Determination of an energy distribution from stopping potential data

The energy spectrum of electrons just inside an irradiated surface is obtained in terms of the derivatives of the current—voltage curve for electrons emitted from the surface. For the familiar case of a unidirectional beam, the energy distribution is just the negative of the first derivative. For an (assumed) isotropic distribution inside the surface, a classical surface potential, and a spherically symmetric retarding field, the energy distribution is similar to the unidirectional case except that the first derivative must be multiplied by an energy-dependent factor. If the retarding field is uniform and perpendicular to the surface, the calculation of the energy distribution inside involves both the first and second derivatives.