Advanced Drift Diffusion Simulator for 4H-SiC MOSFETs
Advanced Drift Diffusion Device Simulator for 6H and 4H-SiC MOSFETs MOSFET Device Simulation MOSFET Device Structure Semiconductor Equations Poisson Equation: 2 q n p N D N A n J n q R G t Electron current continuity equation: q Hole current continuity equation: q Electron current equation: J n qn n q(nDn ) Hole current equation:
J p qp p q( pD p ) p J p q R G t Mobility Models Oxide Low field mobility: Matthiessen's rule 1 1 1 1 1 LF B SP SR C Electron Flow LF = Low Field Mobility B = Bulk Mobility SP = Surface Phonon Mobility SR = Surface Roughness mobility Bulk Electron Surface Phonon Trap Surface Roughness Fixed Charge C = Coulomb Scattering Mobility High Field Mobility:
High field mobility: 1 Total 1 1 LF vsat E || Screened Coulomb Scattering Mobility Screened Coulomb Potential: e 2 1 qsc r V (r ) e 4 r H 2D 2D Matrix Element: 2 2 e 2 exp z zi q2 D qsc 2 q22d qsc2
N z 1 2D 2 i z , zi 4 Scattering Rate: Fermis Golden Rule: k k 2 2 H 2 D z , zi Ek Ek k dk 1 cos d k k k 0 0 Screened Coulomb Scattering Mobility: m* e 3 N 2 D z i 1 F z , zi 2 C 16 k BTe F z , zi
2 exp 2 qsc2 8m*k BTe sin 2 2 z zi 1 q q 2 sc 2 sc 8m*k BTe sin 2 2 d e 2 N inv qsc SiC Z avg k BT ID-VGS at Room Temperature -6 x 10 1e-5 5 1e-7 ID (A) ID (A) 4
3 2 1 0 -5 0 VGS 5 10 (Volts) 15 1e-10 0 Circles : Simulated Points Line: Experimental data 5 VGS (Volts) 10 15 Occupied interface trap density Negatively charged interface traps: Ec Qit qN it q D E f E dE it n
E neutral Dit = Interface traps density of states Dita E Ditmid E Ec Ditedge exp a f(E) is the probability density function. 1 f E E Ec 1 Nc 1 exp 2 ne k BT Interface Trap Density of States 14 10 Dit (cm-2eV-1) 1e14 13 10 Donor Acceptor 12 10 2.5e11
11 10 0 Neutrality Point 1 E (eV) 2 3 Figure . Interface trap density of states for 4H-SiC: Constant distribution in midgap and an exponential rise near the band edges. 5 5 10 10 4 4 10 10 Mobility (cm2/Vs) Mobility (cm2/Vs) Mobility Variation with Depth 3
0 50 100 150 z (Angstroms) 200 250 VGS = 14V. Lots of Screening. Coulomb Mobility effect only very close to interface. Surface Roughness mobility dominates Current Density Variation with Depth 400 VGS = 2V VGS = 4V VGS = 6V VGS = 8V VGS = 10V VGS = 12V VGS = 14V 350 300 Jn (A/cm 2) 250 200 150 100 50 0 0
20 40 60 80 z (Angstroms) 100 120 Peak of the current density is some distance away from the interface Nit VGS and Ninv VGS at RmT 14 10 Nit & Ninv (cm-2) 12 10 10 10 8 Ninv 10 Nit 6 10
0 5 10 VGS (Volts) 15 Fixed Oxide Charge Density ~ 1.45e12 cm-2 Screened Coulomb Scattering Mobility Coulomb scattering decreases rapidly with increase in depth inside the semiconductor Oxide charges located away from the interface have less effect on Coulomb scattering Screening is directly proportional to the inversion layer charge density Scattering rate is inversely proportional to electron temperature (energy) Scattering rate is directly proportional to the density of oxide charges and occupied interface traps Future Work Implement oxide charging - interface trap charging model in simulator Implement a robust surface roughness mobility model High temperature high power simulations Modeling of different Power MOSFET structures
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