A method for determining energy gap narrowing in highly doped semiconductors

Abstract

A general experimental method for the determination of the phenomenological energy gap narrowing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaE_{G}</tex> in regions of semiconductor devices that have high concentrations of donor or acceptor impurity atoms is presented. The theoretical grounds for the method are discussed in detail, including the strong influence of Fermi-Dirac statistics on minority-carrier recombination in heavily doped regions. The method requires measurements only of the temperature dependence of de current; therefore it is very accurate. The values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaE_{G}</tex> deduced from the method are insensitive to the mechanisms controlling recombination and to the value of minority-carrier mobility in the heavily doped region; they are also independent of the value of n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> the intrinsic carrier density, at a specific temperature. The values for the Si:As emitters of transistors and diodes were measured in the majority-carrier concentration range from 4 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> to 2 × 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> .