# What are the ripples in STM images?

1. Apr 20, 2010

### LostConjugate

Do they just add waves in to demonstrate the probability wave? They could not be detecting the electron in more than one place.

Is it because they make so many measurements to generate the image that the amplitudes you see are a collection of each measurement?

A good example is the copper image, where electrons are reflected and transmitted everywhere as the surface is very step like.

2. Apr 21, 2010

### LostConjugate

Bump, anyone know?

3. Apr 26, 2010

### collinsmark

Gibbs phenomenon maybe?

4. Apr 26, 2010

### PTM19

The picture shows the shape of a electronic surface. Ripples are due to wavelike nature of electrons and their interference.

The picture is done by having a scanning probe scan the surface, this scanning is very slow compared to electron speeds so the probe is actually reacting to an average density of electrons in a given spot. The surface pictured is a surface having a constant electron density.

5. Apr 26, 2010

### nbo10

It could be mechanical oscillations of of the STM caused by a fast scan speed. Adjusting the PID settings of the feedback loop would help diagnose the issue.

6. May 12, 2010

### LostConjugate

If this is done by multiple scans and the electrons are in motion why is there only one large lump for each electron? Then to top it off the waves detected are not random in any way, they are the exact same amplitude for any angle at each distance r from the electron. And the amplitude looks to be falling as 1/r.

Here is what IBM research labs said about the image:

7. May 12, 2010

### alxm

I would suspect that it's for the same reason that you have 'lumps' of probability around any other atom or molecule: It corresponds to a stationary state of the wave function/probability density. I.e. analogous to a classical standing wave. (as the description said)

You're not seeing a single identifiable electron in multiple states at once. (as PTM19 said)

A very clear-cut example is http://www.almaden.ibm.com/vis/stm/images/stm.gif" fairly well-known image/example of an electron "corral", where metal atoms have been placed in a ring to give rise to a nice standing "wave" of electronic density.

Why would they be random?
I'd wager they're falling off as $$e^{-r}$$, though.

Last edited by a moderator: Apr 25, 2017
8. May 12, 2010

### LostConjugate

The bumps we see in the photos are where it detected an electron. So for each section of the wave an electron or more was found in a pass, and in the largest bump in the center many electrons were found over and over, giving it the highest height. So the electrons are moving but also keep going back to that same spot, it makes no sense that this is a distribution of measurements.

9. May 12, 2010

### Gokul43201

Staff Emeritus
No, the bumps are surface defects and impurities. And the entire image is generated from a single scan of that region of the surface (not a reconstruction of several repeated scans).

The ripples are collective surface modes of the electron gas.

10. May 13, 2010

### alxm

Not a single electron, MANY electrons, and possibly the same one many times.

Of course they're going back to those spots - there's an atom (or several) protruding from the surface in those spots. Electrons like to hang around nuclei.

11. May 13, 2010

### LostConjugate

Oh the larger bumps are atoms. I see, so what we see is the discrete levels the electrons can be found, the waves around the atoms.

The height of the wave crests is very uniform, thats odd for something that is measured as a point particle, seems it should be more blotchy because we may not detect an electron (or as many electrons/measurements) at every angle throughout the scan process.

12. May 13, 2010

### alxm

See, but they're not being measured as a point particle.

They're measuring the tunneling current, which is related to the local density-of-states, not the particular location of any single electron at any particular moment in time.

13. May 13, 2010

### ViewsofMars

This topic reminds me of an article back in 2003. This might be helpful. An excerpt from Eight-fold quantum states blossom in a high-temperature superconductor.

14. May 14, 2010

### Gokul43201

Staff Emeritus
No, the ripples are not the bound electronic states of individual atoms. They are collective excitations of the free electron gas in Cu, subject to various boundary conditions from surfaces, edges and defects.

15. May 14, 2010

### LostConjugate

Why are they so uniform in amplitude?

16. May 14, 2010

### Gokul43201

Staff Emeritus
Not sure what you mean by "so" uniform. In a one dimensional standing wave, the amplitude is the same throughout for any given harmonic (or eigenmode). In two dimensions, it depends on the geometry of the boundaries.

17. May 17, 2010

### LostConjugate

I thought the wavelike nature can not be directly measured because the wave function collapses.

Doesn't this violate the HUP?

18. May 17, 2010

### LostConjugate

This actually makes a bit more sense. I thought they were making a measurement each time a single electron tunnels to the tip.

19. May 17, 2010

### f95toli

No, there is nothing preventing you from observing the result of the wavelike nature; this is no different than e.g. observing optical interference using photodetectors: each point if a "particle" but the shape of the "global" pattern is determined by the wavelike nature of the particles.

[quote[
Doesn't this violate the HUP?[/QUOTE]

No, for several different reasons. The most obvious reason being that the HUP sets a lower limit for the "noise" and an STM is nowhere near that limit in terms of signal-to-noise ratio.

Also, remember that the currents in an STM are very high(relatively speaking): there are an enormous amount of electrons involved so it doesn't really make sense to think of if in terms of single particles.

20. May 17, 2010

### LostConjugate

Ok, I was thinking it was much more accurate.

21. Jan 14, 2012

### jhguth

Those really are not "ripples" that you are looking at. Those are rows of copper atoms at a lower resolution so you don't see that each row consists of a line of closely packed spherical atoms as they are detected and imaged by Scanning Tunneling Microscopy. An STM micrograph is actually a 3D plot of the electrical potential of the surface down to the resolution of a single atom. As the tip of the STM slowly passes over the surface of the specimen, the ultrafine point of the tip reacts to the slight differences in distance between the tip and the substrate or atoms sitting on the substrate.