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physicswiki:band_structure_calculation [2019/04/07 21:56] (current)
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 +==== Band structure calculation ====
 +
 +This physics model is built from two coupled simulations. At first, it calculates the mechanical strain in the structure due internal strain (lattice mismatch), or externally applied strain. After the deformation field is calculated it calculate the band structure with the defined models.
 +
 +=== Crystal Stress ===
 +
 +=== Structural Mechanics ===
 +External effects, or lattice mismatch builds up an internal strain, which effects on the characteristics of the device.
 +Two types of crystal structures are implemented:​ //​Zinc-blende//,​ //​Wurtzite//​. More on [[physicswiki:​structural_mechanics#​crystal_stress|Crystal stress]]
 +
 +The Hook tensor in Voigt notation for Zinc-blende:​
 +
 +\[
 +C_{ZB} = \begin{bmatrix} ​  
 +C_{11} & C_{12} & C_{12} & 0 & 0 & 0 \\
 +C_{12} & C_{11} & C_{12} & 0 & 0 & 0 \\
 +C_{12} & C_{12} & C_{11} & 0 & 0 & 0 \\
 +0&​0&​0&​C_{44}&​0&​0\\
 +0&​0&​0&​0&​C_{44}&​0\\
 +0&​0&​0&​0&​0&​C_{44}\\
 +\end{bmatrix}
 +\]
 +
 +And for wurtzite:
 +
 +
 +\[
 +C_{WZ} = \begin{bmatrix} ​  
 +C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\
 +C_{12} & C_{11} & C_{13} & 0 & 0 & 0 \\
 +C_{13} & C_{13} & C_{33} & 0 & 0 & 0 \\
 +0&​0&​0&​C_{44}&​0&​0\\
 +0&​0&​0&​0&​C_{44}&​0\\
 +0&​0&​0&​0&​0&​\frac{C_{11}-C_{12}}{2}\\
 +\end{bmatrix}
 +\]
 +=== Band Structure ===
 +
 +The band-structure of a semiconductor looks like the following in position space on figure {{ref>​semi_pos}}
 +
 +<figure semi_pos>​
 +;#;
 +{{physicswiki:​semiconductors:​semibands_x.png}}
 +;#;
 +
 +<​caption>​
 +**Figure {{ref>​semi_pos}}** Semiconductor band-structure with Conduction band(CB), and the valence bands: Heavy hole band(HH), Light hole band (LH), Split-off band(SO) ​
 +</​caption>​
 +</​figure>​
 +
 +Upon strain the bands of the semiconductor get shifted in position space, due the [[http://​www.iue.tuwien.ac.at/​phd/​windbacher/​node31.html | Deformation potentials]]. ​
 +
 +The strain effects could be simulated with $6 k.p$, and $8 k.p$ methods with our software. [[physicswiki:​semiconductors:​Band structure|More on]]
 +
 +
 +
 +
 +
  
  • physicswiki/band_structure_calculation.txt
  • Last modified: 2019/04/07 21:56
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