Physics

### Topic Covered

color{blue}{star} INTRODUCTION
color{blue}{star} CLASSIFICATION OF METALS, CONDUCTORS AND SEMICONDUCTORS
color{blue}{star} INTRINSIC SEMICONDUCTOR

### INTRODUCTION

color{blue} ✍️Devices in which a controlled flow of electrons can be obtained are the basic building blocks of all the electronic circuits.

color{blue} ✍️Before the discovery of transistor, such devices were mostly vacuum tubes (also called valves) like the vacuum diode which has two electrodes, viz., anode (often called plate) and cathode; triode which has three electrodes – cathode, plate and grid; tetrode and pentode (respectively with 4 and 5 electrodes).

color{blue} ✍️ In a vacuum tube, the electrons are supplied by a heated cathode and the controlled flow of these electrons in vacuum is obtained by varying the voltage between its different electrodes. Vacuum is required in the inter-electrode space; otherwise the moving electrons may lose their energy on collision with the air molecules in their path.

color{blue} ✍️In these devices the electrons can flow only from the cathode to the anode (i.e., only in one direction). Therefore, such devices are generally referred to as valves.

color{blue} ✍️These vacuum tube devices are bulky, consume high power, operate generally at high voltages (~100 V) and have limited life and low reliability.

color{blue} ✍️The seed of the development of modern solid-state semiconductor electronics start when it was released that some solid-state semiconductors and their junctions offer the possibility of controlling the number and the direction of flow of charge carriers through them. Simple excitations like light, heat or small applied voltage can change the number of mobile charges in a semiconductor.

color{brown} {"Note"} that the supply and flow of charge carriers in the semiconductor devices are within the solid itself, while in the earlier vacuum tubes/valves, the mobile electrons were obtained from a heated cathode and they were made to flow in an evacuated space or vacuum. No external heating or large evacuated space is required by the semiconductor devices.

color{blue} ✍️They are small in size, consume low power, operate at low voltages and have long life and high reliability. Even the Cathode Ray Tubes (CRT) used in television and computer monitors which work on the principle of vacuum tubes are being replaced by Liquid Crystal Display (LCD) monitors with supporting solid state electronics.

color{blue} ✍️Here, we will introduce the basic concepts of semiconductor physics and discuss some semiconductor devices like junction diodes (a 2-electrode device) and bipolar junction transistor (a 3-electrode device).

### CLASSIFICATION OF METALS, CONDUCTORS AND SEMICONDUCTORS

color{brown}bbul("On the basis of conductivity")
color{blue} ✍️On the basis of the relative values of electrical conductivity (sigma) or resistivity (p = 1//s ), the solids are broadly classified as:

color{green}((i) ul{"Metals:"}) They possess very low resistivity (or high conductivity).
color{purple} {r ~ 10^(–2) – 10^–8 W m}
color{purple} {s ~ 10^2 – 108 S m^–1}

color{green} {(ii) ul{"Semiconductors:"}} They have resistivity or conductivity intermediate to metals and insulators.
color{purple}(r ~ 10^(–5) – 10^6 W m)
color{purple}(s ~ 10^5 – 10^(–6) S m^–1)

color{green}((iii)ul {"Insulators:"}) They have high resistivity (or low conductivity).
color{purple}(r ~ 10^11 – 10^(19) W m)
color{purple}(s ~ 10^(–11) – 10^(–19) S m^(–1))

color{blue} ✍️The values of p and sigma given above are indicative of magnitude and could well go outside the ranges as well. Relative values of the resistivity are not the only criteria for distinguishing metals, insulators and semiconductors from each other. There are some other differences

color{blue} ✍️Our interest in this chapter is in the study of semiconductors which could be:
color{blue} {(i)} Elemental semiconductors: Si and Ge
color{blue} {(ii)} Compound semiconductors: Examples are:
color{blue} {• }Inorganic: CdS, GaAs, CdSe, InP, etc.
color{blue} {•} Organic: anthracene, doped pthalocyanines, etc.
color{blue} {• }Organic polymers: polypyrrole, polyaniline, polythiophene, etc.

color{blue} ✍️Most of the currently available semiconductor devices are based on elemental semiconductors S i or G e and compound inorganic semiconductors.

color{blue} ✍️However, after 1990, a few semiconductor devices using organic semiconductors and semiconducting polymers have been developed signalling the birth of a futuristic technology of polymerelectronics and molecular-electronics.

color{brown}bbul("On the basis of energy bands")
color{blue} ✍️According to the Bohr atomic model, in an isolated atom the energy of any of its electrons is decided by the orbit in which it revolves. But when the atoms come together to form a solid they are close to each other.

color{blue} ✍️So the outer orbits of electrons from neighboring atoms would come very close or could even overlap. This would make the nature of electron motion in a solid very different from that in an isolated atom.

color{blue} ✍️Inside the crystal each electron has a unique position and no two electrons see exactly the same pattern of surrounding charges.

color{blue} ✍️Because of this, each electron will have a different energy level. These different energy levels with continuous energy variation form what are called "energy bands."

color{blue} ✍️The energy band which includes the energy levels of the valence electrons is called the valence band. The energy band above the valence band is called the conduction band. With no external energy, all the valence electrons will reside in the valence band.

color{blue} ✍️If the lowest level in the conduction band happens to be lower than the highest level of the valence band, the electrons from the valence band can easily move into the conduction band. Normally the conduction band is empty. But when it overlaps on the valence band electrons can move freely into it. This is the case with metallic conductors.

color{blue} ✍️If there is some gap between the conduction band and the valence band, electrons in the valence band all remain bound and no free electrons are available in the conduction band. This makes the material an insulator.

color{blue} ✍️But some of the electrons from the valence band may gain external energy to cross the gap between the conduction band and the valence band. Then these electrons will move into the conduction band.

color{blue} ✍️At the same time they will create vacant energy levels in the valence band where other valence electrons can move. Thus the process creates the possibility of conduction due to electrons in conduction band as well as due to vacancies in the valence band.

color{blue} ✍️Let us consider what happens in the case of Si or Ge crystal containing N atoms. For Si, the outermost orbit is the third orbit (n = 3), while for Ge it is the fourth orbit (n = 4).

color{blue} ✍️The number of electrons in the outermost orbit is 4 (2s and 2p electrons). Hence, the total number of outer electrons in the crystal is 4N. The maximum possible number of electrons in the outer orbit is 8 (2s + 6p electrons).

color{blue} ✍️So, for the 4N valence electrons there are 8N available energy states.

color{blue} ✍️These 8N discrete energy levels can either form a continuous band or they may be grouped in different bands depending upon the distance between the atoms in the crystal (see box on Band Theory of Solids).

color{blue} ✍️At the distance between the atoms in the crystal lattices of Si and Ge, the energy band of these 8N states is split apart into two which are separated by an energy gap E_g (Fig. 14.1).

color{blue} ✍️The lower band which is completely occupied by the 4N valence electrons at temperature of absolute zero is the valence band. The other band consisting of 4N energy states, called the conduction band, is completely empty at absolute zero.

color{blue} ✍️The lowest energy level in the conduction band is shown as E_C and highest energy level in the valence band is shown as E_V .

color{blue} ✍️Above E_C and below EV there are a large number of closely spaced energy levels, as shown in Fig. 14.1. The gap between the top of the valence band and bottom of the conduction band is called the energy band gap (Energy gap Eg). It may be large, small, or zero, depending upon the material. These different situations, are depicted in Fig. 14.2 and discussed below:

color{brown} {"Case I"}: This refers to a situation, as shown in Fig. 14.2(a). One can have a metal either when the conduction band is partially filled and the balanced band is partially empty or when the conduction and valance bands overlap.

color{blue} ✍️When there is overlap electrons from valence band can easily move into the conduction band. This situation makes a large number of electrons available for electrical conduction.

color{blue} ✍️When the valence band is partially empty, electrons from its lower level can move to higher level making conduction possible. Therefore, the resistance of such materials is low or the conductivity is high.

color{brown} {"Case II:"} In this case, as shown in Fig. 14.2(b), a large band gap E_g exists (E_g > 3 eV). There are no electrons in the conduction band, and therefore no electrical conduction is possible.

color{brown} {ul "Note:"} that the energy gap is so large that electrons cannot be excited from the valence band to the conduction band by thermal excitation. This is the case of insulators.

color{brown} {"Case III :"} This situation is shown in Fig. 14.2(c). Here a finite but small band gap (E_g < 3 eV) exists. Because of the small band gap, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band.

color{blue} ✍️These electrons (though small in numbers) can move in the conduction band. Hence, the resistance of semiconductors is not as high as that of the insulators.

color{blue} ✍️In this section we have made a broad classification of metals, conductors and semiconductors. In the section which follows you will learn the conduction process in semiconductors.

### INTRINSIC SEMICONDUCTOR

color{blue} ✍️We shall take the most common case of Ge and Si whose lattice structure is shown in Fig. 14.3.

color{blue} ✍️These structures are called the diamond-like structures.

color{blue} ✍️Each atom is surrounded by four nearest neighbours. We know that Si and Ge have four valence electrons. In its crystalline structure, every Si or Ge atom tends to share one of its four valence electrons with each of its four nearest neighbour atoms, and also to take share of one electron from each such neighbour.

color{blue} ✍️These shared electron pairs are referred to as forming a covalent bond or simply a valence bond. The two shared electrons can be assumed to shuttle back-andforth between the associated atoms holding them together strongly.

color{blue} ✍️Figure 14.4 schematically shows the 2-dimensional representation of Si or Ge structure shown in Fig. 14.3 which overemphasises the covalent bond. It shows an idealised picture in which no bonds are broken (all bonds are intact). Such a situation arises at low temperatures.

color{blue} ✍️As the temperature increases, more thermal energy becomes available to these electrons and some of these electrons may break–away (becoming free electrons contributing to conduction).

color{blue} ✍️The thermal energy effectively ionises only a few atoms in the crystalline lattice and creates a vacancy in the bond as shown in Fig. 14.5(a).

color{blue} ✍️The neighbourhood, from which the free electron (with charge –q) has come out leaves a vacancy with an effective charge (+q ). This vacancy with the effective positive electronic charge is called a hole. The hole behaves as an apparent free particle with effective positive charge.

In intrinsic semiconductors, the number of free electrons, n_e is equal to the number of holes, n_h.

color{blue} ✍️That is color{blue}(n_e = n_h = n_i)

...............(14.1)
where n_i is called intrinsic "carrier concentration."

color{blue} ✍️Semiconductors posses the unique property in which, apart from electrons, the holes also move. Suppose there is a hole at site 1 as shown in Fig. 14.5

color{blue} {(a).} The movement of holes can be visualised as shown in Fig. 14.5.

color{blue} {(b).} An electron from the covalent bond at site 2 may jump to the vacant site 1 (hole). Thus, after such a jump, the hole is at site 2 and the site 1 has now an electron.

color{blue} ✍️Therefore, apparently, the hole has moved from site 1 to site 2. Note that the electron originally set free [Fig. 14.5(a)] is not involved in this process of hole motion. The free electron moves completely independently as conduction electron and gives rise to an electron current, I_e under an applied electric field.

color{green} {ul {"Remember"}} that the motion of hole is only a convenient way of describing the actual motion of bound electrons, whenever there is an empty bond anywhere in the crystal. Under the action of an electric field, these holes move towards negative potential giving the hole current, I_h. The total current, I is thus the sum of the electron current I_e and the hole current I_h:

color{blue}(I = I_e+I_h)

............ (14.2)

color{blue} ✍️It may be noted that apart from the process of generation of conduction electrons and holes, a simultaneous process of recombination occurs in which the electrons recombine with the holes.

color{blue} ✍️At equilibrium, the rate of generation is equal to the rate of recombination of charge carriers. The recombination occurs due to an electron colliding with a hole.

color{blue} ✍️An intrinsic semiconductor will behave like an insulator at T = 0 K as shown in Fig. 14.6

color{blue} {(a)} It is the thermal energy at higher temperatures (T > 0K), which excites some electrons from the valence band to the conduction band. These thermally excited electrons at T > 0 K, partially occupy the conduction band.

color{blue} ✍️Therefore, the energy-band diagram of an intrinsic semiconductor will be as shown in Fig. 14.6(b).

color{blue} ✍️Here, some electrons are shown in the conduction band. These have come from the valence band leaving equal number of holes there.
Q 3179180016

C, Si and Ge have same lattice structure. Why is C insulator while Si and Ge intrinsic semiconductors?
Class 12 Chapter 14 Example 1
Solution:

The 4 bonding electrons of C, Si or Ge lie, respectively, in the second, third and fourth orbit. Hence, energy required to take out an electron from these atoms (i.e., ionisation energy E_g ) will be least for Ge, followed by Si and highest for C. Hence, number of free electrons for conduction in Ge and Si are significant but negligibly small for C.