The maximum speed of signal transmission in microchips is about one petahertz (one million gigahertz), which is about 100,000 times faster than current transistors. Physicists from the Ludwig-Maximilians-Universität München, the Max Planck Institute of Quantum Optics and Vienna and Graz Universities of Technology have recently published this finding in the scientific journal Nature Communications (13, 1620 (2022). Whether computer chips of this maximum speed can ever actually be produced is, however, questionable. One of the study's lead scientists Dr. Marcus Ossiander was a former colleague in the attoworld-team. In the interview with Elizabeth Rayne he reveals the basic physics behind the latest results and how the team found that petahertz frequencies will be the ultimate limit of electronics.

 

What generates an electric current in a solid?

Starting from the very beginning, we talk about an electric current when charged particles (in this specific experiment electrons, but in other cases also protons, ions, or charged molecules) move through space. In free space, this usually means that there is an electric field that accelerates the charged particles. E.g., when you look at a battery, there is an electric field between its positive and its negative terminal. If you put an electron between the two battery terminals, it will start moving towards the positive terminal and we call that a current. In a solid material - which we usually need to build a computer or optical interconnect for technological reasons - the scenario is a bit more complicated: at any time in the solid, there are a lot of electrons around and they are moving in all directions. If you now average the movement of all those electrons you realize that - as a whole - their movement cancels (i.e., the same number of electrons are moving left as right). This means that although there is lots of movement, there is no net current. To induce a current we must somehow create an asymmetry in the electron movement, i.e., make more move left than right or opposite. To do this, we again want to apply an electric field (attach the two terminals of a battery to two spots of the solid). This makes most electrons *prefer* to go along the direction of the applied electric field.

 

What is the role of quantum mechanics here?

Electrons cannot always do what they (or we) want. If they can depends on the solid material and that is where quantum mechanics kicks in: all solids possess the (infamous) band structure. While a bit abstract at first, you can interpret it as a set of rules all electrons in a solid must obey, much like traffic rules in a city: there are speed limits that depend on the direction electrons want to go, there are speeds that are forbidden, but most importantly, there is only a limited amount of spaces available and every available space can only be taken by a single electron.

If you compare the three most important types of solids: metals, semiconductors, and dielectrics, they correspond to different filling levels of the band structure (the available states/spaces).

- Metals have lots of free space in the band structure. If you want to create a current, you can apply an electric field the electrons can react to it. This corresponds to late-night traffic in a city. Cars can go wherever and when you tell all of them to go a certain direction they will. Therefore, metals conduct currents well. In metals, we call the states that electrons are usually in the 'conduction band'.

- In semiconductors, all available states/spaces are taken, therefore, even if you apply an electric field, and the electrons would prefer to go one direction more than the other, they cannot just turn around because there are no available states/spaces. There is a way around this 'blockage' though: when you supply the electrons extra energy - e.g. by shining light on the semiconductor - you can put them in energy regions of the band structure that are normally not available to them but that have a lot of free spaces. Because there are so many free states, electrons that you kick in those energy regions are free to do whatever they want and can react to your electric fields - thus semiconductors can conduct currents after you shine light on them. In the city example think of rush hour - all streets are full and congested. Even if you ask cars to go another direction they cannot because the streets are so full. However, there are toll roads that are barely driven on because they are very expensive. If you pay the toll for the cars (shine the light), they are free to go anywhere you tell them because the toll roads are empty. In semiconductors, we call the normal states all electrons are in the 'valence band' and the extra states that are usually empty (the toll roads) the 'conduction band'. In short, when we want to conduct currents in semiconductors, we first must take electrons from the valence band and put them in the conduction band so they will conduct our current.

- Dielectrics are at first glance like semiconductors, all available states/spaces are taken, therefore, even if you apply an electric field, they cannot change their direction and there is no current. However, the toll roads are incredibly expensive, such that you can usually not make them conductive, even when you supply extra energy in the form of light.

One of the achievements in our current work is that we were able to create light pulses with very high photon energies, much larger than people can usually use. We call the energy of our light (similar to its 'color') vacuum ultraviolet or extreme ultraviolet. This means the light pulses have more energy than infrared light, visible light, and ultraviolet light. Therefore, we can supply large energies to the electrons in dielectrics and use them like other people would use semiconductors. This allows us to design switches and transistors that can react incredibly fast.

 

Why is it possible for electrons to absorb very different energies from laser pulses, ultimately causing the amount of energy transferred to the electrons to not be precisely defined?

There are two parts to answer this question. The first part is how our laser light looks: the laws of physics (Heisenberg Uncertainty) require that ultrashort laser pulses are always broadband. When you make a laser pulse shorter, you make its spectrum broader. Therefore, our very short laser pulses always contain many different colours (i.e., energies) that can be absorbed. This is exactly the opposite of what many people often expect a laser is: one pristine colour of exactly one wavelength (or energy) but nonetheless, all our light is fully coherent.

The second part comes back to the band structure from above: the absorption of laser light that is relevant to technology takes an electron from the valence band and puts it into the conduction band. The exact energy that is required for this transition is given by the difference between the energy of the state you take the electron from and the energy of the state you put it into. They are called 'bands' because, in a solid, there are many allowed states very close to each other, in contrast to the case of an atom, where the allowed energy levels are precisely defined and 'sharp'.

Therefore, when you shine a short light pulse - which contains many energies - on a solid, you compare what are all the possible energy differences between all the states in the valence and the conduction band. Then you compare those many energy differences with the many energies contained in your light pulse to see which energies can be absorbed. Usually, there is a broad overlap between those two sets causing the exact energy transferred to not be precisely defined because there are so many allowed possibilities.

 

Going off that, how do the electrons react differently to the electric field depending on how much energy they carry?

When you know the energy an electron carries in a solid, you can check in which part of the band structure of a solid the electron currently is. This means you can check the rules which the solid currently imposes on the electron and the electron cannot escape those rules. These rules can include, how fast an electron moves and in which direction it will move when you apply an electric field. It sounds peculiar but sometimes, the rules say that even if you apply a field in a certain direction, the electron must move in the opposite direction according to the band structure and that is what the electron will do then.

 

How did you finally determine that one petahertz is the upper limit for optoelectronic processes, and why are realistic upper limits (for technology like computers etc.) much lower?

Using our novel extreme ultraviolet injection technique, we were able to push electrons from the valence to the conduction band in a dielectric within one femtosecond, i.e., we switched the dielectric from an isolator to a conductor at the speed necessary to realize a petahertz switch. By exactly tracking what the electrons do after we put them in the conduction band, we could show that any faster switching time would put them into regions of the band structure where they will cause harm to the signals we would like to transmit. This is explained by a combination of the previous questions:

Switching faster and faster will require shorter and shorter light pulses. That means, the light pulses must also get spectrally broader and they will cause electrons to go in more regions of the band structure. Switching beyond a petahertz would cause the electrons to go to band structure regions where the electrons suddenly move in the opposite direction than we tell them to, deteriorating the switching performance. By comparing the band structure of the material we used (lithium fluoride) with the band structure of other materials, we could show that we pretty much reached the maximum of what is theoretically possible for any existing material before these reversal effects occur.

However, the experimental setup we used for this experiment is roughly the size and cost of a one-bedroom apartment - and this is to realize a single switch. It will still take a while to miniaturize the lasers and setups needed to reach such extreme time scales in millions of parallel switches required for a processor and at a size and cost that can make it into our living rooms.