Recurrence formulae determining radial matrix elements of r 4 between quasirelativistic hydrogenic wavefunctions are derived. In the diagonal case they are a generalisation of the well known Kramer's relations. The formulae are also transformed to the basis of the Dirac wavefunctions.

An analytic expression for the tempoerature coefficient of the open-circuit voltage has been derived in general, which may be applied to different kinds of p-n junction solar cells. Based on the dominance of the saturation dark current density, the simplified expression have also been developed and justified by experimental measurements. It has been shown that the negative temperature coefficient of the open-circuit voltage is decreased with the increasing light level and the interaction between minority carriers and the high-low junction. Hence, the temperature coefficient of the open circuit voltage is good measure for providing a guide to test the effectivness of a high-low junction in a back-surface-field (BSF) solar cell. Moreover, based on the measured temperature coefficient of the open-circuit voltage from the BSF solar cells fabricated on thin epitaxial substrate, a new method for measuring the effective energy-gap narrowing in the highly doped emitter has been proposed and studied. It has shown that the effective energy-gap narrowing measured is in good agreement with the eempirical expression proposed by Slotboom.

A simple technique for measuring the interface-state density of a Schottky barrier diode fabricated on the moderately doped semiconductor is presented. It requires the I-V characteristics and substrate doping concentration as inputs which can be easily measured by existing techniques. Checked by the Schottky capacitance spectroscopy method, the proposed technique is proved to be highly accurate for various metal-Si and metal silicide-Si Schottky barrier diodes.

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