Piezoelectric Effect and EM Radiation

[Samson4]

It's my understanding that deforming a piezoelectric crystal causes electric charges to build up on the outer faces of the material. What I would like to know is if these charges behave like the free charges in a metal. More specifically, does deforming a piezoelectric crystal effect how em radiation penetrates the surfaces that become charged? This is considering crystals with no electrodes.

 

[Cutter Ketch]

The answer to this isn’t simple. Part of the reason is that the same assymetry of the crystal lattice that causes the piezo-electric effect also causes other effects that aren’t officially directly related but wind up occurring together and influencing each other.

When you squeeze a crystal (stress) the crystal lattice (atomic cores bound together by electrons which are in covalent bonds in all the piezo materials) bends just a little (strain). The lattice of a piezo electric is assymetric in a way that the negative charge in the bonds bends a little one way while the positive atom cores shift the other. Net charge only appears on the surface. To see why, picture a rectangle filled with positive charge. Superposed over it picture a rectangle filled with negative charge. Right now the rectangle is neutral. Now picture displacing the negative charge a little to the left. All the charge moved, but most of the area is still neutral. A little excess negative charge appears on the left surface and a little excess positive charge appears on the right surface. Note that these are still bound charges. It’s not like a metal. The charge can’t move, and it hasn’t become free to interact with EM waves. The distortion is only slight and the charge has pretty much the same band structure and interacts with light about the same, transparent or absorbing, as the unstressed crystal. The lattice is elastic, and the harder you squeeze the more charge you get. (or inversely the more field you apply the more the lattice bends)

The polarized crystal is now like a parallel plate capacitor. The charge creates an electric field. The dc electric field doesn’t directly effect EM radiation. However the electric field can affect the polarizability and therefore the index of refraction through the electrooptic effect. Given the assymetry, the index change is not uniform in all directions so the crystal becomes birefringent. Squeezing the crystal displaces the atoms and this also results in birefringence through the stressoptic effect. This too makes the crystal birefringent.

These three effects, piezoelectric, electrooptic, and stressoptic often occur together to differing degrees and can influence each other. For example we use Lithium Niobate as a Pockel’s cell Q-switch in high power laser cavities. We apply an electric field to create birefringence. The electro optic effect is very fast and on short time scales you get one value of birefringence. However the electric field also causes stress via the piezoelectric effect. The piezo stress causes the crystal to distort, but it takes acoustic time scales to complete the strain. As the lattice strains you get extra birefringence through the stressoptic effect. This means the required electric field to get the desired birefringence changes completely depending on the time scale because of the interaction of these three effects. Yikes!

 

[Samson4]

Beautifully articulate. Thank you very much Cutter Ketch.