Ambipolar Diffusion of Free Carriers in Insulating CdS Crystals

A new method is described for measuring ambipolar diffusion of free carriers in insulating materials. Strongly absorbed light producing electron-hole pairs is shone on one surface of the material through a transparent noninjecting contact. These carrier pairs set up a concentration gradient extending into the interior due to ambipolar diffusion. To describe this process, the theory of ambipolar diffusion is extended to the insulator case of unequal lifetimes for electrons and holes and significant trapping of both types of carriers. Simultaneously, excess space charge of the same sign as the majority photocarriers is injected through an Ohmic contact on the opposite face and space-charge-limited current (SCLC) flow is established. The point of equality of these two charge distributions establishes an effective thickness $x_0$. To a good approximation, $x_0$ can be inserted into the SCLC density formula which, for shallow trapping, is $J=\frac{K{V}^2}{{x_0}^3}$ where $K$ is a constant. The thickness $x_0$ depends on the illumination intensity and therefore introduces an intensity dependence into the SCLC formula. A technique is described with which the ambipolar diffusion length $L_a$ of free carriers can be calculated from this intensity dependence. The procedure was tested with insulating CdS crystals. The results show that $L_a\approx 1\mu$ at room temperature from which the minority carrier (hole) recombination lifetime ${\tau }_p\approx 5\times {10}^{-8\mathrm{}}$ sec is obtained. These values are in good agreement with earlier estimates.