Resistivity‐Dopant Density Relationship for Phosphorus‐Doped Silicon

New data for the resistivity‐dopant density relationship for phosphorus‐doped silicon have been obtained for phosphorus densities between 10 13 and 10 20 cm −3 and temperatures of 296°K (23°C) and 300°K. For dopant densities less than 10 18 cm −3 , results were calculated from resistivity and junction capacitance‐voltage measurements on processed wafers. For more heavily doped material, data were obtained from Hall effect and resistivity measurements on specimens cut from bulk silicon slices. The results differ by 5–15% from the commonly used Irvin curve, always in the direction of lower dopant density for a given resistivity. For comparison with the electrical measurements, phosphorus densities were also obtained by neutron activation analysis and the photometric technique. The values from these methods were within 10% of the electrical results. Analytical fits were determined for the resistivity‐dopant density product as a function of resistivity and dopant density for temperatures of 23°C and 300°K. Similar fits were obtained for the calculated electron mobility as a function of resistivity and electron density.