1) Consider the two atomic resolution STM constant current images of the clean Si (111) surface . When atomically clean, the Si surface atoms re-arrange themselves in a 7x7 "reconstruction".
The two images have been acquired from the same area of the surface but at opposites tip biases. The empty states image shows topographic information while the filled states image shows a convolution of topographic and electronic effects.
1. Identify the empty and filled states images.
2. Using STM textbooks or papers, identify the unit cell of the 7x7 superstructure on both images. Use the drawing tools to draw the 7x7 unit cell.
3. Column B and C contain the tip height recorded along a 5nm line (represented by the red arrows) running across the same 4 atoms on both images. Column A contains the distance along the line. Plot the tip height profiles across the 4 atoms at both tip biases on the same graph. Devise a way of separating the electronic effect from the topography using the height profiles and comment on the magnitude of the electronic effect.
4. Using textbooks, find out why electronic effects only appear on the filled states image.
2) The STS curve has been acquired from a semiconductor surface. This localised I(V) curves can be analysed to extract electronic information such as the band egdes position relative to the Fermi level.
1. Plot Log(I) against V. Identify the band edges position. Is the semiconductor n-type or p-type?
2. Raw I(V) curves are often converted into the normalised conductivity dln(I)/dln(V) which is equal to (dI / dV) / (I/V). Plot I/V against V
3. Plot dI / dV against V
4. Plot (dI / dV) / (I/V) against V. What is the cause of the divergence in the band gap region?
3) Atomic Force Microscopy
Analysis of force-distance data
The data below is taken from a real set of experiments where a cell probe is used to measure the adhesion between a yeast cell and a mica surface in an aqueous environment
1. Calculate a spring constant value from the dimensions of the cantilever and 'cleavelands' method using the data provided
2. Use the best estimation of spring constant to process the force- distance data provided to produce:-
a) Force vs piezo extension curve
b) Force vs separation distance curve
c) Calculate the adhesion between the cell and the surface
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Density of Tungsten kg/m^3 19300
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Sphere Diameter (um)
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Frequency (kHz)
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0.00
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29.50
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8.07
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22.90
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8.24
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22.00
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12.48
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17.60
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16.68
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12.60
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17.22
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11.20
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18.31
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10.10
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22.63
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8.38
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24.12
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8.06
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Cantilever Dimensions and properties
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length (um)
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200
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width (um)
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18
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thickness (um)
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0.6
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Youngs Modulus (N/m^2)
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1.25 x 10^11
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