# Journal Club Week 7 Answers

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### G. Binnig and H. Rohrer (1999), In touch with atoms, Reviews of Modern Physics, Vol. 71, No. 2

Below are the best student submissions for the skim-read questions and summary questions, congratulations to those students! The rest of the answers can be downloaded as a PDF or seen below.

Why do physicists often argue that two objects never really ‘touch’?

Everything we “touch” is made of atoms. Almost all of the mass of an atom is centralised in its small, dense nucleus. Surrounding the nucleus is mostly empty space and some smaller orbiting electrons. Electrons have a particle-wave duality, meaning that they have the characteristics of a particle and a wave – they are also negatively-charged. Particles are attracted to particles of opposite charges and repel those of similar charges. Therefore, electrons are prevented from coming in direct contact with other electrons – their wave packets may overlap, but they can never touch each other. Therefore, when we “touch” anything, the electromagnetic force of repulsion between our electrons and the object’s electrons means that we are actually hovering around the object by a negligible distance.
Ayesha

What is a wavefunction?

A wave function is a mathematical description of a particle’s quantum state; it can be found by solving Schrodinger’s wave equation at a certain point in time. It doesn’t give a precise position or momentum of the particle (this can be linked to Heisenberg’s uncertainty principle), just the probability that you would find the particle in a particular place. However, this probability can only be found after squaring the wave function as it involves imaginary numbers. Interpretations of the wave function are much debated however, some physicists believe it to be a solely mathematical equation that can be used to find important information about a particle, others believe it to be more ‘real’. Due to the complex nature of quantum mechanics, many prefer to not question it and ‘just calculate’, believing there can be no true interpretation. The wavefunction collapses once the system is observed, this means that the system can no-longer be modelled as a wave and it 'becomes' a particle with a position that can be measured.
Sophie

What is quantum mechanical tunnelling?

According to classical physics, if the energy of a particle or wave is less than the energy of the barrier it is trying to cross, it simply won’t be able to cross it. However, in quantum physics, every particle is modelled as a wave function and this seemingly straightforward notion turns out to not be the case. When the wave function meets a barrier, most of the wave function is reflected, but some of the wave function continues into the barrier. The amplitude of the wave function decreases exponentially as it moves through the barrier, it is what is known as an evanescence wave. This means that so long as the barrier isn’t infinitely thick, the wave function can exit the other side of the barrier, meaning that there is a very small, but non-zero, probability that the particle is found on the other side of the barrier. This is known as quantum tunnelling. Even though the probability of the event occurring is very small, when there are a large number of particles in a system it is likely that tunnel effects will be observed.
Molly

What are piezoelectric tubes?

The piezoelectric (meaning pressing electricity) effect allows us to squeeze special crystals and get electricity to flow through them. Picture a crystal: a matrix of atoms and molecules bonded in a regimented way based on countless repetitions of the same basic atomic building block. The majority of crystals are symmetrical but piezoelectric crystals aren’t. Under normal circumstances piezoelectric crystals are electrically neutral; a positive charge in one place cancels out a negative in another. But when we stretch or squeeze them, we upset this balance. Some atoms group together or move apart causing net electrical charges to appear carrying through the entire structure. One face of the crystal will be left positive whilst the other negative. The reverse is also true. If we apply a voltage across the crystal atoms inside are subject to ‘electrical pressure’. They move to rebalance themselves, causing the crystal to slightly change shape.
James

What is a cantilever?

A cantilever is a rigid structural element which extends horizontally and is supported at only one end. Typically, it extends from a flat, vertical surface such as a wall, to which it must be rigidly attached. When a load is applied to the cantilever, the cantilever transfers that load to the fixed end by bending.
Ayesha

How does a Scanning Tunnelling Microscope (STM) work?

An STM uses a sharp metal wire tip to scan very close to a surface whilst applying an electric voltage. Due to the quantum tunnelling effect, some electrons will jump across the air barrier between the probe tip and the sample and by monitoring the current (the tunnelling current) that passes through the sample, you can accurately tell the size of the gap. A feedback loop is used to maintain a constant tunnelling current, meaning that it will keep the size of the air barrier between the probe and the surface the same. Therefore, the probe tip will move relative to the contours of the sample surface. The probe's movements can then be recorded to give a topological representation of the surface. Since the value of the tunnelling current and the size of the gap between the probe and the sample are related, you can also use the STM to maintain a constant horizontal position of the probe and measure the changing tunnelling current to get the same result.
Kitty
The Scanning Tunnelling Microscope is an application of both a mechanical system and quantum behaviour. A very fine tip, consisting of just a few atoms, comes in proximity to a sample, and when a voltage is applied there is a “potential barrier” that exists between the sample and the tip. The potential barrier is the energy required for the electrons in the sample to jump up to the tip. In classical physics, if the energy required to overcome the potential barrier is not enough, then it is impossible for such a thing to happen. However, in the quantum world a particle exists as a “wavefunction” – a wave like distribution of the probability of finding a particle. There is a chance that the electron will cross the potential barrier as the wavefunction will decrease appreciably as it comes into contact with the potential barrier, but it will not die down completely. This phenomenon is known as “quantum tunnelling”. We can make use of this interesting behaviour by adjusting the distance between the sample and the tip using piezoelectric materials – materials which change in length when a voltage is applied – to achieve a constant tunnelling current. Looking at the voltage applied to the piezoelectric materials will tell us the change in length, and so we will be able to distinguish the change in length of the sample and therefore create an image of what the surface of the sample looks like at the nanoscale.
Jared

What does Figure 2 show? Why is it remarkable?

Figure 2 shows a quantum corral, a ring of atoms arranged on a substrate. The tip of a low-temperature STM positioned some iron atoms to form a ring on top of a piece of copper. The iron atoms reflected the electrons from the copper into the centre, creating a wave pattern predicted by quantum mechanics that was able to be imaged using the same STM that positioned the atoms. This image is remarkable not only because its result can be correctly predicted by quantum mechanics, but also because of the amazing resolution of the image, demonstrating a huge leap in our ability to observe and understand interactions at the nanometre scale.
Molly
Figure 2 shows a ring of iron atoms on a copper surface, and a wave-like pattern within this ring. This is remarkable for several reasons, firstly it is incredible that scientists were able to create a ring of 48 iron atoms on a nanometre level, with such precision and accuracy, this is truly a feat of science. In addition to this, the ability to record this at a molecular level was unparalleled at the time and shows the incredible nature of STMs. And finally, the wave-like interior of the ring is remarkable as it shows that electrons exhibit wave-like features, in the days of classical physics, many had assumed, like Newton, that electrons acted as particles, and only particles. As quantum mechanics progressed and Young performed his double slit experiment, it became widely accepted that particles exhibited both particle and wave properties, an example being light. However, figure 2 shows without a doubt that electrons can act as waves and the fact that it can be detected at such a minute level is astounding.
Sophie

“They are fragile individuals, whose properties and functions depend strongly on their context and which are usually quite different from those in the isolated state.” This is the description of atoms, molecules and nanometer-sized objects given in III. Change and Challenge. What does this quote bring to your mind about the atomic world?

Within this statement, the author provides a brief overview into the complications of the observer effect. Observing something on an atomic scale without altering it is extremely difficult and the combination of adhesive and electrostatic forces during the STM process may lead to deformations and displacements. This gives us an understanding of the delicate nature of the atomic world, and the issue of attempting to observe the nature of how things operate - in doing so we may observe either altered properties, or create entirely new ones.
Ejiroghene
In P.W. Anderson’s paper, ‘More is Different,’ he summarises this concept in a different manner: “[A]t each new level of complexity entirely new properties appear, and the understanding of the new behaviours requires research which I think is as fundamental in its nature as any other.” The core concept, however, is the same—taken together, particles are often more than the sum of their parts. Looking around at our world, it’s easy to miss the complexity of the atomic world when the two seem unrelated and abstract. Though the rules of quantum mechanics may not apply on larger scales, in seeing and understanding the interactions that occur on the smallest of levels using an STM, we are better able to understand the systems they coalesce to form. Though Anderson might have been more sceptical about Binnig and Rohrer’s thoughts that “this [could] be the starting point for the human bottom-up approach to functionality,” I believe he would have agreed on the importance of probing this area of research as a method of understanding our world, no matter how small.
Acacia

ABSTRACT

 What is the rough size of an atom? 10-10 m What is the rough size of a water molecule? Around 3×10-10 m What do they mean by the term ‘local probe’? A tool that looks at a material in a particular location. At the scale of atomic structures, what will local probes be able to sense? Individual atoms and their arrangements.

BACK TO THE FUTURE OF MECHANICS

 (P1, C1) What do the authors mean by the term ’electronics’? The motion of electrons in and the deformation of their arrangements. (P1, C1) What do the authors mean by the term ‘mechanics’? The motion of the mass of atomic cores and the deformation of their arrangements. (P1, C1) Why do the authors consider the atomic cores to be, at best, the ‘guardian of the electron’? Because the electrons give rise to the electronic, chemical and mechanical properties of materials whereas the atomic cores’ do not affect or define the macroscopic properties of materials so strongly. (P1, C1) Why might you argue that atomic cores are much more than the ‘guardian of the electron’? The electronic states are caused by the interaction between the electrons and the atomic cores. Without the atomic cores, we’d simply have an electron gas which does not have the wide variety of properties as material systems. (P1, C1) What can a Scanning Tunnelling Microscope (STM) do? Sense and manipulate atoms/molecules/tiny objects. (P1, C1) Analyse the individual words of the phrase ‘The STM is a mechanically positioned, electrically sensitive kind of nanofinger’ to understand what an STM is. Mechanically positioned – it is moved externally through classical means. Electrically sensitive – it has the ability to sense the electrons of a material. Nanofinger – it is designed to be thin so that the probe is essentially atomically sharp. (P1, C1) Looking at Figure 1, how might you improve your earlier definition of ‘local probe’? A local probe interacts with an object in such a way that its interaction deteriorates rapidly with distance away from the probe so that the probe only feels that atom(s) closest to it whilst not affecting any of the atoms further away. (P1, C1) What does ‘inhomogeneity’ mean? The opposite of homogeneous (which means having the same composition throughout so that it is considered uniform). We can think of it as being non-uniform. (P1, C1) What had been the focus of condensed matter physics? Periodic structures – structures that are uniform and repeating such as crystals. (P1, C1) Why do we consider an inhomogeneity to be a local phenomenon? Because the breaking up of a uniform pattern (homogeneity) can occur in a specific place. Imagine a perfect grid of points (e.g. graph paper) – if we could rub out one small part of one of the lines, then we’ve introduced inhomogeneity and it occurs at a particular location (it is local). (P2, C1) Why would such a small local probe (atomically thin) need a ‘high precision nanodrive’ when scanning a material? We need to move the tip with precision to maintain close proximity to a sample. With this in mind, we need to be able to alter the position of the tip incredibly deftly, thus we need high precision motors. (P2, C1) What are ‘continuous and reproducible displacements’? We want to be able to alter the position smoothly not in discrete steps, to be able to be precise about the location of atoms. We want it to be reproducible so that we can be sure that the movements of the tip correspond to features on the surface. (P2, C1) Why is good vibration isolation necessary? To ensure that any movement of the tip is caused by the machine itself (so that it can be recorded) and so that the tip doesn’t damage the sample through non-intentional movements. (P2, C1) Why does the concept of contact blur when we get to the nanometer level? As we are in the range of quantum mechanics. Imagine one atom attempting to ‘touch’ another. The atoms themselves don’t have clear boundaries – their ‘edge’ is a blur of the electrons that they contain (the electron cloud). When one atom comes near to another, the electron clouds overlap and repel. No subatomic particles make contact with any others. (P2, C1) What does resolution mean in the context of creating an image? The degree of detail that is visible.

Before you read the paragraph that begins ‘In STM, the interaction can be described…’, we need to get a more basic understanding of how an STM works. Read this brief article from ‘How an STM Works’ now. The diagram below may also be useful. ‘Describe how an STM works’ will be one of our summary questions this week, so draft out an initial answer now.

 (P2, C1) As the scanning tip (or probe) gets further from the surface of a material, what happens to the tunnelling current? The tunnelling current decreases exponentially with increasing distance between the tip and the surface. Where x is the tip-surface distance and I is the tunnelling current. I0 is a constant and l is the decay length. (P2, C1) What is the rough estimate of the decay length for most tip/sample combinations? 0.05 nm (P2, C1) Why would the STM be less effective if the decay length was longer? As you’d be less certain that the frontmost atom of the tip was carrying the current and therefore the STM would not necessarily be probing the local area. (P2, C1) Why do the authors state that ‘atomic resolution was inevitable’? As the required distance between the tip and surface needed to achieve a current in the measurable range was less than 1 nm. This distance is in the range of the size of an atom. (P2, C1) Why do you think that thermal fluctuations (think of these for now as random fluctuations in the movements of atoms in the material) of atoms in a lattice can be ‘averaged out’? As the fluctuations are random, they’re equally likely to occur in any direction and so the average position of an atom that is fixed within a lattice is going to be at its lattice point. (P2, C2) What is meant by describing an STM as ‘an electronic-mechanical hybrid’? The interaction is electronic – the tunnelling of electrons from the tip to the sample. The feedback loop leads to a mechanical alteration in the position of the tip which is really what an STM is monitoring. (P2, C2) What is the constant interaction/mechanical mode of an STM? Where the feedback loop is designed to keep a constant tunnelling current between the tip and the surface and so adjusts the height of the tip as the tip scans over features so that the tip remains at a constant above the local surface. By relaying the height of the tip, this builds up the surface contour of the sample. (P2, C2) How else can an STM be operated? What are the limitations? An STM can be used in a constant height mode, where the tunnelling current changes as the surface gets closer to and further from the tip (when the surface is closer, the tunnelling current increases and vice versa). The size of the tunnelling current can be associated with the size of surface features. This mode can only be used for very smooth surfaces (where no bumps on the surface will knock into the tip) and is limited in its speed by how fast you can measure the current.

The article discusses a ‘magical Si(111) 7x7 reconstruction’ which was used to persuade the community that the STM was a powerful tool. This image can be seen here.

1. COLOURFUL TOUCH
 (P2, C2) What do the authors mean by the term ‘colourful touch’? That local probes provide a ‘rainbow of possibilities’ for making contact with a surface by altering the type of interaction between a tip and surface or by altering the surrounding medium that it all takes place within. (P3, C1) What are the two main reasons for using an STM? To image a surface or to work with/alter a surface.

Due to the STM using a tunnelling current to ascertain where the surface is, an accurate topography of a surface relies on the electronic structure of the surface remaining constant. In the simplest case, if we imagine a hypothetical smooth surface that is in one location metallic whilst insulating in another then an STM not going to register this surface as smooth and continuous (in fact, it won’t register the insulating surface at all). This property of tunnelling current – that it samples the local electronic properties of a surface – can actually be useful, though, as the authors take note of in (P3, C1)

 (P3, C1) What is the downside of the slightly more recent Scanning Near-field Optical Microscope (SNOM) compared to the STM? It doesn’t have an atomic scale resolution. (P3, C1&2) What is an advantage of the atomic force microscope (AFM) over the STM? It can image surfaces of non-conducting samples. It provides force detection (for many different types of forces, both vertically and laterally). (P3, C2) What are van der Waals forces? We looked at this very briefly in a previous week whilst discussing Gecko tape. A collective term for intermolecular forces (attractive or repulsive) between atoms, molecules and surfaces that are caused by fluctuating polarisations of electric charge within the interacting molecules.

 (P3, C2) What are the two operating modes of an atomic force microscope (AFM)? Describe them briefly. Static/contact mode where the tip is moved across the surface of a material and the deflection of the cantilever is noted (or the sample is moved to keep a constant deflection). Dynamic mode where the cantilever is oscillated, with the oscillations being driven initially by the AFM. The amplitude and frequency of these oscillations change when the tip interacts with a sample. (P3, C2) Why is the AFM ‘more mechanical in nature’ than the STM? Both the STM and AFM have a mechanical feedback loop – the position of the sample relative to the tip is altered mechanically by a piezoelectric tube. But the interaction between the AFM tip and the sample is mechanical in its nature (contact or tapping) whereas the tip of the STM’s interaction with a surface is electronic in nature. (P3, C2) Given that the usage of the cantilever is based upon Hooke’s law, discuss some of the practicalities that might be involved in choosing a cantilever. You want to get the right cantilever for the situation you have. The spring constant of the cantilever needs to be tailored to the size of the forces you’re expecting to see on a given surface (and the resolution of your optical tracking). You want to create large enough deflections in your cantilever to be easily picked up by the optical tracking, but not so large as to overbend the cantilever (past its elastic limit) and snap it. (P3, C2) We have met this idea before, but what is microfabrication? Answer courtesy of Alex from Week 4: Microfabrication is “the process of making structures that are extremely small - one-millionth of a metre or even smaller. An example of when this is used in making integrated circuits or microchips” (P3, C2) Why is it difficult to achieve atomic resolution with an AFM? Because the tip and sample can be deformed by their interaction such that the tip is no longer atomically sharp, so the resolution becomes smeared. (P3, C2) Why are AFMs not typically operated in air? As, in air, any humidity will leave a thin watery film on both the tip and sample creating a strong capillary force that brings the two together. (P4, C1&2 and Figure 2) What does Figure 2 show? Why is it remarkable? (This will be one of our summary questions this week) Figure 2 shows a ring of iron atoms positioned deftly on a piece of copper. What is remarkable is that the same tool that imaged them also positioned all of the atoms there in the first place. By altering the strength of the interaction between tip and surface, an STM can transition between being a tool for altering the position of atoms and a probe of the surface. The wavelike structure within the circle is also remarkable and shows how the STM is actually sampling the electronic properties of a material. The waves come from the confinement of the electrons on the surface of copper within the iron ring. This shows the wavelike properties of electrons, behaving as waves to form a standing wave pattern.

III. CHANGE AND CHALLENGE

 “They are fragile individuals, whose properties and functions depend strongly on their context and which are usually quite different from those in the isolated state.” This quote will be used in one of our summary questions this week. For now, just take a few moments to really think about what the authors might mean by this. (P4, C2 and P5, C1) Why isn’t the STM strictly non-invasive? As by its very nature, it has to interact with the sample to image it. It calls to my mind the Heisenberg uncertainty principle, but on a larger scale. We can’t make measurements without affecting the thing we are trying to measure in some way. In the case of the Heisenberg uncertainty principle it is because of the delicate balances of quantum mechanics, in the case of the STM it is because we’re given the sample an electric shock (and sometimes crashing the tip straight into the surface). (P5, C1) How has the invasive nature of STM been used to advance the technique? By using the STM to physically manipulate atoms on a surface. (P5, C1) How can working in a liquid environment be beneficial (or why is the liquid-solid interface thought by the authors to be the interface of the future)? As “liquids provide a very adaptive environment for protection, process control, and modification of surfaces, they carry ionic charges and atomic and molecular species, and they remove many of the ‘‘traffic restrictions’’ typical for a two-dimensional solid surface.”

Around now the authors begin to dig into some of the more advanced applications of local-probe microscopy. We won’t have any questions on this part, but it would be very beneficial to carry on reading this section to see how the STM and AFM develops from a tool to look and manipulate atoms to more exotic ventures.

1. NATURE’S WAY
 (P6, C2) Why do the authors draw links between the local probe microscopy techniques and nature itself? As nature is built on the nanoscale, using nanofunctionality to create life itself. The AFM and STM are probing systems at this scale and so there is a parallel to be drawn to nature when these techniques can sense and change systems on this nanometre scale.

#### GENERAL INFORMATION

Remember, reading a paper isn't like reading a piece of fiction or a newspaper article. Don't get frustrated if it doesn't immediately make sense - you might need to do a little research of your own to understand some of the ideas. This article gives you an idea of how scientists read differently.

Each question refers to a specific part of the paper e.g. Page 2, Column 3 is written as (P2, C3).

Next week, we'll publish solutions to the questions and the best submitted summaries from students across the country.

#### NEXT WEEK

We're going to be looking at exoplanets. This gives a brief introduction to exoplanets. It might be good idea to understand the basics of some of the method used to find exoplanets here.