Power and computing

The Wall Street Journal last week had an article (sorry about the paywall) titled "There’s Not Enough Power for America’s High-Tech Ambitions", about how there is enormous demand for more data centers (think Amazon Web Services and the like), and electricity production can't readily keep up.  I've written about this before, and this is part of the motivation for programs like FuSE (NSF's Future of Semiconductors call).  It seems that we are going to be faced with a choice: slow down the growth of computing demand (which seems unlikely, particularly with the rise of AI-related computing, to say nothing of cryptocurrencies); develop massive new electrical generating capacity (much as I like nuclear power, it's hard for me to believe that small modular reactors will really be installed at scale at data centers); or develop approaches to computing that are far more energy efficient; or some combination.  

The standard computing architecture that's been employed since the 1940s is attributed to von Neumann.  Binary numbers (1, 0) are represented by two different voltage levels (say some \(V\) for a 1 and \(V \approx 0\) for a 0); memory functions and logical operations happen in two different places (e.g., your DRAM and your CPU), with information shuttled back and forth as needed.  The key ingredient in conventional computers is the field-effect transistor (FET), a voltage-activated switch, in which a third (gate) electrode can switch the current flow between a source electrode and a drain electrode.  

The idea that we should try to lower power consumption of computing hardware is far from new.  Indeed, NSF ran a science and technology center for a decade at Berkeley about exploring more energy-efficient approaches.  The simplest approach, as Moore's Law cooked along in the 1970s, 80s, and 90s, was to steadily try to reduce the magnitude of the operating voltages on chips.  Very roughly speaking, power consumption goes as \(V^{2}\).  The losses in the wiring and transistors scale like \(I \cdot V\); the losses in the capacitors that are parts of the transistors scale like some fraction of the stored energy, which is also like \(V^{2}\).  For FETs to still work, one wants to keep the same amount of gated charge density when switching, meaning that the capacitance per area has to stay the same, so dropping \(V\) means reducing the thickness of the gate dielectric layer.  This went on for a while with SiO2 as the insulator, and eventually in the early 2000s the switch was made to a higher dielectric constant material because SiO2 could not be made any thinner.  Since the 1970s, the operating voltage \(V\) has fallen from 5 V to around 1 V.  There are also clever schemes now to try to vary the voltage dynamically.  For example, one might be willing to live with higher error rates in the least significant bits of some calculations (like video or audio playback) if it means lower power consumption.  With conventional architectures, voltage scaling has been taken about as far as it can go.

Way back in 2006, I went to a conference and Eli Yablonovitch talked at me over dinner about how we needed to be thinking about far lower voltage operations.  Basically, his argument was that if we are using voltages that are far greater than the thermal voltage noise in our wires and devices, we are wasting energy.  With conventional transistors, though, we're kind of stuck because of issues like subthreshold swing.  

So what are the options?  There are many ideas out there. 

• Change materials.  There are materials that have metal-insulator transitions, for example, such that it might be possible to trigger dramatic changes in conduction (for switching purposes) with small stimuli, evading the device physics responsible for the subthreshold slope argument.  
• Change architectures.  Having memory and logic physically separated isn't the only way to do digital computing.  The idea of "logic-in-memory" computing goes back to before I was born.  
• Radically change architectures.  As I've written before, there is great interest in neuromorphic computing, trying to make devices with connectivity and function designed to mimic the way neurons work in biological brains.  This would likely mean analog rather than digital logic and memory, complex history-dependent responses, and trying to get vastly improved connectivity.  As was published last week in Science, 1 cubic millimeter of brain tissue contains 57,000 cells and 150,000,000 synapses.  Trying to duplicate that level of 3D integration at scale is going to be very hard.  The approach of just making something that starts with crazy but uncontrolled connectivity and training it somehow (e.g., this idea from 2002) may reappear.
• Update: A user on twitter pointed out that the time may finally be right for superconducting electronics.  Here is a recent article in IEEE Spectrum about this, and here is a youtube video of a pretty good intro.  The technology of interest is "rapid single-flux quantum" (RSFQ) logic, where information is stored in circulating current loops in devices based on Josephson junctions.  The compelling aspects include intrinsically ultralow power dissipation b/c of superconductivity, and intrinsically fast timescales (clock speeds of hundreds of GHz) because of the frequency scales associated with the Josephson effect.  I'm a bit skeptical, because these ideas have been around for 30+ years and the integration challenges are still significant, but maybe now the economic motivation is finally sufficient.

A huge driving constraint on everything is economics.  We are not going to decide that computing is so important that we will sacrifice refrigeration, for example; basic societal needs will limit what fraction of total generating capacity we devote to computing, and that includes concerns about impact of power generation on climate.  Likewise, switching materials or architectures is going to be very expensive at least initially, and is unlikely to be quick.  It will be interesting to see where we are in another decade.... 

Wind-up nanotechnology

When I was a kid, I used to take allowance money and occasionally buy rubber-band-powered balsa wood airplanes at a local store.  Maybe you've seen these.  You wind up the rubber band, which stretches the elastomer and stores energy in the elastic strain of the polymer, as in Hooke's Law (though I suspect the rubber band goes well beyond the linear regime when it's really wound up, because of the higher order twisting that happens).  Rhett Alain wrote about how well you can store energy like this.  It turns out that the stored energy per mass of the rubber band can get pretty substantial. 

Carbon nanotubes are one of the most elastically strong materials out there.  A bit over a decade ago, a group at Michigan State did a serious theoretical analysis of how much energy you could store in a twisted yarn made from single-walled carbon nanotubes.  They found that the specific energy storage could get as large as several MJ/kg, as much as four times what you get with lithium ion batteries!

Now, a group in Japan has actually put this to the test, in this Nature Nano paper.  They get up to 2.1 MJ/kg, over the lithium ion battery mark, and the specific power (when they release the energy) at about \(10^{6}\) W/kg is not too far away from "non-cyclable" energy storage media, like TNT.  Very cool!  

Moiré and making superlattices

One of the biggest condensed matter trends in recent years has been the stacking of 2D materials and the development of moiré lattices.  The idea is, take a layer of 2D material and stack it either (1) on itself but with a twist angle, or (2) on another material with a slightly different lattice constant.  Because of interactions between the layers, the electrons in the material have an effective potential energy that has a spatial periodicity associated with the moiré pattern that results.  Twisted stacking hexagonal lattice materials (like graphene or many of the transition metal dichalcogenides) results in a triangular moiré lattice with a moiré lattice constant that depends on twist angle.  Some of the most interesting physics in these systems seems to pop out when the moiré lattice constant is on the order of a few nm to 10 nm or so.  The upside of the moiré approach is that it can produce such an effective lattice over large areas with really good precision and uniformity (provided that the twist angle can really be controlled - see here and here, for example.)  You might imagine using lithography to make designer superlattices, but getting the kind of cleanliness and homogeneity at these very small length scales is very challenging.

It's not surprising, then, that people are interested in somehow applying superlattice potentials to nearby monolayer systems.  Earlier this year, Nature Materials ran three papers published sequentially in one issue on this topic, and this is the accompanying News and Views article.

• In one approach, a MoSe2/WS2 bilayer is made and the charge in the bilayer is tuned so that the bilayer system is a Mott insulator, with charges localized in exactly the moiré lattice sites.  That results in an electrostatic potential that varies on the moiré lattice scale that can then influence a nearby monolayer, which then shows cool moiré/flat band physics itself.
• Closely related, investigators used a small-angle twisted bilayer of graphene.  That provides a moiré periodic dielectric environment for a nearby single layer of WSe2.  They can optically excite Rydberg excitons in the WSe2, excitons that are comparatively big and puffy and thus quite sensitive to their dielectric environment.  
• Similarly, twisted bilayer WS2 can be used to apply a periodic Coulomb potential to a nearby bilayer of graphene, resulting in correlated insulating states in the graphene that otherwise wouldn't be there.

Clearly this is a growth industry.  Clever, creative ways to introduce highly ordered superlattice potentials on very small lengthscales with other symmetries besides triangular lattices would be very interesting.

The future of the semiconductor industry, + The Mechanical Universe

 Three items of interest:

• This article is a nice review of present semiconductor memory technology.  The electron micrographs in Fig. 1 and the scaling history in Fig. 3 are impressive.
• This article in IEEE Spectrum is a very interesting look at how some people think we will get to chips for AI applications that contain a trillion (\(10^{12}\)) transistors.  For perspective, the processor in my laptop used to write this has about 40 billion transistors.  (The article is nice, though the first figure commits the terrible sin of having no y-axis number or label; clearly it's supposed to represent exponential growth as a function of time in several different parameters.)
• Caltech announced the passing of David Goodstein, renowned author of States of Matter and several books about the energy transition.  I'd written about my encounter with him, and I wanted to take this opportunity to pass along a working link to the youtube playlist for The Mechanical Universe.  While the animation can look a little dated, it's worth noting that when this was made in the 1980s, the CGI was cutting edge stuff that was presented at siggraph.

Electronic structure and a couple of fun links

Real life has been very busy recently.  Posting will hopefully pick up soon.  

One brief item.  Earlier this week, Rice hosted Gabi Kotliar for a distinguished lecture, and he gave a very nice, pedagogical talk about different approaches to electronic structure calculations.  When we teach undergraduate chemistry on the one hand and solid state physics on the other, we largely neglect electron-electron interactions (except for very particular issues, like Hund's Rules).  Trying to solve the many-electron problem fully is extremely difficult.  Often, approximating by solving the single-electron problem (e.g. finding the allowed single-electron states for a spatially periodic potential as in a crystal) and then "filling up"* those states gives decent results.   As we see in introductory courses, one can try different types of single-electron states.  We can start with atomic-like orbitals localized to each site, and end up doing tight binding / LCAO / Hückel (when applied to molecules).  Alternately, we can do the nearly-free electron approach and think about Bloch waves.  Density functional theory, discussed here, is more sophisticated but can struggle with situations when electron-electron interactions are strong.

One of Prof. Kotliar's big contributions is something called dynamical mean field theory, an approach to strongly interacting problems.  In a "mean field" theory, the idea is to reduce a many-particle interacting problem to an effective single-particle problem, where that single particle feels an interaction based on the averaged response of the other particles.  Arguably the most famous example is in models of magnetism.  We know how to write the energy of a spin \(\mathbf{s}_{i}\) in terms of its interactions \(J\) with other spins \(\mathbf{s}_{j}\) as \(\sum_{j} J \mathbf{s}_{i}\cdot \mathbf{s}_{j}\).  If there are \(z\) such neighbors that interact with spin \(i\), then we can try instead writing that energy as \(zJ \mathbf{s}_{i} \cdot \langle \mathbf{s}_{i}\rangle\), where the angle brackets signify the average.  From there, we can get a self-consistent equation for \(\langle \mathbf{s}_{i}\rangle\).  

Dynamical mean field theory is rather similar in spirit; there are non-perturbative ways to solve some strong-interaction "quantum impurity" problems.  DMFT is like a way of approximating a whole lattice of strongly interacting sites as a self-consistent quantum impurity problem for one site.  The solutions are not for wave functions but for the spectral function.  We still can't solve every strongly interacting problem, but Prof. Kotliar makes a good case that we have made real progress in how to think about many systems, and when the atomic details matter.

*Here, "filling up" means writing the many-electron wave function as a totally antisymmetric linear combination of single-electron states, including the spin states.

PS - two fun links:

• Don't forget to fill out your grant reports, or you can hold up the works for an entire university!
• PIs, don't forget to keep running on the funding hamster wheel!

Thoughts on undergrad solid-state content

Figuring out what to include in an undergraduate introduction to solid-state physics course is always a challenge.   Books like the present incarnation of Kittel are overstuffed with more content than can readily fit in a one-semester course, and because that book has grown organically from edition to edition, it's organizationally not the most pedagogical.  I'm a big fan of and have been teaching from my friend Steve Simon's Oxford Solid State Basics, which is great but a bit short for a (US) one-semester class.  Prof. Simon is interested in collecting opinions on what other topics would be good to include in a hypothetical second edition or second volume, and we thought that crowdsourcing it to this blog's readership could be fun.  As food for thought, some possibilities that occurred to me were:

• A slightly longer discussion of field-effect transistors, since they're the basis for so much modern technology
• A chapter or two on materials of reduced dimensionality (2D electron gas, 1D quantum wires, quantum point contacts, quantum dots; graphene and other 2D materials)
• A discussion of fermiology (Shubnikov-DeHaas, DeHaas-van Alphen) - this is in Kittel, but it's difficult to explain in an accessible way
• An introduction to the quantum Hall effect
• Some mention of topology (anomalous velocity?  Berry connection?)
• An intro to superconductivity (though without second quantization and the gap equation, this ends up being phenomenology)
• Some discussion of Ginzburg-Landau treatment of phase transitions (though I tend to think of that as a topic for a statistical/thermal physics course)
• An intro to Fermi liquid theory
• Some additional discussion of electronic structure methods beyond the tight binding and nearly-free electron approaches in the present book (Wannier functions, an intro to density functional theory)

What do people think about this?

Items of interest

The time since the APS meeting has been very busy, hence the lack of posting.  A few items of interest:

• The present issue of Nature Physics has several articles about physics education that I really want to read. 
• This past week we hosted N. Peter Armitage for a really fun colloquium "On Ising's Model of Magnetism" (a title that he acknowledged borrowing from Peierls).  In addition to some excellent science about spin chains, the talk included a lot of history of science about Ising that I hadn't known.  An interesting yet trivial tidbit: when he was in Germany and later Luxembourg, the pronunciation was "eeesing", while after emigrating to the US, he changed it to "eye-sing", so however you've been saying it to yourself, you're not wrong.  The fact that the Isings survived the war in Europe is amazing, given that he was a Jew in an occupied country.  Someone should write a biography....
• When I participated in a DOD-related program 13 years ago, I had the privilege to meet General Al Gray, former commandant of the US Marine Corps.  He just passed away this week, and people had collected Grayisms (pdf), his takes on leadership and management.  I'm generally not a big fan of leadership guides and advice books, but this is good stuff, told concisely.
• It took a while, but a Scientific American article that I wrote is now out in the April issue.
• Integrating nitrogen-vacancy centers for magnetic field sensing directly into the diamond anvils seems like a great way to make progress on characterizing possible superconductivity in hydrides at high pressures.
• Congratulations to Peter Woit on 20 (!!) years of blogging at Not Even Wrong.