Heterojunctions at equilibrium

What is at issue in these junctions is the energy of the two band edges. There are some simple rules of thumb which indicate the trends one can expect in band edges as a function of which elements are changed across the junction. We will see in Chapter 5 that there are very good reasons for these rules, and we will examine their basis in the materials physics of bonding in semiconductors in that chapter. The commonly cited rules of thumb are  

Linearity and Transitivity Because the intrinsic energy gap and band edge positions do not change in one semiconductor just because it is joined to another, if you know the relative band edge positions for two semiconductors the band edge discontinuity can be determined. Mathematically, the statement of this linearity principle is 

The Common Anion Rule When the anion (the electron accepting atom such as As in GaAs and InAs) is in common across a semiconductor heterojunction, the change in the conduction band edge is greater than the change in the valence band edge across the semiconductor heterojunction. Mathematically, AEv AEc- 

When arbitrary doping is allowed in a semiconductor heterojunction or when the Fermi energies of undoped materials do not match spontaneously, electron transfer causes band bending as in homojunctions, bringing the Fermi energies to equilibrium. The following discussion describes how to determine the effect of electron flow on the potentials at the heterojunction. There are many possible configurations of a heterojunction and only a few examples are discussed here. 

the slopes of the connecting segments must match where they intercept the points marked in Step (2) to satisfy the electrostatic continuity equation. 

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