# Semiconductor for beginner #2 ## Introduction

I majored in physics during my university years and focused on theoretical physics.

However, during my master’s program, I unexpectedly delved into research on high-energy physics or particle physics experiments involving semiconductor detection devices.

Given the potentially extensive content, feel free to explore based on your specific areas of interest. And most importantly, enjoy the read!

## How to see the crystal structure

In conclusion, we use X-rays.

By the way, how do you grasp the shape and structure of something you cannot see?

For example, suppose there is a transparent object in front of you and many pebbles around you.

How would you predict the shape of the object?

Perhaps you throw a pebble at the object.

The basic idea is the same: you direct X-rays at the crystal and see where they bounce back to determine the crystal structure.

So, the next question that arises is why use X-rays? This is about the nature of light and humans.

Snow crystals and salt crystals can be seen with the naked eye, but silicon crystals are so minute that they cannot be seen with the naked eye.

When I talked about single crystals, I think I mentioned that the atoms are arranged neatly in a single structure.

The distance between atoms is 0.24 nm, which is 10-9 m in nanometers. It is a very short distance.

The human eye relies on light for vision. Light is said to be a wave, and the distance of one cycle of the wave is called the wavelength.

When we consider one set of these mountains and valleys, the wavelength is the linear distance from the starting point to the original starting point and back again).

And light has various wavelengths.

The wavelengths that the human eye can perceive are the wavelengths of visible light (see image below).

However, the shortest wavelength of visible light is 400 nm, which is blue light.

Compared to the 0.24 nm distance between atoms mentioned earlier, it is so large that it is impossible to distinguish it with the naked eye.

The table below shows that the wavelengths of X-rays and X-rays can be used to identify the distance between atoms.

The energy of radiation increases as the wavelength gets shorter, so handling gamma rays and other types of radiation can be quite hazardous.

This is because radiation damages the DNA of living organisms.

This is why X-rays are used for X-rays. In other words, in terms of what and how to use them, X-rays are best for crystal structure analysis.

To summarize again what we have said so far, as long as we use visible light to identify the space between atoms, we cannot discern the structure of crystals.

In other words, no matter how good an optical microscope you bring, it is impossible. So, let’s use X-rays.

Next, to understand the behavior of X-rays when they are irradiated onto a crystal, we will talk about light diffraction and diffraction gratings (we will replace diffraction gratings with crystals later).

For example, suppose that light is irradiated onto a certain obstacle.

If we call the moment of collision with the obstacle diffraction (also called scattering), there are two types of diffraction possible. (The part of the x-ray that shows the bone is reflected, and the part that does not show any other organs is transmitted.)

So what is a diffraction grating?

Think of it here as a regularly arranged concave-convex shape made to do something using diffraction.

For example, look at the back of a CD or DVD. That is made to be concave and convex in order to read using diffraction. This is a diffraction grating.

Let us look at the diffraction conditions of a diffraction grating.

The diffraction condition is that light intensifies in the direction where the optical path difference L between the light diffracted in the neighboring grooves becomes an integer multiple of the light wavelength λ.

For simplicity, let us consider the case of measuring visible light.

Notice : translate from Japanese to English

For example, consider the case where light is incident perpendicularly, n as a positive integer,

$$n\lambda=L=dsin\theta$$

can be expressed as The left side means that there are n lights of wavelength λ.

The right side is the geometrical calculation of the distance.

d is the distance between adjacent grooves.

Usually n=1 diffraction is used, and is called first-order diffracted light.

Looking at the above equation, when the wavelength λ on the left side changes, the diffraction angle θ on the right side also changes. Therefore, assuming n=1, the wavelength λ can be determined by measuring the diffraction angle θ.

In addition, when measuring visible light, the groove spacing d is about 1μm.

So note that “the wavelength to be measured using a diffraction grating and the spacing between the grooves of the diffraction grating are about the same size.

This means that the spacing between the grooves of the diffraction grating is conveniently set to such a size for the purpose of use.

However, in the measurement, not only the diffraction angle θ but also the intensity of diffracted light is measured.

The resulting spectrum is plotted with the intensity of diffracted light on the vertical axis and the wavelength on the horizontal axis.

Now, let’s replace the diffraction grating with a crystal.

The crystals we are dealing with are single crystals.

I mentioned that in a single crystal, atoms are arranged in a regular pattern.

The principle is the same as in the case of diffraction gratings, except that X-rays can penetrate into the interior of the crystal.

Therefore, we need to consider not only surface diffraction but also diffraction by internal atoms.

This makes it a little more complicated, but it can be understood if you understand diffraction in a diffraction grating.

First, look at the figure below, assuming that each circle is an atom, regularly arranged at a distance d.

Notice : translate from Japanese to English

Again, given the optical path difference as well,

$$n\lambda＝L=2dsin\theta$$

Assuming n is first-order diffraction (n=1), decide what kind of X-rays to use (at what wavelength λ), and then measure the diffraction angle to find the distance between atoms in silicon (also known as the Bragg diffraction condition).

We know the distance between the atoms. This finally led to the story that we now know the structure of the crystal.

That was quite a long story. LOL.

As a digression, Laue in Germany discovered that X-ray irradiation of a crystal causes diffraction, and later Bragg and his son derived Bragg’s diffraction condition from this diffraction phenomenon.

The method of examining crystals is called the Laue method, which some physics students may have done in their student experiments.

The Nobel Prize in Physics was awarded to Laue in 1914 and to Bragg and his son in 1915. Incidentally, the Bragg child was 25 years old at the time.

## Crystal Structure of Silicon

The above method gave us a way to find out the crystal structure.

And what we found out is that the crystal structure of silicon and silicon dioxide is as follows. Incidentally, this structure of silicon is the same as that of diamond.

Diamond is composed of carbon, and of course, pencil lead (graphite) is also composed of carbon.

The difference between diamond and graphite lies in their different crystal structures.

Even if the atoms are the same, the difference in crystal structure can greatly change the value.

Notice : translate from Japanese to English

ケイ素元素 : silicon element

Look at the image of silicon. The black lines connect the blue atoms.

This is an electron, and it takes two electrons to make one bond. To understand why two electrons are needed, look at the image below.

Notice : translate from Japanese to English

Siの電子配列 : Electron array of Si
は電子 : is the electron

Looking at the left side of the image, the number of outermost shell electrons is four.

This M-shell can hold up to 8 electrons.

So, let’s bring the remaining 4 electrons from other silicon atoms.

That is the right side of the image: one silicon atom has 8 electrons around it.

Think of this as each atom sharing the missing piece.

And that is the force that binds the atoms together (covalent bonding).

## Group IV(14) Atoms

The outermost shell of silicon had four electrons.

Thus, an atom with four electrons in its outermost shell is called a group IV(14) atom.

You may have heard of the periodic table, which was created by a man named Mendeleev to classify the elements.

The period represents rows and the group represents columns. In other words, the 14th row is group 14.

Since the masses are lighter from the top to the bottom, group IV is C (carbon), Si (silicon), and Ge (germanium) in order of lightest to lightest mass.

This would explain why diamond (carbon) has the same structure as silicon.

I mentioned that silicon and germanium are used as semiconductors.

Then, you may have wondered what about diamond.

Actually, diamonds also work as semiconductors.

The reason why it is not so widely used is because it is expensive.

Also, it is difficult to process. Incidentally, the diamond cut is called the Brillian cut.

In 1919, Belgian mathematician and jeweler Tolkowsky theoretically derived the most beautiful and brilliant cut by mathematically considering the optical properties of diamonds such as reflection and refractive index.

If it were to be put into practical use, would it be lined up as a sparkling transistor even at Tiffany’s and given to women at Christmas?

## Compound semiconductors

Silicon, diamond, and germanium can all be used as semiconductors. And I told you that their crystal structures have a total of eight electrons making four bonds.

This is a feat only possible with group IV atoms.

However, diamond structures (tetrahedrons) can also be made with elements other than group IV atoms.

The way to do this is to combine two or more elements.

And it is called a compound. Specifically, it is a compound semiconductor of group III(13) and V(15).

It works by placing a group V atom at each vertex of the tetrahedron and a group III atom at the center of the tetrahedron.

This is because group III has 3 outermost shell electrons and group V has 5 outermost shell electrons.

For silicon, 4+4=8, and for this compound, 3+5=8, which is a match.

When the outermost shell atoms are 8, the compound is relatively stable.

Therefore, group 18 (noble gases) with 8 atoms are stable from the start and do not create reactions with other atoms.

The most common combination of Group III and Group V is GaAs, which is called gallium arsenide (official name).

Compound semiconductors such as GaAs and single semiconductors such as Si have several different properties.

The most important point is that compound semiconductors can be made to glow by passing electricity through them.

It is important to note here that you cannot make a compound semiconductor glow simply by passing electricity through it; special processing is required.

However, in the case of Si, no matter what special processing is applied, it is not possible to produce strong light for practical use. I will discuss the reason for this later.

GaAs is a compound of As, and As is toxic. In other words, it is more dangerous to handle than Si.

The crystal structure of GaAs is basically a tetrahedron, the same as that of Si.

citation URL : https://ebrary.net/82321/computer_science/carrier_physics_junction_electrostatics

Such a structure with four As around a Ga and four Gas around an As is called a sphalerite structure (sen-azenite structure).

Looking at combinations other than GaAs, there are various combinations such as InAs and GaP.

In this combination of compounds, the lower down the periodic table, the longer the wavelength of the emission (closer to red), and the higher up the periodic table, the shorter the wavelength (closer to blue).

So we can make new semiconductors by taking advantage of this interesting feature.

For example, InAs, GaAs, GaP, and InGaN emit longer wavelengths in that order.

Research on making semiconductors glow had succeeded in emitting red and green light by around 1990, but not blue.

The reason why blue is so important is that from the three primary colors of color, it will be possible to create all other colors. The term RGB, which stands for Red, Green, and Blue, refers to these three colors.

citation URL : 色の基本概念！光の三原色と色の三原色 (iro-color.com)

And it is a well-known story that it was Japanese researchers who arrived at this blue luminescence.

It turns out that if you use elements at the top of the periodic table, you can make compounds with shorter wavelengths.

Therefore, a small number of researchers turned their attention to GaN (gallium nitride), a combination of nitrogen N and gallium Ga.

But why was it so difficult to make this compound? GaN was not easy to grow crystals.

In 1993, the company succeeded in emitting blue light, which was then applied to various parts such as displays and traffic signals.

Furthermore, a blue semiconductor laser was developed, which is now applied to Blu-ray discs and other products.

Thus, research on semiconductor materials has opened up new markets, and research on the next semiconductors is still being conducted today.

Studying the process of semiconductors is very profound and interesting, as it also gives us a background of our modern lifestyle ☆.

## Electron Movement as Seen from the Conduction Band and Valence Band

Earlier, we talked about colors, such as making semiconductors glow. Here, you will get an idea of how light is emitted when electrons move.

The content itself is already located in condensed matter physics. Therefore, it is interesting, but some mathematical formulas will appear.

If you are allergic, we recommend that you only meditate on the formulas if necessary.

In order to operate various devices such as transistors, it is necessary to pass current through semiconductors.

Therefore, looking at the nature of the current flowing in semiconductors will deepen your understanding: we studied the crystal structures (tetrahedron) of Si, GaAs, and other semiconductors.

Atoms are connected to each other by covalent bonds formed by electrons, represented by black straight bars (look at the left side of the figure below).

Notice : translate from Japanese to English

ケイ素元素 : silicon element

In this figure, the two outermost electrons are represented as black bars; the remaining electrons are not depicted. Notice : translate from Japanese to English

Siの電子配列 : Electron array of Si
は電子 : is the electron

Electrons other than the outermost electrons (K-shell and L-shell in the above figure) are more stable toward the inner side because they are more strongly bound to the nucleus (binding force).

This is because the nucleus is composed of protons and neutrons, and the positive charge of protons and negative charge of electrons attract each other (Coulomb’s law).

citation URL : https://lpilen23.wordpress.com/2017/12/06/the-coulombs-law/

Look at the equation in the figure above.

As the distance r between the electron and proton approaches, the Coulomb force F increases.

Conversely, as the distance r increases, the Coulomb force F decreases.

Thus, when we consider the binding force, we find that the binding force acting on the outermost electron is the smallest and easiest to move.

So basically, when you think of covalent bonding or any kind of electron motion, you should think of outermost-shell electrons.

In the normal state, electrons are packed up to the outermost orbitals.

This normal state is when the temperature is low.

The low temperature is also referred to as low energy, and is a stable state.

Conversely, when the temperature is high, the energy is high. The image is that when the temperature is high, particles move actively and their kinetic energy is high.

By the way, electrons can go beyond this outermost orbit.

This condition becomes possible when the temperature is raised or when doped semiconductors (to be discussed later) are used.

Orbitals beyond the outermost orbital are bound to neighboring atoms and can move widely in space (also known as free electrons).

We need to distinguish between electrons that can move freely and those that cannot.

It is easy to understand this by using energy.

This is the band diagram. The orbitals in which electrons can move freely are called the conduction band, and those in which electrons cannot move freely are called the valence band.

fig.z Relationship between bands (zones) and energy

Notice : translate from Japanese to English

バンドギャップ(禁止帯) : Band gap (forbidden band)

バンドギャップエネルギー : Band gap energy

バンド図 : Band diagram

Let’s look at the diagram above. There are three types of bands.

There are three types of bands: the valence band, the prohibition band, and the conduction band.

The valence band is full of electrons and cannot move. In the forbidden band, there are no electrons.

In the conduction band, there are electrons, and these electrons have high energy and can move freely.

So how do electrons in the valence band move to the conduction band, which has higher energy, and become free electrons?

The electrons in the valence band receive light energy from the outside and move up to the conduction band.

Conversely, the energy can drop from the conduction band to the valence band and the electrons can move there.

When this happens, the electrons lose energy and settle back into the valence band, emitting light.

This luminescence is the light produced by the semiconductor.

However, if the band gap is too large,

there are not enough free electrons in the conduction band to begin with (when the band gap is too energetic to bring electrons from the valence band), or it is difficult to make the semiconductor emit light (because the number of electrons in the conduction band is too small),

so it is necessary to narrow the band gap Therefore, there is room for various improvements, such as narrowing the band gap by ingenuity, and researchers are doing various things to improve it.

The band gap energy of silicon is 1.1 eV and that of GaAs is 1.42 eV. As you may have already noticed,

devices that use this energy increase by receiving light or decrease by emitting light fall into the category of light-receiving or light-emitting devices,

so you can now see the relationship between electrons and light in semiconductors.

Thus, there is an energy conservation law between electrons and light.

This means that the required light energy corresponds to the size of the band gap, and the wavelength differs according to these correspondences, and different wavelengths mean different colors. For example, the band gap energy of Si of 1.1 eV corresponds to a light wavelength of 1.1 μm ($$1.1×10^{-6}$$m), and the band gap energy of GaAs of 1.42 eV corresponds to a light wavelength of 0.87 μm (870 nm) (see below).

Since visible light is the region of light that the human eye can perceive, in the case of Si, it corresponds to the case of infrared light, which is not visible when light is emitted, and in the case of GaAs, it also corresponds to visible light, where red is just barely visible.

I believe that the dots of what I have discussed so far can be connected like lines.

In semiconductor engineering, the unit of energy is not J (joule) but eV (electron volt).

1eV corresponds to the kinetic energy received by an electron when it moves between electrodes with a potential difference of 1V, since e represents the amount of charge (electric elementary quantity) of one electron.

Of course, it is possible to convert the unit to J, but it is easier to use eV for convenience of handling.

For example,

$$1eV=1.602×10^{-19}J$$

But obviously, the value on the right side would be troublesome when dealing with 1.42eV, etc. Thus, we also need to choose units flexibly.

Also, the energy of light is according to quantum mechanics (which I will talk about when I get a chance),

$$E=h×ν= \frac{hc}{λ}$$

can be expressed as (Planck constant h, speed of light c, wavelength λ, and frequency ν).

Since Planck constant h ($$6.626×10^{-34}$$m2kg/s) and light speed c ($$2.2998×10^8$$m/s) are already fixed constants,

we can interpret the expression to mean that light energy changes if wavelength λ changes.

By the way, substituting this Planck constant and the value of the speed of light,

$$λ\mu m≃\frac{1.24}{E[eV]}$$

which can be expressed as This is useful because it allows for a quick conversion between bandgap energy and wavelength.

It is because of this formula that we were able to get the wavelength from the bandgap energies of Si and GaAs mentioned earlier.

## What is a carrier? What is an electron? What is a hole?

There is a basic term that you should know before going to the third lecture.

That is carrier. A carrier is a particle that carries an electrical charge.

For example, a free electron is a negatively charged particle.

A hole (hole), which we will discuss next, behaves like a particle that appears to be positively charged.

There is a reason why holes are not called particles.

A hole is not a particle, but a hole (hole) through which an electron has escaped from a neutral state can be viewed as being positively charged relative to it.

The following example will help you understand this difference between a free electron and a hole.

We will now come back to the explanation of terms.

We will talk about genuine semiconductors and impurity semiconductors (this is a review of the previous sections).

A true semiconductor is a semiconductor that contains no impurities.

Silicon and germanium semiconductors fall into this category.

On the other hand, impurity semiconductors are compound semiconductors (the terminology is just different).

A compound is a substance composed of two or more elements.

In other words, an impurity semiconductor is a semiconductor in which the amount of carriers can be adjusted by adding impurities to a genuine semiconductor.

Now, let us look at it concretely as a figure.

Notice : translate from Japanese to English

The characteristics of using Si as a true semiconductor include group 14 elements, outermost electrons (four), covalent bonding, and being true.

Now let us look at impurity semiconductors.

There are two types of impurity semiconductors: P-type and N-type. This can be explained by the concept of free electron and hole carriers.

Notice : translate from Japanese to English

13族元素 : group of 13 elements

The above figure shows a group 14 element Si (four outermost electrons) plus a group 13 element (three outermost electrons).

As a result, only one hole is created around the group 13 element.

When another electron enters this hole, a new hole is created where the other electron was originally located.

In this way, the hole can swim around like a free electron.

The reduction of one electron (two negative charges are reduced by one: (-2Q)-(-Q)=(-Q)) can be viewed in another relative way, as the arrival of a positively charged particle (two negative charges are added to one positive charge: (-2Q)+(+Q)=(-Q)).

In other words, it looks like a positively charged particle is moving. In other words, a P-type semiconductor is a semiconductor that uses a hole as a carrier.

Notice : translate from Japanese to English

Once the P-type is known, it is clear that N-type semiconductors are semiconductors that use free electrons as carriers.

In other words, a group 15 element (five outermost electrons) is mixed with a group 14 element (four outermost electrons) as an impurity, and one or more electrons are free to move about.

If we can understand the P-type and N-type, we can understand the PN junction.

In the lectures that follow, we will discuss the contents related to the number of carriers in semiconductors, when carriers flow (current flow), summarize these topics, discuss the structure of the pn junction, the most important semiconductor device, and finally continue with transistors and devices that use the pn junction.