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Where m is an empirical exponent (≈3 for electrons). Accelerated life tests stress devices at elevated V_d and V_g, monitoring parameters like linear drain current (I_dlin) or transconductance (g_m). A 10% degradation is a common failure criterion. It seems you are looking for an article

Where (E_m) is the maximum lateral field near drain, (\Phi_b) is the barrier height for impact ionization, and λ is the mean free path. High (E_m) (short channel, high V_dd) exponentially increases hot carrier generation. The HCI lifetime τ is often modeled via: Where (E_m) is the maximum lateral field near

[ I_sub = I_d \cdot A \cdot \exp\left(-\frac\Phi_bq \lambda E_m\right) ] It seems you are looking for an article

[ V_T = V_FB + 2\phi_F + \frac\sqrt4\epsilon_s q N_A \phi_FC_ox ]