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In this paper, we propose the design optimization of underlapped Si1-xGe x -source tunneling field-effect transistors (TFETs) with a gate-all-around structure. The band-to-band tunneling rates, tunneling barrier widths, I-V transfer characteristics, threshold voltages, on/off current ratios, and subthreshold swings (SSs) were analyzed by varying the Ge mole fraction of the Si1-xGe x source using a commercial device simulator. In particular, a Si0.2Ge0.8-source TFET among our proposed TFETs exhibits an on/off current ratio of approximately