Replacing the depletion approximation

The general solution recently offered for the surface and step-junction problem has a parabolic potential vs position asymptote extending toward the surface or junction. The vertex of this asymptotic parabola defines a spatial origin that is invariant with respect to the general solution and that facilitates analysis. In a depleted surface or junction problem, for example, the expression x/L_D=?√s2(W?1) relates position and potential with an error less than one-third of one percent from W = 3 to W = ∞ in the absence of an inversion layer, where W is normalized potential referred to the bulk potential and L_D is the general Debye length. An accurate asymptotic expression relating position and potential toward the bulk (away from the surface or junction) is (x/L_d) =?0.41209-In W when the same spatial origin is employed. A single exponential expression serves to bridge the gap between the asymptotic expressions with accuracy overall of ±3%. Because these expressions are far more accurate than the corresponding depletion-approximation expression and yet are very simple and easy to use, we offer this approximate treatment of the surface and equilibrium-step-junction problems as a replacement for the depletion approximation. The location of the depletion-approximation boundary is pinpointed for several junctions.