Accurate first principles band gap predictions in strain engineered ternary III-V semiconductors

Tuning the band gap in ternary III-V semiconductors via modification of the composition or the strain in the material is a major approach for the design of optoelectronic materials. Experimental approaches screening a large range of possible target structures are hampered by the tremendous effort to optimize the material synthesis for every target structure. We present an approach based on density functional theory efficiently capable of providing the band gap as a function of composition and strain. Using a specific density functional designed for accurate band gap computation (TB09) together with a band unfolding procedure and special quasirandom structures, we develop a computational protocol to predict band gaps. The approach's accuracy is validated by comparison to selected experimental data. We thus map the band gap over the phase space of composition and strain (we call this the “band gap phase diagram”) for several important III-V compound semiconductors: GaAsP, GaAsN, GaPSb, GaAsSb, GaPBi, and GaAsBi. We show the application of these diagrams for identifying the most promising materials for device design. Furthermore, our computational protocol can easily be generalized to explore the vast chemical space of III-V materials with all other possible combinations of III and V elements.

Figure 1

Variation of the band gap under isotropic compressive strain for ${\mathrm{GaAs}}_{0.963}{\mathrm{P}}_{0.037}$. The $\mathrm{\Gamma }$, L, and X BSW of the folded supercell conduction band are given in parentheses in the format ($\mathrm{\Gamma }$:L:X). The vertical lines in (a) separate regions where the CBM changes character. In (b), the strain resolution is increased to determine the point of direct-indirect transition more accurately, indicated by the red circle (where the highest BSW changes from $\mathrm{\Gamma }$ to L).

Figure 2

Isotropic strain for GaAsP. The variation of band gap magnitudes (${\mathrm{E}}_{\text{g}}$) and type as a function of composition and strain. The dashed black horizontal line indicates unstrained GaAsP. The black circles are the calculated DIT points. The direct and indirect enclosed regions describe the nature of band gap being direct and indirect, respectively. The hatched pattern region is the “uncertainty region” (see Sec. 3).

Figure 3

Biaxial strain for GaAsP. The variation of band gap magnitudes (${\mathrm{E}}_{\text{g}}$) and type as a function of composition and strain. The dashed black horizontal line indicates unstrained GaAsP. The black circles are the calculated DIT points. The DIT points are fitted with a fifth-order polynomial. The direct and indirect enclosed regions describe the nature of band gap being direct and indirect, respectively. The hatched pattern region is the “uncertainty region” (see Sec. 3). Solid black lines indicate the substrate lines under “epitaxial growth” model.

Figure 4

Isotropic strain for GaAsN (up to 12% N). The variation of band gap magnitudes (${\mathrm{E}}_{\text{g}}$) and type as a function of composition and strain. The dashed black horizontal line indicates unstrained GaAsN. The black circles are the calculated DIT points. Beyond 7% N, the DIT is outside the investigated strain regime. 10 SQS cells are used for each configuration and strain point. The band gaps plotted are the average band gaps. The error bars indicate the standard deviation in DIT points estimation. The direct and indirect enclosed regions describe the nature of band gap being direct and indirect, respectively.

Figure 5

Biaxial strain for GaAsN (up to 12% N). The variation of band gap magnitudes (${\mathrm{E}}_{\text{g}}$) and type as a function of composition and strain. The dashed black horizontal line indicates unstrained GaAsN. 10 SQS cells are used for each configuration and strain point. The band gaps plotted are the average band gaps. All the band gaps are direct in nature. Solid black lines indicate the substrate lines under the “epitaxial growth” model.

Figure 6

Band gap phase diagram for ternary III-V semiconductors GaEY (E = P, As; Y = Sb, Bi) under biaxial strain. The band gap magnitudes (${\mathrm{E}}_{\text{g}}$) are shown in the color bar. The dashed black horizontal line indicates unstrained structures. The black circles are the calculated DIT points. The direct and indirect enclosed regions describe the nature of band gap being direct and indirect, respectively. The hatched pattern region is the “uncertainty region” (see Sec. 3). Solid black lines indicate the substrate lines under the “epitaxial growth” model.

Figure 7

Proposals on how the band gap phase diagram of biaxially strained GaAsP can be used in designing optoelectronic devices. (a) Defines the bound of composition region for creating a QWH with direct band gap GaAsP on GaAs substrate. (b) Choosing the different composition regions appropriately to make a multijunction photovoltaic with successive direct and indirect cells on the GaAs substrate. (c) In the vicinity of the transition point, the band gap properties of the GaAsP epilayer on the GaP substrate can be changed by appropriately varying the composition. (d) Depending on the choice of substrate, GaAs or Si, the particular composition indicated by the vertical line can be made direct or indirect band gap, respectively.