Bandgap changes in excited intrinsic (heavily doped) Si and Ge semiconductors

Our results for the bandgap changes in highly excited intrinsic (heavily doped-HD) Si (Ge) for any majority-carrier density N and temperature T have been investigated and expressed in terms of (i) the bandgap narrowing (BGN>0) due to many-body carrier–carrier interactions and screening effect on carrier-impurity (or electron–hole) potential energies, (ii) the bandgap widening (BGW<0) due to the effects of Fermi Dirac statistics, and (iii) the apparent BGN defined by ABGN≡BGN+BGW