Method for measuring impurity distributions in semiconductor crystals

A method for measuring the doping profile and its gradient in thin layers of semiconductor crystals is described. A sine-wave signal applied to an appropriate p-n junction on the surface of a crystal gives rise to second and third harmonics in the output signal due to the nonlinear capacitance-voltage characteristic of the junction. Expressions are derived which relate the second and third harmonic distortion factors to the impurity concentration and its gradient as a function of the distance into the crystal. Measurements of the impurity profile in the base layer of some silicon and germanium transistors have been made.