Silicon Photonics: Fundamentals and Devices

2.6 Heterojunctions and Band Lineup

Heterojunctions are junctions formed by two dissimilar semiconductors having different band gaps, permittivities, electron affinities, and so on. While the focus in this text is on heterojunctions made of Si and other group IV materials, we present in this section a few general concepts and definitions by using the well-studied materials combination of GaAs and its alloy Ga_1−xAl_xAs.

The lattice constants of GaAs and AlAs are respectively 5.6533 and 5.6612 Ǻ. The 0.14% lattice mismatch between the two is still further reduced between GaAs and its alloy GaAlAs. This combination is an example of lattice-matched heteroepitaxy, in which the alloy is grown on GaAs substrate. The band gap of the alloy is expressed as

(2.26)

When a heterojunction is made by growing the alloy on GaAs, the difference in the band gap ΔE_g = 1.247x is consumed by two steps ΔE_C and ΔE_V , occurring respectively at the conduction and valence band edges at the heterointerface as indicated in Figure 2.6a. There are different theories to calculate the band offsets ΔE_C and ΔE_V ; however, in actual calculations the experimentally determined ratio ΔE_C : ΔE_V ≈ 60 : 40 is considered.

Example 2.5

Consider the Ga_0.7Al_0.3As–GaAs heterojunction. Since x = 0.3, ΔE_g = 0.3745 eV and ΔE_C and ΔE_V are, respectively, 0.2245 and 0.1497 eV.

Figure 2.6 Different types of band alignment: (a) type ...