---
title: "STM: a current contour is not simply a height map"
description: "How did tunneling current resolve surface structure, and why can the same surface look different at another bias?"
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[Diffraction, phase and surface structure](https://sandboxphysics.com/stories/probe-evidence/#structure)

Apparatus · Observation · Inference

# STM: a current contour is not simply a height map

Sandbox Physics · 2026-10-22

How did tunneling current resolve surface structure, and why can the same surface look different at another bias?

1. Biased tip and conducting specimen
2. Tunneling through a small gap
3. Current feedback during scanning
4. Interpret a bias-dependent contour

The feedback coordinate is the tip motion required to hold a current. It includes electronic contrast and instrument response.

## The gap made the current sensitive

Binnig and Rohrer’s lecture traces local tunneling spectroscopy into scanning tunneling microscopy. A conducting tip brought very close to a conducting specimen permits tunneling at an applied bias. The strong distance dependence turns tiny changes of the junction into measurable current changes.

The development needed vibration isolation, stable approach, sharp tips and scanning control; Christoph Gerber and Edmund Weibel also contributed. A barrier-transmission equation alone does not supply a working microscope.

Sources: [1] [2]

## A barrier estimate explains sensitivity

For a simple constant vacuum barrier, low-bias current decays approximately exponentially with gap. The decay parameter depends on electron mass and an effective barrier energy. A one-electronvolt-scale change of barrier or a change of tip state can therefore alter the current without the surface moving.

The expression is only a distance-sensitivity limit. It neglects detailed tip and sample densities of states, voltage-dependent barrier shape and lateral structure. It must not be fitted to every pixel as if the barrier were known and uniform.

$$
I\propto e^{-2\kappa z},\qquad\kappa=\frac{\sqrt{2m_e\Phi}}{\hbar}
$$

Sources: [1]

## The silicon traces retained a reconstruction pattern

The lecture presents the silicon (111) seven-by-seven reconstruction as both a relief assembled from original recorder traces and a processed top view. Keeping those representations together shows the passage from measured scan lines to an interpreted surface image.

The pattern constrained competing surface models; it did not directly reveal all subsurface atomic coordinates. Bias dependence and the electronic character of tunneling mean that bright features need not coincide with a simple geometrical atom center.

Sources: [1]

## Feedback adds a bandwidth limit

Constant-current scanning adjusts height to maintain a setpoint. If the scan outruns the feedback, slopes and edges can be distorted; multiple tip apexes can repeat structures. Constant-height scanning instead retains current variations and has a different risk of collision.

At different biases the accessible sample states and tip response change. A contrast reversal can therefore be electronic rather than a physical inversion of the surface. Quantitative interpretation needs junction conditions and a tunneling model.

Sources: [1]

## Use the barrier model without calling it an STM

The existing tunneling Lab tests transmission through a prescribed barrier. It contains no complete raster, current feedback or local-density-of-states imaging. The historical article is complete as a reading path; the independently planned STM instrument remains a separate implementation task.

Sources: [1]

## Explore the related models

Each link states what the existing model can explain and where the historical measurement goes further.

### [Explore barrier sensitivity](https://sandboxphysics.com/labs/quantum-tunneling/)

Compare transmission as barrier width and height change.

A one-dimensional barrier does not implement an STM surface, tip or feedback scan.

## Sources and reading notes

The original joint lecture was read in the hosted volume, including the recorder-trace and silicon figures. The displayed barrier estimate is a separate modern approximation.

1. [G. Binnig & H. Rohrer, Scanning tunneling microscopy: from birth to adolescence (1986), Figs.4–6](https://www.nobelprize.org/uploads/2018/06/rohrer-lecture.pdf)

   Tunneling, vibration isolation, recorder traces and silicon reconstruction passages read in the hosted original lecture. [Read the hosted original](https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics81-90-2.pdf)

2. [H. Rohrer, Nobel Foundation interview transcript (2008)](https://www.nobelprize.org/prizes/physics/1986/rohrer/interview/)

   Primary interview transcript read: surface electronic wavefunctions, partnership and the early team.

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