13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u

13.2 Obtain the binding energy of the nuclei 5626Fe and 20983 Bi in units of MeV from the following data: m ( 5626Fe ) = 55.934939 u m ( 20983 Bi ) = 208.980388 u

13.6 Suppose, we think of fission of a 5626Fe nucleus into two equal fragments, 1328 Al . Is the fission energetically possible? Argue by working out Q of the process. Given m ( 5626Fe ) = 55.93494 u and m ( 1328 Al ) = 27.98191 u. 321 Reprint 2025-26 Physics 13.7 The fission properties of 23994 Pu are very similar to those of 23592 U . The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure 23994 Pu undergo fission? 13.8 How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as 2 1 H+ 21 H → 32 He+n+3.27 MeV 13.9 Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.) 13.10 From the relation R = R0A1/3, where R0 is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A). Reprint 2025-26 Chapter Fourteen SEMICONDUCTOR ELECTRONICS: MATERIALS, DEVICES AND SIMPLE CIRCUITS 14.1 INTRODUCTION Devices in which a controlled flow of electrons can be obtained are the basic building blocks of all the electronic circuits. Before the discovery of transistor in 1948, 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). 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. 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. These vacuum tube devices are bulky, consume high power, operate generally at high voltages (~100 V) and have limited life and low reliability. The seed of the development of modern solid-state semiconductor electronics goes back to 1930’s when it was realised 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. Note that the supply Reprint 2025-26 Physics 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. 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. Much before the full implications of the semiconductor devices was formally understood, a naturally occurring crystal of galena (Lead sulphide, PbS) with a metal point contact attached to it was used as detector of radio waves. In the following sections, 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). A few circuits illustrating their applications will also be described. 14.2 CLASSIFICATION OF METALS, CONDUCTORS AND SEMICONDUCTORS On the basis of conductivity On the basis of the relative values of electrical conductivity (s ) or resistivity (r = 1/s ), the solids are broadly classified as: (i) Metals: They possess very low resistivity (or high conductivity). r ~ 10–2 – 10–8 W m s ~ 102 – 108 S m–1 (ii) Semiconductors: They have resistivity or conductivity intermediate to metals and insulators. r ~ 10–5 – 106 W m s ~ 105 – 10–6 S m–1 (iii)Insulators: They have high resistivity (or low conductivity). r ~ 1011 – 1019 W m s ~ 10–11 – 10–19 S m–1 The values of r and s 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, which will become clear as we go along in this chapter. Our interest in this chapter is in the study of semiconductors which could be: (i) Elemental semiconductors: Si and Ge (ii) Compound semiconductors: Examples are: · Inorganic: CdS, GaAs, CdSe, InP, etc. · Organic: anthracene, doped pthalocyanines, etc. · Organic polymers: polypyrrole, polyaniline, polythiophene, etc. Most of the currently available semiconductor devices are based on 324 elemental semiconductors Si or Ge and compound inorganic semiconductors. However, after 1990, a few semiconductor devices using Reprint 2025-26 Semiconductor Electronics: Materials, Devices and Simple Circuits organic semiconductors and semiconducting polymers have been developed signalling the birth of a futuristic technology of polymer- electronics and molecular-electronics. In this chapter, we will restrict ourselves to the study of inorganic semiconductors, particularly elemental semiconductors Si and Ge. The general concepts introduced here for discussing the elemental semiconductors, by-and-large, apply to most of the compound semiconductors as well. On the basis of energy bands 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. So the outer orbits of electrons from neighbouring 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. Inside the crystal each electron has a unique position and no two electrons see exactly the same pattern of surrounding charges. 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. 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. 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. 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. 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. 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. 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). 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). So, for the 4N valence electrons there are 8N available energy states. 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). 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 Eg (Fig. 14.1). The lower band which is completely occupied by the 4N valence electrons at temperature of absolute 325 zero is the valence band. The other band consisting of 4N energy states, called the conduction band, is completely emptyReprint 2025-26at absolute zero. Physics The lowest energy level in the conduction band is shown as EC and highest energy level in the valence band is shown as EV. Above EC 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: Case I: This refers to a situation, as shown in Fig. 14.2(a). One can have a metal either when the conduction band FIGURE 14.1 The energy band positions in a is partially filled and the balanced band semiconductor at 0 K. The upper band, called the is partially empty or when the conduction conduction band, consists of infinitely large number and valance bands overlap. When there of closely spaced energy states. The lower band, is overlap electrons from valence band can called the valence band, consists of closely spaced easily move into the conduction band. completely filled energy states. This situation makes a large number of electrons available for electrical conduction. 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. FIGURE 14.2 Difference between energy bands of (a) metals, 326 (b) insulators and (c) semiconductors. Reprint 2025-26 Semiconductor Electronics: Materials, Devices and Simple Circuits Case II: In this case, as shown in Fig. 14.2(b), a large band gap Eg exists (Eg > 3 eV). There are no electrons in the conduction band, and therefore no electrical conduction is possible. 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. Case III: This situation is shown in Fig. 14.2(c). Here a finite but small band gap (Eg < 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. 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. 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.