Unified Model for Trap-Limited Conduction via Field-Driven Interactions and Poole-Frenkel Emission

Abstract

In the widely accepted trap-limited space-charge-limited current (T-SCLC) model, limitations arise due to the underestimation of excess carriers generated by field-driven emission from charge-filled traps. This limitation exists because the model cannot adequately characterize field-dependent emission rates. In contrast, Poole-Frenkel (P-F) emission can describe field-dependent emission rates based on the Coulomb interaction between free carriers and positively charged trap centers. However, it focuses solely on the trap-detrap process within individual trap centers. In this work, we propose a novel field-dependent emission current model within the P-F emission framework, specifically under trap-limited conditions. Utilizing the Shockley-Read-Hall (SRH) framework, we aim to eliminate ambiguities in the free-to-trapped carrier density ratio and to directly evaluate recombination centers. Additionally, we employ a quantitative approach to probabilistically describe the dynamic behavior of excess carriers, incorporating the trap-barrier lowering effect and the recombination process within the drift regime. Our model diverges from conventional methods by explicitly incorporating field-dependent trap dynamics, providing a more comprehensive view of trap-limited carrier transport that encompasses discrete, exponential, and Gaussian trap distributions. This approach extends its utility across various conduction regimes, from trap-limited to trap-filled-limited conditions, making it adaptable to a range of materials. Through experimental validation, we present practical techniques for generating trap-limited systems and evaluating them in experimental settings, thereby enhancing the model's practical relevance. Key improvements introduced by our model include: 1) explaining variations in current magnitude based on injection level; 2) resolving the observed P-F factor anomaly by accounting for injection-level effects; and 3) providing a more realistic voltage dependence with enhanced curvature in the I-V characteristics compared to the traditional T-SCLC model with P-F effects. These enhancements ultimately offer a deeper understanding of trap-limited transport properties in various semiconductor systems.