A stepped metal surface has a true crystallographic step height of (one atomic layer)

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Seeing atoms: electron and scanning-probe microscopy

Problem

A stepped metal surface has a true crystallographic step height of

d_{\rm true}=2.0\,\mathrm{\text{\AA}}

(one atomic layer). A constant-current STM image of the step is recorded at two sample biases. Using the tunnelling exponent for a

4\,\mathrm{eV}

work function,

\kappa=1.02\,\mathrm{\text{\AA}^{-1}}

, treat the constant-current condition as

\rho_1 e^{-2\kappa z_1}=\rho_2 e^{-2\kappa (z_2-d_{\rm true})}

for the local densities of states

\rho_1,\rho_2

(integrated over the bias window) on the lower and upper terraces. Here

z_1

and

z_2

are the tip heights over the lower and upper terraces, both measured from the lower terrace, so

z_2-d_{\rm true}

is the gap over the upper terrace and

z_2-z_1

is the apparent step height the tip traces out. ((a)) At

+0.5\,\mathrm{V}

sample bias the apparent step height read off the image is

2.6\,\mathrm{\text{\AA}}

. Find the ratio

\rho_2/\rho_1

(upper terrace LDOS to lower terrace LDOS) implied by the discrepancy from

d_{\rm true}

. ((b)) At

-0.5\,\mathrm{V}

sample bias the apparent step height is

1.7\,\mathrm{\text{\AA}}

. Find

\rho_2/\rho_1

for this bias.

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