The extrinsic case. Basic development

In a one-dimensional n-type material, the equation of motion for the majority carriers can be written 

Inserting these into the transport equation, eqn. (77), we obtain, for the frequency-dependent terms 

In the bulk of the semiconductor, the potential will be defined as zero. This differs slightly from the convention adopted in Sect. 3, but simplifies the resultant analysis. For a reverse-biased n-type semiconductor, it follows that the potential f in the depletion layer will be negative. In this region, the Boltzmann distribution gives 

At the other surface of the semiconductor, i.e. away from the electrolyte, we may suppose that we have an ohmic contact. If the total width of the semiconductor is Ls, this leads to the boundary conditions 

Further integration is possible using the integrating factor exp(- e0 p0lkT). Recalling that 0 = — d / 0/dx and 

---