Landau was right! Ferroelectrics exhibit negative capacitance

Landau was right! Ferroelectrics exhibit negative capacitance

Lev Landau, who was an exceptional theoretical physicist and a Nobel laureate, probably never would have foreseen how his groundbreaking work on the theory of phase transitions in 1937 would lead to continuous heated debate among electronic device researchers more than 70 years later. The origin of these controversial discussions was the proposal by Sayeef Salahuddin and Supriyo Datta in 2008 that ferroelectric materials could exhibit a negative capacitance, which would enable transistors to overcome the fundamental Boltzmann-limit of power dissipation, one of the biggest roadblocks for further miniaturization.

How does this relate to Landau? A popular phenomenological model for ferroelectrics was conceived in the 1940s based on his aforementioned theory of phase transitions, thus often just called Landau theory. In its simplest form, Landau theory predicts a negative capacitance in ferroelectric materials, which, however, by itself is unstable. Only when adding a positive capacitance material (e.g. a dielectric), according to the theory, the negative capacitance could be stabilized and therefore would be useful for devices. The negative capacitance in Landau theory stems from the double-well energy landscape of the ferroelectric, which manifests itself as an 'S'-shaped polarization-electric field characteristic. However, no experimental proof of such an 'S'-shaped curve was ever reported, casting doubt on the idea to use ferroelectric negative capacitance to improve electronic devices.

I began working on this problem when I was visiting the lab of Prof. Salahuddin at the University of California, Berkeley in 2016. During that time, I had the pleasure to work with Asif Khan (now professor at Georgia Tech), who was one of the first scientists to observe negative capacitance effects in ferroelectrics and from whom I learned a lot about the intricacies of measuring and understanding these phenomena. At the same time, an important paper was published by the group of Prof. Cheol Seong Hwang from Seoul National University using fast voltage pulses (instead of the typical small-signal capacitance measurements) to observe negative capacitance in ferroelectric/dielectric capacitors. While mostly overlooked by the community, this publication would become the blueprint for the experiments that led to our discovery of the 'S'-shaped curve, but at the time I did not fully grasp its implications.

When I returned from Berkeley to start my Ph.D. at NaMLab in Dresden, Germany in September 2016, my colleague Franz Fengler suggested to fabricate a first set of ferroelectric/dielectric capacitors based on some back-of-the-envelope calculations I did using basic Landau theory. However, when I could not observe a negative capacitance using small-signal capacitance measurements on these samples, I was quite disappointed and concluded that the simple Landau approach I used was wrong. Ironically, these were the exact same samples which we later used to confirm negative capacitance in agreement with Landau theory as reported in our paper published in Nature. During the following year, I had almost forgotten those first samples and mostly focused on improving my theoretical understanding of negative capacitance and fabricating new samples.

In January 2018, when I finally decided to try out the fast pulsed measurements Prof. Hwang's group suggested in 2016, I remembered these old samples. In the first attempt, I was able to measure a capacitance enhancement, which is indicative of negative capacitance and I went for lunch to further think about the results. While doing so, it occurred to me that I could simply calculate the electric field and polarization of the ferroelectric from the measured data, which should give me a hint of what was happening in the material. When I came back to the office and re-plotted the data, a beautiful 'S'-shaped curve appeared on the screen, exactly what Landau theory predicted and which nobody had managed to see before. This first discovery of the 'S'-shaped curve would not have been possible without the support of my colleagues at NaMLab and TU Dresden, as well as our collaborators from NIMP in Romania who did some further physical analyses of our samples to exclude other possible explanations for these results. After additionally confirming the measurement on a different set of samples, I asked Asif Khan about his opinion on the data and he encouraged me to submit a manuscript to Nature, which, in hindsight, I do appreciate a lot. 

When I recently gave a talk on the possibility of measuring the 'S'-shaped curve in a ferroelectric at the International Electron Devices Meeting in San Francisco in December 2018, one of the determined opponents of negative capacitance commented something along the lines of "This is not what Landau had in mind.", which was probably meant as criticism, but to which I would respond in the following way. While Lev Landau indeed never had a negative capacitance in mind when he worked on his famous theory of phase transitions all those decades ago, our discovery is still a testament to the universality and timeless elegance of his theories. To conclude with a quote from one of my former colleagues at NaMLab, Milan Pešić, whose first reaction to the measured 'S'-shaped curve I distinctly remember: "Landau was right all along!"

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