Silicon Photonics周治平(James Zhou)武汉光电国家实验室（筹）华中科技大学School of Electrical and Computer Engineering Georgia Institute of TechnologyFor Graduate Class of Spring 2007 at HUST1Outline •Fundamentals–Wave and Photon–Photon in Semiconductors•A Selection of Silicon Photonic Devices –Light Controlling Devices–Sources and DetectorsSilicon Photonics: An IntroductionReferences: 1.by Graham T. Reed and Andrew P. Knights2. Fundamentals of Photonicsby Bahaa E. A. Saleh and Malvin Carl Teich3. Silicon Photonics Research,Intel Corp.2Fundamentals34•Wave–Frequency –Wavelength –Phase–Polarization –InterferenceWave and Photon•Photon–Energy –Position –Momentum –Polarization –Interference –UncertaintyWave56f =sin θPhase: Angle θf =sin ωtPhase: Angle ωt ω=2πf7f =sin [kz ±ωt ]k =2π/λPhase: kz ±ωtwhich describes wave characters in space andtime.*At a fixed time, the relative phasedifference between the waves is a function of k and z only.8Wave: PolarizationPolarization: The direction of the electric fieldassociated with the propagating wave.1.Plane2.Transverse3.PolarizedPlane polarized light; Elliptical polarized light, Un-polarized light.9Wave:InterferenceThe summation of two waves at a given point in space.1.In phase:Constructive 2.Out of phase:Cancel one another 3.Out of some phase:Same frequency, butshifted phase and amplitude.Assume: a) same polarizationb) coherentWave SummarySatisfies the wave equation;Has intensity, power, and energy;Can be characterized by wavelength, amplitude, phase, polarization, interference, diffraction, …1011•Wave–Frequency–Wavelength–Phase–Polarization–Interference Wave and Photon•Photon –Energy –Position –Momentum –Polarization –Interference–Uncertainty12Photon 1.Light consists of particles calledphotons.2. A photon has zero rest mass andcarries electromagnetic energy andmomentum.3.It also carries an intrinsic angularmomentum (or spin) that governs itspolarization properties.4.The photon travels at the speed oflight in vacuum (C 0); its speed isretarded in matter.5.Photons also have a wavelikecharacter that determines theirlocalization properties in space andthe rules by which they interfere anddiffract.Photon: Energywhere h= 6.63 x l0-34J-s is Planck’s constant E=hν=ħωand ħ= h/2π. Energy may be added to, ortaken from, this mode only in units of hv.13Photon: PositionThe photon location is not precisely determined.It is governed by the optical intensity I(r) inaccordance with the following probabilistic law:Probabilistic reflection or transmission of a photon at a beamsplitter1415Photon:Momentum16Photon: PolarizationLight is characterized as a sum of modes ofdifferent frequencies, directions, and polarizations.The polarization of a photon is that of its mode.Probabilistic outcomes for a single linearly polarized photonPhoton: Polarization-SpinPhotons possess intrinsic angular momentum (spin). The magnitude of the photon spin is quantized to the two values: S = ±ħRight-handed (left-handed) circularly polarized photons have their spin vector parallel (anti-parallel) to their momentum vector.A linearly polarized photon is equivalent to the superposition of aright-and left-circularly polarized photon, each with probability 1/2.17Photon: InterferenceYoung’s experiment can be carried out even when there is only a single photon in the apparatus at a given time. The outcome of this experiment can be understood in the context of photon optics by using the photon-position rule.1819Photon:TimePhoton:Time-Energy UncertaintyThe energy uncertainty of a photon, and the time during which it may be detected, must satisfyTo summarize: A monochromatic photon (σνÆ0) has an eternal duration within which it can be observed (σt Æ∞). In contrast, a photon associated with an optical wavepacket is localized in time and is therefore polychromatic with a corresponding energy uncertainty. Thus a wavepacket photon can be viewed as a confined traveling packet of energy.Photon: Summary20Photon: Summary21Photon in Semiconductors •SEMICONDUCTORS-Energy Bands and Charge Carriers-Electron and Hole Concentrations-Generation, Recombination, and Injection-Junctions•INTERACTIONS OF PHOTONS WITH ELECTRONS-Band-to-Band Absorption and Emission-Rates of Absorption and Emission-Refractive Index22Electronics is the technology of controlling the flow of electrons whereas photonics is the technology of controlling the flow of photons. Electronics and photonics have been joined together in semiconductor optoelectronic devices where photons generate mobile electrons, and electrons generate and control the flow of photons.The compatibility of semiconductor optoelectronic devices and electronic devices has, in recent years, led to substantive advances in both technologies. Semiconductors are used as optical detectors, sources (light-emitting diodes and lasers), amplifiers, waveguides, modulators, sensors, and nonlinear optical elements.23Semiconductors absorb and emit photons by undergoing transitions between different allowed energy levels, with unique properties in following respects:•The proximity of the atoms in a solid (semiconductor material) results in one set of energy levels representing the entire system.•The energy levels of semiconductors take the form of groups of closely spaced levels that form bands.•Thermal and optical interactions can pass on energy to an electron, causing it to jump across the band gap. An electron can also decay from the conduction band into the valence band to fill an empty state by means ofelectron-hole recombination.24Two processes are fundamental to the operation of almost all semiconductor optoelectronic devices:•The absorption of a photon can create an electron-hole pair.The resulting mobile charge carriers can alter the electrical properties of the material. This process is responsible for the operation of photodetectors.•The recombination of an electron and a hole canresult in the emission of a photon.This process isresponsible for the operation of semiconductor lightsources. Spontaneous radiative electron-holerecombination: light generation in the light-emittingdiode. Stimulated electron-hole recombination: source of photons in the semiconductor laser.25Semiconductors: Energy BandsThe solution of the Schrödinger equation for the electron energy, in the periodic potential created by the collection of atoms in a crystal lattice, results in a splitting of the atomic energy levels and the formation of energy bands.26Semiconductors: Charge CarriersIn the absence of thermal excitations,the valence band of Si and Ge is completely filled and the conduction band is completely empty: the material cannot conduct electricity.As the temperature increases, some electrons will be excited into the empty conduction band. Each electron excitation will create a free electron in the conduction band and a free hole in the valence band.The two charge carriers are free to drift under the effect of the applied electric field and thereby to generate an electric current. The conductivity of a semiconductor increases sharply with temperature as an increasing number of mobile carriers are thermally generated.27Semiconductors: Energy-Momentum Relations The energy E andmomentum p of anelectron in free spaceare related by E=p2/2m0= ħ2k2/2m0.The E-k relation is asimple parabola.28Semiconductors: Direct-and Indirect-GapA transition between the top of the valence band and the bottom of the conduction band in an indirect-gap semiconductor requires a substantial change in the electron’s momentum.Si is an indirect-gap semiconductor, whereas GaAs is a direct-gap semiconductor. Direct-gap semiconductors such as GaAs are efficient photon emitters,whereas indirect-gap semiconductors such as Si cannot be efficiently used as light emitters.But, …29Semiconductors: Electron and Hole Concentrations •The density of allowed energy levels (density of states)•The probability that each of these levels is occupied.The quantum state of an electron in a semiconductor material is characterized by its energy E, its wavevector k, and its spin. The state is described by a wavefunction satisfying certain boundary conditions.An electron near the conduction band edge may be described as a particle of mass m c confined to a 3-D cubic box with a 3-D infinite rectangular potential well. Thus, the number of states with electron wavenumbers between k and k + ∆k, per unit volume, is D(k)∆k = [(d/dk)(k3/3π2)]∆k = (k2/ π2)∆k, so that the density of states isD(k) = k2/ π23031•The probability that each of these levels is occupied.The laws of statistical mechanics dictate that under conditions of thermal equilibrium at temperature T , the probability that a given state of energy E is occupied by an electron is determined by the Fermi function :The function f(E)is not itself a probability distribution, and it does not integrate to unity; rather, it is a sequence of occupation probabilities of successive energy levels.•Thermal-Equilibrium Carrier Concentrations Let n(E)∆E and p(E)∆E be the number of electrons and holes per unit volume, respectively, with energy lying between E and E + ∆E. The densities n(E) and p(E)can be obtained by multiplying the densities of states at energy level E by the probabilities of occupancy of the level by electrons or holes, so thatn(E) = D c(E)f(E), p(E) = D v(E)[1 –f(E)].The concentrations of electrons and holes n and p are then obtained from the integrals32Thermal-Equilibrium Carrier Concentrations•3334•Thermal-Equilibrium Carrier Concentrations35•Thermal-Equilibrium Carrier Concentrations•Generation and Recombination in Thermal Equilibrium 1.The thermal excitation of electrons from the valence band intothe conduction band results in the generation of electron-hole pairs.2.Thermal equilibrium requires that this generation process beaccompanied by a simultaneous deexcitation. This process,called electron-hole recombination, occurs when an electron decays from the conduction band to fill a hole in the valence band.3.The energy released by the electron may take the form of anemitted photon,in which case the process is called radiative recombination.4.Nonradiative recombination includes the transfer of energy tolattice vibrations or to another free electron (Auger process).36•Generation and Recombination in Thermal EquilibriumElectron-hole generation and recombination Electron-hole recombinationVia a trap37•Electron-Hole Injection1.A semiconductor in thermal equilibrium with carrierconcentrations n0and p0has equal rates of generationand recombination, G0= kn0p0.2.Now let additional electron-hole pairs be generated ata steady rate R by means of an external (nonthermal)injection mechanism. A new steady state will bereached in which the concentrations are n= n0+ ∆nand p = p0+ ∆p. Since the electrons and holes arecreated in pairs ∆n=∆p, equating the new rates ofgeneration and recombination leads:G0+ R = knpor R=k(np-n0p0)3839•Electron-Hole InjectionThe parameter τmay be regarded as the electron-hole recombination lifetime of the injected excess electron-hole pairs. This is readily understood by noting that theinjected carrier concentration is governed by the rateequationSome manipulates will lead towhereAt a steady rate of R, the steady-state injectedconcentration may be determined fromSemiconductors: JunctionsHomojunctions:between differently doped regions of ajunction.semiconductor material. Example: the p-nA p-n junction in thermal equilibrium at T > 0 K.40Biased Junction:An externally applied potential will alter the potential difference between the p-and n-regions.Energy-band diagram and carrier concentrationsin a forward-biased p-n junction.4142The p-i-n Junction Diode :A p-n junction with adepletion layer that encompasses the entire intrinsic region.Advantages: 1) Small junction capacitance and fast response; 2) Large depletion layer permits more incident light to be captured, thereby increasesthe photodetection efficiency.Electron energy, fixed-charge density, and electric field magnitude for a p-i-n diode in thermal equilibrium.Heterojunctions:between different semiconductor materials.layer is of narrower bandgap than the outer layers.43Heterojunctions:between different semiconductor materials. In photonics, the combination of different semiconductors can be advantageous in several respects:•Junctions between materials of different bandgapcreate localized jumps in the energy-band diagram,providing a barrier to prevent selected charge carriersfrom entering undesired regions.•Discontinuities in the energy-band diagram can beuseful for confining charge carriers to a desired region of space.•Heterojunctions of materials with different refractive indices create optical waveguides that confine anddirect photons.44Heterojunctions:between different semiconductor materials.•Heterojunctions are useful for creating energy-banddiscontinuities that accelerate carriers at specificlocations. The additional kinetic energy suddenlyimparted to a carrier can be useful for selectivelyenhancing the probability of impact ionization in amultilayer avalanche photodiode.•Semiconductors of different bandgap type (direct and indirect) can be used in the same device to selectregions of the structure where light is emitted. Onlysemiconductors of the direct-gap type can efficientlyemit light.45-Energy Bands and Charge Carriers-Electron and Hole Concentrations-Generation, Recombination, and Injection -Junctions46Photon in Semiconductors •SEMICONDUCTORS-Energy Bands and Charge Carriers-Electron and Hole Concentrations-Generation, Recombination, and Injection-Junctions•INTERACTIONS OF PHOTONS WITH ELECTRONS-Band-to-Band Absorption and Emission-Rates of Absorption and Emission-Refractive Index47Examples of absorption and emission of photons in a semiconductor.(a) Band-to-Band (Inter-band) Transitions in GaAs.(b) Impurity-to-Band Transitions in Ge:Hg.(c) Free-Carrier (Intraband) Transitions.4849Observed optical absorption coefficient αversus photon energy for Si and GaAs in thermal equilibrium at T = 300 K.Si is relatively transparent in the band λ= 1.1 to 12 µm.Intrinsic GaAs is relatively transparent in the band λ= 0.87 to 12 µm.Direct-gapsemiconductorshave a moreabruptabsorption edgethan indirect-gap materials. Absorption coefficient versus photon energy for Ge, Si, GaAs,and selected other III-V binary semiconductors at T = 300 K.50。
