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nnp:optics:absorption_spectrum [2017/01/11 11:25] zoltan.jehn [Transition Matrix Element] |
nnp:optics:absorption_spectrum [2017/02/20 21:25] (current) stefan.birner [Eigenvalues] |
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- | ====== Results ====== | + | ===== Absorption Spectrum ===== |
+ | |||
+ | With the optics features of **nextnano++**, the optical absorption spectrum can be calculated for various polarization directions. | ||
+ | |||
+ | ==== Physics Model ==== | ||
+ | |||
+ | The absorption rate in a semiconductor can be written as | ||
+ | |||
+ | \[ | ||
+ | R_{ba} = \frac{2}{V} \sum_{k_a} \sum_{k_b} \frac{2 \pi}{ \hbar} |H_{ba}| ^2 \delta(E_b - E_a -\hbar \omega)(1-f_a) \cdot f_b, | ||
+ | \] | ||
+ | |||
+ | where the matrix element $|H_{ba}|$ depends on the polarization of light and the $\bf k$ vector. | ||
+ | |||
+ | ==== Input File ==== | ||
+ | |||
+ | |||
+ | ===== Results ===== | ||
==== Transition Matrix Element ==== | ==== Transition Matrix Element ==== | ||
- | The transition matrix element $H_{ab}(k)$ is plotted in the function of $\vec{k}$ for a 1D structure in figure {{ref>absk}} | + | The transition matrix element $H_{ab}({\bf k})$ is plotted as a function of ${\bf k}=(k_x,k_y)$ for a quantum well structure (1D simulation) in figure {{ref>absk}} |
<figure absk> | <figure absk> | ||
;#; | ;#; | ||
- | <dataplot dimension=2 xlabel="k_x" ylabel="k_y" ylegends="" 600x400> | + | <dataplot dimension=2 xlabel="k_x (nm^{-1})" ylabel="k_y (nm^{-1})" ylegends="" 600x400> |
-3.68039679527 -3.68039679527 20.0033226842 | -3.68039679527 -3.68039679527 20.0033226842 | ||
Line 370: | Line 388: | ||
</dataplot> | </dataplot> | ||
;#; | ;#; | ||
- | <caption>Transition matrix element in the $\vec{k}$ space</caption> | + | <caption>Transition matrix element in ${\bf k}$ space</caption> |
</figure> | </figure> | ||
==== Eigenvalues ==== | ==== Eigenvalues ==== | ||
- | The first eigenfunction's energy in the kp-space is plotted in figure {{ref>edisp}} for electrons, and in figure {{ref>hdisp}} for holes. | + | The dispersion of the ground state energy is plotted with respect to $\bf k$ space in figure {{ref>edisp}} for electrons, and in figure {{ref>hdisp}} for holes, respectively. |
<figure edisp> | <figure edisp> | ||
;#; | ;#; | ||
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+ | 3.68039679527 3.68039679527 -1.17995996739 | ||
+ | </dataplot> | ||
;#; | ;#; | ||
- | <caption>Energy dispersion relation in the $\vec{k}$ space for electrons</caption> | + | <caption>Energy dispersion relation $E(k_x,k_y)$ for the lowest electron eigenvalue</caption> |
</figure> | </figure> | ||
Line 388: | Line 768: | ||
<figure hdisp> | <figure hdisp> | ||
;#; | ;#; | ||
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+ | -1.22679889202 -0.817865908146 3.16069886045 | ||
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+ | -0.408932954073 -0.817865908146 2.95076172742 | ||
+ | 0 -0.817865908146 2.92227889516 | ||
+ | 0.408932954073 -0.817865908146 2.95076176227 | ||
+ | 0.817865908146 -0.817865908146 3.03297207263 | ||
+ | 1.22679889202 -0.817865908146 3.16069883522 | ||
+ | 1.63573181629 -0.817865908146 3.3239275849 | ||
+ | 2.04466485977 -0.817865908146 3.51342775781 | ||
+ | 2.45359778404 -0.817865908146 3.7219016958 | ||
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+ | 3.27146363258 -0.817865908146 4.17640480232 | ||
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+ | 0.817865908146 -0.408932954073 2.95076176227 | ||
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+ | 2.45359778404 -0.408932954073 3.66716495683 | ||
+ | 2.86253070831 -0.408932954073 3.8947528626 | ||
+ | 3.27146363258 -0.408932954073 4.13165701038 | ||
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+ | -0.817865908146 0.408932954073 2.95076176227 | ||
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+ | 0.817865908146 0.408932954073 2.95076172742 | ||
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+ | 2.45359778404 0.408932954073 3.66716498152 | ||
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+ | 0.817865908146 0.817865908146 3.03297203742 | ||
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+ | -0.817865908146 1.22679889202 3.16069883522 | ||
+ | -0.408932954073 1.22679889202 3.08534484889 | ||
+ | 0 1.22679889202 3.05938600272 | ||
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+ | 0.817865908146 1.22679889202 3.16069886045 | ||
+ | 1.22679889202 1.22679889202 3.27890195817 | ||
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+ | 2.04466485977 1.22679889202 3.61092351641 | ||
+ | 2.45359778404 1.22679889202 3.81006272919 | ||
+ | 2.86253070831 1.22679889202 4.02404304149 | ||
+ | 3.27146363258 1.22679889202 4.24930149758 | ||
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+ | 0.817865908146 2.45359778404 3.72190172715 | ||
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+ | -0.817865908146 2.86253070831 3.94408567659 | ||
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+ | 0 2.86253070831 3.87806893214 | ||
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+ | 0.817865908146 2.86253070831 3.94408567842 | ||
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+ | 2.86253070831 2.86253070831 4.58746914725 | ||
+ | 3.27146363258 2.86253070831 4.77360211484 | ||
+ | 3.68039679527 2.86253070831 4.97289875816 | ||
+ | -3.68039679527 3.27146363258 5.14027881135 | ||
+ | -3.27146363258 3.27146363258 4.95002866071 | ||
+ | -2.86253070831 3.27146363258 4.77360208073 | ||
+ | -2.45359778404 3.27146363258 4.61291022306 | ||
+ | -2.04466485977 3.27146363258 4.47022606074 | ||
+ | -1.63573181629 3.27146363258 4.34811768765 | ||
+ | -1.22679889202 3.27146363258 4.24930147615 | ||
+ | -0.817865908146 3.27146363258 4.17640481493 | ||
+ | -0.408932954073 3.27146363258 4.13165697486 | ||
+ | 0 3.27146363258 4.11656537092 | ||
+ | 0.408932954073 3.27146363258 4.13165697153 | ||
+ | 0.817865908146 3.27146363258 4.17640482466 | ||
+ | 1.22679889202 3.27146363258 4.24930149758 | ||
+ | 1.63573181629 3.27146363258 4.34811768349 | ||
+ | 2.04466485977 3.27146363258 4.47022607936 | ||
+ | 2.45359778404 3.27146363258 4.61291020168 | ||
+ | 2.86253070831 3.27146363258 4.77360208181 | ||
+ | 3.27146363258 3.27146363258 4.95002862907 | ||
+ | 3.68039679527 3.27146363258 5.1402788242 | ||
+ | -3.68039679527 3.68039679527 5.32195113308 | ||
+ | -3.27146363258 3.68039679527 5.14027886168 | ||
+ | -2.86253070831 3.68039679527 4.97289872152 | ||
+ | -2.45359778404 3.68039679527 4.82150056386 | ||
+ | -2.04466485977 3.68039679527 4.68802903982 | ||
+ | -1.63573181629 3.68039679527 4.57461234221 | ||
+ | -1.22679889202 3.68039679527 4.4834338311 | ||
+ | -0.817865908146 3.68039679527 4.41654822468 | ||
+ | -0.408932954073 3.68039679527 4.3756590303 | ||
+ | 0 3.68039679527 4.3618992577 | ||
+ | 0.408932954073 3.68039679527 4.37565907366 | ||
+ | 0.817865908146 3.68039679527 4.41654819403 | ||
+ | 1.22679889202 3.68039679527 4.48343380365 | ||
+ | 1.63573181629 3.68039679527 4.57461229112 | ||
+ | 2.04466485977 3.68039679527 4.68802902715 | ||
+ | 2.45359778404 3.68039679527 4.82150057848 | ||
+ | 2.86253070831 3.68039679527 4.97289872625 | ||
+ | 3.27146363258 3.68039679527 5.14027884292 | ||
+ | 3.68039679527 3.68039679527 5.32195115805 | ||
+ | </dataplot> | ||
;#; | ;#; | ||
- | <caption>Energy dispersion relation in the $\vec{k}$ space for holes</caption> | + | <caption>Energy dispersion relation $E(k_x,k_y)$ for the highest hole eigenvalue</caption> |
</figure> | </figure> | ||