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physicswiki:semiconductors:hexaqw:hexaqw [2019/04/09 13:06] (current)
zoltan.jehn created
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 +==== Hexagonal Quantum Wire ====
 +
 +
 +
 +Click to download {{physicswiki:​hexaqw:​hexaqw.xsproj?​linkonly | Project }} and {{physicswiki:​hexaqw:​hexaqw.pdf?​linkonly | Documentation}}
 +
 +=== Introduction ===
 +
 +Quantum wires in the main focus of research in the past decades. They poses interesting features, when it comes the quantum effects or just their geometrical properties. ​
 +In this tutorial we are going to simulate a cross section of a simple hexagonal quantum wire.     
 +
 +=== Structure ===
 +
 +<​figure>​
 +;#;
 +<​latex> ​
 + ​\input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​hexaqw/​hexastr.tex}
 +</​latex>​
 +;#;
 +<​caption>​ **Figure 1.** Structure of the simulated hexagonal QWire</​caption>​
 +</​figure>​
 +
 +
 +We used the structure which is schematically drawn in figure 1. with the labeled parameters. It consists a GaAs hexagonal quantum-wire embedded in an AlAs matrix. The edge length of the hexagon is 8nm, and the growth direction is in the 001 axis, while the x, y axis in the simulation plane overlaps with the 100,010 axis. 
 +
 +
 +=== Band-structure ===
 +
 +The GaAs wire forms a quantum well in the AlAs matrix. The mismatch between AlAs and GaAs is very low, which results negligible band deformation. The band profile along the middle of the structure in the y axis is plotted in figure 2.
 +
 +<​figure>​
 +;#;
 +<​latex> ​
 + ​\input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​hexaqw/​bandstry.tex}
 +</​latex>​
 +;#;
 +<​caption>​ **Figure 2.** The slice of the band-structure in the y direction. </​caption>​
 +</​figure>​
 +
 +
 +
 +It shows that due no internal strain in the structure there is no band splitting between light-hole, and heavy-hole bands. ​
 +
 +=== Eigenfunctions ===
 +
 +We calculated the wave-functions from single-band approach, and the first several one functions are plotted in figures 3,4,5,6
 +
 +<​figure>​
 +;#;
 +<​latex> ​
 + ​\includegraphics[width=0.99\textwidth]{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​hexaqw/​WG_G_0.png}
 +</​latex>​
 +;#;
 +<​caption>​ **Figure 3.** Electron ground-wave function. </​caption>​
 +</​figure>​
 +
 +<​figure>​
 +;#;
 +<​latex> ​
 +\includegraphics[width=0.99\textwidth]{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​hexaqw/​WG_G_1.png}
 +</​latex>​
 +;#;
 +<​caption>​ **Figure 4.** Electron first excited state </​caption>​
 +</​figure>​
 +
 +<​figure>​
 +;#;
 +<​latex> ​
 +\includegraphics[width=0.99\textwidth]{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​hexaqw/​WG_HH_0.png}
 +</​latex>​
 +;#;
 +<​caption>​ **Figure 5.** Hole ground-state function </​caption>​
 +</​figure>​
 +
 +<​figure>​
 +;#;
 +<​latex> ​
 +\includegraphics[width=0.99\textwidth]{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​hexaqw/​WG_HH_1.png}
 +</​latex>​
 +;#;
 +<​caption>​ **Figure 6.** Hole excited state function </​caption>​
 +</​figure>​
 +
 +
 +=== Charge calculation ===
 +
 +
 +We can calculate the charge density in the hexagonal wire from classical approach, and from the quantum mechanical approach - from the Wavefunctions. ​
 +
 +The results are depicted in figures 7, 8.
 +
 +
 +<​figure>​
 +;#;
 +<​latex> ​
 +\includegraphics[width=0.99\textwidth]{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​hexaqw/​G_dens_qm.png}
 +</​latex>​
 +;#;
 +<​caption>​ **Figure 7.** Quantum mechanical density of electrons in the wire </​caption>​
 +</​figure>​
 +
 +
 +<​figure>​
 +;#;
 +<​latex> ​
 +\includegraphics[width=0.99\textwidth]{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​hexaqw/​G_dens.png}
 +</​latex>​
 +;#;
 +<​caption>​ **Figure 8.** Classical density of electrons in the Wire</​caption>​
 +</​figure>​
  
  • physicswiki/semiconductors/hexaqw/hexaqw.txt
  • Last modified: 2019/04/09 13:06
  • by zoltan.jehn