Ferroelectric Memory: Materials Science, Explained.

There’s something irresistibly satisfying about rolling your fingers over a textured surface and watching the fibers fold over into a pattern. Back and forth, you trace the fibers with your hand and watch them align in the direction of your movement. It might be just as satisfying as making it a scientific analogy – in this case, to ferroelectric memory.

When we trace our finger along a microfiber (or sequin) surface, we are effectively encoding information. If you drew your name in the microfiber couch, for example, it would stay that way forever until an equal and opposite force would erase it. We can apply this phenomenon to ferroelectrics – a type of material that can reorient in the presence of an electric field. When we apply a bias to the material, we can encode information and it’ll stay there without the need of an external force acting upon it. Not unless we apply a bias of the same magnitude but opposite direction, e.g., your hand rolling over the couch’s surface in the opposite direction.

What we have just described is the idea of ferroelectric memory. We can encode information into tiny chips, like the ones in your phone that you use to store pictures, phone numbers, and whatever you like. But what makes ferroelectric memory so enticing compared to traditional forms of random-access memory (RAM) is that it is non-volatile. Meaning, if we left the microfiber couch untouched, the name would be there for a very long time, even after you took away the source of the initial writing.

Ferroelectric memory, in contrast to standard commercial memory devices today, poses a significant advantage in power savings because memory can be stored without a constant supply of electricity. A group at Northwestern estimates that if we switched all our devices to ferroelectric memory, the cost savings in electricity would be 6 billion USD annually for the United States alone.

The crystalline nature of matter

But what is the underlying phenomenon that gives certain materials this exciting property? The answer is ferroelectricity: a characteristic of materials which have a spontaneous electric polarization. To understand this definition fully, let’s break it up and examine each component individually. The dictionary definition of spontaneous suggests that the material performs something “suddenly or instantly.” The second part, “electric” indicates that we need a source of power, or bias, like the same one we used in the microfiber example. Lastly, “polarization” indicates that the material can orient itself in a particular direction (think of a similar “polarizing” political debate as having two distinct sides). Combining these ideas, we can now understand that a ferroelectric material will orient itself suddenly when exposed to some source of bias.

But what does it mean for a material to “orient” in a specific direction? And at what scale does this occur?

We’ll have to consider the crystalline nature of matter to answer these questions. In solid-state matter, atoms are arranged in periodic building blocks called crystals whose specific size, shape, and position can significantly affect its properties. In a non-ferroelectric crystal, these atoms are arranged symmetrically so that the net, spatial charge in the crystal is zero. This type of atomic positioning is called centrosymmetric. One good example of a centrosymmetric crystal is diamond – it has a trihedral structure with symmetrical covalent bonds between all carbon atoms which results in no net electric field.

 In ferroelectric crystals, however, one of the atoms can be shifted in a way that is off-centered and results in an asymmetrical crystal structure. This creates a directional net charge, or dipole moment. This type of crystal positioning is called non-centrosymmetric and it the root of all ferroelectricity.

Centrosymmetric (left) and noncentrosymetric (right) crystal structure. The slight elongation of the c-axis causes the center atom to be off-centered, creating a net dipole moment in the crystal.

Centrosymmetric (left) and noncentrosymetric (right) crystal structure. The slight elongation of the c-axis causes the center atom to be off-centered, creating a net dipole moment in the crystal.

The directionality of ferroelectric crystals

A dipole is fundamentally a vector, meaning it has both a magnitude and a direction. This direction is what we call the orientation, or polarization direction, of the ferroelectric crystal. We can think of this polarization direction as essentially an indicator of the dipole pointing up, down, left, or right. Not only do the crystals in a ferroelectric orient in a specific direction, but they also do this in groups.

We can go back to thinking about the sequin pillow. When we brush our finger across its surface, we aren’t just reorienting one sequin, but a group of sequins that add up together to form a pattern. Regions in a ferroelectric with the same polarization direction are called domains.

Another example we can use to understand domains is a large city grid like Manhattan or Chicago. There are many roads oriented parallel to one other forming a unidirectional region. That is, until they encounter another region with roads and neighborhoods going in a different direction. We can also think of the street that borders regions with different directions as a domain wall, or boundary in which the orientation changes suddenly. In ferroelectric materials the width of the domains are typically on the order of several tens of nanometers to one micrometer – for comparison, that is three times smaller than the width of a human hair. The width of a domain wall is even smaller and is estimated to be around 100-150 atoms.

Plan of the City of New York, with the recent and intended Improvements, Drawn from actual survey by William Bridges City Surveyor; AD 1807.

Plan of the City of New York, with the recent and intended Improvements, Drawn from actual survey by William Bridges City Surveyor; AD 1807.

Domain walls of Lead zirconia titanate after various heat treatments. The periodic stripes are similar to city grids of New York. (Nature Communications, doi: 10.1038/ncomms5677).

Domain walls of Lead zirconia titanate after various heat treatments. The periodic stripes are similar to city grids of New York. (Nature Communications, doi: 10.1038/ncomms5677).

Connecting crystals to computers

We can take advantage of ferroelectrics’ unique property of switchable polarization to encode information into our electronics. By applying a bias, we can orient the ferroelectric’s dipole to a specific direction. As seen in the figure below, when we apply an electric field the dipoles will orient themselves in the direction of the electric field. Following the rule of “opposites attract” the negative ends of the dipole will face the positive direction of the current, and vice versa (for a more in depth understanding of the driving force that causes ferroelectric switching see Landau theory). We call this behavior domain switching.

The fundamental definition of ferroelectrics tells us that when we take away this bias, the dipoles will still maintain the form of their previous state. While the material will relax a little bit when we remove the electric field, it will still maintain most of its directionality. We call this the remnant polarization and is the property of ferroelectric materials we use to store information.

Ferroelectric domains represented as arrows will switch in the direction of a biasing field. The positive ends of the domain will face the negative bias and the negative ends will face the positive bias. After the bias is removed, most of the directionality will stay in the ferroelectric material.

Ferroelectric domains represented as arrows will switch in the direction of a biasing field. The positive ends of the domain will face the negative bias and the negative ends will face the positive bias. After the bias is removed, most of the directionality will stay in the ferroelectric material.

To bridge the gap between dipole orientation and computer memory, it’s helpful to think of “up” and “down” as 1 and 0, respectively. By applying an electric field to a ferroelectric device, we can start to encode information as arrays of 1’s and 0’s. The best part about this is when we take away the electric field, the information is still stored due to the remnant polarization which allows the ferroelectric to “remember” its previous state.

How we analyze and study ferroelectrics

 Just to make things a little more interesting we’re going to introduce the concept of a ferroelectric hysteresis loop. Hysteresis is the dependence of a material’s history on its current state. As you might have guessed, not all ferroelectrics are created equal, and we sometimes want to investigate how “good” they are at being ferroelectric. To do that we measure an electric field-polarization (P-E) loop. For this type of measurement, we apply a bias just as in the case to store information, but we monitor the device’s polarization as a function of the magnitude and direction of the bias. A domain will not switch from “up” to completely “down” until the magnitude of the bias is large enough. In fact, the domains will reorient themselves gradually as we increase the electric field or driving force. This gives rise to a hysteresis as every future polarization state is dependent on the previous state.

Polarization-Electric Field (P-E) Loops of a classical ferroelectric and dielectric. Each fully saturated state represents an “up” or “down” domain orientation. A dielectric behaves linearly in response to an electric field, so its characteristic P-E loop is a straight line.

Polarization-Electric Field (P-E) Loops of a classical ferroelectric and dielectric. Each fully saturated state represents an “up” or “down” domain orientation. A dielectric behaves linearly in response to an electric field, so its characteristic P-E loop is a straight line.

Polarization does not vary linearly with an electric field for ferroelectric materials. The shape of our P-E loop will have a characteristic appearance, as seen above. Other materials like dielectrics do not have a spontaneous polarization and their P-E loops will resemble a straight line. Certain features of the P-E loop, such as where it crosses the x- and y-axis gives us characteristic information about our ferroelectric material. The up and down states correspond to the points at which the ferroelectric is completely saturated either in the positive or negative direction, respectively.

Let’s get technical

Here are some major characteristics we look at when we evaluate P-E loops:

  • Remnant polarization: When E is zero, i.e. crosses the x-axis, the material retains most of its previous directionality and is said to have a remnant polarization corresponding to this value.

  • Saturation polarization: The limit at which applying any additional electric field will not result in a higher polarization state; a completely up or down state.

  • Coercive Field: A measure of the strength of the reversing polarizing field E which is required to erase the remnant polarization of the material.

P-E loops are the bread and butter of the ferroelectrics’ community. Materials scientist (and electrical engineers) use P-E loops to evaluate and test new ferroelectric materials in addition to other techniques.

In summary, the unique noncentrosymetric properties of ferroelectric materials allows us to store information by reorienting domains in the presence of an electric field. We can erase the memory by applying a field in the negative direction, and we can also store information without an external supply of power. Researching ferroelectric materials helps us to enable better functioning electronic devices which will hopefully consume less power and store more information in the future.

Further Suggested Reading:

Ferroelectric Ceramics: Tutorial reviews, theory, processing, and applications, (chapter 2) L. Eric Cross, N. Setter, E.L. Colla (1993).

Radiant Technologies, Ferroelectric Devices. https://www.ferrodevices.com/1/297/files/Presentation2-FerroelectricCapacitors.pdf

Takasu, H. Journal of Electroceramics (2000) 4: 327. https://doi.org/10.1023/A:1009910525462