光電子英文課件：Chapter 3 Light Emitting Diodes

1、Chapter 3 Light Emitting DiodesOutlineEnergy Band DiagramsIntrinsic carrier concentrationNondegenerate Semiconductor and Degenerate SemiconductorCarrier diffusion, Generation and recombination processesDirect and Indirect Bandgap Semiconductors: Ek DiagramContinuity equationThermionic emission proce

2、ss, High field effects and Tunneling processpn junction principles and Junction breakdownLighting Emitting Diodes, LED Materials and LED Characteristics1. Energy Band DiagramsMetal: energy bands overlap and continuousSemiconductor: Valance band (VB), Conduction Band (CB), separated bybandgap (Eg), E

3、g= Ec-Ev;X: electron affinity, the width of CBhvEg: create electron-hole pairconductorinsulatorsemiconductorbandwidth Eg2eVThe electrons are easily excited to the conduction band2. Intrinsic carrier concentrationDensity of State (DOS) g(E): the number of electronic states in a band per unit energy p

4、er unit volume of the crystal.g(E) depends on the electron energy in the CB and VB. The DOS increases with energy as g(E) (E-Ec)1/2The carrier concentration in thermal equilibrium condition the steady-state conditions at a given temperature without any external excitations i.e. light, pressure, elec

5、tric field.Intrinsic semiconductor: contains relatively small amounts of impurities compared with the thermally generated electron and holes.Fermi-Dirac statistics f(E): the probability of finding an electron in quantum states with energy E (states implies a wavefunction). It is a fundamental proper

6、ty of a collection of interacting electrons in thermal equilibrium.EF=ev, fermi energyin the dark,no voltage EF=0Boltzmann Statistics:Fermi-Dirac statistics can be replaced by Boltzmann statistics, such semiconductors are called nondegererate.In the intrinsic semiconductor there will not be many imp

7、urities in the conduction band.The electron density in the conduction band:NC: effective density of states in the CB:for GaAsfor SiThe hole density p in the valance band:Nv: effective density of states in the VB:The Fermi level for an intrinsic semiconductor :At room temperature , the intrinsic Ferm

8、i level Ei of an intrinsic semiconductor lies very close to the middle of the bandgap.The intrinsic carrier density is:It is useful to express the electron and hole densities in terms of the intrinsic carrier concentration ni and the intrinsic Fermi level Ei discussing extrinsic semiconductor:For sh

9、allow acceptors in Si and Ga, under a complete ionization condition The corresponding Fermi level :For shallow donors in Si and Ga, under a complete ionization condition, the Fermi level in terms of the effective density of states Nc and the donor concentration ND:Those semiconductors for which nNc

10、and pNc or pNv are called degenerate semiconductors. For heavily doped n-type or p-type semiconductor, EF will be above Ec or below Ev.An important aspect of high doping is the bandgap narrowing effect, that is, high impurity concentration causes a reduction of the bandgap. The bandgap reduction Eg

11、for silicon at room temperature:meV4. Degenerate SemiconductorThe carriers tend to move from a region to high concentration to a region of low concentration. This current component is called diffusion current (Jn). is called the diffusion coefficient, also called the diffusivityDiffusion current res

12、ults from the random thermal motion of carriers in a concentration gradient.5. Carrier diffusion (1)Equation (1) can be written in a more useful form the theorem for the equipartition of energy for the one-dimensional case.(2)(3)(4)Equation(5) is Einstein relation. It relates the two important const

13、ants (diffusivity and mobility) that characterize carrier transport by diffusion and by drift in a semiconductor.(5)The total current includes both drift current and diffusion current. The total current density at any point of the semiconductor is the sum for the drift and diffusion components.Simil

14、ar for hole concentration:The total conduction current density is:(6)(7)(8)In thermal equilibrium the relationship pn=ni2. If excess carriers are introduced to a semiconductor so that pnni2-Nonequilibrium situation.The process of introducing excess carriers is called carrier injection.Most semicondu

15、ctor devices operated by the creation of charge carriers in excess of thermal equilibrium values.Carrier injectionRecombination processRelease energy(a photon or heat to lattice)Radiative recombination(a photon is emitted) Nonradiative recombination(otherwise condition) 6. Generation and recombinati

16、on processesIn terms of the band diagram, the thermal energy enables a valence electron to make an upward transition to the conduction band, leaving a hole in the valence band. This process is called the carrier generation. The reverse process is called recombination. (1) Recombination Process (band

17、 to band recombination):When shining a light on the semiconductor to produce electron-hole pairs, the net recombination rate U is:R: direct recombination; : the proportionality constantGth: the generation ratenno ,pno represent electron and hole densities in an n-type semiconductor at thermal equili

18、brium; n, p: excess carriers concentration(the lifetime of the excess minority carriers)(9)(10)Direct generation recombination of electron-hole pairs: (a) at thermal equilibrium (b) under illuminated(2) Indirect recombinationThe electrons at the bottom of the conduction band have nonzero momentum wi

19、th respect to the holes at the top of the valence band, a direct transition that conserves both energy and momentum is not possible without a simultaneous lattice interaction. The dominant recombination process in such semiconductor is indirect transition via localized energy stated in the forbidden

20、 energy gap.In indirect recombination, the deviation of the recombination rate is more complicated. The recombination rate U is given by:(11)vth : the thermal velocity of carrier Nt : the concentration of recombination center in semiconductorn: the capture cross section of electrons, it describes th

21、e effectiveness of the center to capture and electron and is a measure of how close the electron has to come to the center to be captured.p: the capture cross section of holes.Indirect generation-recombination processes at thermal equilibrium.(3) Surface RecombinationThe figure shows schematically t

22、he bonds at a semiconductor surface. Because of the abrupt discontinuity of the lattice structure at the surface, a large number of localized energy states or generation-recombination centers may be introduced at the surface region. These energy states, called surface states, may greatly enhance the

23、 recombination rate at the surface region. has its dimension in centimeters per second, it is called the low-injection surface recombination velocity SlrFor a low injection condition, and for the limiting case where electron concentration at the surface is essentially equal to the bulk majority carr

24、ier concentration, the total number of carriers recombining at the surface per unit area and unit time can be simplified to:(12)ps: the hole concentration at the surfaceNst: the recombination center density per unit area in the surface region. (13)(4) Auger recombinationThe Auger recombination proce

25、ss occurs by the transfer of the energy and momentum released by the recombination of an electron-hole pair to a third particle that can be either an electron or a hole.Auger RecombinationBecause the Auger process involves three particles, the rate of Auger recombination can be expressed as:or(14)(1

26、)A second electron in the conduction band absorbs the electron becomes an energetic electron. (2)After the Auger process, the second electron becomes an energetic electron.(3)The energetic electron loses its energy to the lattice by scattering events.7. Direct and Indirect Bandgap Semiconductors: Ek

27、 DiagramDirect bandgap semiconductor: the minimum of the CB is directly above the maximum of the VB. (e.g. GaAs)The majority of light-emitting devices use direct bandgap semiconductors to make use of direct recombination.Indirect bandgap semiconductor: the minimum of the CB is not directly above the

28、 maximum of the VB, but it is displaced on the k-axis. (Si, Ge, GaP)The recombination process in this semiconductors occurs via a recombination center within the defects or impurities.In the previous section we considered individuals effects such as drift due to an electric field, diffusion due to c

29、oncentration gradient, and recombination of carriers though intermediate-level recombination centers. Consider the overall effect when drift, diffusion, and recombination occurs simultaneously in a semiconductor materials.The governing equation is called the continuity equation.For the one-dimension

30、al case under low-injection condition, the continuity equations for minority carriers (i.e. np in a p-type semiconductor or pn in a n-type semiconductor )(15)(16)8. Continuity equationAt the semiconductor surface, carriers may recombine with the recombination centers due to the dangling bonds of the

31、 surface region (Auger recombination). If the carriers have sufficient energy, they may be “thermionically” emitted into the vacuum. This is called the thermionic emission process.The electron density with energies above qX can be obtained from an expression (similar to that for the electron density

32、 in the conduction band except that the lower limit of the integration is qX instead of Ec):(17)9. Thermionic emission process(a) The band diagram of two isolated semiconductors with a distance d. (b) One-dimensional potential barrier. (c) Schematic representation of the wave function across the pot

33、ential barrier.Two isolated semiconductor are brought close together. The distance between them is d, the potential barrier height qV0 is equal to the electron affinity qX. If the distance is sufficient small, the electrons in the left-side semiconductor may transport across the barrier and move to

34、the right-side semiconductor, even if the electron energy is much less than the barrier height. This process is associated with the quantum tunneling phenomenon.The tunneling transmission coefficient (C/A)2 is:(18)To have a finite transmission coefficient, requires a small tunneling distance d, a lo

35、w potential barrier qV0 and a small effective mass. The results could be used for tunnel diode.10. Tunneling process (a) The band diagram of two isolated semiconductors with a distance d. (b) One-dimensional potential barrier. (c) Schematic representation of the wave function across the potential ba

36、rrier.Low electric-field, the drift velocity is linely proportional to the applied field.At sufficiently large field, the drift velocity approaches saturation velocity.Drift velocity versus electric field in Si.811. High field effectsElectron distributions under various conditions of electric fields

37、 for a two-valley semiconductor.Upper valley density n2, m2, u2; Lower valley density n1, m1, u1;(19)(20)12. pn junction principlesThe behavior of single-crystal semiconductor materials both p-type and n-type region that form a p-n junction.Most modern junctions are made by plarnar technology.Main s

38、teps:Oxidation;Lithography;Diffusion and Ion Implantation;Metalization(a) The wafer after the development. (b) The wafer after SiO2 removal. (c) The final result after a complete lithography process. (d) A p-n junction is formed in the diffusion or implantation process. (e) The wafer after metali-za

39、tion. (f) A p-n junction after the compete process.important!Two important pn-junction:The abrupt junction: a p-n junction formed by shallow diffusion or low energy ion implantation. The impurity distribution of the junction can be approximated by an abrupt transition of doing concentration between

40、the n-type and p-type regions.The linearly graded junction: For either deep diffusion of high-energy ion implantations, the impurity profiles may be approximated by linearly graded junction the impurity distribution varies linearly across the junction.(b) Linearly graded junction.(a) Abrupt junction

41、.Abrupt junction:(a) Space charge distribution in the depletion region at thermal equilibrium. (b) Electric-field distribution. The shaded area corresponds to the built-in potential.Form a pn junctionElectric fieldBuilt-in potentialPotential EnergyCarrier densityNet space(1) Ideal current-voltage Ch

42、aracteristic for abrupt junctionA. Open Circuit the potential across a pn junction, going from p to n-type semiconductor, in an open circuit.The total depletion layer width:If the space charge distribution of a one-side abrupt p+-n junction, where NAND. In this case, the depletion layer width of the

43、 p-side is much smaller than the n-side and W can be simplified to:The built-in voltage V0:(21)(22)(23)The maximum field at x=wThe potential distribution is:(24)(25)B. Forward BiasUnder forward bias, the injected minority carrier recombine with the majority carriers at the minority carriers move awa

44、y from the boundaries.Under idealized assumption, the total current is constant throughout the device and is the sum of the hole diffusion current and the electron diffusion current.Js is the saturation current density:(26)(27)(a) Forward bias.The depletion layer Capacitance(28)C. Reverse BiasUnder

45、reverse bias, the reverse current is small and the negative terminal results in more exposed negative acceptor ions and thus a wider SCL.(b) Reverse bias.(29)Ideal current-voltage characteristics. (a) Cartesian plot. (b) Semilog plot.The ideal diode equation, adequately describes the current-voltage

46、 characteristics of germanium p-n junction at low current densities. For silicon and gallium arsenide p-n junctions, the ideal equation can only give qualitative agreement because of the generation or recombination of carriers in the depletion region. (2) Generation-Recombination and high-Injection

47、Characteristic for abrupt junctionCarrier concentrations in the depletion region fall far below their equilibrium concentrations. The dominant generation-recombination processes are those of electron and hole emission through bandgap generation-recombination centers. The capture process are not impo

48、rtant because their rates are proportional to the concentration of free carriers which is very small in the reverse biased depletion region.The reverse-bias condition: The current due to generation in the depletion region is:The total reverse current for p+-n junction, that is for NAND and for Vr3kT

49、/q, can be approximated by the sum of both the diffusion current in the neutral regions and the generation current in the depletion region.(30)(31)For semiconductors with large values of ni, Such as Germanium, the diffusion current dominates at room temperature the reverse current follows the ideal

50、diode equation. But if ni is small, such as Si , the generation current in the depletion region may dominate.g: the generation lifetimer: the effective recombination lifetime given byThe concentration of both electrons and holes exceed their equilibrium values. The carriers will attempt to return to

51、 their equilibrium values by recombination, Therefore, the dominant generation-recombination process in the depletion region are the capture process.The forward-bias condition: The recombination current is:The total forward current is the sum of ideal diffusion current and recombination current:(32)

52、(33)In general, the experimental results can be represented empirically by: the ideality factor the diffusion current dominates: =1the recombination current dominate:=2Both current are comparable, between 12(34)(3) Temperature effectOperating temperature has a profound effect on device performance.

53、In both the forward-bias and reverse-bias conditions, the magnitude of the diffusion and the recombination-generation current depends strongly on temperature.The forward-bias:Temperature dependence of the current-voltage characteristics of a Si diode2. (a) Forward bias.The ratio depends on the tempe

54、rature and the semiconductor bandgap.(34)At room temperature for small voltage, the recombination current generally dominates, whereas at higher forward voltages the diffusion current usually dominates.At a given forward bias, the temperature increases, the diffusion current increase more rapidly th

55、an the recombination current.Therefore, the ideal diode equation will be followed over a wide range of forward bias as the temperature increases.The reverse-bias for a p+-n junction:Temperature dependenceof the current-voltage characteristics of a Si diode2. (b) Reverse bias.(35)The ratio is proport

56、ional to the intrinsic carrier density ni.As the temperature increases, the diffusion current eventuallydominates.At low temperature, the generation current dominates and the reversecurrent varies VR in abrupt junction.13.Junction breakdownWhen a sufficiently large reverse voltage is applied to a p-

57、n junction, the junction breaks down and conducts a very large current.Two important breakdown mechanisms:Tunneling effect; Avalanche MultipilcationEnergy band diagrams under junction-breakdown conditions. (a) Tunneling effect (b) Avalanche multiplication.n- and p- regionquite high dopingVB: breakdo

58、wn voltageChart of the electromagnetic spectrum from the ultraviolet region to the infrared region.14. Lighting Emitting DiodesOptical absorption for (a) hv = Eg, (b) hv Eg, and (c) hv Eg.Optical absorption. (a) Semiconductor under illumination. (b) Exponential decay of photon flux. A. principles:LE

59、D: essentially a pn junction diodes typically made from a direct bandgap. semiconductor ( eg. GaAs) spontaneous radiationThe recombination zone is called the active region B. Device structure The p-side is on the surface. It is important to lattice-match the LED layer to the substrate crystal. It is

60、 possible to shape the surface of the semiconductor into a dome, or hemisphere, so that light rays to surface at angles less than c and therefore do not experience TIR.III-V nitride LED grown on sapphire substrate.visible spectrum: - ternary alloys based on alloying GaAs and GaP, which denoted as Ga