The 2023 list of quantum device simulation

Introduction

With all this fuss about quantum things, I think it’s high time I updated the list of simulators post I did some years ago. I am completely remaking this post, instead of adding to the previous, because now things are more clear to me and to the community at large where each subdomain lies. Since this will be a list from my own experience, feel free to contact me with the software that you would like to see added in this list.

Also, it’s a list for technologies that can host Quantum Information carriers based on solid state device types, that is: semiconducting, superconducting, or even photonic. That is, with the possibility of inclusion of materials science and effects like topological. It is not about trapped ions and optical lattices, although apparently, you can do that too with Wannier functions, a method I will mention here.

Materials

In any type of solid state simulation, the materials play a fundamental role. However, we don’t always have to do some quantum mechanics simulation for different materials in order to do a simulation of the final device. This is because many of the effects get ‘wrapped up’ in simple variables, or do not affect the performance of the device.

Automating device data analysis

Lately, there have been some efforts to incorporate machine learning in experimental measurements, which are generally quite known in the community, and especially the quantum one (see here for example). While these types of work are currently ‘hot’, I decided to do a small post here about the small cousin of ML, which is automation. That is: Extracting information from large datasets of experiments.

This came about from my recently published work done at Grenoble, in which I had the chance to work with a large number of well-organized experiments. And I think it goes nicely with my previous post which is about automation in materials simulation.

Here, instead, I will present some common methods of extracting pinch-off voltages using Python. I did a previous post on a similar subject. Together they can be quite handy for extracting information fast from 1D data. Of course, they can be generalized for 2D also, but the here we focus on device measurements and not spectroscopy. In fact, for the 2D plots I analysed, I handled them as a list of 1D data, so I applied immediately similar routines, instead of 2D ones.

My experience with aiida

Me and aiida go way back, but sadly, I never got the opportunity to use it extensively until now. Lately, as I got more exposure, I feel the same as the first time I started experimenting with it: Lost!

I decided to do this post, not to do criticism – if anything, I am the last person to do it, as I have one or two repos that I need to find the time to finish documenting. I just like the idea and its purpose and would like to talk about it as a user, so that you don’t feel alone. Since it’s changing versions fast, it’s quite possible the issues I point out here will be solved soon.

If someone doesn’t know of what aiida is, it is an automation software than lets you run multiple simulations, read the outputs, adjust, re-run and basically it is like a little robot that does a lot of the boring work for you, while it’s fairly updated on new methods and algorithms (check this example).

‘Connecting the nodes’ in the knowledge graph: Renormalization

One of the things that excites me about learning is the process of creating connections between different things. I believe, this is also the process of learning that is persistent throughout our lives, and in my opinion it can be as powerful as the process of learning in our childhood.

I therefore decided to start writing down notions that I read and which connect to notions I had read before. It’s funny how this can also be converted into a ‘computational’ network, and observe how clusters are formed between its nodes. The difference is that here I will not be connecting words between them, but rather presenting the same word, with the same conceptual meaning, used in different sub-domains in physics. Maybe the most appropriate measure here is when the network would ‘break down’. That is, when the meaning between different uses will change completely.

The Finite Elements Method convergence survival guide

Ok, people, let’s face it. Many of us had no idea about the maths behind Finite Elements Method (FEM) simulations when we initially started using them. And most of us have felt that horrible feeling when we repeatedly saw the message ‘No convergence’ instead of a nice output. What is horrible about it is that, unless you or your group develops the software, you probably have no idea where to start looking for fixing the problem.

I heard from a lot of people in my field (electronics) that they have felt discouraged with FEM and did not even want to touch it. But I’m here to tell you that there is hope! I decided to write this guide after almost 10 years of using this type of software (on and off), first for nanoelectonics and then for semiconducting quantum technologies. It might be that the issue is actually more important in the latter, because of the differences in magnitude (or the scale of things) between classical and quantum effects (yes, not everything is quantum in quantum TCAD). But this is a user’s and not developer’s guide, so I will also keep it math-and code-free.

3D and 2D reciprocal lattice vectors (Python example)

When I started using Density Functional Theory and, even more, when trying to re-create its results in a meaningful piece of material, like a nanoribbon or a nanowire, a lot of the problems came during geometry creation. This is natural, as DFT is a theory to derive quantities like eigenenergies, in a crystal lattice with periodicity. But when trying to switch to a model that is finite in one or more directions, you have to start a sort of mix and match procedure.

During this time (and assuming you are not the one who writes the software), visualizing vectors is maybe the less useful thing to do. Still, there are cases where you need it in order to get a better understanding of things, like visualizing Weyl points.

Extracting pinch-off and threshold voltages in quantum transistors

Many times I needed to extract threshold voltages from experimental results. I remember in my PhD days, this was quite a debate, and we could generally agree there is no optimum way of doing it. The problem mostly lied in that you are not exactly sure in which part of the plot the current starts to flow, or the channel is depleted. In room temperature transistors, this was mainly due to the intermediate region of thermal population of the bands. In quantum transistors, we are playing in the low temperature field and most of the time dopants are thought to be frozen.

What is really certain is that all voltages that you compare against will need to be extracted using the same method.

Since what we are interested in is changes in the curvature of the plot, we expect to play around with derivatives a lot. But for this, there is the extra problem that experimental results can be very noisy. Once you take the derivative, you introduce further noise, that goes even worse in the second derivative (see figure below).

Characteristics of a transistor with 2 pinch-off positions in the classical regime. First derivative (blue plot) shows pronounced amount of noise.

On the universality of Landau theories

There is a lot of buzz going on about topological materials and the quantum Hall effect these days that mark the 40 years since its discovery. If you know a few things about topological materials, you will definitely know that the theory behind them is about a macroscopic mechanism that originates from microscopic (quantum) effects.

There is a similar class of problems, maybe less famous at the present time, namely that of polarization in materials, which has its own counterpart “The modern theory of polarization” that was developed in the ’90s. What these two have in common is exactly the emergence of macroscopic phenomena from microscopic ones.

Vector potential with an angle to the periodic direction

One of the most difficult aspects in Tight Binding models is the incorporation of the magnetic field. And that is because a lot of the things that exist in simple analytical expressions in quantum mechanics, change when we are talking about a Tight Binding model, and especially one derived from First Principles using Density Functional Theory as that discussed here.

One of the problems that could emerge is that there exists an angle between the periodic direction and the direction the magnetic field is applied. This differs from the case of the Peierls phase, defined as,

Interview on ΒΗΜΑ Science

Our work at CEA in collaboration with CNRS has been published on the printed version of the Greek newspaper ΒΗΜΑ. I am happy that the project I am currently working on and the way it connects to the work I was doing at Aristotle University of Thessaloniki have gained publicity.

You can find it on-line here (requires subscription):

https://www.tovima.gr/printed_post/i-kvantiki-yperoxilfsta-skaria/?fbclid=IwAR1NnkS8YSNVDYs7OCHQnAqsIAOJZHKqVZsb6GhZgxGi2HrCfWMbBDqz4v8