An improved effective-mass-theory equation for phosphorus doped in silicon

A new multi-valley effective-mass-theory (EMT) equation is derived for the phosphorus doped in silicon. This equation admits solutions which agree with the measured ground state energy and the square modulus of the ground-state wavefunction |ΨA1(0)|2|ΨA1(0)|2 at the donor site accurately. This avoids the use of the so-called “central-cell correction” approximation method to calculate the hyperfine constant at the donor site. Furthermore, the energy levels for the upper lying states of T2 and E can also be predicted relatively accurately. The newly derived EMT equation has applications in the characterization of semiconductor or spintronics devices.

► A more accurate EMT equation was derived with the valley-orbit effect taken into account. ► Both the ground state energy and the wavefunction at the donor site can be calculated accurately. ► The “central-cell correction” artificial method can be avoided. ► Application can be found in spin qubit characterization and spintronics.