Transcript Slide 1
MOSFET Device Simulation MOSFET Device Structure Semiconductor Equations Poisson Equation: q n p N D N A 2 n J n q R G t Electron current continuity equation: q Hole current continuity equation: q Electron current equation: J n qnn q(nDn ) Hole current equation: J p qp p q( pD p ) p J p q R G t Simulation Methodology Set up the device dimensions, material properties, temperature, bias voltages, doping profile, etc. Discretization of the semiconductor equations Newton’s Method for better accuracy Y Converged? N Iterative Gummel Block Method. Solve for , n, p Initial Guess for , n and p N Current Continuity? Y Extract , electron and hole concentrations, mobility, current density, IV characteristics, etc. Mobility Models Oxide Low field mobility: Matthiessen's rule 1 LF 1 B 1 SP 1 SR 1 Electron Flow C LF = Low Field Mobility B = Bulk Mobility Bulk SP = Surface Phonon Mobility Electron Surface Phonon SR = Surface Roughness mobility Trap Surface Roughness C = Trapped interface charge mobility High Field Mobility: High field mobility: HF Fixed Charge LF 1 LF E|| 1 vsat Caughey – Thomas Model for bulk mobility: n 300 T D 1 N ref n 0 T n n nmin n 1 n Temperature dependence: T nmin Doping dependence: 1 n D n Surface Phonon Mobility: SP 1 SP q ac mc n E n 2 1 E 3 T ac = Surface acoustic phonon relaxation time E┴ = Perpendicular E. Field n, n = calculated from phonon scattering equation Surface Roughness Mobility: 1 SR SR = Surface roughness parameter. E2 SR Higher the value of SR, smoother is the surface and lesser is the degradation in total mobility Interface Trap Charge Mobility: Corresponds to effect of coulomb scattering of mobile charged carriers by fixed charge and interface trap charge. The term also accounts for the screening of these charges by electrons at strong inversion. 1 C nf Nit Temp T 300 ne 1 screen_fit screen_factor it nf = Fixed oxide charge Nit = Occupied interface trap density ne = Inversion layer electron concentration temp = Temperature dependence screen_fit, screen_factor = fitting parameters for the screening effect it = from Coulomb Scattering model 4H SiC 200m x 200m MOSFET: Id-Vgs Simulation Fit at T=27oC 4H SiC 200m x 200m MOSFET: Id-Vds Simulation Fit at T=27oC Bulk Mobility …. n 300 T D 1 N ref n 0 T n nmin n nmin Parameter 6H SiC 4H SiC n0 in cm2/Vs 500.0 1071.0 nmin in cm2/Vs 0.0 5.0 Bulk mobility at Room Temperature and D ~ 1015 is n 2.4 2.5 4H SiC: ~ 800 cm2/Vs Nref 1.1e18 1.9e17 n 0.45 0.40 6H SiC: ~ 400 cm2/Vs Surface Phonon Mobility …. 1 SP n E n 3 n bulk ac 2 2 1 E 3 T 1 h3vs2 ac 2 * 8 m mc Z A2 2 q 9h n 3 k B 16 2 qm 2 1 3 Units 6H 4H m1, m2, m3 - 0.22, 0.90, 1.43 0.29, 0.58, 0.33 m┴ - 0.44 0.41 m║ - 1.43 0.33 mc - 0.35 0.39 m* - 0.44 0.41 ZA eV 17.5 15.0 bulk gm/cm3 3.2 3.2 n (cm/s)-1 2.99e-9 2.29e-9 n (V/cm)-2/3K 0.1217 0.1246 Surface Roughness Mobility …. 1 SR E2 SR Parameter 6H 4H SR (V/s) 1e13 5.82e14 4H SR Value is taken from Linewih (2002) paper 1 SR 1 Cit Effect of surface roughness is negligible as compared to the effect of interface traps on the total mobility. Interface Trap Charge Mobility …. 1 C nf Nit Temp T 300 ne 1 screen_fit screen_factor it 6H 4H nf 5.4 x 1011 2.2 x 1012 Nit at RmT ~ 2 x 1012 ~3 x 1012 it 1.5 x 1011 1.5 x 1011 screen_fit 1.5 x 1018 1 x 1018 screen_factor 0.8 0.7 Occupied interface trap density (Nit) Ec Qit qNit q Dit E f E dE Ev Dit = Density of traps per unit energy f(E) is the probability density function. It is directly proportional to the mobile charge concentration (ne). Hence as MOSFET goes towards stronger inversion, the occupied interface trap density increases. E Ec Dita E Ditmid Ditedge exp a f E 1 1 E Ec 1 Nc exp 2 ne k T B 4H SiC has a higher bandgap than 6H SiC (by 0.2eV). Ditedge value for 4H SiC is obtained by extrapolating the Dit-E curve for 6H SiC by 0.1eV. This gives a very high Ditedge value for 4H SiC because of the exponential relation between Dit and E near the band edge. Hence 4H SiC has much higher interface traps than 6H SiC. Extrapolation of Dit-E curve for 6H SiC to get Dit-E characteristics for 4H SiC Final Dit-E curve for 4H that is used: Dit_edge = 2.15 x 1013 cm-2eV-1 Dit_mid = 6.5 x 1011 cm-2eV-1 6H 4H Ditmid (cm-2eV-1) 1 x 1013 2.19 x 1013 Ditedge (cm-2eV-1) 8 x 1011 8 x 1011 Nit vs. position for different Vgs. T=27oC Occupied interface trap density increases with increase in Vgs. This is because the inversion layer electron concentration increases with increase in Vgs causing more traps to get filled Device: 4H SiC MOSFET W/L: 200 m / 200 m Bias: Vgs = 2 to 4V Vds = 4V Nit vs. position for different Temperatures Occupied interface trap density decreases with increase in temperature because trapped electrons can escape by gaining sufficient energy at higher temperatures. So as the temperature increases, effect of interface trap charge decreases, increasing overall mobility Device: 4H SiC MOSFET W/L: 200 m / 200 m Bias: Vgs = 6V Vds = 1V Comparing effects of Surface Roughness and Interface traps at different Temperatures The change in Id values for a tenfold improvement of the surface roughness factor, is very small at all three temperatures. Thus surface roughness does not change the current with change in temperature. The increase in current with temperature is caused by the reduction of filled interface trap density as temperature increases. Device: 4H SiC MOSFET W/L: 200 m / 200 m Bias: Vgs = 6V Vds = 0-8V Future Work… • Better screening model based on BrooksHerring ionized impurity scattering model • Surface roughness calculation to get proper value for SR • Fitting data at higher temperatures • High power MOSFET simulation • Investigating gate leakage in SiC MOSFETs • Building a Graphical User Interface for the simulator