# Energy Bands | Bohr’s Atomic Model | Energy Levels | Silicon

Table of Contents

## INTRODUCTION

The study of the atomic structure and energy bands is the most important for electronics engineering. The fact is that the size of an atom is so small that it is virtually not possible to see it even with the most powerful microscope. Therefore, we have to employ an indirect method for the knowledge of its structure. The method consists of studying the properties of atom experimentally. After this, a guess is made about the possible structure of the atom, which can satisfy the properties studied experimentally. many scientists have present different theories regarding the structure of the atom. However, for the purpose of understanding and learning electronics, the study of Bohr’s atomic model is adequate. Although many refinements on Bohr’s atomic model have since been made, we still believe in the laws which Bohrs applied to the atomic world. In this chapter, we shall study Bohr’s atomic model in order to understand and learn the problems facing the electronic world.

## Bohr’s Atomic Model

In 1913, Neils Bohr, Danish Physicist gave a clear explanation of the atomic structure. According to Bohr:
(i) An atom consists of a positively charged nucleus around which negatively charged electrons rotate or revolve in different circular orbits.

(ii) The electrons can revolve only around the nucleus only in certain permitted orbits i.e. orbits of certain radii are allowed.

(iii) The electrons in each permitted orbit have a certain fixed energy amount. The orbit is larger (i.e. larger radius), the greater is the energy of electrons.

(iv) If an electron is provided additional energy (e.g.heat, light, etc.), it is moved to the higher orbit. The atom in a state of excitation. This state does not last long, cause the electron soon back to the original lower orbit. As it falls, it releases back the acquired energy in the shape or form of heat, light, or other radiations.

Fig. 4.1 shows the structure of the silicon atom. It has 14 electrons. Two electrons revolve or rotate in the 1st orbit, 8 in the 2nd orbit, and 4 in the 3rd orbits. The 1st, 2nd, 3rd orbits, etc. are also called K, L, M orbits respectively. These electrons can revolve or move only in permitted orbits (i.e. orbits of *radii r1, r2, and r3) and not in any type of arbitrary orbit. Thus, all radii between r1 and r2 or between r2 and r3 are forbidden. Each orbit has a fixed and particular amount of energy associated with it. If an electron in the first orbit is to be lifted or moved to the second orbit, just the **right amount of energy should be provided to it. When this electron jumps from the 2nd orbits to 1st, it will send back the acquired energy in the shape or form of electromagnetic radiations.

## Energy Levels

It has already been discussed that every orbit has a fixed amount of particular energy associated with it. The electrons moving in a particular orbit having the energy of that orbit. The larger the orbit, the larger its energy. It becomes clear that outer orbit electrons having more energy than the inner orbit. An easy way of representing the energy of different orbits is shown in Fig. 4.2 (ii). This is called an energy level diagram. The first orbit indicates the first energy level, the second orbit represents the second energy level, and so on. The greater the orbit of an electron, the larger is its energy and higher is the energy level.

## Energy Bands

In the case of uni or single isolated atom, the electrons in an orbit having definite energy. However, an atom in a solid is largely influenced by the closely-packed neighboring atoms. The result is that the electron in any orbit of such an atom can have a range of energies instead of a single energy. This is called the energy band. The range of energies that have an electron in a solid is called an energy band.

The system of energy band can be easily understood by referring to Fig. 4.3. Fig. 4.3 (ii) represents
the energy levels of a single isolated atom of silicon. Each orbit of an atom has energy.
Therefore, an electron can have only single energy according to the orbit in which it exists.
However, when the atom is in a solid-state, the electron in any orbit may have a range of energies. For instance, electrons in the first orbit have slightly change energies because of no two electrons in this orbit visible exactly the same charge environment. Since there are millions of first orbit electrons, the slightly different or change energy levels form a band, called first energy band [See Fig. 4.3 (iii)]. The electrons in the first orbit may have any energy range in this band. Similarly, second orbit electrons form a second energy band and so on.

### Important Energy Bands in Solids

As discussed above, individual K, L, M, etc. energy levels of an isolated atom are transferred into corresponding bands when the atom is in a solid-state. Though there are a huge number of energy bands in solids, the following are of most particular importance [See Fig. 4.4] :

### (i) Valence band.

The range of energies (i.e. band) having valence electrons is called a valence band. The electrons in the outermost or last orbit of an atom are called valence electrons. In an ordinary atom, the valence band has electrons of the highest energy. This band may be partially or completely filled. For instance, in the case of inert gases, the valence band is full and for other materials or things, it is only partially filled. The partially filled band can have more electrons.

(ii) Conduction band.

In come materials (e.g. metals), the valence electrons are very loosely attached to the nucleus. Even at normal temperatures, certain valence electrons may get detached to be a free electron. In fact, it is these free electrons which are responsible for the flowing current in a conductor. For this purpose, they have known conduction electrons. The range of energies (i.e. band) possessed by conduction band electrons is called the conduction band. All electrons in the conduction band are of course free electrons. If a substance has an empty or zero conduction band, it means current conduction is impossible in that substance. Normally, insulators have an empty or zero conduction band. On the other side, it is partially filled for conductors.

(iii) Forbidden energy gap.

The separation between the valence band and conduction band on the energy level diagram is called a forbidden energy gap. No or zero electron of a solid can stay in a forbidden energy gap as there is no allowed energy state in this region. The width of the forbidden energy gap is calculated by the bondage of valence electrons to the atom. The larger the energy gap, the high tightly the valence electrons are bound to the nucleus. In order to move an electron from the valence band to the conduction band (i.e. to make the valence electron free), external energy equal to the forbidden energy gap must be provided.

### Classification of Solids and Energy Bands

We also know that some solids are very good conductors of electric current while others are insulators. There is also an intermediate or mid-class of semiconductors. The difference in the behavior of solids material as regards their electrical property can be beautifully explained in terms of energy bands. The electrons in the lower energy band are very tightly attached to the nucleus and play no part in the conduction current process. However, the valence and conduction bands are very specific importance in ascertaining the electrical behavior of different solids.

### (i) Insulators.

Insulators (e.g. wood, glass, etc.) are those substances that can not allow the flowing of electric current through them. In terms of energy band, the valence band is full while the conduction band is empty or zero electrons. Further, the energy gap between conduction band and valence bands is very huge (j 15 eV) as shown in Fig. 4.5. Therefore, a very large electric field is needed to push the valence electrons to the conduction band. For this phenomena, the electrical conductivity of such

matters are extremely low and may be regarded as nil or zero under normal conditions At room temperature, the valence electrons of the insulators do not have the required energy to cross over to the conduction band. However, when the temperature is increased, few of the valence electrons may get enough energy to cross over to the conduction band. Hence, the resistance of an insulator decreases with the rises in temperature i.e. an insulator has a negative temperature coefficient of resistance.

### (ii) Conductors.

Conductors (e.g. copper, aluminium) are those substances which very easily allow the flow of electric current through them. It is due to there are a huge number of free electrons available in a conductor. According to the energy band, the conduction band and valance bands overlap each other as shown in Fig.4.6. because of this overlapping, a very small potential difference across a conductor causes the free electrons to constitute an electric current. Thus, the electrical property of conductors can be satisfactorily explained by the band energy theory of materials.

### (iii) Semicondutors

Semiconductors (e.g. germanium, silicon, etc.) are those materials whose electrical conductivity lies in mid of insulators and conductors. According to the energy band, the conduction band is almost empty and the valence band is almost filled. Further, the energy gap between conduction bands and valence bands is very small as shown in Fig. 4.7. Therefore, a comparatively low electric field (smaller than insulators but much greater than conductors) is needed to push the electrons from the valence band to the conduction band. In short, a semiconductor has :
(a) almost full valence band
(b) almost empty conduction band
(c) low energy gap (j 1 eV) between valence bands and conduction bands.
At very low temperatures, the valence is completely full and the conduction band is 100% empty. Therefore, a semiconductor material virtually acts as an insulator at low temperatures. However, even at normal room temperature, few electrons (about one electron for 1010 atoms) cross over to the conduction
band, imparting small conductivity to the semiconductor. As the temperature is increased, large valence electrons move over to the conduction band, and the conductivity rises. This shows that the current conductivity of a semiconductor improves with the rise in temperature i.e. a semiconductor has a negative temperature coefficient of resistance.

## Silicon

During the infancy of the electronic industry, both silicon and germanium were used in the manufacture or development of semiconductor devices. As the electronic field advanced, it was realized that silicon material was superior to germanium material in many respects. Since silicon is the most widely used material in the manufacture or development of semiconductor devices, we shall continue to discuss the properties and characteristics of this material (as compared to germanium) as and when we get the chance.

(i) Note the atomic structure of silicon and germanium in Fig. 4.8 carefully. The valence shell electrons in germanium are in the 4th orbit while the valence shall electrons in silicon are in the 3rd orbit; near to the nucleus. Therefore, the germanium valence shell electrons are at larger energy levels than those in silicon valence electrons. This means that germanium valence electrons need a few amounts of additional energy to escape or go out from the atom and become free electron. What is the effect of this property? This property makes germanium atom more unstable at larger temperatures. This is the basic reason why silicon is mostly used as a semiconductor material.

(ii) Fig. 4.9 shows the energy level of the silicon atom. The atomic number of silicon is 14 so that its 14 electrons are divided into 3 orbits. Each energy level is associated with some particular amount of energy and is separated from the adjacent bands by the energy gap. No electron can never exist in the energy gap. For an electron to jump from one orbit to the next higher or larger orbit, external energy (e.g. heat) equal to the energy difference of the orbits must be provided. For example, the valence band is shown to have an energy of 0.7 eV. The conduction band is shown to have an energy level of 1.8 eV. Thus for an electron to jump or move from the valence band to the conduction band, and energy = 1.8 – 0.7 = 1.1 eV must be provided. As you will see, the energy band description of substances is most important in understanding concepts regarding many fields of science and engineering including electronics.

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Reference: Principles Of Electronics By V K Mehta And Rohit Mehta