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CHAPTER 3 Semiconductor Science and Light Emitting Diodes 1 The first transistor was demonstrated on Dec. 23, 1947, at Bell Labs by William Shockley. This new invention consisting of P type and N type semiconductive materials (in this case germanium) has completely revolutionized electronics. William Shockley (seated), John Bardeen (left), and Walter Brattain (right) invented the transistor at Bell Labs and thereby ushered in a new era of semiconductor devices. The three inventors shared the Nobel prize in 1956 2 3.1 SEMICONDUCTOR CONCEPTS AND ENERGY BANDS 3 3.1 SEMICONDUCTOR CONCEPTS AND ENERGY BANDS A. Energy Band Diagrams 4 Energy of electron in an atom or a molecule • The energy of the electron in an atom is quantized and can have only certain discrete values. • The same concept also applies to the electron energy in a molecule with several atoms. 5 Energy levels of the Li atom • Li: 1s22s1 – Two electrons in the 1s shell – One electron in the 2s subshell 6 Energy bands of Li metal crystal • When we bring together 1023 Li atoms to form a metal crystal, the interatomic interaction result in the formation of electron energy band. • 2s energy level splits into some 1023 closely spaced energy levels 2s energy band • Other higher energy levels also form bands. 7 Energy band structure of a metal • The energy bands overlap to form one continuous energy band that represents the energy bands structure of a metal. • The 2s energy level in the Li atom is half full The 2s band in the crystal will also be half full. • Metals characteristically have partially filled energy bands. 8 Electron energies in semiconductor crystal • Si: 1s22s22p63s23p2 4 valence electrons • Si crystal: Each Si atom is bonding to four neighbors. The interactions between Si atoms and valence electrons results in the electron energy falling into 2 bands valence band (VB) and conduction band (CB) that are separated by bandgap (Eg) 9 Bandgap • There are no allowed electron energies in the bandgap. • It represents the forbidden electron energies in the crystal. 10 Valence band (VB) • Electron wavefunctions correspond to bonds between the atoms. • Electrons that occupy these wavefunctions are the valence electrons. • At 0 K, all the energy levels in the VB are normally filled with these electrons. 11 Conduction band (CB) • The CB represents electron wavefunctions in the crystal that have higher energies than those in the VB. • CB are normally empty at 0 K. • An electron placed in the CB is free to move around the crystal. 12 Band diagram at 0 K the bottom of CB = Ec Ev the top of VB • Electron affinity : The energy difference between the vacuum level and the bottom of the CB, i.e. the width of the CB. 13 Effective mass • We can treat an electron in the CB as if it were free with the crystal by simply assigning an effective mass mc to it. • Effective mass: – A quantum mechanical quantity that take into account the electron in the CB interacts with a periodic potential energy as it moves through the crystal. mc me The mass of electron in vacuum 14 Creation of an electron-hole pair • When an incident photon (h > Eg) interacts with an electron in the VB The electron absorbs the photon and reach the CB. charge : e free electron in the CB "e " effective mass : m e free hole in the VB "h " charge : e effective mass : mh The empty electronic state, or the missing electron, in the bond. 15 Creation of electron-hole pair 16 Thermal generation of electron-hole pair • Due to thermal energy, the atom in the crystal are constantly vibrating. • Energetic vibrations can rupture bonds and thereby create electron and hole pairs (EHPs) by exciting electrons from the VB to the CB. 17 Recombination • When an electron in the CB meets a hole in the VB, the electron falls from the CB to the VB to fill the hole. Recombination of EHP. Annihilation of an electron from the CB and a hole in the VB. photon, e.g. in GaAs and InP Excess energy lattice vibration (heat), e.g. in Si and Ge 18 In steady state • Thermal generation rate = Recombination rate Electron concentration n in CB = constant Hole concentration p in VB = constant • Both n and p depend on temperature: n = n(T) p = p(T) 19 3.1 SEMICONDUCTOR CONCEPTS AND ENERGY BANDS B. Semiconductor Statistics 20 Two important concepts • Density of states (DOS) • Fermi-Dirac function 21 Density of states (DOS) g(E) • The number of electronic states (electron wavefunctions) in a band per unit energy per unit volume of the crystal. • For an electron confined within a 3-D potential well g(E) (E Ec)1/2 • DOS gives information only available states and not on their actual occupation. 22 Fermi-Dirac function f (E) • The probability of finding an electron in a quantum state with energy E. • It is a fundamental property of a collection of interaction electron in thermal equilibrium. • 1 E EF 1 exp k T B k B : Boltzmann constant, T : temperature (K) f (E) EF : Fermi energy (chemical potential) 23 Fermi energy • If V is the potential difference between two points EF = eV A VA EFA B VB EFB EF = e(VA VB)= eV • For a semiconductor in the dark, in equilibrium, and with no applied voltage or no emf generated EF = 0 EF must uniform across the system 24 f (E) and EF 1-f(E): the probability of finding a hole EF is located in the bandgap f(E = EF) = 1/2 f (E) 1 E EF 1 exp k T B f(E): the probability of finding an electron 25 Electron concentration n in CB • nE(E) = gCB(E) f (E) : the actual number of electrons per unit energy per unit volume in the CB. • nE(E)dE = gCB(E) f (E)dE is the number of electron in the energy range E to E+dE per unit volume in the CB. • Electron concentration in the CB n Ec Ec nE ( E )dE Ec Ec gCB ( E ) f ( E )dE 26 Nondegenerate semiconductor • Whenever (Ec – EF) >> kBT, i.e. EF is at least a few kBT below Ec, then f ( E) exp ( E EF ) / kBT Boltzmann probability function • Such semiconductors are called nondegenerate. • It implies that the number of electrons in the CB is far less than the number states in this band. 27 Electron concentration in CB • For nondegenerate semiconductor (Ec – EF) >> kBT n Ec Ec ( Ec EF ) gCB ( E ) f ( E )dE N c exp k T B 2 m k T in which N c 2 h e B 2 3/2 Nc : Effective density of states at the CB edge Nc is a temperature-dependent constant 28 Effective density of states at the CB edge ( Ec EF ) n N c exp k T B 2 m k T Nc 2 h e B 2 3/2 : Effective density of states at the CB edge • If we take all the sates in the CB and replace them with Nc (number of states per unit volume) at Ec and then multiply this by the Boltzmann probability function, we obtain the concentration n in the CB. 29 Hole concentration in VB • If (EF – EV) >> kBT p Ev 0 ( EF Ev ) gVB ( E )(1 f ( E ))dE N v exp k T B 2 m k T in which N v 2 h h B 2 3/2 Nv : Effective density of states at the VB edge Nv is a temperature-dependent constant 30 nE ( E ) gCB ( E ) f ( E ) pE ( E ) gVB ( E )(1 f ( E )) 31 Electron and hole concentrations ( Ec EF ) 2 m k T • n N c exp , Nc 2 k BT h e B 2 3/2 ( EF Ev ) 2 m k T • p N v exp , Nv 2 k T h B h B 2 3/2 The location of EF determined the electron and hole concentrations. 32 Fermi level in intrinsic crystal • In an intrinsic semiconductor (a pure crystal) n p ( Ec EFi ) ( EFi Ev ) n N c exp p N v exp k T k T B B 1 1 Nc exp ( EFi Ev Ec EFi ) exp (2 EFi 2 Ev Eg ) Nv k BT k BT Nc 1 1 EFi Ev Eg k BT ln Fermi level in 2 2 N v intrinsic crystal Nc Typically, N c N v ln 0 Nv EFi Ev 1 Eg EFi is very approximately in the middle of the bandgap 2 33 Mass action law ( Ec EF ) ( EF Ev ) np N c exp N v exp k BT k BT Ec Ev Eg 2 N c N v exp N N exp n c v i k BT k BT temperature T n is a constant that depends on energygap Eg does not depend on Fermi level EF 2 i • Intrinsic concentration in an undoped (pure) crystal ni = n = p 34 Average energy of electrons in CB • The electron in the CB is “free” in the crystal with an effective mass me Average kinetic energy 1 2 3 me v k BT 2 2 • Thermal velocity (root mean square velocity) v 2 5 10 m/s 35 3.1 SEMICONDUCTOR CONCEPTS AND ENERGY BANDS C. Extrinsic Semiconductors 36 Extrinsic semiconductors • Extrinsic semiconductor Pure crystal + small amount of impurities • e.g. As + Si n-type semiconductor n >> p Arsenic: pentavalent impurities B + Si p-type semiconductor p >> n Boron: trivalent impurities 37 Arsenic doped Si crystal • As+ ion + e- hydrogenic impurity ionization energy ~ 0.05eV • At room temp. ~ kBT = 0.025 eV The fifth valence electron can be readily freed by thermal vibrations of Si lattice 38 Energy diagram for n-type Si doped As Ed : Donor level Ec Ed ~ 0.05 eV 39 Donor impurity • As atom : donates an electron into CB donor impurity • Nd : donor atom concentration • If Nd >> ni n = Nd at room temp. p =ni2/n = ni2/Nd p << ni 40 Conductivity ene eph e : drift mobility of electrons h : drift mobility of holes For n - type semiconductors n Nd , p n / Nd 2 i eN d e e(n / N d ) h 2 i eN d e ( n-type conductivity N d p n / N d ) 2 i 41 Arsenic doped Si crystal • When B substitutes for a Si atom one of its bonds has an electron missing and therefore a hole. • Bonding energy of hole ~ 0.05eV • At room temperature, the thermal vibrations of the lattice can free the hole away from the B site. A free hole exits in the VB. 42 Energy diagram for p-type Si doped B Ea : Acceptor level Ea Ev ~ 0.05 eV • There are acceptor energy levels just above Ev around B site. • These acceptor levels accept electrons from the VB and therefore create holes in the VB. 43 Acceptor impurity • The B atom introduced into the Si crystals acts as an electron acceptor impurity. • Na : acceptor atom concentration • If Na >> ni p Na at room temp. n = ni2/p ni2/Na << p 44 Conductivity ene eph e : drift mobility of electrons h : drift mobility of holes For p - type semiconductors p Na , n n / Na 2 i e(n / N a ) e eN a h 2 i eN a h ( p-type conductivity N a n n / N a ) 2 i 45 Energy band diagrams • EFi: intrinsic, EFn:n-type, EFp: p-type • The energy distance of EF from Ec and Ev determines the electron and hole concentrations by ( Ec EF ) 2 me k BT n N c exp , Nc 2 2 k T h B 3/2 ( E Ev ) 2 m k T p N v exp F , N 2 v k T h B h B 2 3/2 46 n-type semiconductors • • • • n >> p Electrons: majority carriers Holes: minority carriers n nn0 in equilibrium n type nn0 = Nd • p pn0 • Mass action law nn0 pn0 = ni2 47 p-type semiconductors • • • • p >> n Electrons: minority carriers Holes: majority carriers n np0 in equilibrium p type • p pp0 pp0 = Na • Mass action law np0 pp0 = ni2 48 3.1 SEMICONDUCTOR CONCEPTS AND ENERGY BANDS D. Compensation Doping 49 Compensation doping • Compensation doping describes the doping of a semiconductor with both donors and acceptors to control the properties. • A p-type semiconductor can be converted to an n-type semiconductor by simply adding donors until Nd > Na • Electron concentration n Nd Na • The effect of donors compensates for the effect of acceptors and vice versa. 50 When both acceptors and donors are present • Electrons from donors recombine with the holes from the acceptors so that the mass action law np = ni2 is obeyed. We can not simultaneously increase the electron and hole concentrations because that leads to an increase in the recombination rate. • If we have more donors than acceptors n = Nd Na • If we have more acceptors than donors p = Na Nd 51 3.1 SEMICONDUCTOR CONCEPTS AND ENERGY BANDS E. Degenerate and Non-degenerate Semiconductors 52 Non-degenerate semiconductors • Number of states in CB >> Number of electrons Probability of 2 electrons occupying the same state ~ 0 Pauli exclusion principle can be neglected and electron statistics can be described by the Boltzmann statistics f ( E) exp ( E EF ) / kBT 53 Non-degenerate semiconductors • The Boltzmann express ( Ec EF ) 2 m k T n N c exp , Nc 2 k BT h e B 2 3/2 for n is valid only when n << Nc • Those semiconductors for which n << Nc and p << Nv are termed non-degenerate semiconductors. 54 Degenerate semiconductors • When semiconductor has been excessively doped with donors n ~ 1019-1020 cm-3 n is comparable to Nc • The Pauli exclusion principle becomes important and we have to use the Fermi-Dirac statistics. • Such a semiconductor are more metal-like, e.g. resistivity as T . • Semiconductors that have n > Nc or p > Nv are called degenerate semiconductors. 55 Degenerate semiconductors • Heavy doping Donor atoms become so close to each other Their orbitals overlap to form a narrow band, which overlaps and becomes part of the conduction band. • Degenerate n-type semiconductor EFn > Ec • Degenerate p-type semiconductor EFp < Ev 56 Degenerate semiconductors • The dopant concentration is so large that they interact with each other. Not all dopants are ionized Carrier concentration saturates ~ 1020 cm-3 n Nd or p Na • The mass action law np = ni2 is not valid for degenerate semiconductors. 57 3.1 SEMICONDUCTOR CONCEPTS AND ENERGY BANDS F. Energy Band Diagram in an Applied Field 58 Band diagram in an applied field • A n-type semiconductor is connected to a voltage supply of V. • The whole band structure tilts because the electron now has an electrostatic potential energy as well. • EF is not uniform throughout the whole system. • EF = EF(A) – EF(B) = eV • CB, VB and EF all bend by the same amount. - 59 EXAMPLE 3.1.1 Fermi level in semiconductors n-type Si, doped with 1016 cm-3 antimony (Sb) (donor) Nd = 1016cm-3 Calculate EFn – EFi @ 300 K When the wafer is further doped with boron (B), Na = 21017 cm-3 > Nd = 1016cm-3 p-type Calculate EFp – EFi @ 300 K 60 EXAMPLE 3.1.1 Fermi level in semiconductors Solution Nd = 1016cm-3 Nd >> ni (= 1.451010 cm-3) n = Nd = 1016cm-3 • For intrinsic semiconductor ni Nc exp ( Ec EFi ) / kBT • For doped Si n Nc exp ( Ec EFn ) / kBT Nd 61 EXAMPLE 3.1.1 Fermi level in semiconductors Solution ni N c exp ( Ec EFi ) / k BT n N c exp ( Ec EFn ) / k BT N d Nd exp ( EFn EFi ) / k BT ni Nd 1016 EFn EFi k BT ln( ) (0.259 eV) ln( ) 10 ni 1.45 10 0.348 eV 62 EXAMPLE 3.1.1 Fermi level in semiconductors Solution Si doped with boron (B) Na = 2 1017cm-3 > Nd = 1016 cm-3 p = Na – Nd = 2 1017cm-3 1016 cm-3 = 1.9017 cm-3 • For intrinsic semiconductor p ni Nc exp ( EFi Ev ) / k BT • 3 1.45 10 cm For doped Si p N v exp ( EFp Ev ) / k BT 10 63 EXAMPLE 3.1.1 Fermi level in semiconductors Solution p ni N v exp ( EFi Ev ) / k BT p N v exp ( EFp Ev ) / k BT p exp ( EFp EFi ) / k BT ni p 1.9 1017 EFp EFi k BT ln( ) (0.259 eV) ln( ) 10 ni 1.45 10 0.424 eV 64 EXAMPLE 3.1.2 Conductivity • • • n-type Si, Nd = 1016cm-3 phosphorus (P) atoms (donors) e: drift mobility e = 1350 cm2V-1s-1 What is the conductivity? 65 EXAMPLE 3.1.2 Conductivity Solution Since N d 1016 cm 3 ni 1.45 1010 cm 3 n Nd Conductivity ene ep p ene ni 2 N d ) (p Nd (1.6 1019 C)(11016 cm 3 )(1350 cm 2 V 1s 1 ) =2.161cm 1 66 3.2 DIRECT AND INDIRECT BANDGAP SEMICONDUCTOR: E-k DIAGRAMS 67 Infinite potential well • When the electron is within an infinite potential energy well, the wavevector kn is a quantum number n kn , n 1, 2,3, L • The electron momentum is kn • Its energy is quantized ( kn ) 2 En 2me V(x)= V(x)= V(x) Electron e 0 L En increases parabolically with kn • This description can be used to represent the behavior of electrons in a metal. 68 Nearly free electron model • When electrons are in a metal, their average potential energy can be taken very roughly zero. • We take within the metal crystal 0 V ( x) V0 (several eV) outsid the metal crystal so that the electron is contained within the metal. • This is the nearly free electron model of a metal. • This model is too simple since it does not take into the actual variation of the electron potential energy in the crystal. 69 Periodic potential energy in a crystal • The E-k relationship will no longer be simply En = (kn)2/2me 70 Bloch wavefunctions V ( x) : Periodic potential in crystal V ( x) V ( x a ) V ( x 2a ) V ( x ma ), m 1, 2, One has to solve the Schrodinger equation d 2 2me 2 [ E V ( x)] 0 2 dx Solutions are Bloch wavefunctions k ( x) U k ( x) exp( jkx) Bloch wave in the crystal U k ( x ma ) U k ( x) traveling wave periodic function The electron wavefunction in the crystal is a traveling wave that is modulated by Uk(x). 71 E-k diagram • k ( x) U k ( x) exp( jkx) • There are many such Bloch wavefunction solutions to the crystal. • kn acts as a kind of quantum number. • Each k(x) corresponds a particular kn and represents a state with an energy Ek The dependence of Ek on k E-k diagram /a /a 72 Crystal momentum • k :crystal momentum k is the momentum invloved in its interaction with external fields, such as those involved in photon absorption processes. d( k) • Fext dt Fext: the externally applied force , such as due to an electric field E Fext = eE 73 E-k diagram • E-k diagram Energy vs. crystal momentum plot. • Lower E-k curve Valence band (VB). • Upper E-k curve Conduction band (CB). • All the valence electrons at 0K fill the states in the lower E-k diagram. 74 E-k diagram • The E-k curve consists of many discrete points with each point corresponding to a possible state k(x). • In the energy range from Ev to Ec, there are no solutions to the Schrödinger equation. • E-k behavior is not a simple parabolic relationship except near the bottom of the CB and the top of the VB. 75 Direct bandgap semiconductor • e.g. GaAs • The minimum of the CB is directly above the maximum of the VB. • Electron-hole pairs can recombine directly and emit a photon • The majority of light-emitting devices use direct bandgap semiconductors to make use of direct recombination. 76 Indirect bandgap semiconductor • e.g. Si, Ge • The minimum of the CB is not directly above the maximum of the VB, but it is displaced on the k-axis. • An electron at the bottom of the CB cannot recombine directly with a hole at the top of the VB because it is not allowed by the law of conservation of momentum. 77 Indirect bandgap semiconductor with a recombination center • Recombination center – Crystal defects – Impurities • The electron is first captured by the defect at Er. • The change in the energy and momentum of the electron by this capture process is transferred to lattice vibrations, i.e., to phonons. • The captured electron at Er can readily fall down into an empty state at the top of the VB and thereby recombine with a hole. • The electron transition from Ec to Ev involves the emission of further lattice vibration. 78 GaP doped nitrogen impurities • GaP: indirect bandgap semiconductor • Nitrogen (N) impurities Recombination center • The recombination of the electron with a hole at the recombination centers results in photon emission. • The electron transition from Ec to Ev involves photon emission. 79 3.3 pn JUNCTION PRINCIPLES 80 3.3 pn JUNCTION PRINCIPLES A. Open Circuit 81 pn junction • One side is n-type and the other is p-type. • There is an abrupt discontinuity between the p and n region. Metallurgical junction, M • n region: – fixed (immobile) ionized donors – free electrons (in CB) • p region : – fixed ionized acceptors – holes (in VB) 82 Hole concentration gradient • p = pp0 (p-side) > p = pn0 (n-side) Holes diffuse towards the right and enter the n-region and recombine with the electrons (majority carriers) in this region. The n-side near the junction becomes depleted of majority carriers and has exposed positive donors of concentration Nd. 83 Electron concentration gradient • n = nn0 (n-side) > n = np0 (p-side) Electrons diffuse towards the left and enter the p-region and recombine with the holes (majority carriers) The p-side near the junction becomes depleted of majority carriers and has exposed negative acceptors of concentration Na. 84 Space charge layer • The regions on both sides of M becomes depleted of free carriers in comparison with the bulk regions far away from the junction. • There is a space charge layer (SCL) around M. • Also known as the depletion region around M. 85 Electron and hole concentration profiles logarithmic scale • Note: under equilibrium condition (e.g., no applied bias , or photoexcitation) pn = ni2 everywhere. 86 Internal electric field E0 • There is an internal electric field E0 in the SCL. • E0 tries to drift the holes back into the p-region and electrons back into the n-region. • This field drives the carriers in the opposite direction to their diffusion. • In equilibrium – Hole diffusion flux = Hole drift flux – Electron drift flux = Electron diffusion flux 87 Net space charge density net(x) • For uniformly doped p and n regions eNa , Wp x 0 net ( x) eNd , 0 x Wn • For overall charge neutrality N aWp N dWn 88 Depletion widths • NaWp = NdWn • If Na > Nd Wp < Wn Depletion width of heavily doped side < Depletion width of lightly doped side • If Na >> Nd Wp << Wn The depletion region is almost entirely on the lightly doped side. • We generally indicate heavy doped regions with the superscript plus sign as p+. 89 Built-in field Gauss's law net (r ) net (r ) d E net ( x) E (r ) 0 r dx net ( x ') E ( x) dx ' eN a , W p x 0 net ( x) eN d , 0 x Wn eN a x x (eN a ) dx ', E , W p x 0 Wp 0 E ( x) 0 (eN a ) dx ' x (eN d ) dx ', E eN d x , 0 x Wn 0 W 0 p eN aW p eN dWn Bulit-in field where E 0 E (0) 90 Built-in potential x dV E V ( x) E ( x ')dx ' O dx eN a x E0 , W p x 0 E ( x) E eN d x , 0 x Wn 0 Wn V0 V (Wn ) E ( x ')dx ' O eN a N dWo 2 1 V0 E0W0 2 2 ( N a N d ) in which W0 Wn W p Bulit-in potential If we know V0, we can calculate W0. 91 Boltzmann statistics • If carrier concentration in the CB << Nc we can use Boltzmann statistics Effective density of states n( E ) exp( E / kBT ) at the CB edge • The concentrations n1 and n2 of carriers at potential energies E1 and E2 are related by ( E2 E1 ) n2 exp n1 k T B in which E = qV is the potential energy (PE). 92 Potential energy of carriers • Electrons – q = -e – PE = 0 on the p-side far away from M where n = np0 – PE = -eV0 on the n-side far away from M where n = nn0. • Holes – q=e – PE = 0 on the p-side far away from M where p = pp0 – PE = eV0 on the n-side far away from M where p = pn0. 93 Built-in potential nn 0 k BT n p 0 / nn 0 exp(eV0 / k BT ) V0 ln( ) e np0 pn 0 / p p 0 p p0 k BT exp(eV0 / k BT ) V0 ln( ) e pn 0 p p 0 N a , pn 0 ni2 / nn 0 ni2 / N d k BT N a N d V0 ln 2 e ni Built-in potential V0 is related to the dopant and host material properties via Na, Nd, and ni2 [= NcNv exp(-Eg/kBT)] 94 Built-in potential • k BT N a N d V0 ln 2 e ni Eg where n N c N v exp k T B 2 i • V0 is the potential across the pn junction, going from p to n-type semiconductor, in an open circuit. • Once we know V0 from above Eq., we can then calculate the width W0 of the depletion region form eN a N dWo 2 V0 2 ( N a N d ) 95 3.3 pn JUNCTION PRINCIPLES B. Forward Bias 96 Forward Bias • A battery with a voltage V is connected across a pn junction: – Positive terminal p-side. – Negative terminal n-side. The applied voltage drops mostly across the depletion width W. V directly opposes V0 and the potential barrier against diffusion is reduced to (V0-V). 97 Injection of excess minority carriers • The applied voltage effectively reduces the guilt-in potential and the built-in field that acts against diffusion. • Excess holes can diffuse across SCL and enter the nside. • Excess electrons can diffuse across SCL and enter the p-side. Injection of excess minority carriers 98 Small increase in the majority carriers • When holes are injected into the neutral n-side, they draw some electrons from the bulk of n-side (and hence from the battery). • There is a small increase in the electron concentration in the n-side. • Similarly, there is a small increase in the hole concentration in the p-side. 99 Hole concentration just outside SCL • pn(0) = pn (x = 0): the hole concentration just outside the depletion region. • pn(0) is determined by the probability of surmounting the new potential energy barrier e(V0V), pn (0) p p 0 exp[ e(V0 V ) / k BT ] 100 Law of the junction • Holes are injected from the p-side to the n-side pn (0) p p 0 exp[e(V0 V ) / k BT ] pn 0 / p p 0 exp(eV0 / k BT ) pn (0) pn 0 exp(eV / k BT ) • Electrons are injected from the n-side to the p-side n p (0) n p 0 exp(eV / k BT ) Law of the junction where np(0) is the electron concentration just outside the depletion region at x = Wp 101 Current due to diffusion of minority carriers • The current due to holes (electrons) diffusing in the n-region (p-region) can be sustained because more holes (electrons) can be supplied by the p-region (n-region), which can be replenished by the positive (negative) terminal of battery. An electric current can be maintained through a pn junction under forward bias, and that the current flow seems to be due to the diffusion of minority carriers. 102 Excess minority carrier concentration • The hole concentration pn(x) profile on the nside falls exponentially toward to the thermal equilibrium value. pn ( x ') pn ( x ') pn 0 pn (0) exp( x '/ Lh ) pn ( x ') : excess minority carrier concentration Lh : hole diffusion length Lh : Dh h Dh : diffusion coefficient of holes h : mean hole recombination lifetime (minority carrier lifetime) in the n - region The average distance diffused by a minority carrier before it disappears by recombination. 103 Hole diffusion current density Hole diffusion flux pn ( x ') pn ( x ') pn 0 pn (0) exp( x '/ Lh ) dpn ( x ') d pn ( x ') J D ,hole ( x ') Dh (e) eDh dx ' dx ' eDh x' Hole diffusion current p (0) exp n depends on location L L h h 104 Total current • In n-region – Jhole Minority carrier diffusion current – Jelec Majority carrier drift current • In p-region – Jhole Majority carrier drift current – Jelec Minority carrier diffusion current The field in the neutral region is not totally zero but a small value, just sufficient to drift the huge number of majority carriers. • J = Jelec + Jhole= constant 105 Hole diffusion current density eDh x' J D ,hole ( x ') pn (0) exp Lh Lh eV pn (0) pn 0 exp Law of the junction k BT pn 0 ni2 / nn 0 ni2 / N d eV pn (0) pn (0) pno pn 0 exp k BT J D ,hole x ' 0 eDh Lh ni2 eV exp pno k BT Nd eDh ni2 eV pn (0) exp k BT Lh N d 1 1 Hole diffusion current Just outside the depletion region 106 Total current density • We assume that the electron and hole currents do not change across the depletion region because, in general, the width of this region is narrow. eDh ni2 eV J D ,hole x W or W J D ,hole x '0 exp 1 n p k BT Lh N d eDe ni2 eV J D ,elec x W or W exp 1 n p k BT Le N a • The total current density is eDh eV eDe 2 J J D ,hole J D ,elec ni exp 1 k BT Lh N d Le N a eV J J so exp k BT 1 Schockley diode equation 107 J D ,hole eDh ni2 eV exp k BT Lh N d 1 J D ,elec eDe ni2 eV exp k BT Le N a eDh eDe J Lh N d Le N a 2 eV ni exp k BT 1 1 108 Shockley equation eV • J J so exp k BT eDh eDe 1 , where J so Lh N d Le N a 2 ni • The constant Jso depends Na, Nd, ni, Dh, De, Lh and Le. • If we apply a reverse bias V = Vr > kBT/e (= 25 mV) eVr J J so exp k BT 1 J SO JSO is known as the reverse saturation current density. 109 Recombination in SCL • Under forward bias, the minority carriers diffusing and recombining in the neutral regions are supplied by external current. • However, some of the minority carriers will recombine in the depletion region. The external current must therefore also supply the carriers lost in the recombination process in the SCL. 110 Recombination current • • • • • • pM = hole concentration at M nM = electron concentration at M A symmetrical pn junction pM = nM (due to symmetry) area ABC electrons recombining in p-side area BCD holes recombining in n-side Recombination current J recom eABC e eBCD h 1 1 e Wp nM e Wn pM 2 2 e h e : mean electron recombination time in Wp h : mean hole recombination time in Wn 111 Recombination current • PE = 0 at A, PE = e(V0V)/2 at M ( PE M PE A ) e(V0 V ) pM exp exp p p0 k T 2 k T B B k BT N a N d V0 ln 2 , p p 0 N a e ni e(V0 V ) eV pM p p 0 exp ni exp 2 k BT 2k BT J recom 1 1 e W p nM e Wn pM en 2 2 i e h 2 nM W p Wn eV exp 2 k BT e h • From a better quantitative analysis J recom J r 0 exp(eV / 2kBT ) 1 112 Total current • The total current into the diode will supply carriers for minority carrier diffusion in the neutral regions and recombination in SCL. eV J J so exp k BT 1 eV J r 0 exp 2 k BT J recom 1 eV I I 0 exp 1 k BT • : the diode ideality factor • is 1 for diffusion controlled and 2 for SCL recombination controlled characterisitics. 113 3.3 pn JUNCTION PRINCIPLES C. Reverse Bias 114 Reverse Bias • Positive terminal n-side Electrons in n-side move away from SCL • Negative terminal p-side Holes in p-side move away from SCL Wider SCL • The movement of electrons in the n-region towards the positive terminal cannot be sustained because there is no electron supply to this nside. 115 Reverse Bias • Built-in potential V0+Vr • Electric field in SCL E0+E • Small number of holes on the n-side near the SCL become extracted and swept by the field across the SCL over to the p-side. • This small current can be maintained by the diffusion of holes from the n-side bulk to the SCL boundary. 116 Minority carrier diffusion current • pn(0) pn0 exp(eVr/kBT) law of the junction • If Vr > 25 mV = kBT/e pn(0) 0 < pn0 Small concentration gradient Small hole diffusion current toward SCL • Similarly, there is a small electron diffusion current from bulk p-side to SCL. • Within the SCL, these carriers are drifted by the field. 117 Reverse current eVr • J J so exp k BT 1 Shockley equation • If Vr >> KBT/e = 25 mV J Jso Reverse saturation current density eDh eDe • J so Lh N d Le N a 2 ni Dh = hkBT/e, De = ekBT/e Lh = (Dhh)1/2, Le = (Dee)1/2 Jso depends only on the material via ni, h,e, the dopant concentrations, etc., but not on the voltage. Jso depends ni2, and hence is strongly temperature dependent. 118 EHP thermal generation in SCL • The thermal generation of EHPS in the SCL can also contribute to the observed current since the internal field will separate the electron and hole and drift them toward the neutral region. 119 EHP thermal generation in SCL • g: the mean time to generate an EHP by thermal vibrations of lattice (mean thermal generation time) • ni/g :the rate of thermal generation per unit volume • A : the cross-sectional area of the depletion region • WA: the volume of the depletion region The reverse current density component due to thermal generation of EHPs within SCL: J gen ni 1 eWni e AW g A g 120 The total reverse current density • The total reverse current density is the sum of the diffusion and generation component: J rev J diffusion J gen eDh eDe Lh N d Le N a 2 eWni ni g • Jgen increases with Vr because the SCL width W increase with Vr. 121 The total reverse current density • J rev J diffusion J gen eDh eDe Lh N d Le N a 2 eWni ni g The reverse current are predominantly controlled by ni2 and ni. • Since ni ~ exp(Eg /2kBT), the reverse current depends on the temperature. 122 Reverse current J rev ni eDh eDe J diffusion J gen Lh N d Le N a exp( Eg / 2k BT ) 2 eWni ni g I rev Aexp( Eg / k BT ) Bexp( Eg / 2k BT ) Eg 1 ln I rev ln( A) if I rev is controlled by ni2 kB T Eg 1 ln I rev ln( B) if I rev is controlled by ni 2k B T 123 Reverse current Irev in a Ge pn junction • T > 238 K slope of ln(Irev) vs. 1/T 0.63 eV 0.66 eV (Eg of Ge) Irev is controlled by ni2 • T < 238 K slope of ln(Irev) vs. 1/T 0.33 eV (Eg/2 of Ge) Irev is controlled by ni 124 3.3 pn JUNCTION PRINCIPLES D. Depletion Layer Capacitance 125 Stored charge in depletion region • The depletion region of a pn junction has positive and negative charges separated over a distance W similar to a parallel plate capacitor. • Storged charge: +Q +eNdWnA on n-side Q eNaWpA on p-side • Unlike in the case of a parallel plate capacitor, Q does not depend linearly on the voltage V across the device. 126 Depletion layer capacitance • We can define an incremental capacitance: When V changes by dV to V+dV, then W also changes and the Q becomes Q+dQ. The depletion layer capacitance Cdep is defined by Cdep dQ dV 127 Depletion layer width • If the applied voltage is V, the voltage across the depletion layer W is V0 V eN a N dW 2 V0 V 2 ( N a N d ) Built-in potential 2 ( N a N d ) V0 V W eN a N d 1/2 128 Depletion layer capacitance Q eN dWn A eN aW p A Wn Q / (eN d A), W p Q / (eN a A) 2 ( N a N d ) V0 V W eN N a d 1/2 Q 1 1 Q Na Nd Wn W p ( ) eA N a N d eA N a N d eAN a N d 2 ( N a N d ) V0 V Q ( Na Nd ) eN a N d 1/2 Cdep eAN a N d 1 2 ( N a N d ) V0 V dQ dV ( N a N d ) 2 eN a N d 1/2 Cdep eN a N d A 2 ( N a N d ) V0 V 1/2 2 ( N a N d ) eN a N d A W 129 Depletion layer capacitance 1/2 eN a N d 2 ( N a N d ) V0 V • Cdep A A W Cdep is given by the same expression as that for the parallel plate capacitor, A/W, but with W being voltage-dependent. • For reverse bias, V = Vr 1/2 Cdep eN a N d A 2 ( N a N d ) V0 Vr Cdep decreases with increasing Vr – Typically, Cdep~ pF 130 3.3 pn JUNCTION PRINCIPLES E. Recombination Lifetime 131 Excess carrier injection • Consider recombination in a direct bandgap semiconductor. • Suppose that excess electrons and hole have been injected: pp : the excess hole concentration in the neutral p-side. np : the excess electrons concentration in the neutral p-side. pp = np for charge neutrality 132 Net rate of change of np • At any instant: n p n po n p instantaneous minority carrier concentration p p p po n p instantaneous majority carrier concentration • Instantaneous recombination rate nppp • Thermal generation rate of EHPs is Gthermal. • The net rate of change of np is n p t Bn p p p Gthermal in which B is called the direct recombination capture coefficient. 133 Net rate of change of np • In equilibrium n p t 0 • Using np = np0, pp = pp0, we find n p Bn p p p Gthermal Bn p 0 p p 0 Gthermal 0 t Gthermal Bn p 0 p p 0 The rate of change of np is n p t B np p p np0 p p0 Rate of change due to recombination 134 Recombination time e • In many instance n p n p t • Excess minority carrier recombination time (lifetime) e is defined by n p t n p e 135 Weak injection • In practical cases: np >> np0 Actual equilibrium minority carrier concentration • Weak injection: np << pp0 np np , pp pp0 + pp pp0 Na n p t B n p p p n p 0 p p 0 B n p N a n p 0 N a BN a n p Comparing with n p t n p e e 1/ BN a constant Weak injection recombination lifetime 136 Strong injection • Strong injection: np >> pp0 n p t B n p p p n p 0 p p 0 B n p p p n p 0 p p 0 Bn p ( p p 0 p p ) Bn p p p B n p 2 Comparing with n p n p e t e 1 1 Bn p n p Under high level injection conditions the lifetime e is inversely proportional to the injected carrier concentration. 137 EXAMPLE 3.3.1 A direct bandgap pn junction • A symmetrical GaAs pn junction: – A = 1 mm2 (cross sectional area) – Na (p-side doping) = Nd (n-side doping) = 1023 m-3 – B = 7.2110-16 m3s-1 (direct recombination capture coefficient) – ni = 1.8 1012 m-3 – r = 13.2 – h (in the n-side) = 250 cm2V-1s-1 (drift mobility) – e (in the p-side) = 5000 cm2V-1s-1 (drift mobility) – Forward voltage across the diode = 1V 138 EXAMPLE 3.3.1 A direct bandgap pn junction • What is the diode current due to the minority carrier diffusion at 300 K assuming direct recombination? • If the mean minority carrier recombination time in the depletion region is of the order of ~ 10 ns, estimate the recombination component of the current. 139 EXAMPLE 3.3.1 A direct bandgap pn junction Solution • Assuming weak injection 1 1 h e BN a (7.211016 m3s 1 )(11023 m 3 ) 1.39 108 s 140 EXAMPLE 3.3.1 A direct bandgap pn junction Solution • Einstein relation: Diffusion coefficients are Dh h k BT / e, De e k BT / e Dh h k BT / e (0.2585)(250 10 ) 4 6.46 10 4 2 -1 ms De e k BT / e =(0.2585)(5000 104 ) 1.29 102 m 2s-1 141 EXAMPLE 3.3.1 A direct bandgap pn junction Solution • The diffusion length Lh ( Dh h )1/2 [(6.46 104 m 2s -1 )(1.39 108 s)]1/2 3.00 106 m Le ( De e )1/2 [(1.29 102 m 2s -1 )(1.39 108 s)]1/2 1.34 105 m 142 EXAMPLE 3.3.1 A direct bandgap pn junction Solution • The diffusion length Lh ( Dh h )1/2 [(6.46 104 m 2s -1 )(1.39 108 s)]1/2 3.00 106 m Le ( De e )1/2 [(1.29 102 m 2s -1 )(1.39 108 s)]1/2 1.34 105 m 143 EXAMPLE 3.3.1 A direct bandgap pn junction Solution • The reverse saturation current due to diffusion in the neutral regions is IS 0 Dh De 2 A eni Lh N d Le N a 6.46 104 1.29 102 6 19 12 2 (10 ) (1.6 10 )(1.8 10 ) 6 23 5 23 (3.00 10 )(10 ) (1.34 10 )(10 ) 6.13 1021 A 144 EXAMPLE 3.3.1 A direct bandgap pn junction Solution • The forward diffusion current I diff I so exp(eV / K BT ) (6.13 10 27 1.0 V A) exp 0.0258 V 3.9 104 A • The built-in voltage V0 10231023 Na Nd K BT V0 ln( 2 ) (0.0258) ln 1.28 eV 12 2 e ni (1.8 10 ) 145 EXAMPLE 3.3.1 A direct bandgap pn junction Solution • The depletion layer width 2 ( N a N d ) V0 V W eN N a d 1/2 1/2 2(13.2)(8.85 10 Fm )(10 10 )m (1.28 1)V 19 23 3 23 3 (1.6 10 C )(10 m 10 m ) 9.0 108 m or 0.090 m 12 -1 23 23 3 146 EXAMPLE 3.3.1 A direct bandgap pn junction Solution • For a symmetric diode, Wp = Wn = W/2, and taking e = h = r 10 ns Aeni W p Wn Aeni W I r0 2 e h 2 e • (106 )(1.6 1019 )(1.8 1012 ) 9.0 10 8 12 1.3 10 A 9 2 10 10 So that I recom eV 1.0 V 12 I r 0 exp (1.3 10 A)exp 2 k T 2(0.02585) V B 3.3 104 A The diffusion and recombination components are about the same order. 147 3.4 THE pn JUNCTIONN BAND DIAGRAM 148 3.4 THE pn JUNCTION BAND DIAGRAM A. Open Circuit 149 Energy diagram of a pn junction under open circuit • EFp : Fermi level in the p-side • EFn : Fermi level in the n-side • In equilibrium and in the dark EFp = EFn 150 Energy diagram of a pn junction under open circuit • Ec on the n-side is close to EFn whereas on the p-side it is far away from EFp. • EFp = EFn through the whole system. We have to bend the bands Ec and Ev near the junction at M. 151 Energy diagram of a pn junction under open circuit • PE of the electron: 0 (p-region) eV0 (n-region) • The electron in the n-side at Ec must overcome a PE barrier to go to Ec at the p-region • PE barrier = eV0 (V0 : built-in potential) 152 3.4 THE pn JUNCTION BAND DIAGRAM B. Forward and Reverse Bias 153 Energy diagram of a pn junction under forward bias • Applied voltage V Built in potential V0. • PE barrier: eV0 e(V0 V) 154 Energy diagram of a pn junction under forward bias • The electrons in the nside can overcome the PE barrier and diffuse to the p-side. • The diffusing electrons can be replenished by the negative terminal. • Similarly, holes can diffuse from p- to n-side. The positive terminal can replenish those holes. A current flow through the junction and around the circuit. 155 Energy diagram of a pn junction under forward bias • p exp [e(V0V)/kBT] the probability that electron in the n-side overcomes the PE potential and diffuses to the p-side. Forward current exp [e(V0V)/kBT] exp (V/kBT) 156 Energy diagram of a pn junction under reverse bias • When reverse bias: V= Vr . • PE barrier: eV0 e(V0 + Vr) • Field in SCL: E0 E0 + E There is hardly any reverse current because if an electron were to leave the n-side to travel to the positive terminal, it can not be replenished from the p-side. 157 Thermal generations • Thermal generation of EHPs in the SCL – The field separates the pairs – Electrons n-side – Hole p-side • Thermal generation of minority carriers within a diffusion length to the SCL – A thermally generated hole in the n-side can diffuse to the SCL and then drift cross the SCL – A thermally generated electron in the p-side can diffuse to the SCL and then drift cross the SCL Small reverse current 158 Thermal generation of EHPs in SCL • When EHPs are thermally generated in the SCL, the field separates the pairs Electrons fall down the PE hill n-side Holes fall down the PE hill p-side Small reverse current 159 3.5 LIGHT EMITTING DIODES 160 3.5 LIGHT EMITTING DIODES A. Principles 161 Light Emitting Diodes • A light emitting diode (LED) is a pn junction diode typically made from a direct bandgap semiconductor in which the electron hole pair recombination results in the emission of a photon. • Emitted photon energy h Eg Bandgap energy 162 Band diagram of a pn+ junction device • pn+ junction device: – The n side is more heavily doped than the p-side. – The depletion region in a pn+ device extends mainly into the p-side. (a) Without any bias: • Uniform Fermi level • PE barrier = eV0 Built-in potential V0 prevents electrons from diffusing from n+ to p side. 163 Band diagram of a pn+ junction device (b) Forward bias • Built in potential V0 V0 – V It allows the electrons from the n+ side to diffuse or become injected into the p-side. = • The recombination of injected electrons in the depletion region as well as in the neutral p-side results in the spontaneous emission of photons. 164 Active region • Recombination primary occurs within: The depletion region A volume extending over the diffusion length Le of the electrons in the p-side • The recombination zone is called the active region. 165 Injection electroluminescence • The phenomenon of light emission from EHP recombination as a result of minority carrier injection. • Spontaneous emission process The emitted photons are in random direction. 166 3.5 LIGHT EMITTING DIODES B. Device Structure 167 Planar surface emitting LED devices (a) Epitaxial layers: first n+-layer and then the p-layer. (b) p-side is formed by diffusing dopants into the epitaxial n+-layer. • Narrow p-side (~ few m) Photons can escape without being absorbed. • Heavily doped n-side (n+) Most of recombination take place in the p-side. • Segmented back electrode Encourages reflection from the semiconductor-air interface. 168 Lattice mismatch • Lattice mismatch: – The epitaxial layer and the substrate crystal have different lattice parameter Lattice strain in the LED layer Crystal defect Recombination centers Radiationless EHP recombinations • It is important to lattice-match the LED layer to the substrate crystal. 169 Lattice match system • AlGaAs alloys – direct bandgap – bandgap red-emission region • It can be grown on GaAs substrates with excellent lattice match. High efficiency LED devices. 170 TIR in LED • Not all light rays reaching the semiconductor-air interface can escape because of total internal reflection (TIR) • E.g. GaAs-air interface, c 16 Much of the light suffers TIR 171 Domed surface • Domed or hemisphere surface of semiconductor i < c No TIR • Main drawback: – additional difficult process – Increase in expense 172 Plastic dome for LED • The encapsulation of the pn junction within a transparent plastic medium (an epoxy) that has a higher refractive index. More light escape from the LED • Many individual LEDs are sold in similar types of plastic bodies. 173 3.6 LED MATERIALS 174 Photon energy, wavelength and color E h hc (4.14 1015 eV s) (2.9979 1017 nm/s) 1240 eV nm 1240 eV nm (nm) E (eV) 175 LED materials from VIS to IR y = 0.45 y=0 y=1 x=0 176 GaAs1y Py • • • • Ga : group III, As, P: group V GaAs1y Py III-V ternary alloy Eg (GaAs1y Py ) as y y < 0.45 – direct bandgap – EHP recombination is direct – 630 nm < < 870 nm y = 0, GaAs y = 0.45, GaAs0.55P0.45 • y > 0.45 – indirect bandgap – EHP recombination occur through recombination centers and involve lattice vibrations rather than photon emission. 177 N doped indirect GaAs1-yPy (y > 0.45) • N and P atoms – same group V same valency – different electric cores The positive nucleus of N is less shielded by electrons compared with that of the P atom. • If some N atoms are added into GaAsP crystal – N atoms are isoelectric impurities – N atoms substitute for P atoms • same number of bonds • do not act as donors or acceptors A conduction electron near an N atom will be attracted and may become trapped at this site. N atoms introduce localized energy levels, or electron trap EN near the conduction band edge. 178 N doped indirect GaAs1-yPy (y > 0.45) • N atom electron trap • Trapped electron at EN can attract a hole by Coulomb attraction. • Direct recombination between a trapped electron and a hole emits a photon. • h EN– Ec < Eg Inexpensive green, yellow, and orange LEDs • Efficiency < Efficiency (direct bandgap semiconductors) 179 UV and blue LED materials • InxGa1-xN alloy – – – – Direct bandgap Eg as x GaN: Eg = 3.4 eV UV emission InGaN: Eg = 2.7 eV blue emission • Al doped silicon carbide (SiC) – Indirect bandgap – EHP recombination is through an acceptor level Ea • ZnSe (II-VI compound) – Direct bandgap – Drawback: difficulty in appropriately doping to fabricaye efficient pn junction 180 AlxGa1xAs • Al, Ga : group III • As: group V • AlxGa1xAs III-V ternary alloy – Direct bandgap for x < 0.45 – Eg as x – GaAs: Eg = 1.43 eV = 870 nm IR emission – AlxGa1-xAs (x < 0.45) : Eg = 1.941.43 eV = 640 870 nm deep red to IR emission 181 In0.49Ga0.51-xAlxP • Al, Ga, In : group III • P: group V • InGaAlP III-V quarternary alloy – Direct bandgap – Lattice-matched to GaAs substrates when in the composition range In0.49Ga0.34Al0.17P to In0.49Ga0.452Al0.058P – = 590 630 nm Amber, orange, red LEDs – Material for high-intensity visible LEDs 182 In1-xGaxAs1-yPy • Ga, In : group III • P, As: group V • In1-xGaxAs1-yPy III-V quarternary alloy – Direct bandgap – = 870nm (GaAs) 3.5 m (InAs) includes the optical communication wavelength of 1.3 and 1.55 m 183 External quantum efficiency external • ext The efficiency of conversion of electrical energy into an emitted external optical energy. • It incorporates the “internal” efficiency of radiative recombination process and the subsequent efficiency of photon extration from the device. • external Pout (Optical) 100% IV The input of electrical power into an LED • Indirect bandgap LEDs: external < 1% • Direct bandgap LEDs: higher external 184 LED materials orange, 185 3.7 HETEROJUNCTION HIGH INTENSITY LEDs 186 Homo and heterojunctions • Homojunction: A junction (such as a pn junction) between two differently doped semiconductors that are of the same material (same bandgap Eg) • Heterojunction: A junction between two different bandgap semiconductors • Heterojunction device (HD): A semiconductor device structure that has junctions between different bandgap materials 187 Refractive index and bandgap • The refractive index n of semiconductor material depends on its bandgap Eg: n as Eg • By constructing LEDs from heterostructures, we can engineer a dielectric waveguide within the device and thereby channel photons out from the recombination region. 188 Drawbacks of homojunction LEDs The p-region must be narrow to allow the photons to escape without much reabsorption. When the p-side is narrow, some of the injected electrons in the p-side reach the surface by diffusion and recombine through crystal defects near the surface. Radiationless recombination process decreases the light output. 189 Drawbacks of homojunction LEDs • If the recombination occurs over a relative large volume (or distance), due to long electron diffusion lengths, then the chances of reabsorption of emitted photons becomes higher. The amount of reabsorption increases with the material volume. 190 Double heterostructure (DH) device • DH device based on two junctions between different semiconductor materials with different bandgaps. • Different materials – Eg (AlGaAs) 2 eV – Eg (GaAs) 1.4 eV • Two heterjunctions – n+ p heterojunction between n+-AlGaAS and p-GaAs – p p heterojunction between p-GaAS and p-AlGaAs • p-GaAS thin layer – a fraction of m – lightly doped 191 Band diagram with zero bias • No bias Fermi level EF = constant • eV0 : PE barrier between n+-AlGaAS and p-GaAs • Ec = effective PE barrier between p-GaAS and p-AlGaAs Bandgap change between p-GaAs and p-AlGaAs 192 Forward biased band diagram • PE barrier eV0 eV0-V • Electrons in the CB of n+AlGaAs are injected (by diffusion) into p-GaAs • These electrons are confined to the CB of pGaAs by the barrier Ec • Wide gap AlGaAs layers act as confining layers. 193 Double heterojunction LED • EHP recombination presents in the p-GaAs layer • Eg (AlGaAs) > Eg (GaAs) The emitted photons do not get reabsorbed as they escape the active region and can reach the surface of the device. • Since light is also not absorbed in p-AlGaAs, it can be reflected to increase the light output. • DH LED is much more efficient than homojunction LED 194 3.7 LED CHARACTERISTIC 195 Energy of an emitted photon • The energy of an emitted photon from an LED is not simply equal to Eg because electrons in the CB are distributed in energy and so are the holes in the VB. 196 Energy distribution of carriers • Electron concentration in CB as a function of energy: nE(E) = gCB(E)f(E) A peak at (1/2) kBT above Ec Energy spread ~ 2KBT • The hole concentration is similarly spread from Ev in VB nE ( E ) gCB ( E ) f ( E ) pE ( E ) gVB ( E )(1 f ( E )) 197 • Transition 2 (E = h2) – has the maximum probability as both electron and hole concentrations are largest at these energy. Relative intensity is maximum, or close maximum • Idealized spectrum – Energy for the peak emission ~ Eg+KBT – Linewidth (h) ~ 2.5 KBT to 3 KBT 198 Output spectrum from an LED • The output spectrum from an LED depends not only on the semiconductor material but also on the structure of the on junction diode, including the dopant concentration level. 199 Effect of Heavy doping • Electron wavefunctions at the donors overlap to generate a narrow impurity band overlaps the CB and effectively lowers Ec Minimum emitted photon energy < Eg 200 Typical characteristics of a red GaAsP LED • Linewidth = 24 nm 2.7 kBT • LED current injected minority carrier concentration rate of recombination output light intensity • Turn-on voltage ~ 1.5 V from which point the current increases sharply with voltage. 201 Turn-on voltage • The turn-on voltage depends on the semiconductor and generally increases with the energy bandgap Eg • Blue LED Vturn-on~3.5-4.5 V • Yellow LED Vturn-on~ 2 V • GaAs IR LED Vturn-on~ 1 V 202 EXAMPLE 3.8.1 LED Output Spectrum • Typical width of the relative intensity vs. photon energy spectrum ~ 3kBT • Linewidth 1/2 = ? 203 EXAMPLE 3.8.1 LED Output Spectrum Solution • c / v hc / E ph d hc2 dE ph E ph d hc hc 2 E ph E ph 2 E ph dE ph E ph (hc / ) 2 E ph hc We are given E ph (h ) 3k BT 2 E ph 3k BT hc hc 2 204 EXAMPLE 3.8.1 LED Output Spectrum Solution • 2 E ph 3k BT hc hc 2 23 J/K)(300 K) 10 3(1.38 2 870 nm (870 nm) (6.626 1034 J s)(3 1017 nm/s) (870 nm) 2 (6.24 105 nm 1 ) 47.2 nm 1300 nm (1300 nm) 2 (6.24 10 5 nm 1 ) 105.4 nm 1550 nm (1550 nm) 2 (6.24 10 5 nm 1 ) 149.9 nm • These linewidths are typical values and the exact values depend on the LED structure. 205 EXAMPLE 3.8.2 LED Output wavelength variations • • • • Consider a GaAs LED. Eg = 1.42 eV @ 300 KT dEg/dT = 4.5 104 eVK-1 What is the change in the emitted wavelength if the temperature change is 10C ? 206 EXAMPLE 3.8.2 LED Output wavelength variations Solution • c / v hc / Eg d hc dEg 2 dT Eg dT (6.626 1034 )(3 108 ) 4 19 ( 4.5 10 1.6 10 ) 19 2 (1.42 1.6 10 ) 2.77 1010 m K 1 0.277 nm K 1 (d / dT )T (0.277 nm K 1 )(10 K ) 2.8 nm • Eg decrease with T, increases with T. 207 EXAMPLE 3.8.3 InGaAsP on InP substrate • Quarternary alloy In1-xGaxAsyP1-y grown on InP substrate Commercial semiconductor material for IR LED and laser diode. • In1-xGaxAsyP1-y is lattice matched to InP if y 2.2 x • Eg (In1-xGaxAsyP1-y) = 1.350.72y+0.12y2, 0 x 0.47 • Calculate the compositions of InGaAsP quarternary alloy for peak emission at 1.3m. 208 EXAMPLE 3.8.3 InGaAsP on InP substrate Solution • E ph hc Eg k BT hc k BT Eg (in eV) e e 1.3 106 m, T 300 K (6.626 1034 )(3 108 ) Eg 0.0259 eV 0.982 eV 19 6 (1.6 10 )(1.3 10 ) 0.982 eV 1.35 0.72 y 0.12 y 2 y 0.66 y 2.2 x x y / 2.2 0.66 / 2.2 0.3 The quarternary alloy is In0.7Ga0.3As0.66P0.34 209 3.9 LEDS FOR OPTICAL FIBER COMMUNICATIONS 210 Light sources for optical communications • LEDs – – – – simpler to drive more economic have a longer lifetime provide the necessary output power Short haul application (e.g. local networks) • Laser diodes – narrow linewidth – high output power – higher signal bandwidth capability Long-haul and wide bandwidth communications 211 Two types of LED devices • Surface emitting LED (SLED) – The emitted radiation emerges from an area in the plane of the recombination layer • Edge emitting LED (ELED) – The emitted radiation emerges from an area on an edge of the crystal, i.e. from an area on a crystal perpendicular to the active layer. • ELEDs provide a greater intensity light and also a beam that is more collimated than the SLEDs. 212 Light coupling for SLEDs 213 Burrus type device • The method is to etch a well in the planar LED structure and lower the fiber into the well as close as possible to the active region. • An epoxy resin is used to bond the fiber and provide refractive index matching between the fiber and the LED material. 214 A microlens focuses light into fiber • The method is to use a truncated spherical lens (a microlens) with a high refractive index (n = 1.9 -2) to focus the light into the fiber. 215 Structure of a edge emitting LED • The light is guided to the edge of the crystal by a dielectric waveguide formed by wider bandgap semiconductors surrounding a double heterostructure. 216 Light coupling for ELEDs • Light from an edge emitting LED is coupled into a fiber typically by using a hemispherical lens or a GRIN rod lens. • A GRIN rod lens (typical diameter ~ 0.5-2 mm) can be used to focus the light into a fiber. This coupling is particular useful for single mode fibers because their core diameters are typically ~ 10 m. 217 • GRIN rod lenses and a spherical lens (a ball lens) used in coupling light into fibers. 218