Engineering & Science
Arora Silicon Electron Mobility Model: Joint Temperature & Doping Law
Calculate n-type silicon electron mobility μ_n(T, N) (cm^2/(V·s)) across 200–500 K and arbitrary doping N via Narain Arora’s 1982 TCAD temperature-scaled Caughey-Thomas equations.
Why power MOSFETs slow down at 400 K junction temperature—and by how much!
Room-temperature Caughey-Thomas parameters fail as soon as a power Si MOSFET or automotive IC heats up to 400–450 K because all four mobility parameters shift simultaneously with normalized temperature T_n = T / 300 K! Narain D. Arora, John R. Hauser, and David J. Roulston (IEEE Transactions on Electron Devices, 1982) calibrated the industry-standard Sentaurus/Silvaco TCAD model for n-silicon: μ_min = 88 * T_n^-0.57, μ_d = 1252 * T_n^-2.33, N_ref = 1.26 × 10^17 * T_n^2.4, α = 0.88 * T_n^-0.146, and μ_n(T, N) = μ_min + μ_d / (1 + (N / N_ref)^α)!
Watch the thermal derating on an n-drift region doped at N = 1.0 × 10^16 cm^-3: at T = 300 K (T_n = 1.00), μ_n = 1,218.4 cm^2/(V·s); when junction temperature rises to T = 400 K (T_n = 1.3333), acoustic-phonon T^-2.33 scattering slashes μ_n by 44.6% down to 675.6 cm^2/(V·s)—nearly doubling on-state R_DS(on) conduction loss!
| Silicon Operating Condition (T & Donor N) | Reduced Temp Tn = T / 300 | Arora Electron Mobility μn | Device Conduction Impact |
|---|---|---|---|
| 300 K Drift Region (N = 1.0 × 10^16 cm^-3) | 1.0000 | 1,218.4 cm^2/(V·s) | Nominal Datasheet RDS(on) |
| 400 K Hot Junction (N = 1.0 × 10^16 cm^-3) | 1.3333 | 675.6 cm^2/(V·s) (-44.6%!) | Positive Thermal Resistance Coeff |
| 300 K Heavy N+ Collar (N = 1.0 × 10^18 cm^-3) | 1.0000 | 262.1 cm^2/(V·s) | Impurity-Weakened T Dependence |
Arora Joint Temperature & Doping Electron Mobility μ_n(T, N) (cm^2/(V·s))
Evaluates all four temperature-scaled Arora terms at T_n = B2 / 300 K and donor concentration B3 (cm^-3).
=IF(OR(B2 <= 0, B3 <= 0), "Invalid Arora Inputs", ROUND(88 * ((B2 / 300) ^ -0.57) + (1252 * ((B2 / 300) ^ -2.33)) / (1 + (B3 / (1.26E17 * ((B2 / 300) ^ 2.4))) ^ (0.88 * ((B2 / 300) ^ -0.146))), 1))Phonon-Limited Low-Doping Ceiling μ_max(T) = μ_min(T) + μ_d(T) (cm^2/(V·s))
Returns intrinsic/light-doping electron mobility ceiling 88 * T_n^-0.57 + 1252 * T_n^-2.33 (= 1,340.0 at 300 K).
=IF(B2 <= 0, "Invalid Arora Inputs", ROUND(88 * ((B2 / 300) ^ -0.57) + 1252 * ((B2 / 300) ^ -2.33), 1))Try the example
Use the original values or change them to test your understanding.