Talk:Aluminium arsenide antimonide

Electronic Properties section

I suppose I should elaborate on how I extracted the bandgaps, lattice constant, and bandgap-composition relationship from the cited source^[1] for verification purposes. Some of the data that I present in that section isn't explicitly stated in the source, but it can be derived or extracted from the data that is tabulated in there in what I hope is a pretty straightforward process - the math only requires algebra. I try to be mindful to not overstep into the territory of inappropriate synthesis from the source data, although presenting properties calculated from that data should be acceptable.

The source I've cited is, in my opinion, one of the most comprehensive, accessible compilations of data on the fundamental band parameters for III-V semiconductors. Because of its comprehensiveness and scope, I can understand how it may be difficult to parse and verify from a non-expert in the field. I've tried to condense the information in there into something most appropriate for inclusion in a Wikipedia article on the subject.

For the lattice constants and room temperature (T = 300 K) bandgaps of AlAs and AlSb, I refer to Table II^[2] and Table VIII^[3], respectively (I'll use AlSb as my example). The lattice constant of AlSb in angstroms is given as a function of temperature in Kelvin in the first entry of Table VIII:

$a(T)=6.1355+(2.60\cdot 10^{-5})(T-300)$

For room temperature (T = 300 K), the lattice constant $a$ is simply 6.1355 Å, which I then divided by 10 and rounded to get 0.614 nm, which is presented in the article.

The direct ( $E_{g}^{\Gamma }$ ) and indirect ( $E_{g}^{L}{\text{, }}E_{g}^{X}$ ) bandgaps at absolute zero (T = 0 K) are given in these same tables in units of electron volts. Also provided in the tables are the Varshni parameters $\alpha$ and $\beta$ , which can be used to calculate the bandgaps at any other temperature according to equation (2.13) in the source:^[4]

$E_{g}(T)=E_{g}(T=0)-{\frac {\alpha T^{2}}{T+\beta }}$

For $E_{g}^{X}$ in AlSb, the given parameters in Table VIII (with appropriate unit conversions) are $E_{g}^{X}(T=0)=1.696{\text{ eV}}$ , $\alpha (X)=5.8\cdot 10^{-4}{\text{ eV}}/{\text{K}}$ and $\beta (X)=140{\text{ K}}$ . Plugging these into the equation with T = 300 K gives the room temperature indirect bandgap to be $E_{g}^{X}(T=300)=1.62{\text{ eV}}$ . Repeating the same process for $E_{g}^{L}$ and $E_{g}^{\Gamma }$ shows that $E_{g}^{X}$ is the smallest of the three badgaps at room temperature, which makes AlSb an indirect bandgap semiconductor at room temperature. Thus, I give $E_{g}^{X}$ as the bandgap in the article. The same process is repeated with Table II to determine that AlAs is an indirect bandgap semiconductor at room temperature and calculate the magnitude of that bandgap.

Once I've calculated all of the bandgaps of AlAs and AlSb, I can move on to making an equation that models the composition-dependent bandgap of the ternary, AlAsSb. For any general alloy of the form $A_{1-x}B_{x}$ with composition $x$ , the bandgap is typically given as a polynomial, according to the source:^[5]

$E_{g}(x)=(1-x)E_{g}^{A}+xE_{g}^{B}-x(1-x)C(x)$

$E_{g}^{A}$ and $E_{g}^{B}$ are the bandgaps of the pure compounds that I calculated previously, while $C(x)$ is a "bowing parameter" that accounts for the nonlinearity in the composition-dependence of the bandgap. For most of the ternaries given in the source, $C(x)$ is given as a single number (i.e., it's a constant with respect to composition). For AlAs_1-xSb_x, I refer to Table XXIII^[6] for the bowing parameters. In the case of $E_{g}^{X}$ , the recommended bowing parameter that is given is $C=0.28{\text{ eV}}$ . Taking $E_{g}^{A}=1.62{\text{ eV}}$ and $E_{g}^{B}=2.16{\text{ eV}}$ as the indirect X gaps for AlSb and AlAs that I previously calculated, this then gives the composition dependence of $E_{g}^{X}$ in electron volts:

$E_{g}^{X}(x)=2.16(1-x)+1.62x-0.28x(1-x)=0.28x^{2}-0.82x+2.16$

This equation is ultimately plotted as the orange-red curve in the figure. The same process is repeated to get the appropriate equations for $E_{g}^{\Gamma }(x)$ (blue curve) and $E_{g}^{L}(x)$ (yellow curve).

@Dcotos: I want to make you aware of this, since you left the "expert needed" tag on the article. I'm not sure if you'll find an expert in WikiProject Chemicals or elsewhere to verify this data. MaterialsPsych (talk) 23:09, 5 February 2024 (UTC)[reply]

Hi, @MaterialsPsych, thanks for the clarification. It makes sense; I'll remove the tag. Cheers! Dcotos (talk) 07:55, 6 February 2024 (UTC)[reply]

References

^ Vurgaftman, I., Meyer, J. R., Ram-Mohan, L. R. (2001). "Band parameters for III–V compound semiconductors and their alloys". Journal of Applied Physics. 89 (11): 5815–5875. Bibcode:2001JAP....89.5815V. doi:10.1063/1.1368156.
^ Vurgaftman et al. 2001, p. 5826.
^ Vurgaftman et al. 2001, p. 5831.
^ Vurgaftman et al. 2001, p. 5818.
^ Vurgaftman et al. 2001, p. 5837.
^ Vurgaftman et al. 2001, p. 5844.

[VMR-1] Vurgaftman, I., Meyer, J. R., Ram-Mohan, L. R. (2001). "Band parameters for III–V compound semiconductors and their alloys". Journal of Applied Physics. 89 (11): 5815–5875. Bibcode:2001JAP....89.5815V. doi:10.1063/1.1368156.

[FOOTNOTEVurgaftman_et_al.20015826-2] Vurgaftman et al. 2001, p. 5826.

[FOOTNOTEVurgaftman_et_al.20015831-3] Vurgaftman et al. 2001, p. 5831.

[FOOTNOTEVurgaftman_et_al.20015818-4] Vurgaftman et al. 2001, p. 5818.

[FOOTNOTEVurgaftman_et_al.20015837-5] Vurgaftman et al. 2001, p. 5837.

[FOOTNOTEVurgaftman_et_al.20015844-6] Vurgaftman et al. 2001, p. 5844.

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