Empirical tight-binding sp3s* band structure of semiconductors

In summary, the author is trying to find the spin-orbit splitting parameters for certain semiconductors using tight binding, but is having trouble because the temperature is not mentioned in any of the articles he has consulted. The author is looking for a reference that will provide accurate spin-orbit splitting parameters for T = 0 K, but is having difficulty finding one.
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rogdal
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TL;DR Summary
I'm looking for the spin-orbit splitting parameters of certain semiconductors at T = 0 K and their dependance on temperature.
I'm simulating on code the tight-binding sp3s* bandstructure of certain semiconductors, such as GaAs, AlP, InP, ZnSe, etc. with spin-orbit coupling at a temperature of T = 0 K but I'm having trouble at finding the corresponding spin-orbit splitting parameters.

For example, I've found in this article by Vogl et al, A Semi-Empricial Tight-Binding Theory of the Electronic Structure of Semiconductors the following relation of spin-orbit parameters:

1678451111175.png


But the temperature is not said anywhere in that article. In fact, the tight binding parameters without spin-orbit coupling depend a lot on the temperature. At this point, the only information that is certain for me is the following:

1) At T = 300 K the desired parameters appear in this article by Klimeck et al: sp3s* Tight-binding parameters for transport simulations in compound semiconductors

2) At T = 0 K I know from chapter 5 of Supriro Datta's Quantum Transport, Atom to Transistor that the spin-orbit parameters, only for GaAs are D_a = 0.37 eV for Arsenic and D_c = 0.013 eV for Gallium. The other semiconductors are not mentioned.

Based on what I've said above, do you know where I could find the spin-orbit splitting parameters for the semiconductors on Table 4 at T = 0 K, and if it were possible their dependance with the temperature? Any references will be appreciated.

Thank you very much!
 
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  • #2
They will be fairly accurate at low T, since that is where the measurements were probably made.
 
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Thanks, all the articles I've referenced provide semiempirical results for the parameters, but how can they differ that much from each other?

I mean, if the parameters at Table 4 were taken at T = 0 K, Delta_a very similar to the one provided in Datta's book, but Delta_c differs in one order of magnitude. Do you how what fenomena can occur in those measurements so that the results are so different?
 

FAQ: Empirical tight-binding sp3s* band structure of semiconductors

What is empirical tight-binding theory?

Empirical tight-binding theory is a computational approach used to calculate the electronic properties of materials, particularly semiconductors. It simplifies the complex interactions in a solid by using a tight-binding model that considers the overlap of atomic orbitals. The "empirical" aspect refers to the use of parameters derived from experimental data or more accurate quantum mechanical calculations to fit the model to specific materials.

What does the sp3s* notation signify in the context of band structure?

The sp3s* notation refers to the specific hybridization of atomic orbitals used in the empirical tight-binding model. The "sp3" indicates that the model incorporates the hybridization of one s and three p orbitals from the valence shell of the atoms, which is typical for tetrahedral bonding in semiconductors like silicon. The "s*" denotes the inclusion of additional s-type orbitals, which can improve the accuracy of the model by accounting for interactions that are not captured by the standard sp3 hybridization alone.

How does empirical tight-binding improve the calculation of band structures in semiconductors?

Empirical tight-binding improves the calculation of band structures by providing a more computationally efficient way to model the electronic states of semiconductors. It allows for the inclusion of various atomic interactions and local environment effects while reducing the complexity of the underlying quantum mechanical equations. This results in accurate predictions of band gaps, effective masses, and other electronic properties, making it a valuable tool for materials science research.

What are the limitations of using empirical tight-binding models?

While empirical tight-binding models are useful, they do have limitations. They rely on empirical parameters that may not be universally applicable across different materials, which can affect the accuracy of predictions. Additionally, these models may struggle with systems that exhibit strong electron correlation or significant spin-orbit coupling. Furthermore, they typically do not include effects such as lattice vibrations (phonons) or temperature dependence, which can also influence electronic properties.

How can empirical tight-binding models be validated?

Empirical tight-binding models can be validated by comparing their predictions with experimental data, such as band gaps, density of states, and effective masses obtained from techniques like photoemission spectroscopy or transport measurements. Additionally, results can be cross-validated with more sophisticated computational methods, such as density functional theory (DFT), to ensure consistency and reliability. If the empirical tight-binding model provides results that align well with experimental observations and other theoretical approaches, it can be considered validated for the specific material under study.

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