Scanning tunnelling microscopyand
electronic structure
Avdelningen för synkrotronljusfysik, Fysiska institutionen, Lunds universitetSpektroskopi och materiens kvantmekaniska beskrivning FYS T20, VT 2008
What is scanning tunnelling microscopy?
Michael Schmid, TU Wien A. Emundts, Forschungszentrum Jülich,http://www.fz-juelich.de/video/emundts/
What does STM have to do withthe electronic structure?
Everything!
At very low biases STM images the electron densityat the Fermi level.
At higher biases STM images the integrated electron densitybetween the Fermi level and the applied voltage.
Actually, STM images represent a convolution of theelectronic states of the sample and the tip.
Potential
Simplified potentialwith energy level
Wave function
Potential and wave function
sample region
tip region
Tunnelling can occur!
EFermi EFermi
Energy
xSample Tip
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Energy
xSample Tip
-eV
-eV
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Energy
xSample Tip
No bias
Negative bias
Positive bias
Tunnel currents for homogeneous density of states
No net current
Positive net current
Negative net current
Conventions:- bias applied to sample- current measured on tip
Mathematical treatment
Solutionsfor sampleelectrons
sample tip
Gottlieb and Wesoloski,Nanotechnology 17 (2006) R57
Topographic vs electronic contrast
STM image of the TiO2(110) surface byDiebold et al., Tulane University.The (001) direction is along the oxygen andtitanium rows.Brighter areas correspond to a more retractedtip.
Charge density plot of the TiO2(110) surface, U. Diebold,Surf. Sci. Rep. 48 (2003) 53). The contour lines correspondto a progression of charge density, very much like the contourlines on a topographic map.
Interpret the STM image in terms of the oxygen and titaniumrows of the sample(a) in a purely topographic interpretation(b) using the charge density plot.
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Energy
xSample Tip
Real (inhomogeneous) density of states
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Energy
xSample Tip
very smalltunnelling current!
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Energy
xSample Tip
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