Investigation of layers’ properties using brush discharge: Mobility of charge carriers in the layer is zero

Abstract This work is mainly based on the paper “R. Rinkunas, S. Kuskevicius, A contactless method of resistance measurement, Tech. Phys., 59 (2009) 133–137”. This paper contains a proposed contact less method for measuring resistivity of various materials, as well as various ambient parameters related to resistivity, e.g., humidity, intensity of illumination, sample thickness, etc. The mentioned paper describes experimental applications of the proposed method for measuring resistances in the range from 10 7 Ω to 10 13 Ω. In this work, a model of the method proposed previously is presented. On the basis of that model, it has been determined that during charging of an insulating layer of a material (on whose surface the deposited ions are immobile), the charge flux becomes wider as it approaches the surface of the insulator. For example, the diameter of the charge flow region may increase from 0.2 mm (near the needle tip) up to 2 cm near the surface of the insulator. [Those numbers correspond to the distance h = 1 mm between the needle and the substrate, insulating layer thickness 40 μm and needle–substrate voltage of 4000 V. A change of those parameters would cause a change of the size of the spot on the layer surface]. It has been determined experimentally that resistance of the air gap between the needle and the substrate is linearly dependent only on h , whereas the electromotive force, which is responsible for the electric current from the needle to the substrate, also depends only on h . The radial coordinate of the points where the gradient of the electric charge density is largest is equal to h /2 (a zero radial coordinate corresponds to the point that is directly below the needle). During transfer of charge carriers from the needle onto the surface of the insulating layer, the largest potential is obtained at the point corresponding to radial coordinate r = 0, but this potential is still smaller than the electromotive force that causes electric current in the circuit (i.e., the difference between the power supply voltage and the voltage on the capacitor formed by the needle and the substrate, when no charge has been deposited yet). The time dependence of charging current and of the potential difference between the needle and the substrate is not monotonic: at first the current increases, then it begins to decrease, and the potential difference at first decreases, then it begins to increase. The initial parts of those dependences can be explained by the “breakdown” of the capacitor formed by the needle and the substrate, and the subsequent time dependence is determined by the increase of the insulating layer potential due to accumulation of charge on it.