P型硅纳米板压阻特性的理论研究

A Theoretical Study of the Piezoresistivity of a p-Type Silicon Nanoplate

考虑量子尺寸效应与自旋轨道耦合作用,从含有应变的6×6 Luttinger-Kohn哈密顿量出发,采用有限差分方法建立了p型硅纳米板的能带结构模型.基于硅纳米板压阻特性与其能带结构的相关性,采用改进的压阻理论定量分析了厚度、杂质浓度与温度对其压阻系数的影响.研究结果表明:量子尺寸效应强烈改变了硅纳米板的能带结构,是其压阻系数增大的主要因素,而自旋轨道耦合作用仅对含较高应变的硅纳米板的能带结构有较大影响;硅纳米板的压阻系数具有尺寸效应,随厚度减小而增大,随杂质浓度增加或温度升高而减小.在高简并条件下,硅纳米板的压阻系数与温度无关,完全由杂质浓度的大小控制;在非简并条件下,情况刚好相反.最后,利用施加应力前后空穴等能面形状的变化定性分析了硅纳米板压阻特性的起源.

Based on the 6 × 6 Luttinger-Kohn Hamiltonian,including strain, and taking into account of the quantum-size effect and spin-orbit coupling,a band structure model for p-type silicon nanoplate piezoresistors is established using the finite difference meth- od. The effect of thickness, impurity concentration, and temperature on the piezoresistive coefficient of the silicon nanoplate was quantitatively investigated based on its dependence on the band structure. The results indicate that the effect of the quantum confinement of holes, which dramatically alters the band structure,enhances the piezoresistive coefficient of the p-type silicon nanoplate piezoresistors. The spin-orbit coupling,which changes the band-edge energies, plays a significant role in the high strained silicon nanoplates. The size-dependent piezoresistive coefficient of the p-type silicon nanoplate piezoresistors increases as the thickness decreases. The piezoresistive coefficient was also observed to decrease with increased impurity concentration and temperature. In the extreme degen- erate range,the piezoresistive coefficient is controlled only by the impurity concentration and becomes temperature-independent. In the nondegenerate range,the opposite phenomenon occurs. Furthermore, according to the form change of constant energy surfaces for heavy and light holes in the presence of stress,we qualitatively analyze the origin of the longitudinal piezoresistive effect in the silicon nanoplate.