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Artificial Superlattices

Production and Characterization

A tutorial

What is a superlattice?


To build an artificial superlattice we deposit very thin layers of different materials on top of each other to build up a structure that can be thought of as a new material.

For something to be a superlattice, as opposed to a multilayer, the periodicity should be small enough that it becomes the relevant periodicity of the new material.

In the Lego model shown the grey base can be thought of as a substrate, the blue layers as electrodes and the yellow and red layers as two materials which form a superlattice.

Perovskite Oxide Ferroelectrics

The “bricks” we use to make a sample are perovskite oxide ferroelectrics. These are materials which, in a particular non-centrosymmetric phase, have a spontaneous electrical polarization associated with an ionic displacement. In the case of BaTiO3 the dipole originates from the displacement of the Ti ion within the oxygen cage.

Double Well Potential

We can represent this situation with a diagram of energy (U) against polarization (P). This looks like a double well, ie. there are two equal energy minima for the system which have equal and opposite polarizations. In the ferroelectric phase either of these configurations are energetically more stable than a non-polar configuration where P = 0.

Ferroelectric Phase Transition

As the temperature of a ferroelectric material is raised the polarization usually decreases until at a particular temperature there is a phase transition to a higher symmetry phase. The figures show examples of transitions from a ferroelectric to a paraelectric phase (though there can also be transitions from one ferroelectric phase to another, as in BaTiO3). Because the interactions in ferroelectrics are long range ferroelectric phase transitions are usually well described by a mean field theory. The expression shown is a simple Landau expression for the free energy of a ferroelectric as a function of polarization. In this theory the P2 term has linear dependence on temperature. Depending on the sign of the P4 term the transition can be either continuos (second order) or discontinuos (first order). First order transitions may also exhibit temperature hysteresis.


Application of an electric field causes one polarization state to be preferred over the over. In terms of our double well this is like pushing one well up and the other down. When applying a field in the opposite direction to the current polarization state of the sample switching only occurs once a particular value, known as the coercive field is exceeded. This characteristic leads to polarization hysteresis, ie. the systems response to a field depends on it's history. An applied AC field will result in a polarization hysteresis loop as shown above.

Domain Switching

The previous picture might suggest that in a ferroelectric all the dipoles switch at the same time. However this does not usually happen. At applied fields much lower than the field that would be required for the whole crystal to switch at once a ferroelectric material will switch by a process of domain nucleation and growth. Nucleation usually occurs at particular locations in a sample where a particular polarization direction is favored over another and domains will nucleate at the same sites each time the sample switches (i.e. nucleation is inhomgenous). The time scale for domain growth varies strongly on the strength of the applied field and the material and sample geometry, however it is usually seen that the forward growth of domains occurs first and is much faster than the subsequent sideways growth.

Electrostatic boundary conditions

If we consider a uniformly poled ferroelectric slab with polarization P there is a uniform electric displacement D. Electric displacement can only change if there is free charge, so unless there is a electrode to provide screening charged ions will be attracted to the surface or the slab will develop a domain structure so that it does not have an overall electric displacement. It should be noted that the size and direction of the polarization is also highly dependent on the mechanical boundary conditions, or strain, applied to the slab.

Electrostatics of superlattices

An example superlattice

Sputter deposition



Thin Film X-ray Diffraction


An X-ray diffractometer is an essential tool for the characterization of thin films. In particular size effects, such as the one shown here for a 150nm thick PZT film on STO can be used to calibrate growth rates accurately, an essential step in preparing to fabricate superlattices.

Superlattice X-ray Diffraction

X-ray diffraction on superlattices can be used to obtain:

  • Superlattice periodicity
  • Total thickness of sample
  • Quality of sample
  • Degree to which coherency with substrate has been achieved
tutorials/superlattices.txt · Last modified: 2010/08/03 22:25 (external edit)
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