Modeling of transient electrical characteristics for granular semiconductors

Modeling of the electrical large-signal response of granular n-type semiconductors is carried out at following three different levels: (i) simple fully analytical model, (ii) semianalytical numerical model, and (iii) numerical device simulation. The electrical transients induced by both voltage and temperature changes are calculated. The analysis is based on the dynamic electrical model of the grain-boundary (GB) region, the drift-diffusion theory, and electronic trapping in the acceptor-type electronic interface states at the GBs. The electronic trapping is described using the standard rate equation. The models are verified by performing numerical device simulations using SILVACO ATLAS. The agreement between the proposed semianalytical model and ATLAS results is excellent during the whole transient and up to rather high electric fields. Compared to ATLAS, the calculations performed with the present semianalytical model are four orders of magnitude faster on a standard PC computer. The approximative analytical formulas describing the response are valid when the voltage and temperature changes are small. The semianalytical model is also fitted to reported experimental data obtained from dc and transient measurements of ZnO powder samples. The semianalytical model fits to the data well. The current in the GB region has following three components: potential-barrier limited current, charging and discharging current, and capacitive current. The results show that the large-signal transient responses of granular semiconductors are complex, as they vary highly in both duration and magnitude. During a transient the current can change many orders of magnitude. This is mainly caused by the change in the GB trap occupancy.