Modeling and measurement of minority-carrier lifetime versus doping in diffused layers of n⁺-p silicon diodes

Abstract

The results of minority-carrier lifetime measurements in heavily phosphorus-doped n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> diffused layers of p-n junction diodes using a spectral response technique are reported in this paper. Exact modeling of current-flow equations, modified to include bandgap reduction due to high carrier concentration and Auger recombination, is used to compute the dependence of diffused-layer photocurrent J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pth</inf> on the incident light energy and intensity. The photocurrent in the diffused layer is also obtained by subtracting the theoretical value of the space charge and uniformly doped p-region component from the experimentally measured photocurrent of the diode at each wavelength. Note that all calculated values based on light intensity include computed transmittance/reflectance through the oxide layer at each wavelength. The comparison of the values of J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pth</inf> with J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pexp</inf> , using nonlinear least square techniques, then directly gives the lifetime profile in the diffused layer. A simple expression is given for lifetime as a function of doping which may be used in modeling and prediction of device performance. Using this experimental technique it was found that the lifetime in the diffused layer is an order of magnitude less than that corresponding to uniformly doped bulk-silicon values and is very much process dependent; its value being 3.72 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-11</sup> s for surface concentration of 3.0 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and increases to 2.9 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> s at doping concentration of 1.0 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">17</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> .