Isotype heterojunctions with flat valence or conduction band

We show that isotype heterojunctions with a perfectly flat majority or minority carrier band edge can be realized by modulation doping of arbitrary continuous alloy grading. The required impurity distribution is obtained analytically from the knowledge of the compositional grading and band structure parameters in the grading. This analytic relationship is exact for heterojunctions in which the grading fields are negligible in comparison with the atomic fields. We illustrate the design of flat valence-band heterojunctions for application in high-reflectivity low-resistance distributed Bragg reflectors for vertical-cavity lasers. The presented formalism enables the design of isotype heterojunctions with arbitrary band-edge profiles.