Resistance (R) Temperature (T)

CHAPTER 1 Physical Properties of Elements and Semiconductors 1.1 Introduction Semiconductors constitute a large class of substances which have resistivities lying between those of insulators and conductors. The resistivity of semiconductors varies in wide limits, i.e., 10 4 to 10 4 Ω-m and is reduced to a very great extent with an increase in temperature (according to an exponential law) as shown in Fig. 1.1. Typical resistivity values of conductor, semiconductor and insulator are provided in the following table: Typical resistivity values Conductor Semiconductor Insulator 10 6 Ω-cm 50 Ω-cm (Ge) 10 12 Ω-cm (copper) 50 10 3 Ω-cm (Si) (mica) Resistance (R) Temperature (T) Fig. 1.1 The temperature dependence of the resistance in semiconductors. In Mendeleev s periodic table, semiconductors form the group of elements shown in Fig. 1.2. The most typical and extensively employed semiconductors whose electrical properties have been well investigated, are Germanium (Ge), Silicon (Si) and Tellurium (Te). The study of their electrical properties reveals that (i) Semiconductors have negative temperature coefficient of resistance, i.e., the resistance of semiconductor decreases with increase in temperature and vice versa as shown in Fig. 1.1. For example, Germanium is actually an insulator at low temperatures but it becomes good conductor at high temperature. 1

2 A Textbook of Electronics Period Group III IV V VI VII II B C III Si P S IV Ge As Se V Sn Sb Te I Fig. 1.2 Position of semiconductor elements in the Mendeleev Table (ii) The resistivity of semiconductors lies between that of a good insulator and of a metal conductor, i.e., lying in the range 10 4 to 10 4 Ω-m. (iii) The electrical conductivity of a semiconductor is very much affected when a suitable impurity, e.g., Arsenic, Gallium, Indium etc. is added to it. This property of semiconductors is most important. In recent years a number of devices based on semiconductors have been developed that are of great practical applications in electronics. Most important of these are semiconductor diodes, transistors and ICs. A transistor, which is a three terminal device having properties similar to those of a vacuum tube (triode), but requires no cathode power, and at the same time offers the hope of pretty long life. In modern electronic systems, the complete electronic circuit, containing many transistors, resistors, diodes etc. is fabricated on a single chip which is called an Integrated Circuit (IC). As compared to electronic valves, semiconductor devices offer the following advantages: (i) low weight and small size, (ii) no power for the filament (iii) long service life (thousands of hours), (iv) mechanical ruggedness, (v) low power losses and (vi) low supply voltages. At the same time semiconductor devices suffer from a number of disadvantages: (i) marked spread in parameters between devices within the same type; (ii) deterioration in performance with time (ageing); higher noise level than in electronic valves; (iii) unsuitability of most transistors for use at frequencies over tens of megahertz; (iv) low input resistance as compared with vacuum triodes; (v) inability to handle large power and (vi) deterioration in performance after exposure to radioactive emissions. Continuing efforts in research and development, however, are eliminating or minimizing many of the demerits of semiconductor devices. There are semiconductor rectifiers for currents of thousands of amperes. Replacement of Germanium with Silicon makes crystal diodes and transistors suitable for operation at temperatures upto 125 C. There are transistors for operation at hundreds of megahertz, and also microwave devices such as gunn diode, tunnel diode. Semiconductor devices impose a very small drain on power sources and make it possible to miniaturize or even micro-miniaturize components and whole circuits. The minimum power for an electronic valve is 0.1 watt, while for a semiconductor device it may be one microwatt. Of course, semiconductor devices will not replace electronic valves in each and all applications, for the valves are also being continually improved. Simply, crystal diodes and transistors may be advantageous in some uses and electronic valves in others. To understand the operation of semiconductor devices, it is necessary to study the semiconductor materials in some detail.

Physical Properties of Elements and Semiconductors 3 1.2 Atomic Structure and Energy Level To understand how semiconductors work, one must have a good knowledge of atomic structure. We know that matter is composed of compounds and elements. The elements are the basic materials found in nature. When elements are combined to form a new material, we have a compound. The smallest particle that an element can be reduced to and still retain its properties is called an atom. Although the atoms of different elements have different properties, they all contain the same subatomic particles. There are a number of different subatomic particles, but only three of these are of interest in basic electronics the proton, the neutron and the electron. The proton and the neutrons are contained in the nucleus of the atom, and the electrons orbit around the nucleus along elliptical path. The electrons and the protons are the particles that have the electrical properties. Neutrons have no electrical charge. An atom has the same number of electrons and protons, and so it is electrically neutral. If an atom does have more electrons than protons, it is called a negative ion. If it has more protons than electrons, it is called a positive ion. To understand the location and energy of each electron in an atom, one must have the knowledge of following four quantum numbers: (i) Principal Quantum Number (n): This characterises the average distance of an electron from the nucleus and corresponds to the principal energy level in which electron resides. Obviously, n gives some idea about the position of the electron around the nucleus. n can have positive integer values starting from 1, i.e. n = 1, 2, 3,.... The principal energy levels or shells having different values of n are designated by the letters K, L, M, N and so on as per X-ray nomenclature. The maximum numbers of the electrons that can be accomodated in a shell corresponding to n is equal to 2n 2. (ii) Azimuthal Quantum Number (l): This is also called as orbital angular momentum quantum number and gives a measure of the angular momentum of an electron in the orbit. Physically, l indicates the shape of the classical orbit. For a given value of n, l can take all positive integer values from o to (n l). The particular l value defines the subshell, and the subshells with l = 0, 1, 2, 3,... are designated as s, p, d, f, g,... respectively. For a given principal quantum number, the energies of various subshells are in the order of s < p < d < f.... Obviously, an electron in the s-subshell has lower energy than in the p subshell with same n. The magnitude of this angular momentum is = = ll ( + 1 ). (iii) Magnetic Quantum Number (m l ): This is also called as orbital magnetic number and this determines the preferred orientation of the orbitals in space with respect to an applied magnetic field. We know that the magnetic moment of an electron due to its orbital motion gives rise to a magnetic field which can interact with an external magnetic field. The electrons orient themselves in certain preferred region of space around the nucleus under the influence of the external field. For a given value of l, m l can take integer values between 1 to + 1 including 0, i.e. total allowed values of m l are (2l + 1). The magnitude of the component of angular momentum along the direction of the magnetic field is m l =. (iv) Spin Quantum Number (m s ): Electron is spinning about its own axis in the atom. The spin of the electron produces a spin magnetic moment which can either be parallel or anti parallel to the surrounding magnetic field. For an electron there are two spin states. Spin quantum number is concerned with the spinning of the electron about its own axis. Thus m s can take only two possible states, +½ or ½.

4 A Textbook of Electronics Pauli Exclusion Principle: It states that in an atom no two electrons can exist in the same quantum state, i.e. in an atom there cannot be two electrons with the same value of all the four quantum numbers. With the help of this principle, one can write the configuration of electrons. We may note that all the electrons with the same value of n constitute a shell and a shell can have a maximum of 2n 2 electrons. The energy state capacity of different shells and subshells are as follows: K-shell. This corresponds to n = 1 and this has one subshell, namely, 1s. This corresponds to n = 1, l = 0, m l = 0, m s = ± ½ and has 2 states. L-shell. This corresponds to n = 2 and this has two subshells, namely, 2s and 2p.2s sub-shell corresponds to n = 2, l = 0, m l = 0 and has 2 states and 2p subshell correspond to n = 2, l = 1, m l = 0, ± 1 and has 6 states. M-shell. This corresponds to n = 3 and has 3s, 3p and 3d subshells. The 3s subshell corresponds to n = 3, l = 1, and m l = 0, ± 1 and has 6 states. The 3d subshell corresponds to n = 3, l = 2, m l = 0, ± 1, ± 2 and has 10 states. Similarly, one can find subshells in other shells, e.g., N, etc. According to Pauli exclusion principle, the electronic distribution in first four shells are shown in Table 1.1. We may note that in all seven shells are required for all the chemical elements in the periodic table. Table 1.1. Electron distribution in subshells Shell K L M N n 1 2 3 4 l 0 0 1 0 1 2 0 1 2 3 Subshell s s p s p d s p d f No. of electrons 2 2 6 2 6 10 2 6 10 14 The electrons in the inner most shells are very strongly attached to the atom and hence they cannot be easily separated. In other words, the electrons that are very near to the nucleus are most tightly bound and hence have the lowest energy. Clearly, the atoms that have electrons in the closed shells will have very stable configurations. The atomic number Z gives the numbers of electrons orbiting about the nucleus and the superscripts are used to designate the number of electrons in a particular subshell, e.g. Z for silicon is 14 and its electronic configuration is given as 1s 2 2s 2 2p 6 3s 2 3p 2. We may note that silicon has only two electrons in the outer most subshell. Electronic configurations of C, Si, Ge, Sn and Pb belonging to same subgroup (IV A) in the periodic table is given in Table 1.2. Table 1.2. Electronic configuration of some elements of group IV A Element Atomic number (Z) Electronic configuration C 6 1s 2 2s 2 2p 2 Si 14 1s 2 2s 2 2p 6 3s 2 3p 2 Ge 32 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 2 Sn50 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 5s 2 5p 2 Pb 82 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 4f 14 5s 2 5p 6 5d 10 6s 2 6p 2

Physical Properties of Elements and Semiconductors 5 Figure 1.3 shows the representation of the atomic structures of H, B, Si, P and Ge atoms. Fig. 1.3 (a) represents the hydrogen atom. It contains one electron revolving around one proton which is the nucleus. The nucleus of H atom contains no neutrons. Figure 1.3 (b) represents the structure of a Boron atom. Its nucleus contains 5 protons and 5 neutrons. There are 5 electrons revolving around the nucleus in different shells. Of which there are two electrons in the first shell, 2 electrons in the second shell and only 1 electron in the third outermost or valence shell. 3rd shell 2nd shell 1st shell Electron Proton Nucleus 1P (a) Hydrogen atom (H) 1 (b) Boron atom (B) 5 (c) Silicon atom ( Si) 14 (d) Phosphorus atom ( P) 15 (e) Germanium atom ( Ge) 32 Fig. 1.3 Atomic structure of a few atoms. Figure 1.3 (c) represents the structure of a Silicon atom. It contains 14 protons and 14 neutrons in the nucleus. There are 14 electrons revolving around the nucleus in different shells. Of which there are 2 electrons in the first shell, 8 electrons in the second shell and 4 electrons in the outermost or valence shell. Figure 1.3 (d) and 1.3 (e) represent the structure of Phosphorus and Germanium atoms respectively. We note that phosphorus contains 5 electrons in the outermost shell whereas Ge atom contains 4 electrons in the outermost shell which are called valence electrons. The electrons in the inner shells of an atom are strongly bound and do not normally leave the atom. But the electrons which are in the outermost shell, so-called valence shell do not always remain confined to the same atom. Some of these valence electrons move in a random manner and may travel from one atom to another in a crystal lattice. These electrons are called as free electrons. It is due to the presence of these free electrons in a material, that electrical conduction is possible. The electrons in the inner orbits of the atom remain bound to the nucleus and are, therefore, called bound electrons. The tendency of an atom to give up its valence electrons depends on chemical affinity. When an atom is stable, it resists giving up electrons, and when it is unstable, it tends to give

6 A Textbook of Electronics up electrons. The level of stability is determined by the number of valence electrons, because the atom strives to have its outermost or valence shell completely filled. If an atom s valence shell is more than half filled, then atom tends to fill its shell. Since 8 is the maximum electrons that can be held in the valence shell, elements with 5 or more valence electrons make good insulators, since they tend to accept rather than give up electrons. On the other hand, atoms with less than 4 valence electrons tend to give up their electrons, thereby the valence shell is empty, this would allow the next shell, which is already filled, to be the outermost shell. These atoms make the best electrical conductors. The elements Si(14) and Ge(32) have 4 valence electrons, and are neither good conductors and nor good insulators. These are called semiconductors. Most characteristics of semiconductors can be easily explained by means of an energy level diagram. We are familiar that each isolated atom has only a certain number of orbits available. These available orbits represent energy levels for the electrons in the atom. According to Bohr s theory of atomic structure only discrete values of electron energies are possible. An electron energy is usually expressed in electron volt (1 ev = 1.6 10 19 J = 1.6 10 12 erg). An electron can have only certain permissible values, i.e., no electron can exist at an energy level other than a permissible one. Energy level diagram for hydrogen atom is shown in Fig. 1.4. The permissible energy levels for hydrogen atom are numbered n = 1, 2, 3... in increasing order of energy. n = En (ev) 0 n =4 n =3 n =2 Balmer series Paschen series Brackett series 0.85 1.5 3.4 n =1 Lyman series 13.6 Fig. 1.4 Energy level diagram of hydrogen In any atom, an electron orbiting very close to the nucleus in the first shell is strongly bound to the nucleus and possesses only a small amount of energy. The greater the distance of an electron from the nucleus, the greater is its total energy. The total energy of an electron includes Kinetic and Potential energies. Obviously, an electron orbiting far from the nucleus would have a greater energy, and hence it can be easily knocked out of its orbit. This makes it clear that why the valence electrons having maximum energy take part in chemical reactions and in bonding the atoms together to form solids.

Physical Properties of Elements and Semiconductors 7 When radiations impinge on an atom, the inner shell, electrons are excited to higher (outer shell) energy levels. The excited state of electron does not last long and very soon, the electron after emitting out energy in the form of heat, light or other radiations, falls back to the original energy level. 1.3 Energy Band Theory Most of the metals and semiconductors have crystalline structure. A crystal is made of a space array of atoms of molecules in regular repetition in three dimensions of some fundamental building block. The electronic energy levels for a gaseous element are the same as for a single free atom because the individual atoms in a gas are well apart and has negligible influence on each other. However, in a crystal the individual atoms are so closely packed that the resulting energy levels get modified due to interaction between the atoms in a crystal lattice. We may note that when atoms form crystals, the energy levels of the inner shell electrons are not affected appreciably. On the other hand, the energy levels of the outer-shell electrons are considerably altered as these electrons are shared by the adjacent atoms in the crystal. As a consequence of this interaction between the electrons of outer-shell, the energy levels spread up to form a of energy (Fig. 1.5). Isolated atoms 2N electrons 6N states 2N electrons 6N p states Energy 2N electrons 2N states 2N electrons 2N s states Lower energy levels remain unaffected by crystal formation a Interatomic spacing Fig. 1.5 Energy formation in a crystal To make more clear the formation of energy s in a crystal, we consider an example of silicon crystal made up of N atoms. Let us assume that the interatomic spacing can be varied without affecting the fundamental crystal structure. Let, the interaction between adjacent atoms is negligible for very large interatomic spacing, say a (Fig. 1.5). Silicon has 14 electrons and the outermost subshells, namely, 3s and 3p contain 2 electrons each. Thus in a silicon crystal consisting of N atoms, the outermost subshells 3s and 3p consist of 2 N electrons each. Obviously, the 3s subshell has 2 N electrons completely occupying the available 2 N

Forbidden energy gap 8 A Textbook of Electronics states, and the 3p subshell has only 2 N electrons partially occupying the available 6 N states, all at the same energy level. Now, we consider that the interatomic spacing is gradually decreased, i.e. we are moving from right to left (Fig. 1.5). This means that there will be a gradual increase in the interaction between the neighbouring atoms. The atomic wave functions overlap due to this interaction. This makes the crystal an electronic system which obeys the Pauli exclusion principle. Clearly, 2Ns states spread out to form a of energy. Since N is very large (~ 10 23 /cm 3 ) and separation between energy levels is small, the total spread between the minimum and maximum energy levels become large. This spread will have several volts of energy and termed as energy. The lower shaded region in Fig. 1.5 shows this. In this the 2 N states are completely filled with 2 N electrons. Similarly, we see that at the same value of interatomic spacing at p- level, 6 Np states spread up to form a. The upper shaded region in Fig. 1.5 shows this we may note that there are 6 N states available in this but only 2 N states are occupied and remaining 4 N states remain unoccupied. There exists an energy gap (E g ) between two energy s, called as forbidden energy gap, as no electrons can occupy states in this energy gap. With the decrease in atomic spacing this forbidden energy gap decreases and becomes zero with further reduction in the interatomic spacing, say at b (Fig. 1.6). When the interatomic spacing is small enough, the two energy s will overlap. Under these circumstances, the 6 Np states in the upper merge with the 2 Ns states in the lower, giving a total of 8 N states. Half of these 8 N states, i.e. 4 N states are occupied by the 4 N available electrons. Now, these 4 N electrons no longer belong to either p-subshell or s-subshell but belong to the entire crystal. Clearly, at this interatomic spacing, each atom in the crystal can contribute 4 electrons to the crystal. The occupied by these contributed electrons is known as valence. 4N states 0electrons Conduction Energy 0 states E g Crystal lattice spacing 4N states 4N electrons Valence c b Interatomic spacing Fig. 1.6 Energy in a crystal as a function of interatomic spacing Now, if the interatomic spacing is further reduced, say c (Fig. 1.6), the interaction between the atoms becomes very large, and the energy structure becomes as shown in Fig. 1.6. The exact shape of the energy structure depends on : (i) the orientation of the

Physical Properties of Elements and Semiconductors 9 atoms relative to each other in space, and (ii) the atomic number of the atom, which may be obtained from the solution of Schrödinger s wave equation. For spacing c, 4 N states in the valence are completely filled by 4 N electrons. This valence is separated from the upper unfilled or empty by a forbidden energy gap (E g ). However, the forbidden energy gap contains no allowed energy states. The upper energy has 4 N unfilled energy states and this is called as the conduction. 1.4 Energy Band Diagrams in Solids The simple energy level diagram of Fig. 1.4 for electron energies for a single atom is no longer applicable when one discusses a solid. A solid is formed when atoms bond together. In a solid, the orbit of an electron is influenced not only by the charges in its own atom but by electrons and nuclei of every atom in the solid. Each electron in a solid occupies a different position inside the solid and hence no two electrons can have exactly the same pattern of surrounding charges. Obviously, the orbits of electrons in a solid are different. When one is considering a solid in bulk, then the simple energy level diagram in Fig. 1.4 modifies to that shown in Fig. 1.7. All electrons belonging to the first orbits have slightly different energy levels because no two electrons see exactly the same charge environment. Since there are billions of first-orbit electrons in a bulk mass, the slightly different energy levels form a group or. Similarly, the billions of second orbit electrons, all with slightly different energy levels, form the second energy. Similarly all third orbit electrons form the third and so on. Conduction Energy (ev) Energy gap 3rd (Valence ) 2nd 1st Fig. 1.7 Energy s of silicon at absolute zero Silicon is a commonly used semiconductor having atomic number 14. It has 4 electrons in its outermost or valence orbit. Here, the third becomes the valence (Fig. 1.7). In Fig. 1.7, all these three s are shown completely filled. Although the third shell of an isolated atom of silicon is not completely filled as it has only 4 electrons whereas it could

10 A Textbook of Electronics accommodate a maximum of 8 electrons, the third energy or valence of a bulk silicon material behaves as if it is completely filled. It is so, because in solid silicon each atom positions itself between four other silicon atoms, and each of these neighbours share an electron with the central atom. In this manner, each atom now has 8 electrons filling the valence completely as shown in Fig. 1.12 (for Silicon), i.e., all the permissible energy levels in the are occupied by electrons. Obviously, no electron in a filled can move and hence an electron in a completely filled cannot contribute to electric conduction current. At absolute zero temperature, electrons cannot move through the solid silicon material and hence it acts like a perfect insulator. Beyond the valence there is a conduction (Fig. 1.8). At absolute zero temperature, the conduction is empty, i.e., no electron has enough energy to reach in a conduction from valence. Definite amount of energy is needed to shift the electron from the valence to the conduction. This amount differs from one substance to another substance and helps to classify them as conductors, insulators and semiconductors. 1.5 Conductors, Semiconductors and Insulators The structure in a solid determines whether the solid is an insulator or a conductor or a semiconductor. The s are filled upto a certain level by the electrons within each atom. The highest in which electrons are still predominantly attached to their atoms are found is called the valence. This is the in which the valence (outermost) electrons from each atom will be located. These are the electrons that are the possible carriers of electricity. However, in order for an electron to conduct, it must get up to a slightly higher energy so that is free of the grip of its atom. Insulators: Let us consider the case when the valence in full, i.e., when there are no more available energy levels. Then, a valence electron must jump (increase its energy) into the next higher to be free. If the energy gap between the valence and the conduction is too large, then the electron will not be able to make that jump. Such a material will not be a good conductor of electricity, and is called an insulator. Forbidden energy gap in an insulator is about 5 ev or even more (Fig. 1.8 (a)). The theory of solids tells us that an insulator is a material in which the valence s are filled and the forbidden energy gap Conduction Conduction Conduction Conduction Energy (ev) Eg 5 ev or more Valence Valence Valence E g 1 ev Valence (a) (b) (c) (d) Fig. 1.8 Energy diagram exhibiting energy gap in (a) Insulators, (b) and (c) Conductors, and (d) Semiconductors