Indentation response characteristics of a piezoelectric semiconductor layer

The interaction of piezoelectricity with semiconducting property in piezoelectric semiconductors (PSCs) can be utilized to realize the amplification and gain of elastic waves and to tune the electronic property. This not only makes PSCs have enormous potential in multifunctional electronic devices, but also raises many multi-field coupled problems that need to be investigated. This paper considers the axisymmetric frictionless indentation responses of a PSC layer, which is perfectly bonded to a rigid substrate and acted on by a rigid spherical indenter. While both the indenter and the rigid substrate are assumed to be electrically insulating, the interaction of piezoelectricity and semiconducting property of a PSC layer is fully taken into consideration. By the Hankel integral transformation, the indentation problem is reduced to a Fredholm integral equation of the second kind, which is solved numerically. For the PSC ZnO layer, the numerical results for the indentation force, electric potential and contact radius are presented to systemically explore the effect of the layer thickness, indenter size and semiconducting property on the response of the PSC layer under indentation. It is found that the critical thickness, at which the thickness effect may be neglected, is dependent on the indentation depth. The influence range of semiconducting property on indentation response is related to the thickness of the PSC layer. Furthermore, the theoretical results based on the singular integral equation method are verified by the finite element simulation. This study is useful for a better understanding of the interaction between piezoelectricity and semiconducting property of PSC materials, which has potential value for developing indentation techniques to extract the coupling characteristics of PSC materials.