Semiconductor Science and Leds

Home , Band diagram, Double heterostructure, Homojunction, Intrinsic semiconductor

Optoelectronics EE/OPE 451, OPT 444 Fall 2009 Section 1: T/Th 9:30- 10:55 PM

John D. Williams, Ph.D. Department of Electrical and Computer Engineering 406 Optics Building - UAHuntsville, Huntsville, AL 35899 Ph. (256) 824-2898 email: [email protected] Office Hours: Tues/Thurs 2-3PM

JDW, ECE Fall 2009 SEMICONDUCTOR SCIENCE AND LIGHT EMITTING DIODES

• 3.1 Semiconductor Concepts and Energy Bands – A. Energy Band Diagrams – B. Semiconductor Statistics – C. Extrinsic Semiconductors – D. Compensation Doping – E. Degenerate and Nondegenerate Semiconductors – F. Energy Band Diagrams in an Applied Field • 3.2 Direct and Indirect Bandgap Semiconductors: E-k Diagrams • 3.3 pn Junction Principles – A. Open Circuit – B. Forward Bias – C. Reverse Bias – D. Depletion Layer Capacitance – E. Recombination Lifetime • 3.4 The pn Junction Band Diagram – A. Open Circuit – B. Forward and Reverse Bias • 3.5 Light Emitting Diodes – A. Principles – B. Device Structures • 3.6 LED Materials • 3.7 Heterojunction High Intensity LEDs Prentice-Hall Inc. • 3.8 LED Characteristics © 2001 S.O. Kasap • 3.9 LEDs for Optical Fiber Communications ISBN: 0-201-61087-6 • Chapter 3 Homework Problems: 1-11 http://photonics.usask.ca/

Energy Band Diagrams

• Quantization of the atom • Lone atoms act like infinite potential wells in which bound electrons oscillate within allowed states at particular well defined energies • The Schrödinger equation is used to define these allowed energy states 2 2m  e E V (x)  0 x2  E = energy, V = potential energy • Solutions are in the form of waves oscillating at quantized energies and related propagation constants defined by the differential equation Quantum Mechanics and Molecular Binding

• All atoms have specific bound states • Molecular binding requires filling of these allowed states in such a way as to reduce the amount of energy required to fill various states Effect of Periodicity in Solid Systems

• The compression of quantum states into periodic structures results overlap of available quantum states • Pauli exclusion principle states that: – electrons must fill available quantum states from lowest to highest potential – allowed states are defined by orbital solutions obtained from quantum mechanics • As atoms come closer together, orbitals become shared allowing electrons to fill exchange orbitals between the materials • As the number of atoms brought into proximity increases degeneracies occur resulting in allowable energy bands • These bands can be modeled using the Kronig Penning model with solutions that give an electron Density of States

Applet detailing different crystallographic binding types http://jas.eng.buffalo.edu/education/solid/genUnitCell/index.html Quantized States in Solid Li

Allowable Quantum States in Li Overlapping Orbitals in 1 mol of Li 1 mol = 1023 atoms Metal Energy Bands

• Overlapping energy degeneracies in metals • Lead to continuous energy bands • Statistically stable energy for electrons lies within these overlapping bands and only slight excitations lead to conduction b/c the variation in allowable quantum states is nearly continuous Semiconductors

• Semiconductors are distinctly different • In Semiconductors there is no overlapping degeneracy between conduction and valence bands

• The result is a bandgap, Eg, that is present between bound and conducting electron states Eg  Ec  Ev • The width of the conduction band is called the electron affinity, 

• At energies above the Ec+  electrons can be ejected from the material • In silicon for example, all of the valence electrons are used to fill the binding orbitals located in the valance band Bandgap Basics

• The application of excess energy (light, thermal, electrical) or the addition of extra electrons into the system results in conduction by moving electrons into the conduction band • In thermal equilibrium electrons can be excited into the conduction band leaving a hole in the valance band • Holes and electrons propagate in throughout the material via quantum mechanical tunneling from site to site randomly • The application of a driving potential forces electrons and holes to migrate in opposite directions based on charge density

• The effective mass of holes ,mh*, and electrons me* is a quantum mechanical quantity relating the inertial resistance to acceleration of each under a driving force due to electric fields within the periodic structure

Thermal Considerations and Recombination

• The presence of a finite band gap requires that at T=0K, there is no electrical conduction within the material • As temperature increases, more and more free energy present in the semiconductor allows for the population of conduction bands with electrons. http://jas.eng.buffalo.edu/ed – Due to atomic vibrations that increase with temperature allowing for excitation of ucation/semicon/recombinati conduction band energy states on/indirect.html – Production of electrons in the conduction band due to increased free energy generates an equal number of holes in the valance band – This is referred to as thermal generation • When a wondering electron crosses a site within the lattice where a hole is present, the electron releases its free energy and binds to the atoms valence band. This process is called recombination • Electron concentration, n, within the conduction band • Hole concentration, p, within the valance band

Semiconductor Statistics: Density of States

• Many important properties of semiconductors are described by considering electrons in the conduction band and holes in the valance band. • Density of States (DOS), g(E), represents the number of electronics states in a band per unit energy per unit volume of the crystal • We use quantum mechanics (QM) to calculate the DOS by considering how many electron wave functions there are within a given energy range per unit volume • According to QM

where E = E – Ec for electrons in the conduction band DOS Continued Semiconductor Statistics: Fermi Dirac Function

• The Fermi Dirac Function, f(E), is the probability of finding an electron in a quantum state with energy E. This function is a fundamental property of a collection of interacting electrons in thermal equilibrium

• Where kb is the Boltzmann constant, T is the temperature in Kelvin, Ef is the Fermi energy • Fermi Energy = energy required to fill all states at T=0K • The Fermi energy is the chemical potential (or Gibbs free energy) per electron in the material • Changes in the Fermi energy across the material represent the electrical work input or output per electron • In the equilibrium state of a semiconductor with no http://jas.eng.buffalo.edu/educa light or applied voltage, the change in Fermi energy, Ef tion/semicon/fermi/functionAnd = 0, AND Ef must be uniform throughout the system States/functionAndStates.html • Note: The probability of a finding a hole is 1-F(E)

Conduction Band Concentrations in a Semiconductor

• Carrier concentration applet for variable temperature – http://jas.eng.buffalo.edu/education/semicon/fermi/lev elAndDOS/index.html • Note: DOS, g(E), remains constant. The carrier concentration varies as a function of F(E) Electron concentration in the conduction band

where

is the effective density of states at the conduction band edge Valance Band Solution

hole concentration in the valence band

where

is the effective density of states at the Important note: The only assumptions valance band edge specific to these derivations for n and p is that the Fermi energy is only a few kBT away from the band edges Intrinsic Semiconductor

• Intrinsic semiconductors are pure crystals where n = p

• It can be shown that in an intrinsic semiconductor that the Fermi level, Efi, is above Ev and located in the bandgap at 1 1  N   c  E fi  Ev  Eg  kBT ln  2 2  Nv 

• Typically Nc and Nv values are comparable and both occur in the logarithmic term so that Efi is approximately in the middle of the bandgap as shown in previous slides • The product of n and p in an intrinsic semiconductor provides the mass action law

 Eg      kBT  2 np  Nc Nve  ni 2 • Where Eg =Ec – Ev s the bandgap energy, ni is the constant that depends on temperature and material properties, and not the Fermi energy. • Thermal velocity of electrons in an intrinsic semiconductor at room temperature m*v2 3 E  e  k T 2 2 B m v2 105 s Extrinsic Semiconductors

• Semiconductors with small amounts of impurities • These impurities increase/decrease the probability of obtaining an electron in the conduction band • N-type semiconductors – extrinsic semiconductors with excess electrons – Arsenic added to silicon to which have one more valence (available electron) than silicon – Arsenic is called a donor b/c it donates electrons to the system

– For Nd >> ni, at room temperature, the electron concentration inside the conduction band will be nearly equal to Nd such that Nd=n (a) (b) – Number of holes, Electron Energy 2 p = ni /Nd – Conductivity, , depends CB As+ Ec on drift mobilities,, of e– ~0.05 eV E electrons and holes d As+ As+ As+ As+

  ene  eph E Distance into 2 v x n crystal i As atom sites every 106 Si atoms   eN d e  e h (a) The four valence electrons of As Nd (b) Energy band diagram for an n-type Si doped allow it to bond just like Si but the fifth with 1 ppm As. There are donor energy levels just electron is left orbiting the As site. The + below Ec around As sites.   eN d e energy required to release to free fifth- electron into the CB is very small.

• Semiconductors with small amounts of impurities • These impurities increase/decrease the probability of obtaining an electron in the conduction band • P-type semiconductor – Extrinsic with less electrons – Adding Boron (+3) metal which has one fewer electron and yields an increased hole per doped atom Electron energy 6 – Boron is called an acceptor B atom sites every 10 Si atoms Ec x Distance into crystal – For Na >> ni, at room

temperature, the hole h+ concentration inside the B– B– B– B– B– E valence band will be nearly a ~0.05 eV equal to N such that N =p h+ a a Ev – Electron carrier concentration VB is determined by the mass 2 (a) (b) action law as n = ni /Na (a) Boron doped Si crystal. B has only three valence electrons. When it – This value is much smaller than substitutes for a Si atom one of its bonds has an electron missing and therefore a p and thus the conductivity is hole. (b) Energy band diagram for a p-type Si doped with 1 ppm B. There are – given by acceptor energy levels just above Ev around B sites. These acceptor levels accept   eN ah electrons from the VB and therefore create holes in the VB.

Simplified Band Diagrams for Semiconductors

• Notice in the chart below that the Fermi level changes as a function of doping • Notice also that carrier concentration (holes or electrons) also changes as a function of doping • N-type: majority carriers are electrons and minority carriers are holes • P-type: majority carriers are holes and minority carriers are electrons 2 • Mass action law still valid: nnopno=ni where no is the doped equilibrium carrier concentration

E Ec c Ec EFn EFi EFp Ev E v Ev VB

(a) (b) (c)

Energy band diagrams for (a) intrinsic (b) n-type and (c) p-type semiconductors. In all cases, np = ni2. Note that donor and acceptor energy levels are not shown.

• Doping of a semiconductor with both donors and acceptors to control properties • Provides precise control of carrier concentrations n  N  N d a • Utilized extensively where p and n type doping of different regions meet.

Medium Dose Applications

High Dose Applications 0.2 keV to 80 keV Buried channel doping 0.5 keV to 750 keV 35-65 nm ULSI Degenerate and Nondegenerate Semiconductors

• In nondegenerate semiconductors the number of states in the carrier band far exceeds the number of electrons • Thus the probability of two electrons trying to occupy the same allowed state is virtually zero • This means that the Pauli exclusion principle can be neglected and the DOS is represented only by Boltzmann statistics • In this case, E CB CB EFn Impurities E Ec forming a band c is only valid when n << N c g(E) E E • Semiconductors where n<< N and p << N are termed v v c v EFp nondegenerate VB • When a semiconductors has been excessively doped (a) (b) with donors – 19 20 3 (a) Degenerate n-type semiconductor. Large number of donors form a then n may be 10 – 10 /cm band that overlaps the CB. (b) Degenerate p-type semiconductor. n > Np or P>Nv © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) – N is then comparable to Nc and the Pauli exclusion principle comes into play – In this case Fermi Dirac statistics are required – Degenerate semiconductor Energy Band Diagram in an Applied Field

V(x), PE(x) V(x)

Elect ron Energy PE(x) = –eV E

Ec EF

Ec  eV Ev EF  eV

Ev eV A

B n-T ype Semiconduct or

Energy band diagram of an n-type semiconductor connected to a voltage supply of V volts. The whole energy diagram tilts because the electron now has an electrostatic potential energy as well © 1999 S.O. Kasap,Optoelectronics (Prentice Hall) Potential Theory: A More Precise Band Diagram

• The time independent Schrödinger equation for a given potential function is written as 2m   e E V (x) 0 with a general solution of 2 If the potential energy, V, is periodic in nature as that shown below, then one can write it as V(x) V(x  ma) m 1,2,3,...

PE(r) PE of the electron around an r isolated atom

When N atoms are arranged to form the crystal then there is an overlap of individual electron PE functions. V(x) a a 0 PE of the electron, V(x), inside the crystal is periodic with a period a. x x = 0 a 2a 3a x = L

Surface Crystal Surface

The electron potential energy (PE), V(x), inside the crystal is periodic with the same periodicity as that of the crystal, a. Far away outside the crystal, by choice,V = 0 (the electron is free and PE = 0).

• The solution is called a Bloch Wavefunction

jkx k (x) U(x)k e – where U(x) is a periodic function that depends on V(x). The two share the same periodicity • The wavevector, k, in this solution acts like a quantum number and has values from – /a to  /a

• Momentum, p, in the crystal is ħk • External forces: dp d(k) F  qE   dt dt Direct vs. Indirect Bandgap

• Direct Bandgap – Base of the conduction band is matched to the max height of the valence band – Recombination through the emission of a photon (Light!!!!!!) • Indirect Bandgap – direct recombination would require a momentum change (not allowed) – Recombination centers (lattice defects) are required to recombine CB to VB bands – The result is a phonon emission (lattice vibration) that propagates across the lattice E E E

CB Indirect Bandgap, Eg Ec CB Direct Bandgap Photon CB Eg E E c E c E r Phonon v kcb E E VB v v

VB kvb VB –k k –k k –k k

(a) GaAs (b) Si (c) Si with a recombination center

(a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs is therefore a direct bandgap semiconductor. (b) In Si, the minimum of the CB is displaced from the maximum of the VB and Si is an indirect bandgap semiconductor. (c) Recombination of an electron and a hole in Si involves a recombination center . © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) pn Junction Principles p n

B- As+ + h (a) • Consider what happens when e– one side of a semiconductor M M Metallurgical Junction such as Si is doped n-type and E (x) Neutral p-region Eo Neutral n-region –Wp 0 Wn the other is d p-type x (e) • The abrupt discontinuity (b) –E between the two sides is called o a metallurgical junction, M V(x) M V Space charge region o • The M region contains a W W (f) log(n), log(p) p n depletion region of carriers of p po x width W = Wp + Wn where Wn nno PE(x) is the space charge region of n (c) i eV the n-doped Si and vice versa o pno Hole PE(x) npo • An electric field is generated in x x = 0 net x (g) the M region in order to M minimize the free energy at the Electron PE(x) eNd boundary and satisfy the mass –Wp –eV x (d) o 2 W action law ni = pn n

• The result is a bias voltage -eNa generated across the junction Properties of thepn junction.

• n-type Si is doped with 1016 antimony (Sb) atoms/cm3. Note antimony is group V  n dopes • Calculate the Fermi energy with respect to the intrinsic Fermi energy of Silicon

10 3 Intrinsic Carriers ni 1.4510 / cm ni  Nc exp Ec  EFi / kBT 

16 3 Doped Carriers Nd 10 / cm Nd  Nc exp Ec  EFn / kBT  16 Nd  ni  10  E  E  k T ln N / n  0.0259eV ln   0.348eV Fn Fi B  d i     10  n  Nd 1.4510   • If the n-type Si is further doped with 2x1017 boron(B) atoms/cm3 Boron is group III  p dopes • Calculate the position of the Fermi energy with respect to the intrinsic Si Fermi energy at room temperature (300K) and hence with respect to the n-type case for antimony doping

17 3 Na  210 / cm p  ni  Nc exp EFi  Ev / kBT  Intrinsic Carriers

16 3 Nd 10 / cm p  Nc exp EFp  Ev / kBT  Na  Nd Doped Carriers N  N a d p / ni  exp EFp  EFi / kBT  p  N  N a d 1.91017 / cm 3  17 3 E  E  k T ln p / n   0.0259eV ln   0.424eV p 1.910 / cm Fp Fi B  i     10   1.4510  Governing Equations for pn Junctions

• Conservation of charge NaWp  NdWn • The potential established across the boundary on the n-side is derived by integrating the Electric field established by the change in charge density across the boundary

Charge Density

 Force, F  qE  q dx  

Potential V   Edx 

• The Maximum value of the electric field and built in potential generated at the edge of the n- side of the M region are eN W eN W E   d n   a p o   1 eN N W 2 V   E W  d a o o 2 o o 2 (N  N ) a d

Governing Equations for pn Junctions

• One can relate Vo to doping parameters using the ratios of the carriers n2 and n1

n2  (E2  E1 _) nno  eVo  pno  eVo   exp     exp   and  exp   n1  kBT  npo  kBT  ppo  kBT 

Nd  eVo  Na  eVo    exp    exp   ni  kBT  ni  kBT 

k T  N N  V  B ln a d   o  2  e  ni  Forward Bias on pn Junctions

• Applied Bias V-Vo yields –(Vo-V) in exponential term • Resultant equations for carrier concentrations are referred to as the Law of the Junction

2 2  eVo V  ni  eV   eVo V  ni  eV  np (0)  npo exp    exp   pn (0)  pno exp    exp    kBT  Na kBT   kBT  Nd kBT  Hole Diffusion

• The increased length of carrier regions under an applied forward bias lead to excess minority carrier concentrations and a hole diffusion length, L   x'  p (x')  p (x')  p  p (0)exp  L  D   n n no n   h h h  Lh  where D is the diffusion coefficient of holes in the lattice and  is the hole recombination lifetime • Current density due to carrier diffusion is dp (x')  eD   x'  eD n2   eV   n h   h i   J d ,hole  eDh  pn (0)exp   exp  1 dx Lh  Lh  Lh Nd   kBT  

2   J eDeni  eV    p-region SCL n-region J d ,elec  exp  1 Le Na   kBT   J = J + J elec hole Total current Majority carrier diffusion The total current • Yields the Shockley equation and drift current anywhere in the device is J (reverse saturation current density) hole constant. Just outside the depletion region it is due Jelec Minority carrier diffusion 2 2 current to the diffusion of eDhni eDeni minority carriers. J so   Lh Nd Le Na x W –Wp n

eABC eBCD J recom    e  h

eWpnM  eWn pM  J recom   2 e 2 h 1 using M  eV V  2 o   eV  pM  ni exp   2kBT  en W W   eV  i  p n    J recom    exp  2   e  h   2kBT    eni Wp Wn   eV  I    Aexp  1 2   e  h   kBT   Where  is the diode ideality factor and is valued between 1 and 2 Current in pn Junctions

I I = Io[exp(eV/kBT)  1]

mA Reverse I-V characteristics of a pn junction (the positive and V negative current axes have Shockley equation different scales)

nA Space charge layer Where  is the diode ideality factor generation. and is valued between 1 and 2

• V = Vo+Vr • Increased bias leads to thermal generation of electrons and holes • Mean thermal generation time,  g eWn • Reverse current density due to thermal generation of CB electrons J  i gen  • Total reverse current density g

2 2 eDhni eDeni eWni J gen    Lh Nd Le Na  g

  Eg  where ni  exp   2kBT  Reverse current in Ge pn junction

Ge is a direct bandgap semiconductor, thus the pn junction emits a photon and is referred to as a photodiode

Reverse diode current (A) at V = 5 V

10-4 Ge Photodiode 323 K Reverse diode current in a Ge pn junction as a function of temperature in 10-6 0.63 eV a ln(Irev) vs. 1/T plot. Above 238 K, Irev 2 10-8 is controlled by ni and below 238 K it is controlled by ni. The vertical axis is 10-10 a logarithmic scale with actual current 0.33 eV values. (From D. Scansen and S.O. 238 K 10-12 Kasap, Cnd. J. Physics. 70, 1070-1075, 1992.) 10-14  eD eD  eW 10-16 h e 2 J gen    ni  ni 0.002 0.004 0.006 0.008    Lh Nd Le Na   g 1/Temperature (1/K)

• Charge on each side of the diode Q  eN dWn A Q  eN W A a p • Width of the Depletion layer 2N  N V V  W  d a o eN d Na • Depletion Layer Capacitance

dQ A eN N Cdep    A d a dV W 2Nd  Na Vo V 

eN d Na C j  A Junction capacitance 2Nd  Na Vo 

C j Cdep  m ;m 1/ 2 1V /Vo  Recombination Lifetime

• Instantaneous minority carrier concentration np  npo  np • Instantaneous majority carrier concentration pp  ppo  np • Thermal generation rate, Gthermal • Net change of holes in the semiconductor is n p  Bn p  G t p p thermal

np  Bnp p p  npo p po t

• Where B is the direct recombination coefficient np np • Excess minority carrier recombination lifetime, e is defined by   t  e • Weak injections n << p p po np  BN anp np  np t

p  p  N  e 1/ BN a p po a

• Strong injections np >> ppo

n p  Bn p  Bn 2 t p p p

• LEDs modulated under high carrier injection have variable minority carrier concentrations which lead to distortion of the modulated light output Pn Junction Band Diagram

E (a) (b) o Eo–E p n M E E c c e(V –V) E o eVo c E E E c E eV Fn Fp E Fp E Fn E v v E v E p n v p n

SCL I V

E +E (d) o (c) Eo+E E c E c e(Vo+Vr) e(V +V ) Thermal o r E generation Fp E E E E c Fp c v E E E Fn v Fn

E E v v p n p n

I = Very Small V Vr r

Energy band diagrams for a pn junction under (a) open circuit, (b) forward bias and (c) reverse bias conditions. (d) Thermal generation of electron hole pairs in the depletion region results in a small reverse current.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Example: Direct Bandgap pn Junction Symmetrical GaAs pn junction with a cross sectional area A= 1mm2. Compare the diode current due to minority carrier diffusion with the recombination current. 1    1.39108 s due to time changes in 23 3 h e carrier concentration Na ( pside)  Nd (nside) 10 / m BN a 4 2 16 3 B  7.2110 m / s Dh  hkBT / e  6.4610 m / s 2 2 12 3 ni 1.810 / m De  ekBT / e 1.2910 m / s 6  r 13.2 Lh  Dh h  310 m cm 2 L  D  1.34105 m  (n )  250 e e e h side Vs  D D  2 21 Reverse saturation 2  h e  cm Iso  A  eni  6.1310 A current  ( p )  5000  Lh Nd Le Na  e side Vs  eV    4 Forward diffusion Dh  hkBT / e Idiff  I so exp   3.910 A  kBT  current in pn junction De  ekBT / e k T  N N  V 1V V  B ln a d  1.28V Built in bias voltage applied o  2  e  ni  in pn junction T  300K e N  N V V  9 W  a d o  9108 m  mean 110 s Na Nd (cont.)

e N  N V V  W  a d o  9108 m Na Nd 1 9 Wp W n W where  h  e 110 s For a symmetric diode, Wp = Wn 2 In equilibrium with stated mean Aen W W  i  p n  12 carrier recombination time Iro     1.310 A 2   e  h   eV    4 Intrinsic recombination value is nearly equal to Irecom  Iro exp   3.310 A  2kBT  diffusion current for doped pn junction Principles of Light Emitting Diodes • LEDs are pn junctions usually made from direct bandgap semiconductors. Ex GaAs • Direct electron hole pair (EHP) recombination results in emission of a photon

• Photon energy is approximately equal to the bandgap energy Egh • Application of a forward bias drops the depletion region allowing more electrons into the p side of the device and increasing the probability of recombination in the depletion region • The recombination zone is called the active region and is the volume in which photons are generated • Light emission from EHP recombination as a result of minority carrier injection as shown here is called injection electroluminescence • The statistical nature of this process requires that the p side be sufficiently narrow to prevent reabsorption of the emitted photons Electron energy Relative spectral output power p n+ p n+ Ec –40°C eVo E Eg c 1 (a) EF E Eg (b) 25°C F The output spectrum from AlGaAs LED. Values h• Eg Ev normalized to peak emission at 25°C. eVo 85°C Ev

Distance into device V Electron in CB 0 Hole in VB Relative spectral output power 740 800 840 880 900 Wavelength (nm) (a) The energy band diagram of a p-n+ (heavily n-type doped) junction without any bias.–40°C + © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Built-in potential Vo prevents electrons from diffusing fromn to p side. (b)1 The applied bias reduces V and thereby allows electrons to diffuse, be injected, into the p-side. 25°C o The output spectrum from AlGaAs LED. Values Recombination around the junction and within the diffusion length of the electrons in the normalized to peak emission at 25°C. p-side leads to photon emission. 85°C © 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

0 740 800 840 880 900 Wavelength (nm)

• LEDS are typically formed by epitaxially growing doped semiconductors layers on suitable substrate. The substrate is then essentially a mechanical support for the device • However if the epi film and the substrate have mismatched lattice sizes then the lattice strain on the LED leads to crystalline defects that cause indirect recombination of EHPs and a loss of electroluminescence (photon emission). Thus the substrate is usually the same material as the epi layers • To insure that recombination occurs on the p side, the n side is very heavily doped. Photons emitted toward the n side become absorbed or reflected back at the substrate interface. • The use of segmented metal electrodes on the back promotes reflections

Light output Light output

Insulator (oxide) p p + Epit axial layers Epit axial layer n n+ n+ n+ Substrate Substrate

(b) (a) Met al electrode

A schematic illustration of typical planar surface emitting LED devices. (a) p-layer grown epitaxially on an n+ substrate. (b) First n+ is epitaxially grown and then p region is formed by dopant diffusion into the epitaxial layer.

• Not all light reaching the semiconductor air interface escape the surface due to TIR • For example the critical angle for TIR in GaAs-air is only 16o • Thus engineers attempt to shape the surface of the semiconductor into a dome or

hemisphere so that the light rays strike the surface at angles less than c. • The main drawback is the additional processing required to achieve these devices • The common method is to seal a plastic dome to the LED surface that moderates the index

change (nGaAs > nplastic >nair)and increases the critical angle for TIR

(a) (b) (c) Light output Plastic dome Light Domed semiconductor

p pn Junction n+ n+ Substrate Electrodes Electrodes

(a) Some light suffers total internal reflection and cannot escape. (b) Internal reflections can be reduced and hence more light can be collected by shaping the semiconductor into a dome so that the angles of incidence at the semiconductor-air surface are smaller than the critical angle. (b) An economic method of allowing more light to escape from the LED is to encapsulate it in a transparent plastic dome.

• Various direct bandgap semiconductor pn GaAs1 y Py junctions can be used to make LEDs that emit in the red and infrared range y  0.45 • III-V ternary alloys based on GaAs and GaP   870nm allow light in the visible spectrum • Doping of Ga materials with different As, P, and Al ratios maintains the lattice constant while allowing for precise control of the bandgap (photon energy emitted) • GaAsP with As concentrations greater than 0.55% are direct bandgap semiconductors • GaAsP with As concentrations less than 0.55% are indirect bandgap semiconductors • However, adding isoelectronic impurities such as N (same grp V as P) into the semiconductor to substitute for P atoms – Provides a trap for indirect ECP recombination and generates direct bandgap emission between the trap and the hole. – Reduces light efficiency and alters wavelength

LED Materials (cont.)

• Blue LED materials • GaN is a direct bandgap with Eg = 3.4 eV • InGaN alloy has Eg = 2.7 eV (blue) • Less efficient is Al doped SiC (indirect) – Aluminum captures holes and in a similar manner to N in GaAsPN materials and reduces the effective direct emission energy and efficiency of the device • II-VI ZnSe semiconductors provide a direct bandgap blue emission

LED Materials (cont.)

• Red and Infrared • Three to four element alloys.

• Al1-xGaxAs with x<0.43 gives 870 nm • Composition variances provide 650 – 870 nm

• In1-xGaxAl1-yPy can be varied to span 870 nm (GaAs) to 3.5 um (InAs)

LED Materials (cont.)

Eg (eV) 2.6 Quaternary alloys with indirect bandgap Direct bandgap 2.4 GaP Indirect bandgap 2.2 2 1.8 Quaternary alloys with direct bandgap 1.6 InP 1.4 GaAs 1.2 1 In1-xGaxAs 0.8 In Ga As 0.6 0.535 0.465 X InAs 0.4 0.2 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 Lattice constant, a (nm)

Bandgap energy Eg and lattice constant a for various III-V alloys of GaP, GaAs, InP and InAs. A line represents a ternary alloy formed with compounds from the end points of the line. Solid lines are for direct bandgap alloys whereas dashed lines for indirect bandgap alloys. Regions between lines represent quaternary alloys. The line from X to InP represents quaternary alloys In1-xGaxAs1-yPy made from In0.535Ga0.465As and InP which are lattice matched to InP. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Light Emitting Materials and Efficiency • External efficiency Color Wavelength [nm] Voltage [V] Semiconductor Material – Quantifies the efficiency of Gallium arsenide (GaAs) Infrared λ > 760 ΔV < 1.9 conversion from electrical Aluminium gallium arsenide (AlGaAs) energy into emitted external Aluminium gallium arsenide (AlGaAs) optical energy Gallium arsenide phosphide (GaAsP) Red 610 < λ < 760 1.63 < ΔV < 2.03 P (Optical) Aluminium gallium indium phosphide (AlGaInP)   out 100% external IV Gallium(III) phosphide (GaP) Gallium arsenide phosphide (GaAsP) – Typically less than 20% for Orange 590 < λ < 610 2.03 < ΔV < 2.10 Aluminium gallium indium phosphide (AlGaInP) direct bandgap semiconductors Gallium(III) phosphide (GaP) – Less than 1% for indirect Gallium arsenide phosphide (GaAsP) bandgap semiconductors Yellow 570 < λ < 590 2.10 < ΔV < 2.18 Aluminium gallium indium phosphide (AlGaInP) • Efficiency has been increased by Gallium(III) phosphide (GaP) altering the shape, periodicity, and Indium gallium nitride (InGaN) / Gallium(III) material interfaces within a device nitride (GaN) Green 500 < λ < 570 1.9[29] < ΔV < 4.0 Gallium(III) phosphide (GaP) Aluminium gallium indium phosphide (AlGaInP) Aluminium gallium phosphide (AlGaP) • White light (wikipedia) Zinc selenide (ZnSe) Indium gallium nitride (InGaN) • There are two primary ways of Blue 450 < λ < 500 2.48 < ΔV < 3.7 Silicon carbide (SiC) as substrate producing high intensity white-light Silicon (Si) as substrate — (under development) using LEDs. One is to use individual LEDs that emit three primary Violet 400 < λ < 450 2.76 < ΔV < 4.0 Indium gallium nitride (InGaN) colors[36] – red, green, and blue, and Dual blue/red LEDs, Purple multiple types 2.48 < ΔV < 3.7 blue with red phosphor, then mix all the colors to produce or white with purple plastic white light. The other is to use a diamond (C) phosphor material to convert Aluminium nitride (AlN) monochromatic light from a blue or Ultraviolet λ < 400 3.1 < ΔV < 4.4 Aluminium gallium nitride (AlGaN) UV LED to broad-spectrum white Aluminium gallium indium nitride (AlGaInN) — light, much in the same way a (down to 210 nm[30]) fluorescent light bulb works. White Broad spectrum ΔV = 3.5 Blue/UV diode with yellow phosphor http://en.wikipedia.org/wiki/Light-emitting_diode Homojunction vs. heterojunction LEDS

Electron energy • pn junctions betweenp two materialsn + p n+ Ec doped components of theeVo same E Eg c material (and(a) EthusF the same E EF g (b) bandgap) are called homojunctions h• Eg Ev • eVo Require narrow p type wells to Ev channel photons out of the device prior to absorption Distance into device V Electron in CB • Narrow channels leadHole to in indirectVB recombination of electrons that reach n+ p p (a) The energy band diagram of a p-n+ (heavily n-type doped)homojunction junction without any bias. defects located at the top surface of + Built-in potential Vo prevents electrons from diffusing(a) fromAn lG atoA sp side. G(b)aA Thes appliedAlGaAs the p-typebias material, reduces Vo therebyand thereby reducing allows electrons to diffuse, be injected, into the p-side. Recombination around the junction and within the diffusion length of the~ 0electrons.2 m in the efficiency Ec p-side leads to photon emission. E • Junctions formed by two different Electrons in CB c (a) A double © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) 2 eV No bias eVo 1.4 eV heterostructure diode has bandgap semiconductor materials are E F EF two junctions which are called heterojunctions E between two different c Ev – bandgap semiconductors Heterostructure devices (HD) are (b) 2 eV (GaAs and AlGaAs) devices between two different E Holes in VB (b) A simplified energy bandgap semiconductors such as v band diagram with AlGaAs and GaAs exaggerated features. E heterojunction F must be uniform. With (c) Forward biased forward simplified energy band bias diagram. (c) (d) Forward biased LED. Schematic illustration of photons escaping reabsorption in the n+ p p AlGaAs layer and being emitted from the device. (d)

AlGaAs GaAs AlGaAs

• The refractive index, n, depends directly on the n+ p p bandgap. (a) AlGaAs GaAs AlGaAs – wide bandgap semiconductors have lower ~ 0.2 m Ec E refractive indices. Electrons in CB c (a) A double 2 eV No bias eVo 1.4 eV heterostructure diode has – we can engineer the dielectric waveguide E F EF two junctions which are within the device and channel the photons Ec E between two different v bandgap semiconductors out from the recombination region (b) 2 eV (GaAs and AlGaAs) • Adding a double heterostructure (DH) to LEDs E Holes in VB (b) A simplified energy reduces radiationless recombination v band diagram with exaggerated features. EF – Introduces a higher bandgap behind the must be uniform. pn junction that localizes the optical With (c) Forward biased generation region. forward simplified energy band bias diagram. – The additiona p type region is known as a (c) confining layer (d) Forward biased LED. Schematic illustration of – Since the bandgap of AlGaAs is larger than photons escaping that of GaAs emitted photons cannot get reabsorption in the n+ p p AlGaAs layer and being reabsorbed in the AlGaAs regions emitted from the device. (d) – Metal reflects light from the back side of the confining layer improving efficiency AlGaAs GaAs AlGaAs – n+ layer is used as topside of the device to reduce lattice defects in the active region and improve device efficiency © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) • DH LEDs are more efficient than homojunction LEDs

LED Device Characteristics

(a) E (b) (c) (d) Electrons in CB CB

2kBT Relative intensity Relative intensity 1 Eg + kBT /2kBT Ec 1 1 (2.5-3)kBT Eg 1 2 3 h  Ev 0 h 0  Holes in VB h h h    VB      

Carrier concentration Eg per unit energy

(a) Energy band diagram with possible recombination paths. (b) Energy distribution of electrons in the CB and holes in the VB. The highest electron concentration is (1/2)kBT above Ec . (c) The relative light intensity as a function of photon energy based on (b). (d) Relative intensity as a function of wavelength in the output spectrum based on (b) and (c).

• CB conduction as a function of energy is asymmetrical with a peak at 1/2kBT above Ec

• The energy spread of electrons is typically 2kBT • Similar observation is made in the VB. • Highest energy photon emissions have small probability • Highest intensity comes from largest carrier concentration • Intensity falls off again with carrier concentration near the CB band edge LED Device Characteristics

• Spread of available carrier recombination probabilities generates a spread in optical wavelength emitted • Linewidth of the spectral output is typically between 2.5 and 3.5kBT • Notice in figure a that the relative intensity does Relative (a) (b) (c) not match the probabilistic intensity plotted on intensity V the previous slide 655nm Relative light intensity • This is due to the fact that as heavily doped n 1.0 2 type semiconductors used to create efficiency in  0.5 1 active p-type regions create a donor band that 24 nm overlaps the conduction band and lowers the effective output wavelength 0  0 I (mA) 0 I (mA) 600 650 700 0 20 40 0 20 40

(a) A typical output spectrum (relative intensity vs wavelength) from a red GaAsP LED. (b) Typical output light power vs. forward current. (c) Typical I-V characteristics of a red LED. The turn-on voltage is around 1.5V. • Turn on voltage is achieved at low operating © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) currents and remains flat as current is increased • Below the turn on voltage, no light is emitted • The number of populated electrons in the p- type region CB increases and thus the relative light intensity also increases with increasing current Example: LED Output Spectrum

• Width of the relative light intensity vs. Given the energy width of the output spectrum:

photon energy spectrum of an LED is E  h   3k T typically 3k T. What is the linewidth, ph B B  in the output spectrum in terms of 1/2 wavelength? Then substituting in terms of wavelength:

hc hc 2  3kBT  Emitted light is related to photon energy by   2 3kBT   2 3kBT      Eph  hc   hc  c hc          E ph That at various LED wavelengths one receives: Differentiating, wavelength w.r.t photon energy:   870nm   47nm d hc    1300nm  105nm dE E 2 ph ph  149nm  1550nm Small changes in the differential :

hc   2 Eph Eph Example: LED Output Wavelength Variation

• Consider a GaAs LED • GaAs bandgap at 300K is 1.42 eV • Derivative of the bandgap is dE eV g  4.5104 dT K • What is the change in emitted wavelength if the temperature is 10oC? hc k T E   B g e e c hc 6.62610343108  1.24106 eV *m       875nm 19  Eg 1.421.610  1.42eV 34 8 d hc  dEg  6.62610 310  4 19 m        4.510 1.610  2   19 2 dT Eg  dT  1.421.610  K d m nm  2.771010  0.277 dT K K d nm   T  0.277 10K  2.8nm dT K • Since Eg decreases with temperature, the wavelength increases with temperature. This calculated change is within 10% of typical values for GaAs LEDs quoted in the literature

Example: InGaAsP on InP Substrate

• Ternary alloy In1-xGaxAsyP1-y is grown on an InP crystal substrate for LED applications • The device requires sufficiently small lattice strain due to mismatch between the two crystals at the interface to allow for electroluminescence. • Strain reduction in tern requires a value for y =2.2x • The bandgap energy for the alloy in eV is given by the empirical relationship 2 Eg 1.35  0.72y 1.12y 0  x  0.47 • Calculate the composition of InGaAsP ternary alloys for peak emission at a wavelength of 1.3 um hc k T E   B For  1300nm;T  300K g e e

34 8 hc kBT 6.62610 310  Eg    19 6  0.0259eV  0.928eV e e 1.610 1.310 

2 Eg  0.928 1.35  0.72y 1.12y

y  0.66

x  0.66 / 2.2  0.3

• Requires In0.7Ga0.3As0.66P0.34 LEDs for Optical Fiber Communication

• Two types of LEDs fabricated today • Surface emitting LED (SLED) • Edge emitting LED (ELED)

Light

Light Double heterostructure

(a) Surface emitting LED (b) Edge emitting LED

• Etch a well into a passive layer over a DH device and couple the flat end of a fiber as close as possible to the active region of the emitter as possible • Epoxy bonding the blunt end of a fiber to the DH surface produces a Burrus device. Named after its origionator • Remember that the epoxy is chosen in such a means as to reduce TIR of photons exiting the DH device • Alternatively, truncated spherical microlenses with n =19.-2 can also be used to focus emitted light and guide it into a fiber. Lens is bonded to both fiber and LED with index matching glue

Fiber (multimode) Fiber Epoxy resin Microlens (Ti O :SiO glass) Electrode 2 3 2

Etched well Double heterostructure

SiO2 (insulator) Electrode (b) (a) Light is coupled from a surface emitting LED A microlens focuses diverging light from a surface into a multimode fiber using an index matching emitting LED into a multimode optical fiber. epoxy. The fiber is bonded to the LED structure.

• ELEDs provide greater intensity and a 60-70 m more collimated beam • Light is guided through the edge of a crystal using a slab created by three L stacked bandgap materials Stripe electrode surrounding one small one Insulation + p -InP (Eg = 1.35 eV, Cladding layer) • Recall that the larger the bandgap, the + p -InGaAsP (Eg  1 eV, Confining layer) lower the dielectric n-InGaAs (Eg  0.83 eV, Active layer) + – Thus the active region comprised n -InGaAsP (Eg  1 eV, Confining layer) 2 1 3 + Current 200-300 m of InGaAs with a bandgap of 0.83 n -InP (Eg = 1.35 eV, Cladding/Substrate) eV has n1

• Diode is typically diced and polished Active layer to create a smooth transmission edge and then coupled to a graded index (a) (b) lens that is bound to the end of an Light from an edge emitting LED is coupled into a fiber typically by using a lens or a optical fiber GRIN rod lens. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall)