What are the ripples in STM images?

[LostConjugate]

Do they just add waves into 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.

http://www.almaden.ibm.com/vis/stm/images/stm6.jpg

 

[LostConjugate]

Bump, anyone know?

 

[collinsmark]

Gibbs phenomenon maybe?

 

[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.

 

[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.

 

[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:

when they determined that the ripples were due to "surface state electrons." These electrons are free to roam about the surface but not to penetrate into the solid. When one of these electrons encounters an obstacle like a step edge, it is partially reflected. The ripples extending away from the step edges and the various defects in the crystal surface are just the standing waves that are created whenever a wave scatters off of something. The standing waves are about 15 Angstroms (roughly 10 atomic diameters) from crest to crest. The amplitude is largest adjacent to the step edge where it is about 0.04 Angstroms from crest to trough.

 

[alxm]

If this is done by multiple scans and the electrons are in motion why is there only one large lump for each electron?

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.

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.

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

 

[LostConjugate]

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

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.

 

[Gokul43201]

The bumps we see in the photos are where it detected an electron.

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.

 

[alxm]

The bumps we see in the photos are where it detected an electron.

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

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.

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.

 

[LostConjugate]

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.

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, that's 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.

 

[alxm]

The height of the wave crests is very uniform, that's 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.

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.

 

[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.

STM as electronic spyglass:A scanning tunneling microscope constructs images at extremely low temperatures by measuring minute variations in conductance, at a given voltage, between atoms on a surface and the microscope's ultrafine tip. Invented in the 1980s, the STM made it possible to picture and manipulate surface atoms and to form images of the wave patterns of surface electrons.

Electrons -- or their equivalent mathematical counterparts, known as quasiparticles (see background information, below) -- scatter from defects in a crystal or from individual impurity atoms. Because of their wavelike nature, the incident and scattered electron waves can interfere to form standing waves. These are visible because the STM directly senses electronic states occupied in a particular place at a particular energy.

Davis compares the process to photographing ripples in water. "Ripples reflect from the shores of a lake and interfere constructively and destructively, producing standing waves," he says. "On water, standing waves can occur at all possible wavelengths."

Davis adds, "We have this water-wave picture in our minds when we first look at electrons in a metal, and indeed this picture is true for simple materials."

He cites the striking STM images obtained in 1993 by Michael F. Crommie and his colleagues, who confined electrons on a copper surface in a "quantum corral" made of iron atoms. Scattering from the iron and interfering to produce standing waves, the electron waves looked much like water on the surface of a pond.

In more complex materials, however, the waves-on-water picture no longer holds and "grows less true as materials grow more complex," says Davis. "For the cuprates -- but not for metals or semiconductors -- at zero energy there are only four possible quantum states that can generate these interferences. As you go away from zero energy, a beautiful thing occurs. Petals open like an eight-fold blossom, into all available quantum states."
http://www.eurekalert.org/pub_releases/2003-04/dbnl-eqs040803.php

 

[Gokul43201]

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.

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.

 

[LostConjugate]

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.

Why are they so uniform in amplitude?

 

[Gokul43201]

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.

 

[LostConjugate]

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.

Because of their wavelike nature, the incident and scattered electron waves can interfere to form standing waves.

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

These are visible because the STM directly senses electronic states occupied in a particular place at a particular energy.

Doesn't this violate the HUP?

 

[LostConjugate]

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.

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

 

[f95toli]

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

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.

 

[LostConjugate]

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.

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.

Ok, I was thinking it was much more accurate.

 

[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.