The primary resource for this material was a lecture by Peter Grütter.
Why has it been reseached?
The semiconductor industry is probably the primary reason why surface science has received so much attention. It is well established in industry and in science. The development of the tools and techniques has been driven primarily by the semiconductor industry.
Another major driver is catalysis. This is the area of study of how to catalyse reactions/processes so that they can happen more quickly and/or with lower energy requirements. Surfaces can be extremely important for catalysis. With regards to catalysis, the sites of interest on the surface are actually the kinks and defects rather than the flat surface itself.
Small features can be of primary importance in many of these condensed matter fields of study. Dr. Grütter calls attention to the fact that in the semiconductor industry, the doping atoms among the silicon of crucial to the operation of the devices.
Introduction to Surface Science
In this class, we will be talking primarily about solid-vacuum interfaces rather than solid-liquid interfaces. We are building on the knowledge we gained in the introductory sections on vacuum systems.
Surfaces are 3 dimensional. They are not merely two-dimensional planes. They are a layer of transition from bulk conditions to vacuum conditions.
The dipole layer is an interesting physical phenomenon that takes place at the surface of a material. Electron density does not drop off to zero once we are outside the surface atoms. It tapers off, becoming negligible some small distance away from the surface. This distance is on the order of one fermi wavelength, which would vary depending on the material.
So some negative charge ends up outside the surface. The only picture I can find of this effect online is here, even though it is given in terms of electrostatic potential rather than electron density. Rather than a smooth drop in electron density, we end up with a periodic (on the scale of fermi wavelengths) charge density as we look into the surface. Thus, just inside the surface we actually have a higher electron density than we do further into the bulk of the material. This interface between the high internal electron density and the low external electron density is called the dipole layer.
The dipole layer can stop atoms from diffusing out of the surface. As they diffuse towards the surface, they suddenly come up against a larger density of electrons, which push them away. In the image linked above, the diffusion would be taking place from right to left. The lower potential pushes back on the atom’s electrons, causing it to have more difficulty getting through the surface than it had moving throughout the bulk of the material.
A few Observations
As we already know, taking an electron out of the surface will take some energy. The amount of energy depends on several things such as strength of bond to ion core, interaction of electrons with each other, etc. This is known as the work function. There are two versions, one considers the energy needed to move the electron to just outside the solid surface, while the other considers the move of the electron to infinity).
The work function depends primarily on the dipole layer. Can be different work functions for different surfaces (faces) of crystals! Depends on the orientation of the atoms. Work function also depends on step density. What is a step? Consider a perfect planar surface of atoms. Now consider adding another layer to half the surface, so that there is a ‘step’ up to the second layer. There can be many such steps. As a heavy and long-time computer user, one of the first things I visualized was the fact that an angled line on a computer monitor is not smooth, it has ‘steps’ made of straight sections. Similarly with a surface viewed at the nano scale. The closer the steps are to each other, the higher the step density. Step density changes the work function because of the details of the dipole layer at each step.
Question that you must learn to ask yourself: You must ask yourself if what you are studying is affected by small defects in the system. In the history of science this has been overlooked many times. How big of an effect can these things have? Well, it turns out that a 5% difference in work function for Tungsten can be created by step density. Even more astounding, a 1 eV difference in work function can be measured depending on tungsten orientation! 1 eV at the nanometer scale indicates a huge difference in electric field. These hugely different electric fields can help explain why such small defects can often have a large effect on chemical reaction rates via catalysis.
The simplest way to explain surface energy that I can find is from Wikipedia, where it is stated that surface energy can be defined as the excess energy at the surface of a material compared to the bulk of the material.
In class, the first thing we discuss about surface energy is the jelly model (jellium), which is quite similar to the plum pudding model. It feels almost heretical to be talking about this, since this class is in a building named after the man who proved that the plum pudding model was wrong (Ernest Rutherford).
We can calculate surface energy for jellium quite easily. This tends to agree with experiment at low densities, then eventually becomes very broken at higher densities. The more complicated (and accurate) models are quite difficult to calculate. Additionally, the surface energy is very hard to measure experimentally.
Surface energy is crucial to our understanding of many physical aspects of surfaces. For example, it helps us understand how we can grow materials on other materials. Will we get island growth or layer-by-layer growth?
One of the reasons this is difficult to model correctly is that the electron correlation effect between d-orbitals are difficult to calculate. This is why estimating the surface energy of elements such as gold, iron, etc involves very complicated calculations.
It turns out that finding the minima of surface energy will show us the shape of an equilibrium crystal. Real crystals may not completely agree because our physical crystal growth is not perfect. In closing, surface energy is important for studying crystal shapes as well as understanding what materials we can grow on what substrates and how they grow.
There are three major ways in which the surface structure can be very different from the bulk structure.
The spacing between surface atoms and second layer is often not equal to the distance between the 2nd and third. Surface atoms tend to get pulled in little bit because they do not have a bond on one side. This is true for both covalent bonds and metals. This relaxation may be up to three layers deep (distances grow towards lattice standard as we go deeper).
Where the surface structure is different from the bulk. For example, there might be more atoms on the surface layer than in a bulk layer. They may be connected to each other at different angles. Thus, the unit cell of the surface crystal can be very different from the bulk unit cell. We actually cannot calculate some of these structures because they are too complicated.
Related aside, Dr. Grütter began talking about silicon (111). He said, “This was the Guinea Pig or Drosphila of surface science for a number of years.” Apparently about 20 years of work went into understand silicon (111), which has what is called a “7x7 reconstruction” comprised of 64 atoms in 4 layers. The problem was eventually solved by a combination of scanning tunneling microscopy and diffraction studies.
Aside from the aside: This is not the industrially relevant silicon unit cell. That role is filled by silicon (001). Dr. Grütter says that it is very important that one can grow very smooth layers of oxide on silicon (001).
Aside3: Dr. Grütter says that silicon cannot be used as a photon emitting material very well because this would violate momentum conservation. However, gallium arsenide is capable of being a useful photon emitting material.
Most materials are an alloy, there are multiple constituent elements. Will the surface layer be the same composition as a bulk layer? It turns out that often surface layers are usually completely different than the bulk in terms of composition. Surface might be all of one element. Second layer might be a split of some kind. Third layer might be a different split.
This fact has huge implications for surface characteristics such as the ability to catalyze reactions, corrosion resistance, hardness, etc.
We tend to think of surfaces as atomically flat, but they are not. A decent flat surface might have truly flat areas that are 10nm in length. We might be able to get 100nm of nice flat area if we try really hard and employ a lot of tricks.
Some of the forms of imperfections in a surface are:
- monoatomic steps
Curious about what these are? Check out this Wikipedia page which includes some of their definitions.
A fair amount of research has been done on the subject of the effects of these imperfections in surfaces. For example, we have learned that electromigration is affected. Defects can backscatter electrons. This can become important when the surface atoms are a notable number of total atoms in the wire, which happens at the nano scale.