Seminconductors.pdf

Semiconductors 1 2 Aims On completion of this module you should: Be familiar with the concept of energy bands; Understand about the two charge carriers, electrons and holes, in semiconductors; Understand why doping of semiconductors is useful; Be familiar with basic el...

Semiconductors 1 2 Aims On completion of this module you should: Be familiar with the concept of energy bands; Understand about the two charge carriers, electrons and holes, in semiconductors; Understand why doping of semiconductors is useful; Be familiar with basic electronic devices made using semiconductors and how these devices operate. 3 Electronic Properties of Metals: Classical Approach One could argue that metals are good conductors of heat and electricity, whereas semiconductors and insulators are not. In the case of heat conduction, we know that diamond, which is an insulator, conducts even better than most metals. Electrical conductivity is not of much help either: Some semiconductors such as silicon conduct electricity reasonably well. Yet another possibility is to define metals by the fact that they look “shiny” or “metallic.” But this applies to some semiconductors, too, and again silicon can be taken as an example. It turns out that a proper definition has to wait until we treat electronic states in a quantum mechanical model. 4 5 6  ENERGY-BAND MODEL FOR ELECTRICAL CONDUCTION (a) Delocalized valence electrons in a block of sodium (a) Energy levels in a single sodium atom. metal. (b) Arrangement of electrons in a sodium atom. (b) Energy levels in a block of sodium metal; note the expansion of the 3s level into an energy band The outer 3s1 valence electron is loosely bound and is and that the 3s band is shown closer to the 2p level free to be involved in metallic bonding. since bonding has caused a lowering of the 3s levels of the isolated sodium atoms. 7 8  (a) The conventional representation of the electron energy band structure for a solid material at the equilibrium interatomic separation. (b) Electron energy versus interatomic separation for an aggregate of atoms, illustrating how the energy band structure at the equilibrium separation in (a) is generated. 9 10 Concept of Energy Bands 11 Electron volt Electron volt is defined as the amount of energy one electron gains by moving through a potential difference of one volt. Hence, one electron volt is equal to elementary charge (1.60217657 × 10- 19 coulombs (C)) multiplied by one volt. It can be written as eV = (1.60217657 × 10-19 C) (1V) Therefore, 1ev = 1.60217657 × 10-19 J. 12 Carbon (Z=6) 13 14 Fermi Energy: Fermi energy is used to separate the vacant and filled states at 0 K. It is used to know the status of the electrons. Electrons are completely filled below fermi energy level and completely empty above the fermi level at 0K Above 0 K some electrons absorb thermal energy and they jumps to the higher energy levels. 15 Fermi Level / Fermi Energy At higher temperatures a certain fraction, characterized by the Fermi function, will exist above the Fermi level. The Fermi level plays an important role in the band theory of solids. In doped semiconductors, p-type and n-type, the Fermi level is shifted by the impurities, illustrated by their band gaps. The Fermi level is referred to as the electron chemical potential in other contexts. In metals, the Fermi energy gives us information about the velocities of the electrons which participate in ordinary electrical conduction. 16  The amount of energy which can be given to an electron in such conduction processes is on the order of micro-electron volts, so only those electrons very close to the Fermi energy can participate. The Fermi velocity of these conduction electrons can be calculated from the Fermi energy. This speed is a part of the microscopic Ohm's Law for electrical conduction. For a metal, the density of conduction electrons can be implied from the Fermi energy. 17 Density of states (DOS) It tells us how many of these energy levels are available for electrons in a given energy range. Think of it like a "capacity chart" that shows how many seats (energy levels) are available in a stadium (energy band) for spectators (electrons) at different ticket prices (energy levels). The DOS is important because it helps us predict how electrons will behave in the material. For example, when we apply an electric field or change the temperature, electrons will gain or lose energy. Understanding the density of states helps you grasp why semiconductors behave differently under various conditions, which is crucial for designing electronic devices like transistors and solar cells. It gives us a deeper insight into the electronic properties of materials, which is fundamental in materials science and engineering. 18  The Mechanism of Electrical Conduction in Intrinsic Semiconductors Electrical conduction in a semiconductor such as silicon Two-dimensional representation of the diamond cubic lattice of silicon or showing the migration of electrons and holes in an germanium showing positive-ion cores and valence electrons. applied electric field Electron has been excited from a bond at A and has moved to point B When a critical amount of energy is supplied to a valence electron to excite it away from its bonding position, it becomes a free conduction electron and leaves behind a positively charged “hole” in the crystal lattice 19  Electrical Charge Transport in the Crystal Lattice of Pure Silicon Schematic illustration of the movement of holes and electrons in a pure silicon semiconductor during electrical conduction caused by the action of an applied electric field. 20 21  Electron-hole movement Till now we have considered only the contribution to the electric current due to electrons occupying states in the conduction band. However, moving an electron from the valence band to the conduction band leaves an unoccupied state or hole in the energy structure of the valence band, which a nearby electron can move into. As these holes are filled by other electrons, new holes are created. The electric current associated with this filling can be viewed as the collective motion of many negatively charged electrons or the motion of the positively charged electron holes. Assume that each lattice atom contributes one valence electron to the current. As the hole on the right is filled, this hole moves to the left. The current can be interpreted as the flow of positive charge to the left. The density of holes, or the number of holes per unit volume, is represented by p. Each electron that transitions into the conduction band leaves behind a hole. If the conduction band is originally empty, the conduction electron The motion of holes in a crystal lattice. As electrons shift to density p is equal to the hole density, n=p the right, an electron hole moves to the left. 22 Work Function 23  Work Function: The minimum energy given to an electron in a metal to liberate it from the surface of that metal at absolute zero is called work function. It depends upon. 1. The nature of the metal. 2. The surface conditions. There are four different ways of supplying energy to the electrons of a metal. When the energy is supplied to the electrons thermally by heating the metal,then the work function is called thermionic work function. When the energy is supplied to the electrons optically by exposing it with the incident light , then the work function is called photoelectric work function. When the energy is received from electrons or ions that strike the metal surface from outside, then the work function is called secondary emission work function. When the energy is received from the applied electric field, then the work function is called field emission work function. 24 Doped Semiconductors 25  Arsenic has five valence electrons. Silicon has four valence electron. Fig. (a) A donor impurity and (b) an acceptor impurity. The introduction to impurities and acceptors into a semiconductor significantly changes the electronic properties of this material. 26  n-Type (Negative-Type) Extrinsic Semiconductors (a) The addition of a pentavalent phosphorus impurity atom to the tetravalent silicon lattice provides a fifth electron that is weakly attached to the parent phosphorus atom. Only a small amount of energy (0.044 eV) makes this electron mobile and conductive. (b) Under an applied electric field the excess electron becomes conductive and is attracted to the positive terminal of the electrical circuit. With the loss of the extra electron, the phosphorus atom is ionized and acquires a + 1 charge. 27 Group VA impurity atoms such as P, As, and Sb when added to silicon or germanium provide easily ionized electrons for electrical conduction. Since these group VA impurity atoms donate conduction electrons when present in silicon or germanium crystals, they are called donor impurity atoms. Silicon or germanium semiconductors containing group V impurity atoms are called n-type (negative-type) extrinsic semiconductors since the majority charge carriers are elect Electrons at the donor energy level require only a small amount of energy (ΔE = Ec - Ed) to be excited into the Ionization energies (in electron volts) for various conduction band. impurities in silicon. When the extra electron at the donor level jumps to the conduction band, a positive immobile ion is left behind. 28  p-Type (Positive-Type) Extrinsic Semiconductors When a trivalent group IIIA element such as boron (B) is substitutionally introduced in the silicon tetrahedrally bonded lattice, one of the bonding orbitals is missing, and a hole exists in the bonding structure of the silicon 29 Only a small amount of energy (ΔE = Ea - Ev) is necessary to excite an electron from the valence band to the acceptor level, thereby creating an electron hole (charge carrier) in the valence band. 30 Fermi Level in Intrinsic Semiconductor 31 Effect of Temperature on Intrinsic Semiconductivity In contrast to metals, whose conductivities decrease with increasing temperatures, the conductivities of semiconductors increase with increasing temperatures for the temperature range over which this process predominates ni= no. of intrinsic carriers 32 33  n-type p-type n-type Schematic plot of ln σ (conductivity) versus 1/T (K-1) for an n-type extrinsic semiconductor. 34 Why electrons have higher mobility in comparison to holes? One simple reason is that electron is always looking for empty hole (unoccupied state) and is moving rapidly and randomly inside the crystal lattice unless it recombines with hole. However, hole (empty state) is waiting for electron to come and move only when nearby electron takes it’s place. This is slower than the movement of electron. Another way we can explain through band diagram. Free electrons are moving in conduction band whereas free holes are moving in valence band. As valence band is more influenced by the nucleus of atoms Electrical conductivity as a function leading to more scattering, movement of holes in valence band is of reciprocal absolute temperature for intrinsic silicon. slower than that of electrons in conduction band. 35  Direct and Indirect Band Gap Semiconductors A photon of energy Eg, where Eg is the band gap energy, can produce an electron-hole pair in a direct band gap semiconductor quite easily, because the electron does not need to be given very much momentum. Direct However, an electron must also undergo a significant change in its momentum for a photon of energy Eg to produce an electron-hole pair in an indirect band gap semiconductor. This is possible, but it requires such an electron to interact not only with the photon to gain energy, but also with a lattice vibration called a phonon in order to either gain or lose momentum. The indirect process proceeds at a much slower rate, as it requires three entities to intersect in order to proceed: an electron, a photon and a Indirect phonon. Analogy to chemical reactions, where, in a particular reaction step, a reaction between two molecules will proceed at a much greater rate than a process which involves three molecules. 36 37 Effect of Temperature on the Electrical Conductivity of Extrinsic Semiconductors At lower temperatures, the number of impurity atoms per unit volume activated (ionized) determines the electrical conductivity of the silicon. As the temperature is increased, more and more impurity atoms are ionized, and thus the electrical conductivity of extrinsic silicon increases with increasing temperature in the extrinsic range. For a certain temperature range above that required for complete ionization, an increase in temperature does not substantially change the electrical conductivity of an extrinsic semiconductor. For an n-type semiconductor, this temperature range is referred to as the exhaustion range since donor atoms become completely ionized after the loss of their donor electrons. For p-type semiconductors, this range is referred to as the saturation range since acceptor atoms become completely ionized with acceptor electrons. To provide an exhaustion range at about room temperature (300 K), silicon doped with arsenic requires about 1021 carriers/m3 38  n-type Schematic plot of ln σ (conductivity) versus 1/T (K-1) for an n-type extrinsic semiconductor. 39  Donor exhaustion and acceptor saturation temperature ranges are important for semiconductor devices since they provide temperature ranges that have essentially constant electrical conductivities for operation. As the temperature is increased beyond the exhaustion range, the intrinsic range is entered upon. The higher temperatures provide sufficient activation energies for electrons to jump the semiconductor gap (1.1 eV for silicon) so that intrinsic conduction becomes dominant. The slope of the ln σ versus 1/T (K-1) plot becomes much steeper and is –Eg/2k. For silicon-based semiconductors with an energy gap of 1.1 eV, extrinsic conduction can be used up to about 200°C. The upper limit for the use of extrinsic conduction is determined by the temperature at which intrinsic conductivity becomes important. 40 Compound Semiconductors A compound semiconductor is a material made from two or more elements from different groups on the periodic table. These elements are usually, but not always, symmetrically arranged around group 4 of the periodic table. For example, some compound semiconductors are made from elements in groups III and V, like gallium arsenide (GaAs), or groups II and VI, like cadmium telluride (CdTe). Different compound semiconductors do different things. Electric vehicles use silicon carbide (SiC) and smartphone cameras use gallium arsenide (GaAs). 41 42 43  Compound Semiconductors One example of a compound semiconductor is gallium arsenide, GaAs. In a compound semiconductor like GaAs, doping can be accomplished by slightly varying the stoichiometry, i.e., the ratio of Ga atoms to As atoms. A slight increase in the proportion of As produces n-type doping, and a slight increase in the proportion of Ga produces p-type doping. 44  Compound Semiconductors (III-V) In the previous sections, we have discussed the donor and acceptor impurities in a group IV semiconductor, such as silicon. The situation in the group III–V compound semiconductors, such as gallium arsenide, is more complicated. Group II elements, such as beryllium, zinc, and cadmium, can enter the lattice as substitutional impurities, replacing the group III gallium element to become acceptor impurities. Similarly, group VI elements, such as selenium and tellurium, can enter the lattice substitutionally, replacing the group V arsenic element to become donor impurities. The corresponding ionization energies for these impurities are smaller than those for the impurities in silicon. The ionization energies for the donors in gallium arsenide are also smaller than those for the acceptors, because of the smaller effective mass of the electron compared to that of the hole. 45  Group IV elements, such as silicon and germanium, can also be impurity atoms in gallium arsenide. If a silicon atom replaces a gallium atom, the silicon impurity will act as a donor, but if the silicon atom replaces an arsenic atom, then the silicon impurity will act as an acceptor. The same is true for germanium as an impurity atom. Such impurities are called amphoteric. Experimentally in gallium arsenide, it is found that germanium is predominantly an acceptor and silicon is predominantly a donor. 46 47 48 Nanomaterials (Bottom Up Approach) e.g. Graphene Nanomaterials may be any one of the four basic types—metals, ceramics, polymers, and composites. However, unlike these other materials, they are not distinguished on the basis of their chemistry, but rather, size; the nano-prefix denotes that the dimensions of these structural entities are on the order of a nanometer (10–9 m)—as a rule, less than 100 nanometers (equivalent to approximately 500 atom diameters). CNT Carbon nano tube (CNT) 49 2D semiconductor A 2D semiconductor is a material that is only one or a few atoms thick, making it effectively two-dimensional (2D). These materials have unique properties that are different from their 3D counterparts due to their thinness and the way electrons behave in them. What Makes a Semiconductor 2D? To be considered a 2D semiconductor, the material must be extremely thin—often just a single layer of atoms, like a sheet of paper that is only one atom thick. This ultra-thin structure limits the movement of electrons to two dimensions: they can move in the plane of the material (left-right and forward-backward), but they have very little freedom to move vertically (up-down).  Why Are 2D Semiconductors Special? Unique Electronic Properties: Because of their thinness, 2D semiconductors have unique electronic properties. Electrons in these materials experience different forces compared to those in 3D materials, which can lead to faster electron movement and better control of electronic properties. This makes them ideal for use in advanced electronics. High Surface Area: 2D semiconductors have a high surface area relative to their volume, which means a lot of their atoms are exposed on the surface. This can make them very sensitive to changes in their environment, which is useful for sensors. 1.Quantum Effects: At such small scales, quantum mechanical effects become significant. In 2D semiconductors, these effects can enhance their performance in electronic and optical applications. 2. For example, they can have higher electron mobility and different band gaps compared to their bulk counterparts.  Examples of 2D Semiconductors One of the most well-known 2D materials is graphene, but it’s not a semiconductor; it’s a conductor. A true 2D semiconductor is molybdenum disulfide (MoS₂). Unlike graphene, MoS₂ has a band gap, which is essential for controlling electron flow in semiconductor devices. Applications of 2D Semiconductors 2D semiconductors are being explored for use in various advanced technologies, such as: Transistors: For faster and more efficient computer chips. Sensors: Highly sensitive to gases, chemicals, and biomolecules. Flexible Electronics: Due to their thinness and flexibility, they are ideal for use in bendable or wearable devices. Optoelectronics: For devices like LEDs and solar cells, where controlling light is crucial. Conclusion 2D semiconductors represent a new frontier in material science, offering unique properties that differ significantly from traditional 3D materials. Their potential for revolutionizing electronics, sensors, and more makes them an exciting area of study in both research and industry. Electrical Resistivity of Metals The thermal component arises from the vibrations of the positive-ion cores about their equilibrium positions in the metallic crystal lattice. As the temperature is increased, the ion cores vibrate more and more, and a large number of thermally excited elastic waves (called phonons) scatter conduction electrons and decrease the mean free paths and relaxation times between collisions. Thus as the temperature is increased, the electrical resistivities of pure metals increase. The residual component of the electrical resistivity of pure metals is small and is caused by structural imperfections such as dislocations, grain boundaries, and impurity atoms that scatter electrons. The residual component is almost independent of temperature and becomes significant only at low temperatures 53