Bowing parameter

In this formula, Eg, x and b are the optical bandgap, AIN molar fraction and bowing parameter, respectively. In order to determine this relationship, not only precise characterisation of Eg by the optical method but also precise determination of alloy composition x is quite important. The optical bandgap of AlGaN on sapphire in the whole compositional range was first reported by Yoshida et al [2] in 1982. They used optical absorption edge for determination of Eg, and x was determined by electron... 

TABLE 1 Summary of the bowing parameter of optical bandgap and excitonic bandgap of AlGaN reported to date. 

Composition range Substrate Growth technique Structural quality Howto measure x Howto measure Eg Bowing parameter (eV) Ref... 

XRD and PL are the usual compositional techniques used to determine the alloy composition. These non-destructive methods provide fast feedback to the growth and can be very accurate in the III-arsenide/phosphide alloys systems. However, for the M-nitrides, the epitaxial films are normally grown on a mismatched substrate which results in residual stress being present in the films, ft is also sometimes difficult to identify the band-to-band emission and the magnitude of the bowing parameters is not well established. Therefore, one must be cautious when employing these methods to determine the alloy compositions. In addition, these techniques cannot be used to determine the composition of multilayer structures. 

The compositions of the ternary layers were evaluated from the lattice parameters measured using X-ray diffraction (see Datareview A1.2) and from the positions of the photoluminescence peaks. Both methods gave the same results, if the bowing parameters of 3.2 eV and 0.1 eV, for InGaN and AlGaN, respectively, were used (as proposed by Takeuchi et al [25] for strained layers on relaxed GaN on sapphire). 

The parameter A has been called the bowing parameter by Moon... 

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).

As will be discussed subsequently, others reported zero bowing parameter, meaning a linear relationship between the composition and the bandgap. The discrepancy is a sign of the nascent nature of the field. 

The constant c is known as the bowing parameter and is four times larger than the negative deviation of the gap from the linear behavior at x=0.5, where the deviation from linearity is typically greatest. Similar expressions can be written and similar behaviors are observed for the gaps at other points in reciprocal space such as the indirect gap minima at X and L. 

NOTE while simple bowing parameters represent convenient ways to discuss and estimate composition dependences of energy gaps, they are often significant oversimplifications of the actual situation. 

One of the most striking features of the bowing parameter values in Table 6.1 is the negative value for the direct gap in AlGaAs and AllnP. This is particularly... 

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