Macroscopic averaging of electrical properties inside grains of polycrystalline materials

The polycrystalline material film consists of various size crystalline grains that have properties of crystalline material. The grains are usually randomly spatially oriented thus affecting the magnitude of orientation dependent properties. Here we considered resistive and piezoresistive properties of polycrystalline silicon. Depending on the dopant concentration within the grains the depleted regions originated owing to carrier trapping on the grain boundary can have various lengths. As the carrier concentration within depletion region is lower the resistance and piezoresistance can be higher than in the rest of the grain. Results of the calculation show that the deviation of the average parameters such as concentration of free carriers, specific resistivity, piezoresistance coefficient, can be significantly different from that obtained on assumption of uniform free carrier distribution in the crystallite.