| Summary: | 碩士 === 國立交通大學 === 電機資訊學院碩士在職專班 === 93 === A numerical simulation program has been developed in this work to investigate the transmission of electrons through the metal-semiconductor contacts. The semiconductor surface is discretized properly into a number of small intervals and the potential barrier is approximated as a series of piece-wise linear or step functions. The transfer matrix for electron transmission through or cross each interval of simple potential distribution can be obtained by solving the Schrödinger equation using Airy or exponential function. The transmission coefficient of electrons through or across the whole contact barrier is then derived from the cascaded transfer matrices. As a comparison, the conventional WKB approximation method has also been illustrated.
Since the transmission coefficient can be calculated numerically for electron with energy below or above the contact barrier, we propose, for the first time, a unified simulation for electron tunneling through the semiconductor surface and thermionic-emission at the metal-semiconductor interface. The thermionic-emission current across the Schottky barrier is integrated from the transmission coefficient, which is a function of electron energy together with the transition probability of electron between metal and semiconductor. However, the tunneling current through the Schottky barrier is converted into a local generation or recombination process with local rate depending on the local Fermi-level and the potential distribution. The tunneling processes are self-consistently treated with all current transport in the semiconductor.
The transmission coefficient is a function of electron energy as well as the tunneling and thermionic-emission currents as a function of applied voltage for different transmission models and various doping concentrations has been discussed in this paper.
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