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A solution is given for the curvature of a semiconductor element that is strained by substitutional incorporation of a dopant with an arbitrary concentration profile. The result is especially applicable to silicon that is heavily doped with boron to form an etch stop during fabrication of thin structures. For the case without misfit dislocations it is shown that the solution for a linear profile is a good approximation for a range of nonlinear dopant profiles and especially so for the erfc profile that arises from Fickian diffusion with a constant surface concentration.