Low-frequency capacitor with hopping electrical conductivity of the working substance (on the example of a-Si:H)

We propose a structural and electrical schemes of a capacitor based on a 3 μm thick a-Si:H (amorphous hydrogenated silicon) layer separated from the metal plates by 0.3 μm thick dielectric layers of SiO2 (silicon dioxide). We consider room temperatures (T ≈ 300 K) when in the absence of illumination for a-Si:H the hopping mechanism of electron migration via point defects of the structure prevails. For such a capacitor, the dependencies of the capacitance on the frequency of the measuring signal ω/2π in the range from 0.1 to 300 Hz are calculated for the a-Si:H layer with stationary hopping electrical conductivity σdc ≈ 1 ∙ 10−10 (Ohm ∙ cm)−1. It is assumed that there is no end-to-end electron transfer between the a-Si:H layer, dielectric layers and capacitor plates in the small-signal mode of capacitance measurement. It is shown that the real part of the capacitance of the capacitor decreases with increasing angular frequency ω, and the imaginary part is negative and depends non-monotonically on ω. The decrease in the real part of the device capacitance to the geometric capacitance of the series-connected oxide layers and the a-Si:H layer with increasing ω is due to a decrease in the electrical resistance of the capacitor. As a result, with increasing ω, the imaginary part of the capacitance is shunted by the hopping electrical conductivity of the capacitor. The phase shift for a sinusoidal electrical signal supplied to the capacitor is determined depending on the frequency ω/2π in the range of 0.1–300 Hz for the values of electrical conductivities of the hydrogenated amorphous silicon layer σdc ≈ 1 ∙ 10−11, 1 ∙ 10−10, and 1 ∙ 10−9 (Ohm ∙ cm)−1 at the temperature 300 K. With an increase in the electrical conductivity σdc of the a-Si:H layer, the minimum absolute value of the phase shift angle (≈65°) shifts to the high- frequency region (from 1 to 100 Hz). The proposed low-frequency capacitor can find application in electrical circuits for detecting low-frequency electrical signals for the purposes of biomedicine.