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Is there a clearer description of the difference(s) between STM and STS than that on Wikipedia? I also found one other site which gave an equally contradictory, overlapping 'explanation'.

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  • $\begingroup$ Link to Wikipedia? $\endgroup$
    – Qmechanic
    Jul 19 '18 at 19:23
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From what I understand in the STS page, in STM you get the shape of an object while varying the distance and measuring the current.

With STS for each distance you change the voltage and measure the current.

This allows, for each distance of the tip, to measure the energy of the electron cloud.

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Usually, when referring to STM people mean the topography mode operation. Considering that is the most common mode of STM measurement employed by STM groups around the world it is an acceptable misnomer. In this mode, we raster the tip across the surface at a fixed sample bias voltage and employ a feedback loop which controls the voltage on the z-piezo to keep the tunneling current constant. By recording the voltage to the z-piezo, we can effectively map the height of the surface, thereby, giving us an image.

We know that tunneling current can be approximated fairly well by,

$$I \approx \dfrac{4\pi e}{\hbar} \exp\left(-s\sqrt{\dfrac{8m\phi}{\hbar^2}}\right)\rho_t\left(0\right)\int_{-eV}^0\rho_s\left(\epsilon\right)d\epsilon$$

where $\rho_s$ and $\rho_s$ are density of states (DOS) at tip and sample, respectively [A].

enter image description here

Now, holding the tip-sample separation constant, at a given (x, y) location, and put a negative bias voltage on the sample, we have

$$I=I_0 \int_{-eV}^0\rho_s\left(\epsilon\right)d\epsilon$$

In other words, we can measure the integral of the DOS, down to any energy by varying the voltage and recording corresponding tunneling current. By taking a numerical derivative of we get the DOS. To circumvent the noise issues inherent to numerical derivatives one can directly measure DOS by employing a lock-in amplifier [B]. This type of measurement is referred to as Scanning tunneling spectroscopy or STS.

[A] https://oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780199211500.001.0001/acprof-9780199211500

[B] https://en.wikipedia.org/wiki/Lock-in_amplifier

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