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\section{STM images of Silicon (001)}
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As explained in the introduction, the Tersoff-Hamman approximation states that the tunnelling current is proportional to the local density of states of the sample around the Fermi level. The tip is simply approximated by a single $s$-orbital. While quantitatively erroneous, the approximation has been qualitatively confirmed by more elaborated models. However, cases in which tip-induced phenomena occur will fail to be reproduced, even from a qualitative point of view.\\
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\siesta\ is able to produce STM images within the Tersoff-Hamman approximation. In order to simulate the bias, which is experimentally applied between the sample and the probe, \siesta\ integrates the LDOS between two energies. The relationship between the energy window and the bias is given by:
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As explained in the introduction, the Tersoff-Hamann approximation states that the tunnelling current is proportional to the local density of states of the sample around the Fermi level. The tip is simply approximated by a single $s$-orbital. While quantitatively erroneous, the approximation has been qualitatively confirmed by more elaborated models. However, cases in which tip-induced phenomena occur will fail to be reproduced, even from a qualitative point of view.\\
5
\siesta\ is able to produce STM images within the Tersoff-Hamann approximation. In order to simulate the bias, which is experimentally applied between the sample and the probe, \siesta\ integrates the LDOS between two energies. The relationship between the energy window and the bias is given by:
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\varepsilon_{\text{window}} = |q|~V,
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\label{eq:energyWindowBias}
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stm_Si001.tex
