Band gap bowing

Band gap bowing occurs in ternary and quaternary alloys as it does in binary and pseudobinary alloys. The behavior of quaternary alloys and can be treated in the same way. For a typical quaternary of the form Ai xBxCyDi y, Equation 6.13 for the energy of a specific part of the band stractrrre (for example, the direct gap) can be generalized to [2] ... 

The same phenomena that lead to limited solubdity (chemical and size differences between atoms) are responsible for band gap bowing. Thus, large bowing and limited solubility typically go together. 

Little band-gap bowing occurs in amorphous semiconductor alloys and most band offset in Si-Ge alloys occurs in the antibonding (conduction) band. 

The data in Table 3.16 may be used to estimate the band gap energy for unstrained wurtzite-structure MgO of E = 6.9 eV and for rocksalt-structure ZnO of Ee — 7.6 eV, with stronger bowing for the rocksalt-structure than for the wurtzite-structure occurrence of the alloys. Theoretical band-structure calculations for ZnO revealed the high-pressure rocksalt-structure phase as... 

Figure 3. Variation of band gap as a function ofZn (O) concentration, x. Lower points and curve (solid) calculated BGs and smoothed Efx) curve using the estimated bowing parameter, b. Upper points and curve (dashed) experimental data for (Gaj.xZnJ(Nj.xOJ solid solution (38,71) and predicted experimental Eg(x) behavior using the estimated b and the limiting GaN and ZnO band gaps (71).

Examples of alloys that follow virtual crystal behavior (random component of bovraig at least twice the non-random contribution) are InAs-InP, and the direct gap in GaAs-GaP, suggesting that these behave as nearly random alloys. [2] Note that this random alloy bowing can lead to decreases in energy gap below either end point compound gap. The entire band structure is affected and band widths as well as density of states center of mass can change with composition. 

Here Eabcd is the energy of a given band in the quaternary and Eabd, Eabc, Eacd> and Ebcd are the energies of the same band that would have been detErmined from Equation 6.13 for each individual pseudobinary alloy. Thus, Equation 6.17 is a linear interpolation of the pseudobinary alloy values. This approach produces a reasonable estimate of the gap values. [2] There are other methods for estimating the alloy energy gap that increase the effective bowing but the performances of these methods are not particularly improved. 

---