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A new grain boundary model is proposed consisting of 1) a scattering part modeled by reduced mobility, independent of the microscopic details of the boundary, and 2) discrete randomly positioned charging defects. 2D and 3D model implementations are demonstrated, explaining several statistical properties in scaled poly-Si channel devices (particularly vertical NAND devices). In particular, we show that the temperature-dependent activation energy of the transconductance in a short channel poly-Si transistor is a statistical effect that can be modeled with a single grain boundary activation energy.
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Degraeve et al. (2015) studied this question.