A Transfer-matrix Based Compact Gate Tunneling Current Model

Wangzuo Shangguan, Xing Zhou, Siau Ben Chiah, Guan Huei See, Karthik Chandrasekaran
School of Electrical & Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798

The 3rd International Conference on Materials for Advanced Technologies (ICMAT-2005), Symposium L: Materials Physics at Interfaces, Singapore, July 3-8, 2005, Paper L-8-OR21.

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The modeling of gate leakage current has been of great interest in recent years, with the continuous miniaturization of MOS device dimensions. Most gate current models employ the simple WKB approximation for calculation of the transmission coefficient to obtain a simple analytical expression. However, the use of the WKB approximation for the gate tunneling current in ultrathin oxides is controversial. It is quite accurate when dealing with opaque barriers, but for ultrathin and low barriers the WKB approximation breaks down. This becomes especially crucial for large applied voltages, which can lower the tunneling barrier substantially. We present in this paper a MOSFET gate tunneling current based on the transfer matrix method. Due to charge pileup in the semiconductor surface layer, the conduction band edge bends by ?s compared to that deep in the bulk, where ?s is the surface potential. This bending feature of the bands is taken into account in the calculation of the transmission coefficient, which in general, is a complicated function of the incident energy. However, the transmission coefficient can be simplified if the incident energy is much lower than the tunneling barrier height. To obtain an analytical model in closed form applicable for compact modeling, the integration in the tunneling current over the incident energy is approximated by the single tunneling energy approximation. To further reduce the error arising from a variety of explicit or implicit approximations in the calculation, an effective conduction band edge is introduced. The simulation resulting from this simple model show satisfactory agreement with the measurement data. A comparison with results from the WKB approximation will also be presented.