Indentation responses of piezoelectric semiconductors

•The indentation responses of piezoelectric semiconductors are firstly studied.•The existence of semiconductor property lowers the indentation resistance of PSC materials.•The steady carrier concentration in a specific range has obvious screening effect on the electric potential induced by the indentation force.•The electric response is more sensitive to the piezoelectric coupling-semiconductor interaction than the mechanical response. In this paper, the indentation responses of a piezoelectric semiconductor (PSC) half-space by an insulating and rigid spherical indenter are investigated. It is assumed that the contact area between the indenter and the PSC is frictionless. Based on the Hankel integral transformation, the considered indentation problem is reduced to a pair of dual integral equations. Due to the complexity of the coupled governing differential equations, the explicit closed-form expressions for the PSC indentation responses cannot be derived like the piezoelectric counterparts. Therefore, the dual integral equations are converted into the Fredholm integral equation of the second kind, which is numerically solved to determine the concerned responses. These responses include the relationships of the indentation force, the electric potential and the change of carrier concentration with the indentation depth. The numerical results show that the semiconducting property has a significant influence on the indentation characteristics. In addition, the three-dimensional finite element simulations are carried out to validate the theoretical results computed by the singular integral equation method. It turns out that the two results are well consistent. The distributions of the stress and electric potential near the contact area are simulated by finite element method to reveal the effect of the steady carrier concentration. The obtained findings are useful for understanding the interaction between piezoelectricity and semiconducting property.