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 | Ψ A 1 ( 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.