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 11 aa 22 Figure: Primitive unit cell and hexagonal conventional unit cell of GaN 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` GG` = EE UU 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 3.46eV Experiment 3.5eV[1] 3.333.35eV[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 States using EPM mm /mm 0 0.165 0.20 ± 0.02[2] Eg(Γ 3 Γ 5 ) 6.12eV 5.3eV[3] Eg(MM 3 MM 4 ) 7.6eV 7.07.1eV[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. ElNaggar, 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 topmost valence band and bottommost 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 Drift velocity (cm/s) 3.00E07 2.50E07 2.00E07 1.50E07 1.00E07 5.00E06 Bulk MC simulation Use Band Structure for MC. The whole electrical field range simulation reveals: 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 0.00E00 0 100 200 300 400 500 Electrical Field (kv/cm) Figure: Whole electrical field range simulation of drift 3. Low field mobility (ie. the slope of the curve at low electrical field range) changes with the impurity concentration 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 1E17 1E18 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 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. [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: 2DElectron Gas (2DEG) Transport Gate 2DEG Channel S contact AlGaN D contact GaN undoped Buffer Layers/ Transition Layers/ Substrate 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 2DEG GaN PP SSSS GaN BandBending Electron transport AlGaN GaN GaN EE FF Reaching critical thickness EE FF EE FF Surface Donor half empty 2D potential quantum well 10/13
2.2 2DEG potential well modeling E_th Slope Case (a) 0.45eV 0.2eV/3.5nm (a) (b) Case (b) 0.75eV 0.52eV/4.5nm Energy (ev) Picked subbands: 3 subbands Picked subbands: 2 subbands 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 Distance(um) Distance(um) 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 11/13
2.2 2DEG Monte Carlo simulation 3.0E7 Mean velocity (a) 2500 2DEG mobility vs. electron concentration (b) Mean velocity (cm/s) 2.5E7 2.0E7 1.5E7 1.0E7 5.0E6 0.0E0 Case(a) Case(b) 3D 0 100 200 300 400 500 E field(kv/cm) Mobility(cm^2/Vs) 2000 1500 1000 500 Data.1 Data.2 Data.3 Data.4 Data.5 Data.6 Data.7 Data.8 Case(a) Case(b) 0 0.00E00 2.00E13 4.00E13 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 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
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. 13/13
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Backup: 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.
Backup: Heterostructure Cation Anion AlGaN film under tensile strain Gaface [0001] [0001] Relaxed GaN substrate PP PPPP Nface 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
Backup. 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 Note: this is a test run for the solver, the specific parameters for the structure differ from case to case