Describing phenomena from the real world mathematically has a tempting sort of elegance and simplicity, but there’s a danger of oversimplifying. You risk missing out on some of the really complex beauty that’s out there! I always experience a bit of glee when a simple explanation turns out to miss something messy but important, and for that reason I’d like to tell you about defects in crystal structure and why they matter.
Awhile back, we talked about periodic structure in solids, and how the geometric arrangement of atoms in a material determines many of the material properties. For electronics, the density of mobile charge carriers (electrons or holes) and the availability of energy states for those carriers to occupy are the two main relevant material properties. From these we can get metals, which conduct electrons easily, or insulators, which don’t, or semiconductors which are somewhere in between. Modern computing is largely based on devices built from semiconductors, connected to each other using metals, with insulators used for electrical isolation and a few other tricks.
But while it’s helpful to imagine a perfect material, with each atom positioned just where it should be in an infinitely repeating array, nature is messy. We can learn a lot from theoretical material models, but the materials we find in the real world will be different. We call any deviation from perfect crystal lattice structure a defect, and the interesting thing about defects is that they can affect material properties too, especially with nanoscale objects that can have a high ratio of “defect” atoms to “normal” atoms.
There are a few different kinds of defects one finds in natural materials. For example, an atom might be missing from a lattice site which is called a vacancy, or there might be an extra atom where there shouldn’t be which is called an interstitial. There could be a whole plane of atoms that just starts in the middle of the crystal, which is called an edge dislocation. Or two regions with different orientations of their crystal structure might be pressed up against each other, which is called a grain boundary. There are lots of ways that a crystal lattice can get messed up, but remember, for that material, the native crystal lattice is usually the minimal energy solution for packing a bunch of atoms together with those properties. So the most probable outcome for any given region is a perfect lattice, but the material will end up with some deviations from this as well. How many defects there are depends on how energetically favourable the lattice is, but also on how the material was made: if you solidify a crystal really slowly, the atoms are more likely to find the true lowest energy position (sites in the perfect lattice) and there are fewer defects.
These defects all matter because they affect material properties, so if we assume that a material is going to behave as it would with a perfect crystal lattice, we are in for a surprise! If we’re focused on practicalities, like whether the material is as electrically conductive as we think it should be, then the type and concentration of defects in the device is very important, because some defects will reduce current flow and others will enhance it. To understand why, let’s think about the physical mechanisms for current flow through a material.
In a crystal, we have an array of positive nuclei with some tightly bound electrons that are bound to them; we can call these ‘localized’ electrons because they are staying in the same approximate location around the nucleus. Electrons that were more loosely bound to the original atoms are able to move freely through the crystal; when these ‘delocalized’ electrons move through the material, that is what we can measure as current flow. But a large part of the reason we can even have delocalized electrons is due to the periodicity of the lattice, which mathematically allows delocalized wave states for the electrons. When this periodicity is broken, as it is by dislocations and grain boundaries, the wave states can be disrupted, and new bound states that localize electrons to the defect are created. These are often called ‘charge traps’ because they trap the charge carriers in a specific place. However, if we ‘dope’ a material by carefully adding lots of interstitial atoms that have an extra electron, we can avoid disrupting the wave states for electrons, but add more electrons total, which actually increases the conductivity of the material. So in device manufacture, controlled doping is a common use of defects to affect material property, but dislocations and grain boundaries are often avoided because their effect on the material property is usually undesirable.
In nanoscience defects are even more important, because with a nanoscale object that’s just hundreds of atoms across instead of hundreds of billions, the percentage of atoms that are in non-ideal crystal sites can get pretty high. For example, many surface atoms end up as defects that trap charge, and a nanocrystal may be 30% surface atoms! So lots of nanoelectronics research is focused on minimizing the negative impact of defects. However, there’s an interesting contradiction there: the fascinating thing about nanomaterials is their quantum-like properties compared to bulk materials. But quantization in nanomaterials stems largely from the greatly increased number of grain boundaries and surface atoms and defects, because these things all increase as you scale down the size of the material. So there’s a careful balance between mitigating the negative effects of defects, and not getting rid of the nanoscale-specific behaviors that make nanoelectronics interesting in the first place!