Theoretical calculation and experimental evidence of the real and apparent bandgap narrowing due to heavy doping in p-type Si and strained Si1−xGex layers

Based on an analytical approach developed by Jain and Roulston, the different contributions to the bandgap narrowing at T = 0 K due to heavy doping in highly p-type doped Si and strained Si_1-xGe_x-layers are calculated for x < 0.3. The valence band in Si and in strained Si_1-xGe_x layers is not parabolic, it is highly distorted. To take the non-parabolicity into account a dopant concentration-dependent density of states effective mass is defined. within the framework of this formalism we find that the bandgap narrowing (BGN) in Si is not appreciably affected due to the band distortion. The situation for strained Si_1-xGe_x layers is quite different, in that the BGN increases significantly at doping levels exceeding 10¹⁹ cm⁻³. In the earlier published work, BGN of the Si_1−xGe_x layers was either slightly smaller or about the same as in Si. Now at high doping levels, BGN becomes considerably higher than in Si. We will show that the effect of the strain on the Fermi energy is much larger than on the BGN, which will cause a large change in the effective valence band offset. Comparison will be made then between our theoretical calculations and experimental results obtained on two different device structures. The modified effective valence band offset that we have calculated is in very good agreement with the experimental value derived from the published work on long-wavelength optical detectors. The apparent bandgap narrowing in strained p-type Si_1-xGe_x-layers is also calculated and compared with the experimental results on Heterojunction Bipolar Transistors fabricated in our laboratory.