Make a semilog plot showing tunneling current versus...

Make a semilog plot showing tunneling current versus tip-sample separation for an STM. Assume that the tunneling depth is $\lambda=0.1 \mathrm{~nm}$ and the tunneling current is $1 \mathrm{nA}$ when the separation is $z=0.2 \mathrm{~nm} .$ In an STM the circuitry usually limits the measurable currents to the range between $100 \mu \mathrm{A}$ and $10^{-14} \mathrm{~A}$.

Key Concepts

Scanning Tunneling Microscopy (STM)

STM is a technique that uses a sharp conductive tip to probe the surface of a material at very small separations. A current, resulting from quantum tunneling, is measured as the tip approaches the sample, allowing researchers to image surfaces at the atomic level. The tunneling current is extremely sensitive to the tip-sample separation, making the control of this distance crucial.

Exponential Decay of Tunneling Current

The tunneling current in STM exhibits an exponential decay with increasing tip-sample separation. This relationship is typically modeled by an exponential equation where the decay factor is determined by the tunneling barrier properties (often characterized by a parameter like lambda). This exponential dependence is central to understanding how minor changes in separation can lead to large changes in current.

Semilog Plotting

A semilog plot is a graph where one axis (usually the vertical axis representing the current) is scaled logarithmically while the other axis (representing the tip-sample separation) is on a linear scale. This graphing method is particularly useful for visualizing the exponential decay of the tunneling current, as the exponential relationship becomes a straight line on the plot, simplifying analysis and interpretation.

Current Measurement Range

In practical STM instrumentation, the electronic circuitry imposes limits on the measurable current range. This is important because the tunneling current can vary enormously due to its exponential dependence on distance, and the device must be designed to accurately measure currents over a wide dynamic range while preventing noise and saturation issues.

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