What is the Arrhenius model for semiconductor reliability and how do I use it for lifetime prediction?

The Arrhenius model is the fundamental relationship used to predict the lifetime of semiconductor devices based on their operating temperature. It describes how chemical and physical degradation mechanisms accelerate with temperature: (1) The model: MTTF = A × exp(E_a / (k_B × T)). Where MTTF = mean time to failure (hours), A = pre-exponential constant (determined experimentally), E_a = activation energy of the dominant failure mechanism (eV), k_B = Boltzmann constant = 8.617 × 10^-5 eV/K, and T = junction temperature in Kelvin (T_K = T_°C + 273.15). (2) Acceleration factor: the ratio of MTTF at two temperatures: AF = MTTF(T₁) / MTTF(T₂) = exp[E_a / k_B × (1/T₁ - 1/T₂)]. This is used to extrapolate from accelerated test conditions to operating conditions. Example: accelerated test at T₂ = 250°C (523K). Operating at T₁ = 150°C (423K). E_a = 1.7 eV (GaN HEMT). AF = exp[1.7 / 8.617e-5 × (1/423 - 1/523)] = exp[19726 × (2.364e-3 - 1.912e-3)] = exp[19726 × 4.52e-4] = exp[8.92] = 7490. MTTF at 150°C is 7490× longer than at 250°C. If the median failure time at 250°C = 2000 hours: MTTF at 150°C = 2000 × 7490 = 1.5 × 10^7 hours (1710 years). (3) Activation energies for common RF failure mechanisms: GaN HEMT gate degradation: E_a = 1.6-2.0 eV. GaAs pHEMT ohmic contact interdiffusion: E_a = 1.2-1.6 eV. Gold wire bond intermetallic growth: E_a = 1.0-1.2 eV. LDMOS hot carrier injection: E_a = 0.7-1.0 eV. Solder joint fatigue: E_a = 0.5-0.7 eV (not purely Arrhenius; also depends on thermal cycling amplitude). Electromigration: E_a = 0.7-0.9 eV. (4) Using the model for design: step 1: identify the dominant failure mechanism for your device technology (from the manufacturer or literature). Step 2: obtain the activation energy (from manufacturer reliability reports or published data). Step 3: determine the MTTF at the test temperature (from the manufacturer accelerated life test data). Step 4: calculate the MTTF at your operating junction temperature using the acceleration factor. Step 5: verify that the MTTF exceeds your reliability requirement.