{"id":520,"date":"2018-11-19T08:15:52","date_gmt":"2018-11-19T08:15:52","guid":{"rendered":"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=520"},"modified":"2019-04-30T11:11:36","modified_gmt":"2019-04-30T11:11:36","slug":"semiconductor-nanoparticles-3","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/chapter\/semiconductor-nanoparticles-3\/","title":{"rendered":"Semiconductor Nanoparticles-3"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/RSzYsneFvjw\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<strong>Semiconductors<\/strong>\r\n<ul>\r\n \t<li>Semiconductors are materials with a (relatively) small band gap (typically 1eV) between a filled valence band and an empty conduction band.<\/li>\r\n \t<li>Chemical potential, \u03bc (often called Fermi energy) lies in the band gap.<\/li>\r\n \t<li>\u00a0Insulators at T=0, with a small density of electrons excited at finite temperatures.<\/li>\r\n \t<li>Typical semiconductors are Silicon and Germanium or III-V compounds such as GaAs 2 atoms in primitive basis have 4 electrons each (or 3 + 5); 8 electrons fill 4 bands made of s and p orbitals.<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n<strong>Band structure of Semiconductors<\/strong>\r\n\r\n<\/div>\r\n<div>\r\n\r\nGraph of Energy (E) vs. wave vector (k). EF separates filled and empty states.\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-523\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-314.png\" alt=\"\" width=\"414\" height=\"292\" \/>\r\n\r\n<strong>Energy levels of electrons and holes<\/strong>\r\n\r\n&nbsp;\r\n\r\nClose to the band edge minima and maxima we can write:\r\n\r\n<img class=\"aligncenter size-full wp-image-524\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-315.png\" alt=\"\" width=\"140\" height=\"144\" \/><img class=\"aligncenter size-full wp-image-525\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-316.png\" alt=\"\" width=\"179\" height=\"238\" \/>\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">Band gap determines the optical properties - strong absorption when h\u03bd &gt; EG<\/span>\r\n\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Optical absorption<\/strong>\r\n<ul>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">Excitation promotes an electron from the valence band to conduction band.<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">An empty state left in valence band is known as a hole.<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<div><\/div>\r\n<img class=\"aligncenter size-full wp-image-526\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-317.png\" alt=\"\" width=\"335\" height=\"294\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-527\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-318.png\" alt=\"\" width=\"322\" height=\"235\" \/>\r\n<div>\r\n<ul>\r\n \t<li>\u00a0If band minima and maxima are at different points then we have an Indirect semiconductor.<\/li>\r\n \t<li>The classic example is Silicon.<\/li>\r\n \t<li>This affects the optical properties such as absorption where \u2206k \u2248 0<\/li>\r\n<\/ul>\r\n<img class=\"aligncenter size-full wp-image-528\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-319.png\" alt=\"\" width=\"381\" height=\"420\" \/>\r\n<p style=\"text-align: justify\"><strong>Hole picture<\/strong><\/p>\r\n&nbsp;\r\n\r\nRemove one electron from a filled band and electricity can be conducted by the movement of all of the electrons present.\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The sum of this motion is equivalent to one positively charged particle: <strong>a hole<\/strong><\/p>\r\n<img class=\"aligncenter size-full wp-image-529\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-320.png\" alt=\"\" width=\"445\" height=\"163\" \/>\r\n\r\n&nbsp;\r\n\r\nHoles and their properties\r\n\r\n<\/div>\r\n<div><img class=\"aligncenter size-full wp-image-530\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-321.png\" alt=\"\" width=\"340\" height=\"58\" \/><img class=\"aligncenter size-full wp-image-531\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-322.png\" alt=\"\" width=\"628\" height=\"280\" \/><\/div>\r\n<div><\/div>\r\n<div><strong><span style=\"font-size: 1em;text-align: initial\">Effective masses<\/span><\/strong><\/div>\r\n<div><\/div>\r\n<div><span style=\"text-align: initial;font-size: 1em\">Force accelerates the electron or hole:<\/span><\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-532\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-323.png\" alt=\"\" width=\"499\" height=\"328\" \/><strong>Meaning of the effective mass<\/strong>\r\n\r\n<\/div>\r\n<div>\r\n<ul>\r\n \t<li>Effective mass changes as we move through a band in k-space <strong>positive<\/strong> (electron-like) at the bottom, becoming <strong>negative <\/strong>(hole-like) at the top<\/li>\r\n<\/ul>\r\n<img class=\"aligncenter size-full wp-image-533\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-324.png\" alt=\"\" width=\"226\" height=\"252\" \/>\r\n\r\nTypical values in semiconductors are in the range 0.01 to 0.5 me\r\n\r\n&nbsp;\r\n\r\n<strong>Concentrations of Electrons and Holes<\/strong>\r\n\r\n&nbsp;\r\n\r\nCalculate carrier density from density of states and distribution function:\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-534\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-325.png\" alt=\"\" width=\"424\" height=\"78\" \/>\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">For most semiconductors the chemical potential, ?, (often also called the Fermi\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">Energy (EF)), lies in the band gap so:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-535\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-326.png\" alt=\"\" width=\"575\" height=\"145\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-536\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-327.png\" alt=\"\" width=\"611\" height=\"353\" \/><img class=\"aligncenter size-full wp-image-537\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-328.png\" alt=\"\" width=\"560\" height=\"263\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>LAW OF MASS ACTION<\/strong>\r\n\r\n&nbsp;\r\n\r\nDensities of holes and electrons depend on\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-538\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-329.png\" alt=\"\" width=\"632\" height=\"318\" \/>\r\n\r\n<strong>Intrinsic Semiconductors<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">A semiconductor is said to be intrinsic if it is undoped, and the only source of electrons and holes is by its thermal excitation from the valence band to the conduction band.<\/p>\r\n<img class=\"aligncenter size-full wp-image-539\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-330.png\" alt=\"\" width=\"575\" height=\"60\" \/>\r\n<p style=\"text-align: justify\">We can use this relation to measure the Band Gap, by measuring the carrier densities from the Hall Effect At low temperatures ni 0 and impurities are important<\/p>\r\n&nbsp;\r\n\r\n<strong>Doping Semiconductors<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">We can control the numbers of electrons and holes in a semiconductor by adding impurities which dope the material.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Donors donate an electron to make the material more n-type. A typical example is by adding a group V element (such as As or P) to a group IV semiconductor such as silicon.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Four of the electrons participate in the sp3 bonds as if they were from silicon, but the fifth electron is left over. Extra charge on P nucleus creates a +ive core, and the fifth electron can be bound to this, but the binding is weak.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>Shallow Donors<\/strong>\r\n\r\n&nbsp;\r\n\r\nImpurity binding looks like a hydrogen atom Binding energy\r\n\r\n<img class=\"aligncenter size-full wp-image-540\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-331.png\" alt=\"\" width=\"262\" height=\"76\" \/>\r\n\r\n&nbsp;\r\n\r\nBinding energy is very small because:\r\n\r\n(i)\u00a0\u00a0 The effective mass is small (typically m* = 0.1 me)\r\n<p style=\"text-align: justify\">(ii)\u00a0\u00a0 The wave function is large (much more than the crystal unit cell), so we must include the relative<\/p>\r\n<p style=\"text-align: justify\">dielectric constant of the medium \u03b5r, - typically \u224810.<\/p>\r\n\u2234\u00a0 \u2217 \u2248 10<sup>\u22123<\/sup>\u00a0 R<sub>0<\/sub> = 13.6 meV (155K)\r\n\r\n&nbsp;\r\n\r\n<strong><span style=\"font-size: 1em;text-align: initial\">Acceptors<\/span><\/strong>\r\n\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Dope semiconductors with holes by adding group III elements to a group IV material. e.g. put Ga into silicon.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">One valence electron is missing. This creates a vacant state, a hole, which binds to the ion core of the Ga which is negatively charged. Binding energy is:<\/p>\r\n<img class=\"aligncenter size-full wp-image-541\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-332.png\" alt=\"\" width=\"256\" height=\"75\" \/>\r\n\r\nWhere is the energy level?\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Ionized Acceptor or Donor is a free hole or electron at the top or the bottom of the band<\/p>\r\n\u2234 Acceptor is R* above the valence band edge\r\n\r\nDonor is R* below the conduction band edge\r\n\r\n&nbsp;\r\n\r\n<strong>Extrinsic Carrier Densities<\/strong>\r\n\r\n&nbsp;\r\n\r\nDensity of impurities (e.g. Donors) usually much less than N<sub>C<\/sub>, N<sub>V.<\/sub> Impurities can be ionized N<sub>d<\/sub><sup>+<\/sup> , or neutral N<span style=\"font-size: 12.8px\">d<\/span><span style=\"text-align: initial;text-indent: 1em;font-size: 1em\"><sup>0<\/sup> so:<\/span>\r\n\r\nN<sub>d<\/sub>= N<sub>d<\/sub><sup>+<\/sup>+N<sub>d<\/sub><sup>0<\/sup>\r\n\r\n&nbsp;\r\n\r\nUsing charge neutrality we have:\r\n\r\nn=p+N<sub>d<\/sub><sup>+<\/sup>\r\n\r\n&nbsp;\r\n\r\nSimple argument:\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">At high (e.g. Room) Temperature kT &gt; R* therefore all donors will be ionized but the density of holes created by excitation across the band gap is still small<\/p>\r\n\u2234 n \u2248N<sub>d<\/sub><sup>+<\/sup>=N<sub>d<\/sub>\r\n\r\n&nbsp;\r\n\r\n<strong><span style=\"text-align: initial;font-size: 1em\">Chemical Potential \u03bc<\/span><\/strong>\r\n\r\n&nbsp;\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">At high (room) temperature most impurities are ionized<\/span>\r\n\r\n<\/div>\r\n<div>\r\n\r\n\u2234 n \u2248N<sub>d<\/sub><sup>+<\/sup>=N<sub>d<\/sub>\r\n\r\n&nbsp;\r\n\r\n\u03bc\u00a0 lies below the Donor level so that most impurities are empty (ionized), but is still close to conduction band.\r\n\r\n&nbsp;\r\n\r\nMinority Carriers\r\n\r\n&nbsp;\r\n\r\nBy Law of Mass action the (very small) density of holes is:\r\n\r\np=n<sub>i<\/sub>(T)2\u2044\u00a0N<sub>d<\/sub>\r\n\r\n&nbsp;\r\n\r\nTemperature dependent density and chemical potential\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-542\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-333.png\" alt=\"\" width=\"345\" height=\"442\" \/>\r\n<ul>\r\n \t<li>Density is constant in region around room temperature.<\/li>\r\n \t<li>High temperature gives Intrinsic behaviour.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\nConductivity of Semiconductors\r\n\r\n<img class=\"aligncenter size-full wp-image-544\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-335.png\" alt=\"\" width=\"254\" height=\"64\" \/>\r\n\r\n\u03bc, is the mobility, which is defined by v = \u03bc E, the drift velocity per unit electric field.\r\n\r\n&nbsp;\r\n\r\nConductivity is dominated by variation in densities.\r\n\r\n&nbsp;\r\n\r\nMobility is determined by scattering rate:\r\n\r\n&nbsp;\r\n\r\nLow T: impurity scattering gives \u03bc\u00a0 ~ T<sup>3\/2<\/sup>\r\n\r\n&nbsp;\r\n\r\nHigh T: phonon scattering gives \u03bc\u00a0 ~ T<sup>3\/2<\/sup>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>p-n junction<\/strong><\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-545\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-336.png\" alt=\"\" width=\"624\" height=\"270\" \/>\r\n\r\np-n junctions\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nWhat is current flow across junction?\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 J=nev\r\n\r\nWhat is v? - due to diffusion of carriers with diffusion coefficient D and lifetime\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 .\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-546\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-337.png\" alt=\"\" width=\"629\" height=\"584\" \/>\r\n\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>Low Dimensional Structures and Materials<\/strong>\r\n\r\n&nbsp;\r\n\r\n\u2022\u00a0 Anisotropic Materials\r\n\r\n\u2022 Artificial layered structures - Quantum Wells and Superlattices\r\n\r\n\u2022\u00a0 Electric or Magnetic Fields applied in one direction.\r\n\r\n<img class=\"aligncenter size-full wp-image-547\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-338.png\" alt=\"\" width=\"239\" height=\"184\" \/>\r\n<p style=\"text-align: center\"><strong>Heterojunctions<\/strong><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-548\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-339.png\" alt=\"\" width=\"673\" height=\"284\" \/>\r\n\r\n<strong><span style=\"text-align: initial;font-size: 1em\">Reduced Dimensionality<\/span><\/strong>\r\n\r\n<\/div>\r\n<div>\r\n\r\nQuantum Well removes 1 Dimension by quantization\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-549\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-340.png\" alt=\"\" width=\"285\" height=\"151\" \/>\r\n\r\n&nbsp;\r\n\r\nElectron is bound in well and can only move in plane\r\n\r\n&nbsp;\r\n\r\n2-D system - motion in x, y plane\r\n\r\n&nbsp;\r\n\r\nQuantum Well - Type I\r\n\r\n&nbsp;\r\n\r\nTypical Materials:\r\n\r\n1: GaAs\r\n\r\n2: (Al<sub>0.35<\/sub>Ga<sub>0.65<\/sub>)<sub>As<\/sub>\r\n\r\n<span style=\"font-size: 1em;text-align: initial\">(Eg = 1.5 eV)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (Eg = 2.0 eV)<\/span>\r\n\r\n<\/div>\r\n<div>\r\n\r\nEnergy levels are quantized in Z-direction with values En for both electrons and holes\r\n\r\n<img class=\"aligncenter size-full wp-image-550\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-341.png\" alt=\"\" width=\"245\" height=\"74\" \/><img class=\"aligncenter size-full wp-image-551\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-342.png\" alt=\"\" width=\"322\" height=\"231\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>Infinite well - Particle in a box<\/strong>\r\n\r\n<img class=\"aligncenter size-full wp-image-552\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-343.png\" alt=\"\" width=\"507\" height=\"381\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>Density of States\u00a0<\/strong>\r\n\r\ng(k)dk\r\n\r\ng(\u03b5)d\u03b5\r\n\r\n<\/div>\r\n<div><\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-553\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-344.png\" alt=\"\" width=\"701\" height=\"361\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>Optical Properties<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>3-D <\/strong>Absorption coefficient is proportional to the density of states:\r\n\r\n\u2234\u03b1\u00a0 ~\u00a0 \u03b51\/2\r\n\r\nModified close to the band gap due to \u2018excitons\u2019\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-554\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-345.png\" alt=\"\" width=\"371\" height=\"217\" \/>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>2-D<\/strong>\u00a0<strong>Big Changes<\/strong>\r\n\r\n&nbsp;\r\n\r\nMultiple Band gaps -\r\n\r\nBand gap shift -\r\n\r\nSharper edge-\r\n\r\n&nbsp;\r\n\r\nFor wide wells the sum of many 2-D absorptions becomes equivalent to the 3-D absorption shape (\u03b51\/2)\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-555\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-346.png\" alt=\"\" width=\"434\" height=\"276\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-557\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-348.png\" alt=\"\" width=\"511\" height=\"484\" \/>\r\n\r\n&nbsp;\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">\u2022\u00a0 Sharp peaks due to excitons<\/span>\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">\u2022\u00a0 peaks doubled due to heavy and light holes<\/span>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>Semiconducting Lasers<\/strong>\r\n\r\n&nbsp;\r\n\r\nForward biased p-n junction\r\n<ul>\r\n \t<li>Quantum Well laser<\/li>\r\n \t<li>Fibre Optic Communications,<\/li>\r\n \t<li>CD players, laser pointers<\/li>\r\n<\/ul>\r\n<img class=\"aligncenter size-full wp-image-558\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-349.png\" alt=\"\" width=\"303\" height=\"361\" \/>\r\n\r\n<strong>How do we achieve low dimensionality?<\/strong>\r\n\r\n&nbsp;\r\n\r\nNaturally anisotropic crystals\r\n<p style=\"text-align: justify\">Controlled growth of layers and\/or apply external potential Deposit thin layers of single crystals to create<\/p>\r\n\u2018heterostructures\u2019\r\n\r\n&nbsp;\r\n\r\n<strong>Two Main techniques:<\/strong>\r\n\r\n&nbsp;\r\n\r\nI) Molecular Beam Epitaxy (MBE)\r\n\r\nII) Metal Organic Vapour Phase Epitaxy (MOVPE)\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Molecular Beam Epitaxy (MBE)<\/strong>\r\n<div>\r\n<ul>\r\n \t<li>Ultra High Vacuum molecular (Molecular Beam) evaporation of species of elements<\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">Epitaxy-\u00a0\u00a0 maintaining crystal\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">structure of the \u2018substrate\u2019 - which\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">is a single crystal<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-559\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-350.png\" alt=\"\" width=\"337\" height=\"341\" \/>\r\n\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Semiconductor Nanoparticles-3<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/RSzYsneFvjw\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/RSzYsneFvjw\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Semiconductors<\/strong><\/p>\n<ul>\n<li>Semiconductors are materials with a (relatively) small band gap (typically 1eV) between a filled valence band and an empty conduction band.<\/li>\n<li>Chemical potential, \u03bc (often called Fermi energy) lies in the band gap.<\/li>\n<li>\u00a0Insulators at T=0, with a small density of electrons excited at finite temperatures.<\/li>\n<li>Typical semiconductors are Silicon and Germanium or III-V compounds such as GaAs 2 atoms in primitive basis have 4 electrons each (or 3 + 5); 8 electrons fill 4 bands made of s and p orbitals.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>Band structure of Semiconductors<\/strong><\/p>\n<\/div>\n<div>\n<p>Graph of Energy (E) vs. wave vector (k). EF separates filled and empty states.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-523\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-314.png\" alt=\"\" width=\"414\" height=\"292\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-314.png 414w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-314-300x212.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-314-65x46.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-314-225x159.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-314-350x247.png 350w\" sizes=\"auto, (max-width: 414px) 100vw, 414px\" \/><\/p>\n<p><strong>Energy levels of electrons and holes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Close to the band edge minima and maxima we can write:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-524\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-315.png\" alt=\"\" width=\"140\" height=\"144\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-315.png 140w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-315-65x67.png 65w\" sizes=\"auto, (max-width: 140px) 100vw, 140px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-525\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-316.png\" alt=\"\" width=\"179\" height=\"238\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-316.png 179w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-316-65x86.png 65w\" sizes=\"auto, (max-width: 179px) 100vw, 179px\" \/><\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">Band gap determines the optical properties &#8211; strong absorption when h\u03bd &gt; EG<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Optical absorption<\/strong><\/p>\n<ul>\n<li><span style=\"text-align: initial;font-size: 1em\">Excitation promotes an electron from the valence band to conduction band.<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">An empty state left in valence band is known as a hole.<\/span><\/li>\n<\/ul>\n<\/div>\n<div><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-526\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-317.png\" alt=\"\" width=\"335\" height=\"294\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-317.png 335w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-317-300x263.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-317-65x57.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-317-225x197.png 225w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-527\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-318.png\" alt=\"\" width=\"322\" height=\"235\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-318.png 322w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-318-300x219.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-318-65x47.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-318-225x164.png 225w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/p>\n<div>\n<ul>\n<li>\u00a0If band minima and maxima are at different points then we have an Indirect semiconductor.<\/li>\n<li>The classic example is Silicon.<\/li>\n<li>This affects the optical properties such as absorption where \u2206k \u2248 0<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-528\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-319.png\" alt=\"\" width=\"381\" height=\"420\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-319.png 381w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-319-272x300.png 272w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-319-65x72.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-319-225x248.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-319-350x386.png 350w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/p>\n<p style=\"text-align: justify\"><strong>Hole picture<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Remove one electron from a filled band and electricity can be conducted by the movement of all of the electrons present.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The sum of this motion is equivalent to one positively charged particle: <strong>a hole<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-529\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-320.png\" alt=\"\" width=\"445\" height=\"163\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-320.png 445w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-320-300x110.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-320-65x24.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-320-225x82.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-320-350x128.png 350w\" sizes=\"auto, (max-width: 445px) 100vw, 445px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Holes and their properties<\/p>\n<\/div>\n<div><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-530\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-321.png\" alt=\"\" width=\"340\" height=\"58\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-321.png 340w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-321-300x51.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-321-65x11.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-321-225x38.png 225w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-531\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-322.png\" alt=\"\" width=\"628\" height=\"280\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-322.png 628w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-322-300x134.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-322-65x29.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-322-225x100.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-322-350x156.png 350w\" sizes=\"auto, (max-width: 628px) 100vw, 628px\" \/><\/div>\n<div><\/div>\n<div><strong><span style=\"font-size: 1em;text-align: initial\">Effective masses<\/span><\/strong><\/div>\n<div><\/div>\n<div><span style=\"text-align: initial;font-size: 1em\">Force accelerates the electron or hole:<\/span><\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-532\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-323.png\" alt=\"\" width=\"499\" height=\"328\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-323.png 499w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-323-300x197.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-323-65x43.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-323-225x148.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-323-350x230.png 350w\" sizes=\"auto, (max-width: 499px) 100vw, 499px\" \/><strong>Meaning of the effective mass<\/strong><\/p>\n<\/div>\n<div>\n<ul>\n<li>Effective mass changes as we move through a band in k-space <strong>positive<\/strong> (electron-like) at the bottom, becoming <strong>negative <\/strong>(hole-like) at the top<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-533\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-324.png\" alt=\"\" width=\"226\" height=\"252\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-324.png 226w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-324-65x72.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-324-225x251.png 225w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><\/p>\n<p>Typical values in semiconductors are in the range 0.01 to 0.5 me<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Concentrations of Electrons and Holes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Calculate carrier density from density of states and distribution function:<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-534\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-325.png\" alt=\"\" width=\"424\" height=\"78\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-325.png 424w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-325-300x55.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-325-65x12.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-325-225x41.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-325-350x64.png 350w\" sizes=\"auto, (max-width: 424px) 100vw, 424px\" \/><\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">For most semiconductors the chemical potential, ?, (often also called the Fermi\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">Energy (EF)), lies in the band gap so:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-535\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-326.png\" alt=\"\" width=\"575\" height=\"145\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-326.png 575w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-326-300x76.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-326-65x16.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-326-225x57.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-326-350x88.png 350w\" sizes=\"auto, (max-width: 575px) 100vw, 575px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-536\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-327.png\" alt=\"\" width=\"611\" height=\"353\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-327.png 611w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-327-300x173.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-327-65x38.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-327-225x130.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-327-350x202.png 350w\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-537\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-328.png\" alt=\"\" width=\"560\" height=\"263\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-328.png 560w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-328-300x141.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-328-65x31.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-328-225x106.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-328-350x164.png 350w\" sizes=\"auto, (max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>LAW OF MASS ACTION<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Densities of holes and electrons depend on<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-538\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-329.png\" alt=\"\" width=\"632\" height=\"318\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-329.png 632w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-329-300x151.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-329-65x33.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-329-225x113.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-329-350x176.png 350w\" sizes=\"auto, (max-width: 632px) 100vw, 632px\" \/><\/p>\n<p><strong>Intrinsic Semiconductors<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A semiconductor is said to be intrinsic if it is undoped, and the only source of electrons and holes is by its thermal excitation from the valence band to the conduction band.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-539\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-330.png\" alt=\"\" width=\"575\" height=\"60\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-330.png 575w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-330-300x31.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-330-65x7.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-330-225x23.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-330-350x37.png 350w\" sizes=\"auto, (max-width: 575px) 100vw, 575px\" \/><\/p>\n<p style=\"text-align: justify\">We can use this relation to measure the Band Gap, by measuring the carrier densities from the Hall Effect At low temperatures ni 0 and impurities are important<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Doping Semiconductors<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">We can control the numbers of electrons and holes in a semiconductor by adding impurities which dope the material.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Donors donate an electron to make the material more n-type. A typical example is by adding a group V element (such as As or P) to a group IV semiconductor such as silicon.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Four of the electrons participate in the sp3 bonds as if they were from silicon, but the fifth electron is left over. Extra charge on P nucleus creates a +ive core, and the fifth electron can be bound to this, but the binding is weak.<\/span><\/p>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>Shallow Donors<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Impurity binding looks like a hydrogen atom Binding energy<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-540\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-331.png\" alt=\"\" width=\"262\" height=\"76\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-331.png 262w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-331-65x19.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-331-225x65.png 225w\" sizes=\"auto, (max-width: 262px) 100vw, 262px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Binding energy is very small because:<\/p>\n<p>(i)\u00a0\u00a0 The effective mass is small (typically m* = 0.1 me)<\/p>\n<p style=\"text-align: justify\">(ii)\u00a0\u00a0 The wave function is large (much more than the crystal unit cell), so we must include the relative<\/p>\n<p style=\"text-align: justify\">dielectric constant of the medium \u03b5r, &#8211; typically \u224810.<\/p>\n<p>\u2234\u00a0 \u2217 \u2248 10<sup>\u22123<\/sup>\u00a0 R<sub>0<\/sub> = 13.6 meV (155K)<\/p>\n<p>&nbsp;<\/p>\n<p><strong><span style=\"font-size: 1em;text-align: initial\">Acceptors<\/span><\/strong><\/p>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Dope semiconductors with holes by adding group III elements to a group IV material. e.g. put Ga into silicon.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">One valence electron is missing. This creates a vacant state, a hole, which binds to the ion core of the Ga which is negatively charged. Binding energy is:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-541\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-332.png\" alt=\"\" width=\"256\" height=\"75\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-332.png 256w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-332-65x19.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-332-225x66.png 225w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/p>\n<p>Where is the energy level?<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Ionized Acceptor or Donor is a free hole or electron at the top or the bottom of the band<\/p>\n<p>\u2234 Acceptor is R* above the valence band edge<\/p>\n<p>Donor is R* below the conduction band edge<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Extrinsic Carrier Densities<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Density of impurities (e.g. Donors) usually much less than N<sub>C<\/sub>, N<sub>V.<\/sub> Impurities can be ionized N<sub>d<\/sub><sup>+<\/sup> , or neutral N<span style=\"font-size: 12.8px\">d<\/span><span style=\"text-align: initial;text-indent: 1em;font-size: 1em\"><sup>0<\/sup> so:<\/span><\/p>\n<p>N<sub>d<\/sub>= N<sub>d<\/sub><sup>+<\/sup>+N<sub>d<\/sub><sup>0<\/sup><\/p>\n<p>&nbsp;<\/p>\n<p>Using charge neutrality we have:<\/p>\n<p>n=p+N<sub>d<\/sub><sup>+<\/sup><\/p>\n<p>&nbsp;<\/p>\n<p>Simple argument:<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">At high (e.g. Room) Temperature kT &gt; R* therefore all donors will be ionized but the density of holes created by excitation across the band gap is still small<\/p>\n<p>\u2234 n \u2248N<sub>d<\/sub><sup>+<\/sup>=N<sub>d<\/sub><\/p>\n<p>&nbsp;<\/p>\n<p><strong><span style=\"text-align: initial;font-size: 1em\">Chemical Potential \u03bc<\/span><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">At high (room) temperature most impurities are ionized<\/span><\/p>\n<\/div>\n<div>\n<p>\u2234 n \u2248N<sub>d<\/sub><sup>+<\/sup>=N<sub>d<\/sub><\/p>\n<p>&nbsp;<\/p>\n<p>\u03bc\u00a0 lies below the Donor level so that most impurities are empty (ionized), but is still close to conduction band.<\/p>\n<p>&nbsp;<\/p>\n<p>Minority Carriers<\/p>\n<p>&nbsp;<\/p>\n<p>By Law of Mass action the (very small) density of holes is:<\/p>\n<p>p=n<sub>i<\/sub>(T)2\u2044\u00a0N<sub>d<\/sub><\/p>\n<p>&nbsp;<\/p>\n<p>Temperature dependent density and chemical potential<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-542\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-333.png\" alt=\"\" width=\"345\" height=\"442\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-333.png 345w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-333-234x300.png 234w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-333-65x83.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-333-225x288.png 225w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><\/p>\n<ul>\n<li>Density is constant in region around room temperature.<\/li>\n<li>High temperature gives Intrinsic behaviour.<\/li>\n<\/ul>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p>Conductivity of Semiconductors<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-544\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-335.png\" alt=\"\" width=\"254\" height=\"64\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-335.png 254w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-335-65x16.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-335-225x57.png 225w\" sizes=\"auto, (max-width: 254px) 100vw, 254px\" \/><\/p>\n<p>\u03bc, is the mobility, which is defined by v = \u03bc E, the drift velocity per unit electric field.<\/p>\n<p>&nbsp;<\/p>\n<p>Conductivity is dominated by variation in densities.<\/p>\n<p>&nbsp;<\/p>\n<p>Mobility is determined by scattering rate:<\/p>\n<p>&nbsp;<\/p>\n<p>Low T: impurity scattering gives \u03bc\u00a0 ~ T<sup>3\/2<\/sup><\/p>\n<p>&nbsp;<\/p>\n<p>High T: phonon scattering gives \u03bc\u00a0 ~ T<sup>3\/2<\/sup><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>p-n junction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-545\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-336.png\" alt=\"\" width=\"624\" height=\"270\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-336.png 624w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-336-300x130.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-336-65x28.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-336-225x97.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-336-350x151.png 350w\" sizes=\"auto, (max-width: 624px) 100vw, 624px\" \/><\/p>\n<p>p-n junctions<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>What is current flow across junction?\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 J=nev<\/p>\n<p>What is v? &#8211; due to diffusion of carriers with diffusion coefficient D and lifetime\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 .<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-546\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-337.png\" alt=\"\" width=\"629\" height=\"584\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-337.png 629w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-337-300x279.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-337-65x60.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-337-225x209.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-337-350x325.png 350w\" sizes=\"auto, (max-width: 629px) 100vw, 629px\" \/><\/p>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>Low Dimensional Structures and Materials<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>\u2022\u00a0 Anisotropic Materials<\/p>\n<p>\u2022 Artificial layered structures &#8211; Quantum Wells and Superlattices<\/p>\n<p>\u2022\u00a0 Electric or Magnetic Fields applied in one direction.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-547\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-338.png\" alt=\"\" width=\"239\" height=\"184\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-338.png 239w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-338-65x50.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-338-225x173.png 225w\" sizes=\"auto, (max-width: 239px) 100vw, 239px\" \/><\/p>\n<p style=\"text-align: center\"><strong>Heterojunctions<\/strong><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-548\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-339.png\" alt=\"\" width=\"673\" height=\"284\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-339.png 673w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-339-300x127.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-339-65x27.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-339-225x95.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-339-350x148.png 350w\" sizes=\"auto, (max-width: 673px) 100vw, 673px\" \/><\/p>\n<p><strong><span style=\"text-align: initial;font-size: 1em\">Reduced Dimensionality<\/span><\/strong><\/p>\n<\/div>\n<div>\n<p>Quantum Well removes 1 Dimension by quantization<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-549\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-340.png\" alt=\"\" width=\"285\" height=\"151\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-340.png 285w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-340-65x34.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-340-225x119.png 225w\" sizes=\"auto, (max-width: 285px) 100vw, 285px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Electron is bound in well and can only move in plane<\/p>\n<p>&nbsp;<\/p>\n<p>2-D system &#8211; motion in x, y plane<\/p>\n<p>&nbsp;<\/p>\n<p>Quantum Well &#8211; Type I<\/p>\n<p>&nbsp;<\/p>\n<p>Typical Materials:<\/p>\n<p>1: GaAs<\/p>\n<p>2: (Al<sub>0.35<\/sub>Ga<sub>0.65<\/sub>)<sub>As<\/sub><\/p>\n<p><span style=\"font-size: 1em;text-align: initial\">(Eg = 1.5 eV)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (Eg = 2.0 eV)<\/span><\/p>\n<\/div>\n<div>\n<p>Energy levels are quantized in Z-direction with values En for both electrons and holes<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-550\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-341.png\" alt=\"\" width=\"245\" height=\"74\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-341.png 245w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-341-65x20.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-341-225x68.png 225w\" sizes=\"auto, (max-width: 245px) 100vw, 245px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-551\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-342.png\" alt=\"\" width=\"322\" height=\"231\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-342.png 322w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-342-300x215.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-342-65x47.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-342-225x161.png 225w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Infinite well &#8211; Particle in a box<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-552\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-343.png\" alt=\"\" width=\"507\" height=\"381\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-343.png 507w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-343-300x225.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-343-65x49.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-343-225x169.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-343-350x263.png 350w\" sizes=\"auto, (max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Density of States\u00a0<\/strong><\/p>\n<p>g(k)dk<\/p>\n<p>g(\u03b5)d\u03b5<\/p>\n<\/div>\n<div><\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-553\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-344.png\" alt=\"\" width=\"701\" height=\"361\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-344.png 701w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-344-300x154.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-344-65x33.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-344-225x116.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-344-350x180.png 350w\" sizes=\"auto, (max-width: 701px) 100vw, 701px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Optical Properties<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>3-D <\/strong>Absorption coefficient is proportional to the density of states:<\/p>\n<p>\u2234\u03b1\u00a0 ~\u00a0 \u03b51\/2<\/p>\n<p>Modified close to the band gap due to \u2018excitons\u2019<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-554\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-345.png\" alt=\"\" width=\"371\" height=\"217\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-345.png 371w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-345-300x175.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-345-65x38.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-345-225x132.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-345-350x205.png 350w\" sizes=\"auto, (max-width: 371px) 100vw, 371px\" \/><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>2-D<\/strong>\u00a0<strong>Big Changes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Multiple Band gaps &#8211;<\/p>\n<p>Band gap shift &#8211;<\/p>\n<p>Sharper edge-<\/p>\n<p>&nbsp;<\/p>\n<p>For wide wells the sum of many 2-D absorptions becomes equivalent to the 3-D absorption shape (\u03b51\/2)<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-555\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-346.png\" alt=\"\" width=\"434\" height=\"276\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-346.png 434w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-346-300x191.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-346-65x41.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-346-225x143.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-346-350x223.png 350w\" sizes=\"auto, (max-width: 434px) 100vw, 434px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-557\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-348.png\" alt=\"\" width=\"511\" height=\"484\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-348.png 511w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-348-300x284.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-348-65x62.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-348-225x213.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-348-350x332.png 350w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">\u2022\u00a0 Sharp peaks due to excitons<\/span><\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">\u2022\u00a0 peaks doubled due to heavy and light holes<\/span><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>Semiconducting Lasers<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Forward biased p-n junction<\/p>\n<ul>\n<li>Quantum Well laser<\/li>\n<li>Fibre Optic Communications,<\/li>\n<li>CD players, laser pointers<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-558\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-349.png\" alt=\"\" width=\"303\" height=\"361\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-349.png 303w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-349-252x300.png 252w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-349-65x77.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-349-225x268.png 225w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><\/p>\n<p><strong>How do we achieve low dimensionality?<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Naturally anisotropic crystals<\/p>\n<p style=\"text-align: justify\">Controlled growth of layers and\/or apply external potential Deposit thin layers of single crystals to create<\/p>\n<p>\u2018heterostructures\u2019<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Two Main techniques:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>I) Molecular Beam Epitaxy (MBE)<\/p>\n<p>II) Metal Organic Vapour Phase Epitaxy (MOVPE)<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Molecular Beam Epitaxy (MBE)<\/strong><\/p>\n<div>\n<ul>\n<li>Ultra High Vacuum molecular (Molecular Beam) evaporation of species of elements<\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">Epitaxy-\u00a0\u00a0 maintaining crystal\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">structure of the \u2018substrate\u2019 &#8211; which\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">is a single crystal<\/span><\/li>\n<\/ul>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-559\" src=\"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/96\/2018\/11\/2-350.png\" alt=\"\" width=\"337\" height=\"341\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-350.png 337w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-350-296x300.png 296w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-350-65x66.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-content\/uploads\/sites\/96\/2018\/11\/2-350-225x228.png 225w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Semiconductor Nanoparticles-3<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/RSzYsneFvjw\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"author":3,"menu_order":22,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-520","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/pressbooks\/v2\/chapters\/520","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":6,"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/pressbooks\/v2\/chapters\/520\/revisions"}],"predecessor-version":[{"id":931,"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/pressbooks\/v2\/chapters\/520\/revisions\/931"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/pressbooks\/v2\/chapters\/520\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/wp\/v2\/media?parent=520"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/pressbooks\/v2\/chapter-type?post=520"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/wp\/v2\/contributor?post=520"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/wp-json\/wp\/v2\/license?post=520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}