Modeling of SiC & GaN: Interfaces, Transport & Devices

Modeling of SiC & GaN: Interfaces, Transport & Devices University of Maryland Neil Goldsman Ziyang Xiao, Chris Darmody Dev Ettisserry & Akin Akturk Army Research Lab Aivars Lelis, Dan Habersat & Ron Green

Modeling of SiC & GaN: Interfaces, Transport & Devices Outline 1. Neil Goldsman a) Summary of Key Earlier Results b) SiC vs. GaN 2. Chris Darmody a) Device Simulation of SiC Trench MOSFETs 3. Ziyang Xiao a) GaN: Band Structure & Monte Carlo Transport b) AlGaN: 2D Electron Gas, Energy Bands & Monte Carlo 4. Neil Goldsman a) Oxide Reliability & Oxygen Vacancies

SiC & GaN Device Virtual Fab, Design and Analysis Platform E X P E R I M E N T Device Modeling (I-V & Performance) Process & Fabrication Modeling (Device Structure & Defect Generation) NO Monte Carlo: (Transport) Σ YES CoolSPICE Circuit Design Density Functional Theory (Defects) Device Meet Specs?

Summary of Key Results: Transition Region & Atomic Origin of Defects Reliability: Threshold Instabilities Due to Oxide Vacancies and Carboxyl Substitutions in SiO 2 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 Operating Temperature Thermal Conductivity High High Low High Medium Medium SiC & GaN: Both Wide Bandgap and Attractive Characteristics Extending work to include GaN

That s it for Introduction 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

Simulation of SiC TrenchMOS Devices and Interfaces University 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 Semiconductor Equations in Drift-Diffusion Model: εε ϕ = qq( nn + pp NN AA + NN DD + ) JJ nn = qqqqμμ nn ϕ + qqdd nn nn Gate Poly Gate Oxide 10 20 n+ Source 6.5x10 16 Source/Body Contact p Body JJ pp = qqqqμμ pp ϕ qqdd pp pp nn tt = 1 qq JJ nn RR nn + GG nn pp tt = 1 qq JJ nn RR pp + GG pp n: Electron Concentration p: Hole Concentration Φ: Potential J n : Electron Current Density J p : Hole Current Density μ n : Electron Mobility μ p : Hole Mobility 1.7x10 15 10 20 n- Drift Region n+ Drain 3/16

Saturation Region Electron Conc. Source Well Gate Channel P Body Vg=15V Vd=50V Vs=Vb=0V Drain 4/16

Saturation Channel Electron Conc. Source Well Gate Oxide t ch = 2nm P Body Vg=15V Vd=50V Vs=Vb=0V 5/16

Saturation Region Electron Conc. Source Well Gate Channel Pinch-off Vg=15V Vd=50V Vs=Vb=0V Drain 6/16

Pinch-off: Saturation Electron Conc. Vg=15V Vd=50V Vs=Vb=0V Gate Oxide Region 7/16

Saturation Region Potential Profile Gate Source/Body Vg=15V Vd=50V Vs=Vb=0V Drain 8/16

Linear Region Operation Gate Source/Body Channel Drain Vg=20V Vd=5V Vs=Vb=0V 9/16

Channel Formed: Linear Region Source Well Gate Oxide P Body 10/16

Off Device Operation Gate Source/Body No channel formed Pinch-off region Drain Vg=0V Vd=600V Vs=Vb=0V 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 L Δ μμ SSSS = ħ 3 2mmmmEE 2 2 LL 2 Ω SSSS True Potential 13/16

4H-SiC Structure and Supercells Primitive Cell 2x2x1 Supercell Transformed Axes Si C Hexagonal Lattice A-Face (1 210) Si-Face (0001) M-Face (1 100) 14/16

Surface Roughness Model from DFT SiO2 Extracted Interface (0001) Potential 4H-SiC Extract realistic interface potentials from DFT simulations Create scattering matrix elements for Monte Carlo Sim. 1 μμ [ ϕ kk VVϕ kk dddd] 2 15/16

Modeling Strategy Overview Atomic Level Structure: DFT time Atomic Level e - Transport: Monte Carlo 0 1 4 3 2 0 z Power TrenchMOS: Device Sim. 16/16

GaN and GaN/AlGaN Heterostructure Properties Investigation and Simulations Ziyang (Christian) Xiao Neil 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: aa 1 = aa 1,0,0 aa 2 = aa 1 2, 3 2, 0 aa 3 = cc 0,0,1 aa 33 aa 22 aa 11 Figure: Primitive unit cell and hexagonal conventional unit 02/13

1.1 GaN Reciprocal Lattice The reciprocal lattice of a Wurtzite crystal is also a hexagonal lattice, with: Reciprocal lattice unit vector: bb 1 = 2ππ 1, 1, 0 aa 3 bb 2 = 2ππ aa 0, 2 3, 0 bb 3 = 2ππ 0,0,1 cc High 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: Where: ħ 2 kk + GG 2 2mm UU GG + VV GG GG` UU GG` = EE UU GG GG` E is the allowed electron energy states GG is the reciprocal lattice vectors UU GG is the Fourier transformation constant for Bloch functions VV GG is the Fourier transformation constant for V(r) VV GG = 1 Ω Ω dd rr VV rr ee ii GG rr V(r) is the periodic lattice atomic potential 04/13

1.2 Band Structure Calculation Band Structure for Mobility and Transport Properties including Velocity Overshoot Eg(Γ 1 - Γ 6 ) EPM 3.46e V Experiment 3.5eV[1] 3.33-3.35eV[4] Energy (ev) 3 4 U 3 1 6 5 AA LL MM ΓΓ AA HH KK ΓΓ Figure: Calculated band structures and Density of mm /mm 0 0.165 0.20 ± 0.02[2] Eg(Γ 3 - Γ 5 ) Eg(MM 3 - MM 4 ) 6.12e V 7.6e V 5.3eV[3] 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 05/13

1.2 Band Structure Calculation Energy: ev (a) 8 7 Energy: ev 8 M Γ K (b) 6 5 4-0.5-1 -1.5-2 -2.5 Bottom most Conduction Band Top most Valence Band Bandgap 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 6 4 2 0-2 - 4 M kk xx Γ K kk yy Plane A 06/13

1.3 GaN Bulk Monte Carlo Simulation 3.00E+07 2.50E+07 Bulk MC simulation Use Band Structure for MC. The whole electrical field range simulation reveals: Drift velocity (cm/s) 2.00E+07 1.50E+07 1.00E+07 5.00E+06 0.00E+00 0 100 200 300 400 500 Electrical Field (kv/cm) 1. A peak velocity of 2.83 10 7 cm/s at 150kV/cm 2. A saturation velocity beyond 250kV/cm at about 2.2~2.3 10 7 cm/s 3. Low field mobility (ie. the slope of the curve at low electrical field range) changes with the impurity concentration Figure: Whole electrical field range simulation of drift velocity with purity concentration at 10 17 cccc 3 07/13

1.3 GaN bulk MC simulation Mobility (cm^2/vs) 800 700 600 500 400 300 200 100 Bulk GaN mobility vs. Impurity concentration 0 1E+17 1E+18 Impurity Conc. (cm^-3) Monte Carlo Data. 1 Data.2 Data.3 Data.4 Bulk low field mobility vs. Impurity concentration extracted from MC simulation. The experimental data sets Data.1 4 are mobility values taken from 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 [1] M. Asif Khan et al, Appl. Phys. Lett. data.,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 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 S contact Gate AlGaN GaN un-doped D contact Buffer Layers/ Transition Layers/ Substrate 2DEG Channel 1. GaN/AlGaN heterostructure is the center of the device. 2. A 2DEG is formed at the interface without doping in either AlGaN or GaN layer or bias Figure: General device structure of a GaN/AlGaN based HEMT 09/13

2.1 Formation of 2DEG AlGaN AlGaN Surface Donor full - - - - - - + + + + + + PP SSSS + PP PPPP - - - - AlGaN 2DE G GaN PP SSSS GaN + + + Band-Bending Electron transport AlGaN GaN GaN EE FF Reaching critical thickness EE FF EE FF Surface Donor half 2D potential 10/13

2.2 2DEG potential well modeling (a) (b) E_th Slope 0.2eV/3.5n Case (a) 0.45eV m Case (b) 0.75eV 0.52eV/4.5n m Energy (ev) Picked subbands: 3 subbands Distance(u m) Picked subbands: 2 subbands Distance(u m) Figure: the approximated wave function Ψ 2 for a triangular potential well with illustrated potential well. The potential well parameters are list on the 1. The wave function is calculated from the infinite triangular potential well. 2. The selected subbands are determined by EE ttt. 3. For 2D scattering (electron energy below EE ttt ), the included scattering types are: acoustic scattering and polar optical scattering 11/13

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] 12/13 2.2 2DEG Monte Carlo simulation Mean velocity (cm/s) 3.0E+7 2.5E+7 2.0E+7 1.5E+7 1.0E+7 5.0E+6 0.0E+0 Mean velocity Case(a) Case(b) 3D (a) 0 100 200 300 400 500 E field(kv/cm) 2500 2000 Mobility(cm^2/Vs) 1500 1000 500 2DEG mobility vs. electron concentration (b) Data. 1 Data. 2 Data. 3 Data. 4 Data. 5 Data. 6 0 0.00E+00 2.00E+13 4.00E+13 Electron Sheet Density (cm^-2) [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

13/13 Conclusion 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 cccc 2 /VVVV in our simulation, while 2DEG mobility is around 1500-1700 cccc 2 /VVVV.

Threshold Voltage Shifts Explained on Atomic Level with DFT Dev Ettisserry & Neil Goldsman

19 Investigate Role of Defects in EMI Ideal Oxide Oxide with Defect

20 Effect of Defects on MOSFETs; High Voltage Bias Changes Threshold Voltage (Vt) Positive shift in Vth following HT positive bias stress due to electron trapping. Negative shift in Vth following HT negative bias stress due to hole trapping. The degradation worsens over time! This work focuses on NBTS degradation potentially due to OV hole traps * Measurements by our collaborators at U.S. Army Research Lab, Adelphi, MD. OV = Oxygen Vacancy

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 s exclusion 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 noninteracting Hamiltonians. Uses electron density (one function in space) as the fundamental property instead of ψ tot. + + + = J I J I J I I I I j i j i I i I i I i i e R R e Z Z M r r e R r e Z m H 2 2 2 2, 2 2 2 2 1 2 2 1 2 ˆ Total wavefunction 21

DFT Shows Oxygen vacancy (OV) defects give rise to charge trapping centers Structural and electronic properties of OVs in MOS oxide regions were studied. 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

Transient modeling of OV hole trap activation under NBTS (contd..) The time-dependent total concentration of activated hole traps (positive charges) is translated to voltage shift in negative direction. ΔVV tt = qq NN 6 ii=2 CC Experimental xx ii (tt) Simulated 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). [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. 23

Thank you! Any questions?

Back-up: Pseudopotential -Z/r 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.

Back-up: Heterostructure Cation Ani on + - AlGaN film under tensile strain Ga-face [0001] [000-1] N-face Figure: the spontaneous polarization of bulk GaN (AlGaN) is due to the lack of symmetry along the [0001] direction Relaxed GaN substrate Figure: Due to the lattice mismatch between AlGaN film and GaN substrate, the film is under biaxial tensile strain, which results in piezoelectric polarization PP PPPP

Note: this is a test run for the solver, the specific parameters for the structure differ from case to case Back-up. heterostructure Poisson solver Parameter inputs: x = 0.2 for AAAA xx GGGG 1 xx NN NN DD GGGGGG = 10 17 cccc 3 EE FF AAAAAAAAAA = EE gg AAAAAAAAAA 2 σσ iiiiiiiiiiiiiiiiii = 10 13 cccc 2 ww σσ = 0.02nnnn