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We have calculated the offset voltage for a linearly graded p n junction and a step junction. The offset voltage can be written asThe correction term AV given by the above equation is in general dificult to calculate. The analytical methods developed by Gummel and Scharfetter and Chang for a step junction cannot be applied to a linearly graded junction and other types of doping profiles.A unified formula for calculation of the correction term AV is derived in this paper. It can be expressed as where A and B are parameters related to the impunity profiles. This formula can be applied not only to a step junction, but also to a linearly graded junction. Although it can be extended to an exponential junction and other diffusion junctions with error-function or Gaussian-doping profile, we are mainly concerned with a linearly graded junction as well as a step junction in this paper.For an abrupt profile, our calculation results in AV E 2.07kTfq. For a linearly graded junction, AV is a function of the applied voltage and the doping parameters. We have obtained AV 2 1.93kTlq for V, = 2OOkTlq (V, is the total voltage across the p-n junction) for the latter junction. Our values agree quite well with the values of AV reported by others previously. The offset voltage for the linearly graded junction obtained from the intercept of the C 3 -V , curve in this study is very close to the gradient voltage V, reported by Chawla and Gummel.

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