HARTREE CONTRIBUTION TO THE BAND-GAP RENORMALIZATION IN SEMICONDUCTORMICROSTRUCTURES

The effect of band-gap renormalization is usually understood in terms of exchange and correlation. This leads to a reduction of the gap ener gy with increasing carrier density. We show that in low-dimensional sy stems a Hartree contribution also occurs because of the lack of local charge neutrality. This effect reduces the total band-gap renormalizat ion. Explicit expressions are given for quantum wells and quantum wire s and the order of magnitude is studied.