Volume and surface recombination of injected carriers in cylindrical semiconductor ingots

An exact solution to the diffusion-recombination problem is obtained for the case of a sample in the form of a right circular cylinder with arbitrary bulk lifetime, arbitrary surface recombination velocity on the lateral curved surface of the sample, and infinite surface recombination velocity on the (lapped) plane end surfaces of the sample. The latter surfaces may be regarded as electrical contacts to the sample, and in such a case the geometry corresponds precisely to a very commonly used experimental arrangement for recombination measurements. Relations between bulk lifetime, surface recombination velocity and observed time constant are calculated and plotted with the height-radius ratio of the cylinder as parameter for the principal decay mode, and the higher-mode decay scheme is worked out for a few cases of practical interest. Examples Of simultaneous surface recombination and bulk lifetime measurement by observation of the higher-mode decay components are presented.