Phonon-limited mobility for electrons and holes in highly-strained silicon

Strain engineering is a widely used technique for enhancing the mobility of charge carriers in semiconductors, but its effect is not fully understood. In this work, we perform first-principles calculations to explore the variations of the mobility of electrons and holes in silicon upon deformation by uniaxial strain up to 2% in the [100] crystal direction. We compute the π₁₁ and π₁₂ electron piezoresistances based on the low-strain change of resistivity with temperature in the range 200 K to 400 K, in excellent agreement with experiment. We also predict them for holes which were only measured at room temperature. Remarkably, for electrons in the transverse direction, we predict a minimum room-temperature mobility about 1200 cm²/Vs at 0.3% uniaxial tensile strain while we observe a monotonous increase of the longitudinal transport, reaching a value of 2200 cm²/Vs at high strain. We confirm these findings experimentally using four-point bending measurements, establishing the reliability of our first-principles calculations. For holes, we find that the transport is almost unaffected by strain up to 0.3% uniaxial tensile strain and then rises significantly, more than doubling at 2% strain. Our findings open new perspectives to boost the mobility by applying a stress in the [100] direction. This is particularly interesting for holes for which shear strain was thought for a long time to be the only way to enhance the mobility.

应变工程是提升半导体载流子迁移率的常用技术，但其作用机制尚未被完全阐明。本研究通过第一性原理计算（first-principles calculations），探究了硅中电子与空穴的迁移率在[100]晶向施加最大2%单轴应变（uniaxial strain）时的变化规律。我们基于200 K至400 K温度区间内电阻率的低应变响应，计算得到π₁₁与π₁₂电子压阻系数，该结果与实验数据吻合极佳。我们还对仅在室温下完成过测量的空穴压阻系数进行了预测。值得注意的是，对于横向电子，我们预测在0.3%单轴拉伸应变下，其室温迁移率存在约1200 cm²/Vs的极小值；而纵向输运则呈单调递增趋势，在高应变下可达2200 cm²/Vs。我们通过四点弯曲测试（four-point bending measurements）验证了上述发现，证实了第一性原理计算结果的可靠性。对于空穴，我们发现当单轴拉伸应变为0.3%以内时，输运性能几乎不受应变影响；当应变超过该阈值后，空穴迁移率显著提升，在2%应变下增幅超过一倍。本研究为通过[100]方向施加应力提升载流子迁移率提供了全新思路，这对于空穴而言尤为重要——长期以来学界普遍认为，唯有剪切应变方可实现空穴迁移率的提升。