A unified thermionic and thermionic-field emission (TE–TFE) model for ideal Schottky reverse-bias leakage current

We present a unified thermionic emission (TE) and thermionic-field emission (TFE) model for the ideal reverse-bias leakage current in Schottky junctions. The unified TE–TFE analytical model advances upon previous analytical TFE models by Murphy–Good and Padovani–Stratton, which are the two most widely adopted models by the community, in two major aspects: (i) the applicability of the TFE expression therein is extended to near-zero surface electric fields by an error-function correction, allowing for the calculation of the total current by a nontrivial sum of TE (over-the-barrier current) and TFE (below-the-barrier current) contributions; therefore, an accurate description of the TE-to-TFE transition region is captured analytically for the first time; (ii) image-force lowering is considered with much-simpler correction terms. Comparisons with the reference numerical model show that the unified TE–TFE model has excellent accuracy, as well as a 10 000× reduction in computation time. The unified model is further tested against experimental data from Schottky barrier diodes based on Si, 4H-SiC, GaN, and β-Ga2O3, revealing accurate extractions of barrier heights and correct descriptions of the ideal reverse leakage characteristics. With the extended applicable range, improved accuracy, and computational efficiency, the unified TE–TFE model is highly valuable for the design and analysis of devices based on Schottky junctions, as well as for potential integration in technology computer-aided design (TCAD) tools.