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We propose a system of real-space envelope function equations without fittingparameters for modeling the electronic spectrum and wave functions of aphosphorus donor atom embedded in silicon. The approach relies on theBurt-Foreman envelope function representation and leads to coupledeffective-mass Schroedinger equations containing smooth effective potentials.These potentials result from the spatial filtering imposed on the exactpotential energy matrix elements in the envelope function representation. Thecorresponding filter function is determined from the definition of the envelopefunction. The resulting effective potentials and the system of envelopefunctions jointly reproduce the valley-orbit coupling effect in the dopedsilicon. Including the valley-orbit coupling not only of the 1s, but also for2s atomic orbitals, as well as static dielectric screening is found crucial toaccurately reproduce experimental data. The measured binding energies arerecovered with a maximum relative error of 1.53 %. The computed wave functionsare in a good agreement with experimental measurements of the electron densityprovided by scanning tunneling microscopy.

Multi-valley envelope function equations and effective potentials for P impurity in silicon