

• SiC & GaN: Both Wide Bandgap and Attractive Characteristics

• Extending work to include GaN

Questions?

Next, Chris Darmody will describe SiC Trench MOSFET Modeling and SiC/SiO2 DFT Interface Modeling

Ziyang Xiao will follow Chris with GaN Transport Studies

That’s it for Introduction

Simulation of SiCTrenchMOS Devices and

InterfacesUniversity of Maryland

Chris Darmody, Dr. Neil Goldsman

Presentation Outline

• 2D Drift-Diffusion TrenchMOS Simulation• Saturation Region and Pinch-off• Linear Operation• Off Device

• Modeling Interfaces & Atomic Roughness Scattering• Introduction and Traditional Mobility Model• 4H-SiC DFT Supercell• Extract Interface Potential from DFT Calculation

1/16

TrenchMOS Basic Device Structure

2/16

Half-Device Structure and Mesh

6.5x1016

1.7x1015

1020

1020

n+ Source

Source/BodyContact

p Body

n- DriftRegion

n+ Drain

Gate Poly

Gate Oxide

𝛻𝛻 𝜖𝜖𝛻𝛻ϕ = −𝑞𝑞(−𝑛𝑛 + 𝑝𝑝 − 𝑁𝑁𝐴𝐴− + 𝑁𝑁𝐷𝐷+)

𝐽𝐽𝑛𝑛 = −𝑞𝑞𝑛𝑛𝜇𝜇𝑛𝑛𝛻𝛻ϕ+ 𝑞𝑞𝐷𝐷𝑛𝑛𝛻𝛻𝑛𝑛

𝐽𝐽𝑝𝑝 = −𝑞𝑞𝑝𝑝𝜇𝜇𝑝𝑝𝛻𝛻ϕ − 𝑞𝑞𝐷𝐷𝑝𝑝𝛻𝛻𝑝𝑝

𝜕𝜕𝑛𝑛𝜕𝜕𝑡𝑡

=1𝑞𝑞𝛻𝛻 𝐽𝐽𝑛𝑛 − 𝑅𝑅𝑛𝑛 + 𝐺𝐺𝑛𝑛

𝜕𝜕𝑝𝑝𝜕𝜕𝑡𝑡

= −1𝑞𝑞𝛻𝛻 𝐽𝐽𝑛𝑛 − 𝑅𝑅𝑝𝑝 + 𝐺𝐺𝑝𝑝

Semiconductor Equations in Drift-Diffusion Model:

n: Electron Concentrationp: Hole ConcentrationΦ: PotentialJn: Electron Current DensityJp: Hole Current Densityμn: Electron Mobilityμp: Hole Mobility

3/16

Saturation Region Electron Conc.

Vg=15VVd=50VVs=Vb=0V

Channel

Source Well

Gate

Drain

P Body

4/16

Saturation Channel Electron Conc.

Vg=15VVd=50VVs=Vb=0V

tch = 2nm

Source Well

P BodyG

ate

Oxi

de

5/16

Saturation Region Electron Conc.

Vg=15VVd=50VVs=Vb=0V

Channel

Pinch-off

Source Well

Gate

Drain

6/16

Pinch-off: Saturation Electron Conc.

Vg=15VVd=50VVs=Vb=0V

Gate OxideRegion

7/16

Saturation Region Potential Profile

Vg=15VVd=50VVs=Vb=0V

Gate

Drain

Source/Body

8/16

Linear Region Operation

Vg=20VVd=5VVs=Vb=0V

Gate

Drain

Source/Body Channel

9/16

Channel Formed: Linear Region

Source Well

P BodyG

ate

Oxi

de

10/16

Off Device Operation

Gate

Drain

Source/Body

Vg=0VVd=600VVs=Vb=0V

No channelformed

Pinch-off region

11/16

Presentation Outline

• 2D Drift-Diffusion TrenchMOS Simulation• Saturation Region and Pinch-off• Linear Operation• Off Device

• Modeling Interfaces & Atomic Roughness Scattering• Introduction and Traditional Mobility Model• 4H-SiC DFT Supercell• Extract Interface Potential from DFT Calculation

12/16

Atomic Roughness Surface Modeling with DFT

• Key scattering factor at high vertical fields

• Never fully modeled accurately (Si, A, M-faces)

• Can get true surface potential from DFT

• Extract scattering cross-section and put into MC simulation to determine mobility

Old, Simplified Model True Potential

𝜇𝜇𝑆𝑆𝑆𝑆 =ħ3

2𝑚𝑚𝑚𝑚𝐸𝐸2∆2𝐿𝐿2Ω𝑆𝑆𝑆𝑆

ΔL

13/16

4H-SiC Structure and Supercells2x2x1 Supercell

Si-Face (0001)

Transformed AxesPrimitive Cell

Si

C

M-Face(1100)

A-Face(1210)

Hexagonal Lattice

14/16

Surface Roughness Model from DFT

• Extract realistic interface potentials from DFT simulations

• Create scattering matrix elements for Monte Carlo Sim.

• 1𝜇𝜇∝ [∫ϕ𝑘𝑘′∆𝑉𝑉ϕ𝑘𝑘𝑑𝑑𝑑𝑑] 2

Extracted Interface

(0001)Potential

SiO2

4H-SiC

15/16

Modeling Strategy Overview

Atomic Level Structure: DFT

Power TrenchMOS: Device Sim.

time

z1

023

40

Atomic Level e- Transport: Monte Carlo

16/16

GaN and GaN/AlGaNHeterostructure

Properties 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 1

2, 32

, 0

• 𝑎𝑎3 = 𝑐𝑐 0,0,1Figure: Primitive unit cell and hexagonal conventional unit

02/13

𝒂𝒂𝟏𝟏𝒂𝒂𝟐𝟐

𝒂𝒂𝟑𝟑

1.1 GaN Reciprocal Lattice

The reciprocal lattice of a Wurtzite crystal 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

𝑑𝑑𝑑𝑑 𝑉𝑉 𝑑𝑑 𝑚𝑚−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 most

Conduction 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

f [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 GaN layer 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

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) 0.45eV0.2eV/3.5n

m

Case (b) 0.75eV0.52eV/4.5n

m

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.6

(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

13/13

Threshold Voltage Shifts Explained on Atomic Level

with DFT

Dev Ettisserry &Neil Goldsman

• Ideal Oxide • Oxide with Defect

Investigate Role of Defects in EMI

19

Effect of Defects on MOSFETs; High Voltage Bias Changes Threshold Voltage (Vt)

• Positive shift in Vth followingHT positive bias stress due toelectron trapping.

• Negative shift in Vth followingHT negative bias stress due tohole trapping.

• The degradation worsens overtime!

* Measurements by our collaborators at U.S. Army Research Lab,Adelphi, MD.

This work focuses on NBTS degradation potentially due to

OV hole traps

• OV = Oxygen Vacancy

20

Density Functional Theory: Use to Analyze• Schrodinger wave equation that accounts for all the electrons and nuclei in

the system and their interactions.

• The kinetic and potential energies are altered by quantum effects like Pauli’sexclusion – not quantifiable.

• DFT provides a tractable accurate solution for the ground state eigenvalues(energy) and electron density.

– Replaces the complicated interacting system Hamiltonian by a sum of non-interacting Hamiltonians.

– Uses electron density (one function in space) as the fundamental propertyinstead of ψtot.

∑∑∑∑∑≠≠ −

+∇−−

+−

−+∇−=

JI JI

JII

I Iji jiIi Ii

I

ii

e RReZZ

Mrre

RreZ

mH

22

22

,

22

2

21

221

2ˆ

Total wavefunction

21

Structural and electronic properties of OVs in MOS oxide regions were studied.

DFT Shows Oxygen vacancy (OV) defects give rise to charge trapping centers

Structures of OV in oxide regions:(1) Basic Low-energy Dimer, (2) High-energy forward-projected (fp), (3) High-energy back-projected (bp)

• Upon hole capture, basic dimer spontaneously forms positive fp.• fp thermally transforms to bp.• Also, fp and bp are stable when neutral.

22

• The time-dependent total concentration of activated hole traps (positive charges) is translated to voltage shift in negative direction.

• Δ𝑉𝑉 𝑡𝑡 = −𝑞𝑞 𝑁𝑁 ∑𝑖𝑖=26 𝑥𝑥𝑖𝑖(𝑡𝑡)𝐶𝐶

Transient modeling of OV hole trap activation under NBTS (contd..)

[1] A. J. Lelis et. al, IEEE T-ED, vol. 62, no.2, pp.316-323, 2015.[2] M.A. Anders et.al., IIRW pp. 16-19, Oct. 2014.

ExperimentalSimulated NBTS

OV hole trap activation is a serious contributor to HTGB reliability degradation in 4H-SiC MOSFETs (from integrated modeling using DFT and rate equations) .

23

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 GaNsubstrate

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−𝐺𝐺𝑎𝑎𝑁𝑁 = 1017𝑐𝑐𝑚𝑚−3

𝐸𝐸𝐹𝐹−𝐴𝐴𝐴𝐴𝐺𝐺𝑎𝑎𝑁𝑁 =𝐸𝐸𝑔𝑔−𝐴𝐴𝐴𝐴𝐺𝐺𝑎𝑎𝑁𝑁

2

𝜎𝜎𝑖𝑖𝑛𝑛𝑡𝑡𝑖𝑖𝑟𝑟𝑖𝑖𝑎𝑎𝑐𝑐𝑖𝑖 = 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