Metals, semiconductors and semiconductors

Dr. S. H. Burungale

1. Module Metals , Semiconductors and Semiconductors Dr.S.H. Burungale

2. Metals, Semiconductors and Semiconductors The electron theory of solidsaims to explain the structures andproperties of solids through their electronic structure .  The electron theory of solids has been developed in three main stages.

3. The Solid State: Matter is something that has mass and occupies space .It is characterized by a set of properties such as shape, size, mass, melting point, boiling point., color, texture, reactivity, etc. Based on size shape, volume and rigidity, matter is classified into three categories: solid, liquid and gaseous .There are some simplifying features of solids which allow considerable insight into their nature. The solids have definite shape and volume and are rigid. Therefore solids are characterized by rigidity incompressibility and mechanical strength. .These facts indicate that the atoms ions or molecules which make up the solids are very closely packed .They are held together by strong forces of attraction and are not free to move at random. The solids are, therefore, the outcome of well ordered arrangement of building units. A good understanding of nature and properties of solids will provide a wide range of tailor-made materials with specific properties having uses in the development of science and technology. Much of our recent progress is no doubt due to the advances we have made in solid state physics and solid state chemistry.

4. Types of Solids: From the state of aggregation the solids are grouped into two categories: amorphous and crystalline. Crystalline Solids : The Solids whose constituents are arranged in a regular geometrical pattern over the entire lattice are knows as the crystalline Solids .This is proved to be so by X –ray diffraction study .Due to the orderly arranged atoms, ions or molecules the crystalline Solids exhibit different elements of symmetry and accordingly belong to either of the crystal systems.

5. Metallic Crystals: The crystalline Solids having positively charged metal ions in the lattice points, surrounded by a sea of mobile electrons are known as metallic crystals. For example: Copper, Silver, gold, sodium, potassium, iron, cobalt, nickel, etc. Here the binding force is the electrical attraction between positively charged metal ions and negatively charged sea of mobile electrons. On account of this fact the metals are characterized by many typical features. They may be soft or hard sufficiently tough, with moderate to very high melting points, good conductors of heat and electricity. These are malleable, ductile and elastic with high tensile strength; exhibit good Iustre on fresh cut etc. (Exception – mercury). In the present chapter our aim is to discuss crystalline Solids such as metals semiconductors and super-conductors.

6. METALS: The most numerous of all the elements are the metallic elements. All the elements in the s, d and f blocks are metals: aluminium , gallium, indium, thallium, tin, lead and bismuth of the p-block are considered to be metals. Further, germanium and polonium are also sometimes taken to be metallic elements. Thus the metals constitute about eighty percent of the element in the periodic Table. It appears that the element with too little electrons in the valence shell but with too many orbitals behave as metals. No doubt, metals are marvels among elements. The marvelous characteristics such as luster, conductivity, malleability, ductility, etc of metals have been attributed to the metallic bond. Metals mean such to modern man. Every amenity of modern civilization depends heavily on metals. In fact there is no moment when man is not in contact with metallic objects directly or indirectly. In other words the distinctive applications of metals are due to the strange nature of forces that exist within the metals .Hence to understand metals it is wise to make an attempt only through their special features .

7. PROPERTIES OF METALLIC SOLIDS Metals are characterized by a set of physical properties. Let us take a brief account of some of these properties to understand, “What the metals exactly are”. 1. Crystal Structure The distinctive properties of metals depend on their crystal structure .Metals have comparatively high melting points ,high boiling points and high densities .These indicate a close-packing of atoms .X-ray analyses have revealed that the metallic atoms give closest packed structures namely face centered cubic, body centered cubic and hexagonal close-packed

8. Crystal structure of Metals Types of Lattice Co-ordination number Metals Cubic closed packed ( ccp ) or ( fcc ) 12 Cu, Ag, Au, Ca, Sr, Fe, Co, Ni, Ru, Rh, Rd , Os, Ir, Pt, Sc, Y, La etc. 2. Body-centered cubic (bcc) 8 Li, Na, K, Rb , Cs, Ti, Zr , Hf , V, Nb , Ta, Cr, Mo, W etc 3. Hexagonal closepacked 12 Be, Mg, Ca, Sc, Y, La, Ti, Zr, Hf, Co, Ni, Ru, Os, Zn, Cd etc 4. Complex structure 12 As, Sb , Bi, Se, Te, Po, Pa, U, Np , Pu , Ga , In, Ge , Sn etc

9. 2. High Electrical Conductivity : Conduction is mechanism of transmission of energy without transfer of mass. Electrical conduction arises due to the flow of mobile electrons through the vacant space between the metal ions. Conduction is effected by displacement mechanism. When an electric field is applied across a metal electrons enter at one end and kicked out form the other as shown in Fig 4.2 Conductivity is a periodic property. With increase of mobile electrons, conductivity increases. e.g. Na < Mg < Al . Thus aluminum which contributes three valence electrons is the best conductor of electricity. With increase of temperature, atomic vibrations increase. Electrical conductivity therefore decreases with increase of temperature. There is an enormous difference in electrical conductivity between metals and the other kinds of solids

10. Solid matter Bond type Electrical conductivity Silver Metallic 6.3 × 105 Copper Metallic 6.0 × 105 Sodium Metallic 2.4 × 105 Zinc Metallic 1.7 × 105 Sodium chloride Ionic 1 × 10-7 Diamond Covalent 1 × 10-14 Quartz Covalent 1 × 10-14

11. 3. High Thermal Conductivity Among solid substances metals are by far the best conductors of heat. If metal is heated at one end, the heat is carried to the other end. Mobile electrons absorb energy, become more mobile, collide on adjacent electrons and heat is transported to the other end . similar to the electrical conductivity, the metals are characterized by high thermal conductivity. Thermal conduction increases if number of mobile electrons increases e.g. Na < Mg < Al. With rise in temperature, heat conductivity decreases as the vibrational motion of metal ions increases.

12. 4. Metallic Lustre : (Reflectivity) All metals typically have a lustrous shiny appearance .When a beam of light (i.e. electromagnetic radiations) falls on the surface of metal its electric field sets the mobile electrons in the surface of the metal into to and fro oscillations. We know that any moving charge always emits electromagnetic energy. Hence, these oscillating electrons emits electromagnetic energy in the form of light .Thus when light falls on the surface of the metal it seems as if light is being reflected .This reflectivity is known as metallic luster. In other words it may be commented that when a beam of light falls on a clean surface the mobile electrons move to some excited state. When these electrons jump back to ground state, light of all wave lengths is re-emitted. Hence show luster.

13. 5. Emissivity : (Emission of Electrons ) Under the conditions of excitation emission of electrons is called emissivity. When a metal is heated strongly it emits electrons. e.g W at (28000C) 3073 K and Th at (18000C) 2073 K. On heating the mobile electrons acquire kinetic energy and get boiled off the electron sea. This is known as thermionic emission. This property is used in thermionic valves. On the other hand, the metals like sodium, potassium, selenium etc. emit electrons when irradiated with UV light. This is known as photoemissivity . This principle is exploited in photoelectric cells.

14. 6. Melting and Boiling Points : In metallic crystals the force of bonding between metal and metal is the strong electrostatic force of attraction between the positively charged metal ions and the negatively charged sea of mobile electrons. This force is essentially non-rigid and non-directional. Therefore metals have very high melting points and high boiling points. 7. Magnetism: Many metals possessing one or more unpaired electrons especially the d-and fblock elements, shows considerable degree of paramagnetism .

15. MECHANICAL PROPERTIES 8 . Malleability, Ductility and softness Metals are malleable i.e. easily flattened into thin sheet and are ductile i.e. easily drawn into wire .These properties make the metals the most useful materials of construction. Metallic elements have a close-packed structure with high coordination number say 8 to 12. The bonding in metallic crystals is the attraction between positively charged metal ions and the mobile electrons. These forces holding the metal ions together are therefore, non rigid and non-directional. On applying mechanical force one layer of ions slips over the other. As a result metal ions move easily from on e lattice site to the other. But in terms of crystal lattice, nothing is changed. The environment of every metal ion remains the same as before since the delocalized electrons are available everywhere which adjust the positions rapidly and the crystal lattice is restored

16. This explains why the metals are malleable and ductile. The possibility of planes gliding is found to be greatest in cubic close-packed structures, so these are generally softer and more easily deformed than hexagonal. This fact further explains why metals like sodium and potassium can easily be cut with a knife. Thus the softness of metals can be accounted for. In these cases, the electron cloud is very much diffused and the bonding is considerably weaker in the lattices. Aluminium with ccp is highly malleable and ductile while magnesium with hcp is less malleable, less ductile and more brittle.

17. 9. High Tensile Strength: Metals have high tensile strength i.e. metals can resist stretching without breaking. This is attributed to the strong electrostatic force of attraction between the positively charged metal ions and the negatively charged mobile electrons surrounding to them. Thus metallic crystals differ from the covalent crystals or ionic crystals. 10 . Elasticity Elasticity is a property by virtue of which a substance can regain its original form as soon as the deforming force is removed .This property is attributed to the ease with which the metal ions can move from one lattice site to another.

18. THEORIES OF BONDING IN METALS Review: The metallic bond is a type of binding or linkage or attraction or force that holds the atoms of two or more metals together in an alloy or it is the force that links atoms of the pure metal together in a metallic crystal. The metallic bond cannot be an ionic bond as there is no transfer of electrons from electropositive element to electronegative element. It cannot be a directional (covalent) bond since metallic properties persist even in liquid state (e.g. mercury) or in solution (e.g. sodium in liquid ammonia) etc. Different theories have been suggested for metallic bonding from time to time .The successful theory of bonding in metals is one which can explain the following to utmost satisfaction. a) The great mobility of electrons in metallic solids. b) The bonding between a large numbers of identical atoms in a pure metal. c) The bonding between widely different atoms in an alloy and d) The non-rigid and non-directional bonding in metals which is retained even in the liquid state (say in ,mercury) or even for the metals which are dissolved in a suitable solvent e.g. sodium in liquid ammonia .

19. These are at present three theories to explain the metallic features Free Electron theory or Electron Gas Theory Valence Bond theory (VBT) or Pauling’s Atomic orbital theory and Molecular orbital Theory or Band theory

20. 1. The Free Electron Theory of Metals: As early as 1900 the free electron theory was first proposed by Drude and was further refined by Lorentz in 1932. The theory is based upon two assumptions (a) Mutual repulsion between the negative electrons in absent. (b)The potential field due to the positive ions is completely uniform throughout the metallic crystal. According to Drude metal is a lattice through which electrons move as freely as molecules of a gas .This idea was used primarily to account electrical conductivity of metals. According to Lorentz metal is a lattice of rigid spheres (i.e. positive metal ions) embedded (fixed) in a gas of valence electrons which could move freely in the interstices of metal throughout the crystal .

21. Explanation: We know that metals are poor in valence electrons and have low ionization energies. Hence metals lose some of their valence electrons and tend to be electropositive. The electrons so freed are not bound to any single nucleus but spread out around several nuclei. Such free electrons are referred to as non localized or delocalized or mobile electrons and their some total collection is appropriately termed as electron pool or electron cloud or electron gas according to the classical electromagnetic theory. For clear understanding take into consideration If many metal atoms are brought close together the outer energy levels of each can merge together when they begin to overlap. The outer electrons are then in a position to move not just around one atom but around and between all the atoms. These electrons have turned to be delocalized or non localized and are therefore more stable. Thus a block of metal may be visualized as an array of positive ions located in the crystal lattice, immersed in an ocean of mobile electrons. The metallic bond is the force of attraction between metal atoms and all the electrons under their influence.

22. Illustration: Consider a simple metal such as lithium. It crystallizes in the body centred cubic form. Hence each atom of lithium is co- ordinated by eight neighboring lithium atoms. The electronic configuration of lithium is 1s2 2s1 i.e. For lithium metal, one cannot expect ordinary covalent bonding which requires eight pairs of electrons as CN=8 but there is only one such electron per lithium atom. This means that the single electron utilizes all the four valence orbitals ; 2s and 2p’s available to it .Thus the nine electrons from (1+8) lithium atoms have freedom to move simultaneously in all the (9x4) thirty six orbitals forming the unit cell of lithium. The electrons are thus regarded as belonging to the crystal a whole and not just to any particular atom or atoms. Since the theory accounts for electron gas or sea of mobile electrons and the non directional nature of bonding, it can successfully explain the properties of metals such as metallic lustre , malleability, ductility high thermal and electrical conductivity high melting and boiling points etc as already outlines. But the theory fails to explain the following due to the concept of electron gas in metallic solids namely i . Semiconductance ii. Specific heats iii. Calculations of cohesive energy of metallic crystals quantitatively. (Another sincere attempt was made to explain metallic bonding by Prof. L. pauling in 1940. This is known as pauling’s Atomic Orbital of Valence Bond Theory. He pictured metallic bond to be a dynamic covalent bond which oscillates through a number of positions between an atom and its nearest neighbors.

23. 2. The Band Theory (Molecular Orbital Theory) The characteristic physical properties as well as the high co-ordination number (either 8 or 1) suggest that the bonding in metals is quite different from those in other substances. There is ionic contribution and it is also not possible to have 2c2e covalent bonding between all the adjacent pairs of atoms since there are neither sufficient electrons nor sufficient orbitals . A satisfactory explanation has been provided for metallic bonding by the so-called band theory or molecular orbital theory. The configurational study of elements reveals that the presence of empty AOs in the valence shell is a prerequisite for metallic properties. The elements which lack in empty AOs in their valence shell are all non-metals. For example, carbon in excited state and N, O, F, Ne, etc. lack in empty AOs and are therefore non metals.

24. 2. The Band Theory (Molecular Orbital Theory) The characteristic physical properties as well as the high co-ordination number (either 8 or 1) suggest that the bonding in metals is quite different from those in other substances. There is ionic contribution and it is also not possible to have 2c2e covalent bonding between all the adjacent pairs of atoms since there are neither sufficient electrons nor sufficient orbitals . A satisfactory explanation has been provided for metallic bonding by the so-called band theory or molecular orbital theory. The configurational study of elements reveals that the presence of empty AOs in the valence shell is a prerequisite for metallic properties. The elements which lack in empty AOs in their valence shell are all non-metals. For example, carbon in excited state and N, O, F, Ne, etc. lack in empty AOs and are therefore non metals

25. Formation of Energy Bands: Basis: The band theory is put forward by Bloch in 1928. This theory is an extension of MOT to metallic structure. According to MOT formation of energy band may be outlined as follows: We may recall that AOs combine to form MOs of which one half will be bonding type and the other half will be of the anti-bonding type .This mechanism results in the splitting of the original atomic orbital energy levels into different energy MOs. Clue: In metal crystal there are numerous atoms which involve several combinations between their different types of atomic orbitals . Suppose in a metal crystal there are combinations between n orbitals where n may be considered to be 6x1023 (Avogadro Number) So that there will be 3x1023 bonding and 3x1023 antibonding MOs. If the starting AOs are all of similar energy (say 2s AOs in lithium crystal), the resulting boding and anti-bonding MOs give rise to series of very closely spaced energy levels that constitute an energy band

26. 1. Lithium Metal : The electronic structure of lithium atoms is 1s2 2s1 2p0 When two lithium atoms join, a lithium molecule Li2 is formed .Here the 2 s AOs on each of the two Li atoms combine to give tow MOs one bonding and one anti-bonding where the valence electrons occupy the bonding MO and Li2 is formed see Fig 4.8 Now suppose four Li atoms join to form Li4 molecule. In Li4 four AOs would form MOs –two boning and tow anti-bonding. As the number of atoms is the cluster increases the spacing between the various orbitals decreases. And thus with a large number of atoms the energy levels of the orbitals are so close together that the virtually form a continuum i.e. band as shown in Fig 4.10 The numbers of MOs are always equal to the number of AOs involved in bonding. Since there is only one valence electron per atom in lithium and a MO can hold two electrons it follows that only half the Mos in the 2s valence band are filled i.e. the binding MOs are only filled while the anti-bonding MOs are completely empty.

27. Note: As the MOs extend in three dimensions over all the atoms in the crystal the electrons have a very high degree of mobility in crystal lattice. A minute amount of energy is more than sufficient to perturb (push) an electron to empty levels where it moves rapidly and readily. This mechanism explains the high degree of thermal and electrical conductivity of metals. In absence of an electric field equal number of electrons move in all possible directions. But if a positive electrode is placed at one end and a negative at the other then the electrons will move towards the anode (+) much more readily than in the opposite direction and thus the electric current flows as shown in Fig (4.2) In metals conduction occurs because MO extend over the whole crystal and because there is effectively no energy gap between the filled and lithium is because only half the MO band is filled with electrons

28. 2. Beryllium Metal : Be (z=4): 1s2 2s1 2p0 In the valence shell of beryllium atom there are two valence electrons which would just fill the 2 s valence band of MOs. In the isolated beryllium atom, the 2s and 2p AOs are some 160 kJ mol-1 different in energy. But in beryllium metal (say Ben ) the 2p AOs form a 2p band of MOs just similar to the 2s band of MOs formed from the 2s AOs. The striking aspect is that the upper part of the 2s band overlaps with the lower part of 2p band .This overlap causes some of the 2p band occupied while some of the 2s band to be empty. Thus in metallic crystal the energy gap is absent so easy perturbation of electrons from the filled valence band to the empty conduction band. Hence beryllium behaves as a metal. It should be noted that the energy bands thus produced belong to the crystal as a whole and act as a measure of the complete delocalization of electron cloud. This fact will naturally account all the properties of metals that we encounter. For further understanding of formation of energy bands, another pictorial presentation may be shown where energy may be plotted horizontally and the number of electrons that may be accommodated at each value of the energy may then appear as an envelope on the vertical as shown in figure .Here the shading represents the filling up of the bands with the available number of electrons .These are called N (E) curves which show the complete distribution of electrons between the various possible energy states and in turn the distribution of various possible energy states and in turn the distribution of various energy states over the energy range within a band.

29. Band Theory and High Conductivity of Metals According to MOT, energy states extend in 3D over the entire crystal lattice. It provides a great mobility to electrons under suitable circumstances and imparts high conductivity to metals. For alkali metals (ns 1 ), Li, Na, K etc. the lower half of ns band in filled while the upper half if completely empty to serve as a conduction band See Fig 4.10 and Fig 4.12(a) For alkaline earth metals (ns2 ) such as Be ,Mg etc. the ns band is completely full while np band is completely empty where the upper np hand overlaps the lower ns band and as a result there remains no energy gap between the filled valence band and the empty conduction band. This is the situation especially at absolute zero. Consequently at any other temperature the available thermal energy is just sufficient to excite a large number of electrons form the valence band to the conduction band where they can move very freely. Hence the metals exhibit electrical and thermal conductivities

30. i ). The classical free electron theory:Drude and Lorentz developed this theory in 1900. According to this theory, the metals containing free electrons obey the laws of classical mechanics . ( ii). The Quantum free electron theory: Sommerfeld developed this theory during 1928. According to this theory, the free electrons obey quantum laws.  ( iii). The Zone theory: Bloch stated this theory in 1928. According to this theory, the free electrons move in a periodic field provided by the lattice. This theory is also called “Band theory of solids”

31. The classical Free Electron Theory of Metals ( Drude - Lorentz theory of metals Lecture-2postulates :(a). In an atom electrons revolue around the nucleus and a metal is composed of such atoms.(b). The valence electrons of atoms are free to move about the whole volume of the metals like the molecules of a perfect gas in a container. The collection of valence electrons from all the atoms in a given piece of metal forms electrons gas. It is free to move throughout the volume of the metal 

32. (c) These free electrons move in random directions and collide with either positive ions fixed to the lattice or other free electrons. All the collisions are elastic i.e., there is no loss of energy . ( d). The movements of free electrons obey the laws of the classical kinetic theory of gases . ( e). The electron velocities in a metal obey the classical Maxwell – Boltzmann distribution of velocities. 

33. (f). The electrons move in a completely uniform potential field due to ions fixed in the lattice.(g). When an electric field is applied to the metal, the free electrons are accelerated in the direction opposite to the direction of applied electric field. 

34. Success of classical free electron theory:(1). It verifies Ohm’s law.(2). It explains the electrical and thermal conductivities of metals.(3). It derives Wiedemann – Franz law. (i.e., the relation between electrical conductivity and thermal conductivity)(4). It explains optical properties of metalsl . Drawbacks of classical free electron theory:1. The phenomena such a photoelectric effect, Compton effect and the black body radiation couldn’t be explained by classical free electron theory.2. According to the classical free electron theory the value of specific heat of metals is given by 4.5Ru is the Universal gas constant whereas the experimental value is nearly equal to 3Ru. Also according to this theory the value of electronic specific heat is equal to 3/2Ru while the actual value is about 0.01Ru

35. 3.Electrical conductivity of semiconductor or insulators couldn’t be explained using this model . 4 . Though K/ σT is a constant ( Wiedemann – Franz Law) according to the Classical free electron theory, it is not a constant at low temperature . 5 . Ferromagnetism couldn’t be explained by this theory. The theoretical value of paramagnetic susceptibility is greater than the experimental value. 

36. Mean free path Lecture-3The average distance traveled by an electron between two successive collisions inside a metal in the presence of applied field is known as mean free path.   Relaxation TimeThe time taken by the electron to reach equilibrium position from its disturbed position in the presence of an electric field is called relaxation time. Drift velocity• In the presence of electric field, in addition to random velocity there is an additional net velocity associated with electrons called drift velocity.• Due to drift velocity, the electrons with negative charge move opposie to the field direction. 

37. Fermi Level “ The highest energy level that can be occupied at 0K” is called Fermi level.• At 0K, when the metal is not under the influence of an external field, all the levels above the Fermi level are empty, those lying below Fermi level are completely filled.• Fermi energy is the energy state at which the probability of electron occupation is ½ at any temperature above 0k.

38. Fermi-Dirac statistics Lecture-6According to Fermi Dirac statistics, the probability of electron occupation an energy level E is given by F(E) = 1/ 1+exp (E-EF/ kT )   Electrical Resistivity Lecture-7• The main factors affecting the electrical conductivity of solids are i ) temperature and ii) defects (i.e. impurities).• According to Matthiesens’s rule, the resistivity of a solid is given by ρpure = ρpure + ρimpurity where ρpure is temperature dependent resistivity due to thermal vibrations of the lattice and ρimpurity is resistivity due to 

39. In a conductor, electrons can move freely among these orbitals within an energy band as long as the orbitals are not completely occupied. conductor

40. Small Band Gap

41. CLASSIFICATION OF MATERIALS Based on ‘band theory’, solids can be classified into three categories, namely , Insulators semiconductors & conductors . What are Semiconductors? Semiconductors are the materials which have a  conductivity between conductors  (generally metals) and non-conductors or  insulators  (such ceramics). Semiconductors can be compounds such as gallium arsenide or pure elements, such as germanium or silicon. Physics explains the theories, properties and mathematical approach governing semiconductors. Examples of Semiconductors: Gallium arsenide, germanium, and silicon are some of the most  commonly used semiconductors . Silicon is used in electronic circuit fabrication, and gallium arsenide is used in solar cells,  LASER DIODE,

42. Table of Content Holes and Electrons Band Theory Properties of Semiconductors Types of Semiconductors Intrinsic Semiconductor Extrinsic Semiconductor N-Type Semiconductor P-Type Semiconductor Intrinsic vs Extrinsic Applications

43. Holes and Electrons in Semiconductors Holes and electrons  are the types of charge carriers accountable for the  flow of current  in semiconductors.  Holes  (valence electrons) are the positively charged electric charge carrier whereas  electrons  are the negatively charged particles. Both electrons and holes are equal in magnitude but opposite in polarity.

44. Mobility of Electrons and Holes In a semiconductor, the  mobility of electrons is higher than that of the holes . It is mainly because of their different band structures and scattering mechanisms. Electrons travel in the conduction band whereas holes travel in the valence band. When an electric field is applied, holes cannot move as freely as electrons due to their restricted movent . The elevation of electrons from their inner shells to higher shells results in the creation of holes in semiconductors. Since the holes experience stronger atomic force by the nucleus than electrons, holes have lower mobility. The mobility of a particle in a semiconductor is more if;

45. Effective mass of particles is lesser Time between scattering events is more For intrinsic  silicon  at 300 K, the mobility of electrons is 1500 cm 2  (V∙s) -1  and the mobility of holes is 475 cm 2  (V∙s) -1 . The  bond model  of electrons in silicon of valency 4 is shown below. Here, when one of the free electrons (blue dots) leaves the lattice position, it creates a hole (grey dots). This hole thus created takes the opposite charge of the electron and can be imagined as positive charge carriers moving in the lattice. Concept of Electrons and Holes in Semiconductors

46. Band Theory of Semiconductors The introduction of band theory happened during the quantum revolution in science. Walter Heitler and Fritz London discovered the energy bands. We know that the electrons in an atom are present in different energy level. When we try to assemble a lattice of a solid with N atoms, then each level of an atom must split up into N levels in the solid. This splitting up of sharp and tightly packed energy levels forms  Energy Bands . The gap between adjacent bands representing a range of energies that possess no electron is called a  Band Gap .

47. Energy Band Diagram for Semiconductors, Conductors, and Insulators

48. INSULATORS• Bad conductors of electricity• Conduction band is empty and valence band is full, and these band are separated by a large forbidden energy gap.• The best example is Diamond with Eg =7ev. SEMI CONDUCTORS• Forbidden gap is less• Conduction band an d valence band are partially filled at room temperature.• Conductivity increases with temperature as more and more electrons cross over the small energy gap. 22• Examples Si(1.2ev) & Ge (0.7ev) CONDUCTORS• Conduction and valence bands are overlapped• Abundant free electrons already exist in the conduction band at room temperature hence conductivity is high.• The resistively increases with temperature as the mobility of already existing electrons will be reduced due to collisions.• Metals are best examples

49. Conduction Band and Valence Band in Semiconductors Valence Band: The energy band involving the energy levels of valence electrons is known as the valence band. It is the highest occupied energy band. When compared with insulators, the bandgap in semiconductors is smaller. It allows the electrons in the valence band to jump into the conduction band on receiving any external energy . Conduction Band: It is the lowest unoccupied band that includes the energy levels of positive (holes) or negative (free electrons) charge carriers. It has conducting electrons resulting in the flow of current. The conduction band possess high energy level and are generally empty. The conduction band in semiconductors accepts the electrons from the valence band.

50. Fermi Level in Semiconductors Fermi level (denoted by EF) is present between the valence and conduction bands. It is the highest occupied molecular orbital at absolute zero. The charge carriers in this state have their own quantum states and generally do not interact with each other. When the temperature rises above absolute zero, these charge carriers will begin to occupy states above  Fermi level . In a  p-type semiconductor , there is an increase in the density of unfilled states. Thus, accommodating more electrons at the lower energy levels. However, in an  n-type semiconductor , the density of states increases, therefore, accommodating more electrons at higher energy levels.

51. Properties of Semiconductors Semiconductors can conduct electricity under preferable conditions or circumstances. This unique property makes it an excellent material to conduct electricity in a controlled manner as required. Unlike conductors, the charge carriers in semiconductors arise only because of external energy (thermal agitation). It causes a certain number of  valence electrons  to cross the energy gap and jump into the conduction band, leaving an equal amount of unoccupied energy states, i.e. holes. Conduction due to electrons and holes are equally important. Resistivity:  10 -5  to 10 6   Ωm Conductivity:  10 5  to 10 -6  mho/m Temperature coefficient of resistance:  Negative Current Flow:  Due to electrons and holes

52. Why does the Resistivity of Semiconductors go down with Temperature? The difference in resistivity between conductors and semiconductors is due to their difference in charge carrier density. The resistivity of semiconductors decreases with temperature because the number of charge carriers increases rapidly with increase in temperature, making the fractional change i.e. the temperature coefficient negative.

53. Some Important Properties of Semiconductors are: Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor. Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers. Lesser power losses. Semiconductors are smaller in size and possess less weight. Their resistivity is higher than conductors but lesser than insulators. The resistance of semiconductor materials decreases with the increase in temperature and vice-versa.

54. Types of Semiconductors Semiconductors can be classified as: Intrinsic Semiconductor Extrinsic Semiconductor Classification of Semiconductors

55. Classification of Semiconductors Intrinsic Semiconductor An  intrinsic type of semiconductor material  is made to be very pure chemically. It is made up of only a single type of element.

56. Conduction Mechanism in Case of Intrinsic Semiconductors (a) In absence of electric field (b) In presence of electric Field Germanium ( Ge ) and Silicon (Si) are the most common type of  intrinsic semiconductor elements . They have four valence electrons (tetravalent). They are bound to the atom by covalent bond at absolute zero temperature. When the temperature rises, due to collisions, few electrons are unbounded and become free to move through the lattice, thus creating an absence in its original position (hole). These free electrons and holes contribute to the conduction of electricity in the semiconductor. The negative and positive charge carriers are equal in number. The thermal energy is capable of ionizing a few atoms in the lattice, and hence their conductivity is less.

57. The Lattice of Pure Silicon Semiconductor at Different Temperatures At absolute zero Kelvin temperature:  At this temperature, the  covalent bonds  are very strong and there are no free electrons and the semiconductor behaves as a perfect insulator. Above absolute temperature:  With the increase in temperature few valence electrons jump into the conduction band and hence it behaves like a poor conductor. Energy Band Diagram of Intrinsic Semiconductor The energy band diagram of an intrinsic semiconductor is shown below:

58. (a) Intrinsic Semiconductor at T = 0 Kelvin, behaves like an insulator (b) At t>0, four thermally generated electron pairs In intrinsic semiconductors, current flows due to the motion of free electrons as well as holes. The total current is the sum of the electron current I e  due to thermally generated electrons and the hole current I h Total Current (I) = I e  + I h For an intrinsic semiconductor, at finite temperature, the probability of electrons to exist in conduction band decreases exponentially with increasing bandgap ( E g ) n = n e -Eg/2.Kb.T Where, Eg = Energy bandgap K b  =  Boltzmann’s constants

59. Classification of Extrinsic Semiconductor The conductivity of semiconductors can be greatly improved by introducing a small number of suitable replacement atoms called IMPURITIES. The process of adding impurity atoms to the pure semiconductor is called DOPING. Usually, only 1 atom in 10 7  is replaced by a dopant atom in the doped semiconductor. An  extrinsic semiconductor  can be further classified into: N-type Semiconductor P-type Semiconductor P

60. N-Type Semiconductor Mainly due to electrons Entirely neutral I = I h   and n h  >> n e Majority – Electrons and Minority – Holes When a pure semiconductor (Silicon or  Germanium ) is doped by pentavalent impurity (P, As, Sb , Bi) then, four electrons out of five valence electrons bonds with the four electrons of Ge or Si. The fifth electron of the dopant is set free. Thus the impurity atom donates a free electron for conduction in the lattice and is called “ Donar “. Since the number of free electron increases by the addition of an impurity, the negative charge carriers increase. Hence it is called n-type semiconductor. Crystal as a whole is neutral, but the donor atom becomes an immobile positive ion. As conduction is due to a large number of free electrons, the electrons in the n-type semiconductor are the MAJORITY CARRIERS and holes are the MINORITY CARRIERS.

61. P-Type Semiconductor Mainly due to holes Entirely neutral I = I h   and n h  >> n e Majority – Holes and Minority – Electrons When a pure semiconductor is doped with a trivalent impurity (B, Al, In, Ga ) then, the three valence electrons of the impurity bonds with three of the four valence electrons of the semiconductor. This leaves an absence of electron (hole) in the impurity. These impurity atoms which are ready to accept bonded electrons are called “ Acceptors “. With the increase in the number of impurities, holes (the positive charge carriers) are increased. Hence, it is called p-type semiconductor. Crystal as a whole is neutral, but the acceptors become an immobile negative ion. As conduction is due to a large number of holes, the holes in the p-type semiconductor are MAJORITY CARRIERS and electrons are MINORITY CARRIERS.

62. Intrinsic Semiconductor Extrinsic Semiconductor Pure semiconductor Impure semiconductor Density of electrons is equal to the density of holes Density of electrons is not equal to the density of holes Electrical conductivity is low Electrical conductivity is high Dependence on temperature only Dependence on temperature as well as on the amount of impurity No impurities Trivalent impurity, pentavalent impurity Difference Between Intrinsic and Extrinsic Semiconductors

63. Applications of Semiconductors Let us now understand the uses of semiconductors in daily life. Semiconductors are used in almost all electronic devices. Without them, our life would be much different. Their reliability, compactness, low cost and controlled conduction of electricity make them ideal to be used for various purposes in a wide range of components and devices. transistors,  diodes , photosensors , microcontrollers, integrated chips and much more are made up of semiconductors. Uses of Semiconductors in Everyday life Temperature sensors are made with semiconductor devices. They are used in 3D printing machines Used in microchips and self-driving cars Used in calculators, solar plates, computers and other electronic devices. Transistor and MOSFET used as a switch in Electrical Circuits are manufactured using the semiconductors.

64. Industrial Uses of Semiconductors The physical and chemical properties of semiconductors make them capable of designing technological wonders like microchips, transistors,  LEDs , solar cells, etc. The microprocessor used for controlling the operation of space vehicles, trains, robots, etc is made up of transistors and other controlling devices which are manufactured by semiconductor materials. Importance of Semiconductors Here we have discussed some advantages of semiconductors which makes them highly useful everywhere. They are highly portable due to the smaller size They require less input power Semiconductor devices are shockproof They have a longer lifespan They are noise-free while operating

65. Pure Silicon semiconductor at 500K has equal electrons and holes (1.5 × 10 16  m -3 ). Doping by Indium increases n h  to 4.5 × 10 22  m -3 . Calculate the type and electron concentration of doped semiconductor. Since, n 2 i  = n e   n h  (1.5 × 10 16 ) 2  = ne (4.5 × 10 22 ) Therefore, n e  = 5 × 10 9 Given n h  = 4.5×10 23 ⇒ nh >> ne Therefore, the semiconductor is p-type and n e  = 5 × 10 9  m -3

66. Why the valence band in semiconductors is partially empty and the conduction band is partially filled at room temperature? In semiconductors, the conduction band is empty and the valence band is completely filled at Zero Kelvin. No electron from valence band can cross over to conduction band at this temperature. But at room temperature, some electrons in the valence band jump over to the conduction band due to small forbidden gap i.e. 1 eV .

67. In an intrinsic semiconductor, the number of conduction electrons is 7 × 10 19  m 3 . Find the total number of current carriers in the same semiconductor of size 1 cm × 1 cm × 1 mm. In an intrinsic semiconductor; n e  = n h Given, n e  = 7 × 10 19  per m 3 Therefore, n h  = n e  = 7 × 10 19  m 3 So, the total current carrier density = n e  + n h  = 7×10 19  + 7×10 19  = 14×10 19  per m 3 Now, the total number of current carrier = Number density × volume = (14 × 10 19  per m 3  ) × (10 -2 m × 10 -2 m × 10 -3 m) = 14×10 12 .

68. The energy gap of silicon is 1.14 eV . What is the maximum wavelength at which silicon will begin absorbing energy? Since hc /λ = Energy (E) Therefore, λ = hc /E = [(6.628 × 10 -34 ) × (3×10 8 )]/1.14×1.6×10 -19 J = 10.901 × 10 -7  m = 10901 Å.

69. Valence Band Conduction Band Band Gap Mumbai to Karad Highway

70. Conductors In a conductor, electrons can move freely among these orbitals within an energy band as long as the orbitals are not completely occupied.

71. Conductors In conductors, the valence band is empty.

72. Conductors Also in conductors, the energy gap is nonexistent or relatively small.

73. Insulators In insulators, the valence band is full.

74. Insulators Also in insulators, the energy gap is relatively large.

75. Semiconductors In semiconductors, the valence band is full but the energy gap is intermediate.

76. SUPERCONDUCTIONS : CERAMIC SUPERCONDUCTORS Introduction : Metals are good conductors of electricity and their conductivity increases as the temperature decreases. In 1911 the phenomenon of superconductivity was discovered by the Dutch scientist Kamerlingh Onnes when he was studying electrical properties of materials near absolute zero. A superconductor has zero or almost zero electrical resistance. It can therefore carry an electric current without losing energy. In other words the current can flow forever. It was proved that mercury is a superconductor below 4.2 K – (the critical temperature (T) at which the superconducting state is formed. Following the discovery, physicists and chemists made slow but steady progress in the discovery of superconductors with higher values of Tc .

77. After 75 years in 1986 high temperature super conductors were discovered. George Bednorz and Alex Mueller reported a new type of (mixed oxide) superconductor of lanthanum barium and copper (La2-x Ba x CuO4-y) which exhibited superconductivity at 35 K For this significant work Bednorz and Mueller were awarded the Noble Prize for physics in 1987. Meanwhile, Meissner and Ochsenfeld found that some low temperature superconductors exhibit the exclusion of magnetic field below Tc i.e. they do not allow a magnetic field to penetrate their bulk. This is known as Meissner effect. See Fig 4.19 Thus superconductors are essentially diamagnetic. Meissner effect gives rise to ‘Levitation’. Levitation occurs when objects float on air. Here repulsion is encountered between a permanent magnet and a superconductor.

78. Ceramic Superconductor The first non metallic superconductor was found in 1964. This was a metal oxide with a perovskite crystal structure and found to be quite different type of superconductor from the alloys. In March 1987 one of the most significant ceramic superconductor was reported by Wu, Chu and co-workers. This is a mixed oxide type material based on the Y- Ba -Cu-O system formulated as YBa2Cu3O7-x which became superconducting at 93 K. This temperature appeared to be quite significant for practical reasons. This temperature allowed liquid nitrogen to be used as coolant rather than the more expensive liquid helium which was used earlier. Such materials are also called as warm superconductors or high temperature superconductors as they work at higher temperatures than the temperature of liquid nitrogen (B.P. = 77 K).

79. Preparation: There are different methods to prepare mixed oxide superconductors. For massive form chemical fusion of sintering is used. For film type, the methods used are ( i ) Chemical Deposition Method (ii) Chemical Vapor Deposition Method (iii) Electrical Deposition Method For illustration two different methods have been discussed below.

80. (1) Chemical Fusion: The synthesis of high temperature super conductors needs a variety of qualitative considerations. These materials may be prepared by fusing the mixture of metal oxides say oxides of yttrium barium and copper to 1073- 1173 K (800-9000C), in an open alumina crucible or in a sealed gold tube.

81. (2) Chemical Vapor Deposition Method: In electronic devices superconductors are used in the form of thin films. For this purpose the best suited method is chemical vapor deposition. The general procedure is to from a thin film by decomposing a thermally unstable compound on a hot solid substrate material See Fig 4.21 In this method, volatile complexes of metals Cu Y and Ba are held at temperatures T1 T2 and T3 which provide desired vapor pressure of each reactant. The reactants are then swept into the reaction chamber by a reactive carrier gas mixture: Argon, oxygen, and water vapor through traps as shown in Fig 4.23. When conditions are properly controlled, the desired YBa2Cu3O7-x film is deposited on the wedge shaped block, heated to a high temperature by an IR lamp. After deposition, the film may be amorphous it is annealed at high temperature to get the desired crystallinity of the film.

82. Structure Informally this, YBa2 Cu3 O7-x ceramic super conductor, is called “123” (or ‘1-2-3’) superconductor from the proportions of metal atoms in the compound. Its structure is similar to perovskite but with some missing ‘O’ atoms, hence (7-x) in its composition. Its structure comprises three cubic perovskite units stacked one on top of the other giving an elongated (tetragonal) unit cell See Fig 4.21. From the figure it is clear that the lower and upper cubes have Ba2+ ions at the body centre while the smaller Cu +2 ions at each corner. The middle cube had Y3+ ion at the body centre. A perovskite has formula ABO3 and the stoichiometry of the compound would be YBa2Cu3O9. But the actual formula being YBa2Cu3O7-x. There is a massive deficiency of oxygen where about one quarter of the oxygen sites are vacant in the crystal. The copper atoms are surrounded by oxygen polyhedra which are in square –planar and square-pyramidal environments i.e. CuO4 and CuO5 units as shown in Fig 4.20(C)

83. Properties ( i ) Ceramic superconductors have mixed oxide system and are called high temperature superconductors or warm superconductors or mixed superconductors. Many of them contain copper which exists in three oxidation state (+I), (+II) and (+III) where Cu (II) forms many tetragonally distorted octahedral complexes. (ii) They have perovskite structure. (iii) They exhibit critical deficiency of oxygen. (iv) Superconductivity in the YBa2Cu3O7-x is thought to be associated with ready transfer of electrons between cu (I) Cu (II ) and Cu (III) (v) Below critical temperature ( Tc ), at which the superconducting state is formed, the ceramic superconductors show zero electrical resistance. (vi) Superconductors can repel magnets and are thus diamagnetic and hence they exhibit Meissner effect below Tc

84. APPLICATIONS OF SUPERCONDUCTORS Ceramic Superconductors show zero electrical resistance. Thus the cables made of Superconducting materials if used then the 20 % loss of electricity during its transmission through aluminium or copper wires is avoided. Thus ceramic superconductors are useful to carry huge amounts of electricity without much loss. Large magnetic fields can be generated by using the ceramic Superconductors. This property is applied in superfast magnetically levitated trains. Trains which can run with speeds of about 500 km per hour have been built in Japan on the principle of magnetic levitation. Superconductors being diamagnetic they are used in Magnetic Resonance Imaging (MRI) which is a new diagnostic tool. Superconductors are useful in computers satellites and variety of electronic devices. Powerful electromagnets using Superconducting windings are quite useful especially at higher temperatures.

85. Ceramics: Let us conclude with familiarity to ceramics. This terms is often applied to all inorganic non metallic non-molecular materials including crystalline as well as amorphous. The word is derived from Greek word “ Keramos ” meaning burnt earth literally potters clay Ceramics comprise different engineering produced through high temperature processing. They possess greater hardness rigidity and thermal stability than the metals. Ceramics are composed of both cationic and anionic species. The basic difference between ceramics and other kinds of solids lies in the nature of chemical bonding. The typical and traditional examples of ceramics are white wares, tiles and bricks abrasives, refractories , chemical stoneware etc.