Mechanical effects play a role in the electronic behavior of semiconductors in various applications. For example, in strain gauges, the piezoresistive effect is responsible for changes of the current with strain while in MOSFET transistors, strained silicon technologies are used for improving the devices' characteristics. However, the effect of the non-uniformities in the stress fields that develop in the electronic devices are rarely taken into account when addressing the strain effect in semiconductors. In this work, we first address from a general viewpoint the couplings between the mechanical and electronic responses in semiconductors and subsequently specialize the general theory to compute the effect of bending on a p-n junction.

Adopting the framework of continuum mechanics and thermodynamics, we develop, in the first part, a fully-coupled continuum theory of the finitely deformable semiconductor which involves the mechanical and electrostatic fields as well as the electronic free carriers densities and current. To this end, we make use of the general principles of mechanics, electromagnetism, species transport and thermodynamics. These laws are completed by thermodynamically consistent constitutive relations whose specific form involves results of statistical physics. While usual semiconductor equations are recovered in a generalized form, the various couplings between the three interacting physics – mechanics, electrostatics and electronics – are obtained. In particular, the existence of an electronic-induced stress (proportional to the density of free carriers), which to the best of our knowledge was never discussed before, is found in addition to Maxwell stresses. Considering crystalline semiconductors, our model is simplified to small strains and the quantitatively significant coupling is shown to reduce to the effect of strain on the free carriers transport expressed by the generalized drift-diffusion equations. A discussion on the orders of magnitude of the different couplings in the case of silicon allows to consistently neglect the small effects.

Motivated by photovoltaic applications, we subsequently apply our general theory to compute the effect of bending on the current-voltage characteristic of a silicon p-n junction. Accounting for the effect of strain on the band edge energy levels, densities of states and electronic mobilities, we solve the electronic transport equation under non-uniform applied strain. Using asymptotic methods, we compute at first order in terms of applied curvature and strain the change in current induced by the bending of the device. A closed form expression of the strain effect shows that it is predominantly the strain state close to the p-n interface that affects the electronic behavior of the device. These results allow to compute the change in dark current of a typical monocrystalline silicon solar cell when subjected to different strain states: changes is dark-current of the order of 20 % are predicted for strains of the order of 0.2 %.