Course announcements

Retake exam

This announcement is a copy of the forum announcement.
If you have questions, please ask them on the course forum.

Hello everyone!
On Wednesday 24/6 at 9:00 we will have the retake exam. The exam will take 3 hours (or 3:30 if you are eligible for extra time). It will take place at Flux Hall C. If you signed up late for the exam in Osiris, we may not let you in with everyone; however, we will let you in as soon as the exam starts.
On the same day, there will be a public-transport strike. Please take this into account when planning your trip to Flux Hall C, and keep an eye on Brightspace and TU Delft communication for general updates.
The retake exam counts for 100% of the course grade, plus the minitest bonus. The retake is designed like the final exam, and the minitest bonus works exactly as for the final exam.
Just like before, the formula sheet will be included with the exam. The current version is attached here: formula_sheet_combined_duplex.pdf.
Good luck!

Attachments:
- formula_sheet_combined_duplex.pdf: exams/formula_sheet.pdf

Lecture 15: overview I

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hello everyone!
We have now covered all of the course contents, and the final exam will take place next week. We would like to use this week as an opportunity to provide an overview of the course materials and answer all the open questions that you may have.
As usual, if there are any topics that you would like covered, please ask below.

Lecture 14: Doping and devices

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.In the final lecture of the Solid State Physics course, we take a look at what usually gets hidden behind the word “applications”.
So far, we have focused mainly on understanding matter as it appears in nature. This time we shift perspective and ask how the same models can be used to design matter. Building on the previous lecture, Anton will explain doping, a widely used way of controlling the occupation of the valence and conduction bands in equilibrium by changing the composition of a material. Doping is the point where the course starts to turn visibly from explanation into engineering.
From there we move to devices and see how some of the most important solid-state inventions arise from combining semiconductors in clever ways using concepts that should now feel familiar.
Don’t forget to post your questions and/or comments below!

Lecture 13: Semiconductor physics: Basic principles

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Good afternoon, everyone!
In the final week of the Solid State Physics lectures, we will first combine what you have learned so far to describe the basic principles of conduction in semiconductors, which will then open a path to understanding how it can be controlled. Semiconductors are especially interesting because they sit right at the boundary between conductors and insulators, and that is exactly what makes them so controllable.
We will build directly on the last week’s introduction to the electronic band structure and we will focus on the occupation of the valence and conduction bands while changing the familiar perspective a bit.
And since it has been a while already, it will be helpful to revise some of the concepts explained earlier in the course, especially in the free electron model and in the tight binding model:

how we described the motion of electrons and defined the current density in the Drude model.
how the number of electron at each energy in the system is defined by the system parameters and affected by the temperature, which we discussed alongside the Sommerfeld model.
how the presence of a lattice potential, and therefore the band structure, affects the motion of electrons, which we described using the group velocity and the effective mass in the Tight-binding model.

Can you imagine how the occupation of the valence and conduction bands changes at T > 0 \text{K}?
As always, please post below any questions that you may have!

Lecture 12: Band structures in 2D

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hi everyone,
After comparing the nearly free electron model and the tight-binding model, we now look more closely at the macroscopic consequences of band structure. By tracking the position of the Fermi level and the valence of atoms, we can understand why a material behaves as an insulator, a conductor, or a semiconductor, and how this connects to the absorption and emission of photons. We will also move from 1D to 2D and investigate both the tight-binding and nearly free electron pictures there.
Check out the lecture notes for this topic and please let us know any possible question you have.

Lecture 11: Nearly free electron model

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hi all,
In the next lecture we will continue our investigation of electrons in solids with one of my personal favorite topics - we will take an approach that is somewhat opposite to that of the tight binding model. Whereas tight binding assumes a very strong interaction with the atomic lattice, what will we find when we instead consider electrons as interacting weakly with the lattice? That is what makes the nearly free electron model so valuable: it gives us the opposite limit of tight binding, and seeing both side by side helps clarify what is essential and what is model-dependent.
We might be able to start out with the free electron dispersion relation and introduce a slight perturbation that represents the lattice potential! As you will learn, such an approach will also lead to the formation of bands and opening of band gaps in the dispersion relation. To climb that mountain together with us, please put the following tools in your lunch box: your diagonalization skills, your knowledge of Fourier series, and the concepts of dispersion relation and reciprocal space!
Please post any questions you have on the lecture notes below, and we can discuss those during the next session.

Lecture 10: X-Ray Diffraction

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hi everyone!
In the previous lecture we talked about crystal structures, where we introduced a framework to describe 3D structures using concepts including lattices, unit cells and miller planes.
In the coming lecture we introduce one additional concept: the reciprocal lattice, which is closely related to the reciprocal space (k-space) we have already encountered.
With this concept in hand, we can study how waves incident on a crystal are scattered by the lattice. The resulting diffraction patterns can be measured and used to infer microscopic crystal structure. That is what makes diffraction such a powerful experimental tool. For one example, see this paper, where X-ray and neutron diffraction were used to investigate water-DNA interactions.
Prior to reading the lecture notes, it will be useful to refresh

crystallographic terminology (lattice, basis, unit cells, etc.)
interference of waves due to their relative phase

Feel free to ask questions below, or during the lecture so that we can address them during the discussion.

Lecture 9: Crystal structure

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hello everyone,
Again a warm welcome to the first lecture after the midterm.
In the last two lectures, we applied 1D equations of motion to construct LCAO hamiltonian for two or more atoms in a unit cell. It’s time to start looking at a bigger picture - N atoms in 2D/3D.
In this lecture, we will classify different crystalline solids into groups by finding patterns in their crystal structure. By this means, we will find out why many of them exhibit similar behaviour. This is also the language that makes later topics such as diffraction and band structure manageable at all: before you can calculate anything, you need a compact way to describe the solid.
We will learn some new concepts such as lattice, basis, primitive and conventional unit cell of a crystal. It could be overwhelming to hear at the moment, but we hope that the interactive demonstrations in the lecture notes will help. Do check them out.
As usual, if anything is unclear, please post your questions here and we will address them during the lecture.

Minitest 2

This announcement is a copy of the forum announcement.
If you have questions, please ask them on the course forum.

Hi @course!
We have now delved into how the motion of electrons and phonons arises from the microscopic structure of materials. This means it’s time for the second minitest. Its organization is very similar to the first one, but here is all you need to know once again.
Impact
This is again a bonus minitest. Your two best minitest scores can each give you up to a 10% bonus on the points you miss on the final exam, so between this one and the first minitest you can already build up part of that bonus.
Allowed materials

The formula sheet will be included with the minitest.

We are composing the formula sheet collectively in this separate forum topic. If you want to contribute, keep your posts concise.

You may not use calculators (plus they won’t be useful anyway)

Minitest composition and an example
See this post for an example minitest and an explanation of how we design exams.
As always, let us know if you have any questions.
Time and location

The minitest will take place Monday at 13:45 in AS-Exam Hall 4.25.
You do not need to register in MyTUDelft or Osiris for the minitest.
The duration of the minitest is the usual 1.5 hours and not the full scheduled time. Of course, if you are eligible for extra time, you’ll get 15 more minutes.

Lecture 8: Many atoms per unit cell

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hey everyone!
Last lecture we revisited the assumptions behind the Debye model by studying a monoatomic chain and calculating its phonon dispersion relation. The result was different from Debye’s simplified picture, but it still had the two crucial features we wanted: linear behaviour at small k and a maximum frequency.
The system we studied last time is still very simple, while real solids are not. So in the next lecture we make the unit cell richer and ask how that changes the dispersion relation.
To answer that question, we extend the ideas from the previous lecture to a more complicated system. Instead of a monoatomic chain, we study a diatomic one. That extra structure already changes the dispersion relation in an interesting way, and you can see how in the lecture notes. One of the payoffs is that the distinction between acoustic and optical phonons finally starts to emerge naturally from the model.
To get a better understanding of the material discussed in the lecture, we expect you to study the lecture notes and briefly review the following topics:

Derive Newton’s equations of motion
Writing a system of equations in matrix form
Solving an eigenvalue problem
The material discussed in lecture 7

If you have any questions, feel free to ask them below!

Lecture 7: Tight-binding model

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hey, everyone!
Now that the first minitest is behind us, we turn to one of the central models of the course.
At the end of the last lecture, we saw how to start generalizing pairwise atomic interactions to bulk materials. Now it is time to push that further. The tight-binding model is one of the most useful tools in solid-state physics, and this lecture should help make ideas such as phonon dispersion relations and, later on, electronic band structures feel much more concrete.
Prior to reading the lecture notes, it will be useful to refresh the following:

The end of last lecture, where we derive the equations of motion for a triatomic chain
The Debye model, specifically the phonon dispersion relation used there
Be comfortable going to and from complex exponentials and trigonometric functions
Taylor expansions of trigonometric functions (\sin x \approx x, etc.)
The derivatives of inverse trigonometric functions (like \cos^{-1})

Remember the Fermi surface database from the lecture on the Sommerfeld model? This lecture is one of our first real steps toward understanding why those shapes look the way they do.
Be sure to ask your questions below for us to address in the lecture!

Lecture 6: Bonds and Spectra

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Good evening everyone!
After the last couple of lectures about electrons, we again turn our attention towards (you guessed it) phonons!
We discussed the LCAO model, which describes bound electrons. You may have noticed there is something off about this model: it predicts that the energy in a bond between two atoms is lowest when the atoms are right on top of each other!

This Thursday in the lecture on bonds and spectra we will fix that issue by adding a repulsive term to the potential. We will then see how the adjusted potential gives rise to phonons. Physically, this is where the shape of the interatomic potential starts turning directly into vibrational frequencies and measurable material properties. Comparing this new model with the Debye model, we will ask and answer several questions:

Where do the models agree? Where do they disagree?
What does our new model predict the speed of sound to be? (remember v_s was a phenomenological parameter of the Debye model)
Where does the cutoff frequency \omega_c come from in the Debye model?
How can we explain thermal expansion?

As always, you should read the lecture notes in advance. It might also be beneficial to recap the Debye model, since we will be comparing against it.
If you have any questions, be sure to ask them below.

Lecture 5: The LCAO Model

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Good afternoon, everyone!
In the first two weeks of the course, we focused on the collective action of phonons and electrons and how they give rise to macroscopic properties, such as heat capacity and electrical resistance. Now, we look even smaller, down to the level of atoms and the bonds between them. To do this, we’ll need some chemistry (no wait, please keep reading!).
We’ll only use the bare minimum we need. As you may suspect, the atomic details of solids greatly influence their behaviour, such as whether they are metals or insulators. And since we can’t solve the Schrodinger equation for systems of tens of electrons (let alone millions!), we need a new set of tools. The Linear Combination of Atomic Orbitals (LCAO) model is the first such tool we will discuss. This is also where the story of bands really begins: once atomic orbitals start combining into bonding and antibonding states, the road toward band structure is already open.
We ask that you review some quantum mechanics to get the most out of the lecture notes:

Recall the time-independent Schrodinger equation
Know how to diagonalize small matrices for computing eigenvectors and eigenvalues
Review the solution of the Schrödinger equation with a delta-function potential to brush up your quantum mechanics knowledge. You’ve learned this in QM1
Review the quantum numbers of a hydrogen atom (remember n,l,m etc.!)
Check out this excellent video that will save you a lot of time solving eigenvalue problems

https://www.youtube.com/watch?v=e50Bj7jn9IQ
As always, please ask any questions you have below!

Minitest 1

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hi @course!
We have learned how electrons and phonons give rise to macroscopic material properties such as heat capacity and conductivity. This means it’s time for the first minitest.
Below I list the practical things that you need to know about the minitest.
Impact
The minitests are bonus opportunities. Your two best minitest scores can each give you up to a 10% bonus on the points you miss on the final exam, so this first one is a good way to get used to the format and test your understanding.
Time and location

The minitest will take place Monday at 13:45 in AS-Exam Hall 4.25.
The duration of the minitest is the usual 1.5 hours. If you are eligible for extra time, you’ll get 15 extra minutes.
You do not need to register in Osiris for the minitest.

Allowed materials

The formula sheet will be included with the minitest.

We are composing the formula sheet collectively in this separate forum topic. If you want to contribute, keep your posts concise.

You may not use calculators (plus they won’t be useful anyway)

Minitest composition and an example
See this post for an example minitest and an explanation of how we design exams.

As always, let us know if you have any questions.

Lecture 4: Sommerfeld model

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hey everyone!
In the previous lecture we studied the Drude model, in which we modeled electrons as classical free particles which scatter of deviations from a perfect crystal, such as phonons and crystal impurities. However, there is a shortcoming to this model: we do not take the statistical properties of electrons into account. We know electrons are fermions and are thus subject to Pauli’s exclusion principle. This influences the distribution of electrons over different energy levels as no two identical electrons can occupy the same state.
We see that the statistical properties of electrons determine how they are distributed over different energy levels. Knowing this, we ask ourselves the following:

Are there any other physical quantities that influence the distribution of electrons?
And how does the distribution of electrons over different energies look like?

To answer these questions we will study the Sommerfeld free electron theory in the upcoming lecture. We no longer model electrons as classical free particles. Instead we consider the quantum mechanical description of free electrons and describe the distribution of electrons with a well-known distribution function. Do you know which function this is? One of the key conceptual shifts here is that Pauli statistics makes most electrons much less “available” than you might naively expect, which is why the electrons near the Fermi surface become so important.
To better understand the material discussed in the lecture, we expect you to recap the following topics:

Quantum mechanical description of a free particle.
Fermi-Dirac distribution.
Notion of the density of states and how it is used to calculate the total energy and number of particles.
Periodic boundary conditions
k-space.

If you have any questions, feel free to ask them below!

Lecture 3: Drude Model

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hello everyone!
So far we have focused on specific heat as an important observable. But solids have many other measurable properties as well. How do we start modelling electrical transport, and what role do collisions play? (hint: think of scattering )
To answer these questions, we turn to the Drude model and pay special attention to scattering and the Lorentz force. In this model, electrons are treated as classical particles whose motion explains electrical conductivity, and what makes the model interesting is that, despite being quite crude, it already captures a surprising amount of useful intuition about transport in solids.
We will meet again on Tuesday to discuss the material, so please also review

The Lorentz force
Concepts like voltage, electrical current, and conductivity

Looking forward to seeing you all in the next discussion!
Please keep asking questions, discussing, and helping each other below this post

Lecture 2: Debye model

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hello everyone!
On Thursday we will meet again to discuss the limitations of the Einstein model. In which cases do you think the model does not perform well? (hint: look at the plot below )

In order to answer this question, make sure you check out the Debye model . This lecture is especially important because we will learn the two key concepts of the course: dispersion relation and density of states.
It is important that you also review

The Einstein model
Periodic boundary conditions
How to calculate volume integrals in spherical coordinates

Looking forward to see you all for the next lecture!
Don’t forget to ask your questions below this post

Lecture 1: Einstein model

This announcement is a copy of the forum announcement.If you have questions, please ask them on the course forum.Hello everyone and welcome to the course forum!
This Tuesday we will go through how the course is organized and begin the journey towards learning solid state physics.
We begin around 1819, when Pierre Dulong and Alexis Petit measured the molar heat capacity of different chemical elements and realized its value was practically independent of the atomic number.
This value, however, drops when the material cools down. We will see how Einstein explained this drop in 1907, almost a century later, by anticipating quantum mechanics.
That is the question we will discuss in the first lecture. To prepare, please review

The quantum harmonic oscillator (you do not need to know the wave functions)
The equipartition theorem
The Bose-Einstein distribution

If you have previously followed the course ‘Statistical Physics TN2626’ (which you should), then these concepts will likely be familiar.
In the header of each course lecture, you will find the prerequisites that you will need to work through the material. You have encountered these concepts before, and we will not go through them in detail.
This one is a freebie though, since we are just getting started. Still, if you have time, review the notes before the lecture, and please ask your questions about the material and exercises by replying to this topic.

Welcome to the 2026 course run

Welcome to the course!
This announcement is a copy of the course forum announcement.
You will receive a forum invite at your student email address shortly.
If you have questions after joining, please ask them on the course forum.

Please read this announcement carefully: it contains a lot of important information. If you have any questions, ask them below.
First of all, hello! This is us:
@t.vandersar and @anton-akhmerov are the instructors; @Joaquin, @fsfetcu, @Emma, @egijonruiz, @Alex123, and @abermejillo are the TAs, and together we are the course @team.
Solid state physics is a challenging but fascinating subject that underlies much of modern technology, and if you put in the effort you will learn a lot.
Here we explain how the course is organized.
Course resources
Here are the main resources you will use during the course.
Lecture notes
All the course study materials are in the online lecture notes.
The lecture notes cover the full content of the course: the lectures, the exercises after each lecture, and their reference solutions.
These notes are developed and maintained by the course team. If you see room for improvement, we would love to hear your input, either via the source repository or in Site Feedback.
The book

The course structure is heavily inspired by Oxford Solid State Basics by Steve Simon, which is available through the university library. The book provides a more detailed and systematic overview of the material, and we highly recommend it as an auxiliary source. Steve Simon is also an excellent lecturer, and you will likely enjoy his lecture recordings.
This forum
This is the main point of contact in the course outside class and exam hours. We will post announcements and discuss planning in Course activities, and we will answer questions in the public part, Physics Q&A. We welcome active participation from everyone, so do not hesitate to contribute if you know the answer to a question from a fellow student.
While we welcome public discussion, we also respect your right to privacy. If you do not want to disclose your name in a post, you may post anonymously, or ask your question privately by sending a direct message to the course @team. If you have a practical question about your personal circumstances, you can ask @anton-akhmerov and @t.vandersar directly via DM. You may also delete all of your forum activity at any time.

Note: why we don't use MS Teams or Discord

We will post all announcements on Brightspace as well, but the forum is where discussion happens.
We do not use MS Teams because it behaves more like a chat, and once there are many questions it becomes harder to organize or search.
We do not use Discord because we are not allowed to use it for course communication under the privacy rules.

How to follow the course
Schedule
The course schedule is at mytimetable.tudelft.nl.
Lectures

Tuesdays and Thursdays at 13:45 we begin with a review of one course topic. Each topic corresponds to a chapter of the course notes. For example, on Tuesday 17 March we will study the Einstein model, and on Thursday 19 March we will study the Debye model.
Important: The course is intense, and we expect you to prepare for lectures. At the beginning of each lecture you will find expected prior knowledge, which lists what you should review and points to preparation material. Go through it: we will check it during lectures using quick quizzes.
In octal 7 the schedule changes according to the timetable. We will announce all course activities, but always double-check MyTimetable as well.

Exercise classes

Right after the lectures you will work on the problems listed at the end of each chapter of the lecture notes.
We strongly recommend attending these exercise classes, working together in teams, and asking us questions if something is unclear.

psst, click me
You are doing well: halfway through the instructions and still paying attention. Check out this happy duck to relax a bit

Bonus Minitests

The course has three bonus minitests:

Monday 30 March 13:45–15:45

Monday 20 April 13:45–15:45

Friday 1 May 13:45–15:45

Each minitest contains two problems focusing on the two weeks of the course immediately preceding it.

Your two best minitests can each give you up to a 10% bonus on the points you miss on the final exam. The exact formula is F + (M1 + M2) * (10 - F) / 100, where F is the final grade and M1, M2 are your two best minitest grades.

The minitests, as well as the final exam, use a formula sheet. We will let you compose this sheet collectively during the course and will share the exact rules soon.

The level of the minitests and the final exam is the same.

If you are entitled to extra time, inform us directly for the minitests on the spot and declare it via MyTUDelft for the exam.

You do not need to register in Osiris for the minitests.

Contact @anton-akhmerov and @t.vandersar as soon as possible if you are unable to attend a minitest or an exam.

Exams

The final exam takes place Wednesday 20 May 13:30–16:30.
It counts for 100% of the course grade, plus the minitest bonus.
The final exam will contain a problem about semiconductors and one problem for each minitest block. The problems will be a bit shorter than in the minitests.
The retake exam takes place Wednesday 24 June 09:00–12:00, and it is organized in the same way as the final exam.

Practice material
We explain how the exams are designed in this post, how we compose exams, where we also list representative examples.
Additionally, throughout the course several exercises are marked with an asterisk. These are similar in level and style to exam problems.
Language

The course materials are offered in English.
You may use Dutch to communicate with the course team members, or to write your exam solutions.

Conclusion
Phew! That was a lot of information, but now you should be all set. Welcome again to the course!