ELEC 425/ 6261 Lecture Notes 2 & 3

Optical waveguides display 3 types of dispersion: These are the main sources of dispersion in the fibers. Δτ L D Δλ Material dispersion, different wavelength of light travel at different velocities within a given medium. Due to the variation of n1 of the core wrt wavelength of the light. Waveguide dispersion, β depends on the wavelength, so even within a single mode different wavelengths will propagate at slightly different speeds. Due to the variation of group velocity wrt V- number Emitter Very short light pulse Intensity Intensity Intensity Spectrum, ²λ λ λ λ 1 o 2 Input λ 0 Cladding v g (λ 1 ) Core v g (λ 2 ) t Output τ Spread, ²τ All excitation sources are inherently non-monochromatic and emit within a spectrum, ²λ, of wavelengths. Waves in the guide with different free space wavelengths travel at different group velocities due to the wavelength depe of n 1. The waves arrive at the end of the fiber at different times and hence a broadened output pulse. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) t

Optical waveguides display 3 types of dispersion Modal dispersion, in waveguides with more than one propagating mode. Modes travel with different group velocities. Due to the number of modes traveling along the fiber with different group velocity and different path. Intensity 0 Cladding Light pulse t Core High order modelow order mode Axial Broadened light pulse Intensity Spread, Δτ Schematic illustration of light propagation in a slab dielectric waveguide entering the waveguide breaks up into various modes which then propag group velocities down the guide. At the end of the guide, the modes com constitute the output light pulse which is broader than the input light pul 1999 S.O. Kasap, Optoelectronics (Prentice Hall) t

Dispersion coefficient (ps km -1 nm -1 ) 30 Δτ L D m Δλ 20 10 0 Dm Dm + Dw -10 λ 0 D w D m 2 λ d n c dλ 2 Material Dispersion Coefficient -20-30 1.1 1.2 1.3 1.4 1.5 1.6 λ (μm) Δτ L D ω Δ λ Material dispersion coefficient (D m ) for the core material (taken as SiO 2 ), waveguide dispersion coefficient (D w ) (a 4.2 μm) and the total or chromatic dispersion coefficient D ch ( D m + D w ) as a function of free space wavelength, λ. D ω 1.984N g 2 2 2 ( 2πa) 2cn 2 Waveguide Dispersion Coefficient 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Δτ L D P Δλ Δτ L D + D + m ω D p Δλ

Polarization Dispersion Intensity Output light pulse z Δτ t n 1y // y Core E x n 1x // x E y E x E y Δτ Pulse spread t E Input light pulse Suppose that the core refractive index has different values along two orthogonal directions corresponding to electric field oscillation direction (polarizations). We can take x and y axes along these directions. An input light will travel along the fiber with E x and E y polarizations having different group velocities and hence arrive at the output at different times 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Dispersion coefficient (ps km -1 nm -1 ) 20 D m 10 SiO 2-13.5%GeO 2 0 10 D w a (μm) 4.0 3.5 3.0 2.5 20 1.2 1.3 1.4 1.5 1.6 λ (μm) Material and waveguide dispersion coefficients in an optical fiber with a core SiO 2-13.5%GeO 2 for a 2.5 to 4 μm. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Dispersion coefficient (ps km -1 nm -1 ) 30 n 20 10 D m r 0-10 λ 1 λ 2 D ch D m + D w -20-30 D w 1.1 1.2 1.3 1.4 1.5 1.6 1.7 λ (μm) Thin layer of cladding with a depressed index Dispersion flattened fiber example. The material dispersion coefficient (D m ) for the core material and waveguide dispersion coefficient (D w ) for the doubly clad fiber result in a flattened small chromatic dispersion between λ 1 and λ 2. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Fiber Information Digital signal Emitter t Input Photodetector Information Output Input Intensity Output Intensity ² τ 1/2 Very short light pulses 0 T t 0 t ~2² τ 1/2 An optical fiber link for transmitting digital information and the effect of dispersion in the fiber on the output pulses. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

n 2 O 2 1 3 n 1 n (a) Multimode step index fiber. Ray paths are different so that rays arrive at different times. O O' O'' 3 2 1 2 3 n 2 n 1 n (b) Graded index fiber. Ray paths are different but so are the velocities along the paths so that all the rays arrive at the same time. n 2 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

0.5P 0.25P 0.23P O O' O O (a) (b) (c) Graded index (GRIN) rod lenses of different pitches. (a) Point O is on the rod face center and the lens focuses the rays onto O' on to the center of the opposite face. (b) The rays from O on the rod face center are collimated out. (c) O is slightly away from the rod face and the rays are collimated out. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Sources of Loss and Attenuation in Fibers A solid with ions E x Light direction k z Lattice absorption through a crystal. The field in the wave oscillates the ions which consequently generate "mechanical" waves in the crystal; energy is thereby transferred from the wave to lattice vibrations. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

A dielectric particle smaller than wavelength Incident wave Through wave Scattered waves Rayleigh scattering involves the polarization of a small dielectric particle or a region that is much smaller than the light wavelength. The field forces dipole oscillations in the particle (by polarizing it) which leads to the emission of EM waves in "many" directions so that a portion of the light energy is directed away from the incident beam. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Field distribution θ θ Cladding Core θ θ > θ c θ Microbending θ < θ Escaping wave R Sharp bends change the local waveguide geometry that can lead to waves escaping. The zigzagging ray suddenly finds itself with an incidence angle θ that gives rise to either a transmitted wave, or to a greater cladding penetration; the field reaches the outside medium and some light energy is lost. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Attenuation in Optical Fiber 10 5 OH - absorption peaks 1.0 0.5 0.1 0.05 Rayleigh scattering 1310 nm Lattice absorption 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Wavelength (µm) Illustration of a typical attenuation vs. wavelength characteristics of a silica based optical fiber. There are two communications channels at 1310 nm and 1550 nm. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) 1550 nm α P db out α P in (10 1 P 10 log( L P αl /10 ) in out ) G. Keiser (Ref. 1)

Some Concepts of Solid State Materials Contents The Semiconductors in Equilibrium Nonequilibrium Condition Generation-Recombination Generation-Recombination rates Photoluminescence & Electroluminescence Photon Absorption Photon Emission in Semiconductors Basic Transitions Radiative Nonradiative Spontaneous Emission Stimulated Emission Luminescence Efficiency Internal Quantum Efficiency External Quantum Efficiency Photon Absorption Fresnel Loss Critical Angle Loss Energy Band Structures of Semiconductors PN junctions Homojunctions, Heterojunctions Materials III-V semiconductors Ternary Semiconductors Quaternary Semiconductors II-VI Semiconductors IV-VI Semiconductors

The Semiconductors in Equilibrium The thermal equilibrium concentration of carriers is independent of time. The random generation-recombination of electrons-holes occur continuously due to the thermal excitation. In direct band-to-band generation-recombination, the electrons and holes are created-annihilated in pairs: Gn0 Gp0, Rn0 Rp0 -The carriers concentrations are independent of time therefore: Gn0 Gp0 Rn0 Rp0

Nonequilibrium Conditions in Semiconductors When current exist in a semiconductor device, the semiconductor is operating under nonequilibrium conditions. In these conditions excess electrons in conduction band and excess holes in the valance band exist, due to the external excitation (thermal, electrical, optical ), in addition to thermal equilibrium concentrations. n(t) no + δn(t), p(t) po + δp(t) The behavior of the excess carriers in semiconductors (diffusion, drift, recombination, ) which is the fundamental to the operation of semiconductors (electronic, optoelectronic,..) is described by the ambipolar transport equations.

Generation-Recombination In the direct band-to-band the excess electrons and holes are generated and recombined in pair: g n0 g p0, R n0 R p0

Generation-Recombination Rates The recombination rate is proportional to electron and hole concentrations. dn ( t) 2 d ( n0 + δn( t)) dδn( t) α [ ni n( t) p( t)] dt dt dt n ( t ) n 0 + δ n ( t ) p( t) p ( ) 0 + δp t 2 αn i is the thermal equilibrium generation rate.

Generation-Recombination Rates Electron and holes are created and recombined in pairs, therefore, δn(t) δp(t) and no and po are independent of time. d( δn( t)) dt α[ n 2 i ( n 0 + δn( t))( p 0 + δp( t)] αδn( t)[( n 0 + p 0 ) + δn( t)] Considering a p-type material under low-injection condition, d ( δ n dt ( t )) α p t τ 0 α p δ n ( ) 0 t δ n 0 n ( t ) δ n (0 ) e δ n (0 ) e t τno (αpo)-1 is the minority carrier electrons lifetime, constant for low-injections.

Generation-Recombination Rates The recombination rate ( a positive quantity) of excess minority carriers (electrons-holes) for p-type materials is: 0 ' ' ) ( n p n t n R R τ δ Similarly, the recombination rate of excess minority carriers for n-type material is: 0 ' ' ) ( p p n t n R R τ δ

Generation-Recombination Rates where τpo is the minority carrier holes lifetime. For high injections which is in the case of LASER and LED operations, δn >> no and δp >> po so, τno (αδp)-1 and τpo (αδn)-1 If photons are emitted (usually in direct bandgap semiconductors), the process is called radiative (important for the operation of optical devices), otherwise is called nonradiative recombination (takes place via surface or bulk defects and traps).

Generation-Recombination Rates In any carrier decay process the total lifetime τ can be expressed as 1 τ 1 τ r + 1 τ nr where τr and τnr are the radiative and nonradiative lifetimes respectively. The total recombination rate is given by R R + R total r nr R sp Where Rr and Rnr are radiative and nonradiative recombination rates per unit volume respectively and Rsp is called the spontaneous recombination rate.

Photoluminescence & Electroluminescence The recombination of excess carries in direct bandgap semiconductors may result in the emission of photon. This property is generally referred to as luminescence. If the excess electrons and holes are created by photon absorption, then the photon emission from the recombination process is called photoluminescence. If the excess carries are generated by an electric current, then the photon emission from the recombination process is called electroluminescence.

Absorption When semiconductors are illuminated with light, the photons may be absorbed (for Eph hν Eg E2 E1)or they may propagate through the semiconductors (for Eph Eg). There is a finite probability that electrons in the lower level absorb energy from incoming electromagnetic field (light) with frequency of ν (E2 E1)/h and jump to the upper level. dn dt 1 ab B 12 ( Φδν ) N 1 B12 is proportionality constant, δν ν2 - ν1 and Φδν Iν is the photon density in the frequency range of δν.

Absorption dn1 states are raised from E1 to E2 i.e dn1 photons are absorbed. Electrons are created in conduction band and holes in valence band. When photons with an intensity of Iν (x) are traveling through a semiconductor, going from x position to x + dx position (in 1-D system), the energy absorbed by semiconductor per unit of time is given by αiν (x)dx, where α is the absorption coefficient; the relative number of photons absorbed per unit distance (cm-1). di ν ( x ) I ν ( x + dx ) I ν ( x ). dx α I ν ( x ) dx dx di ν ( x) dx αi ν ( x) I αx ν ( x) Iν 0e where Iν(0) Iν0.

Absorption Intensity of the photon flux decreases exponentially with distance. The absorption coefficient in semiconductor is strong function of photon energy and band gap energy. The absorption coefficient for hν < Eg is very small, so the semiconductor appears transparent to photons in this energy range.

Photon Emission in Semiconductors When electrons in semiconductors fall from the conduction band to the valence band, called recombination process, release their energy in form of light (photon), and/or heat (lattice vibration, phonon). N1 and N2 are the concentrations of occupied states in level 1 (E1) and level 2 (E2) respectively. Basic Transitions Radiative Intrinsic emission Energetic carriers Nonradiative Impurities and defect center involvement Auger process

Photon Emission in Semiconductors

Einstein Relationship

Wave attenuation

pn Junction The entire semiconductor is a singlecrystal material: -- p region doped with acceptor impurity atoms --n region doped with donor atoms --the n and p region are separated by the metallurgical junction.

p n B - h+ (a) M Metallurgical Junction As+ e- (d) M Neutral p-region E Neutral n-region E (x) (b) (e) E o - xp 0 xn x (c) en d ρ (x) W -x p xn Space charge region x (f) ev bi e φ (x) - xp Hole PE(x) xn x -en a Electron PE(x)

- the potential barrier : - keeps the large concentration of electrons from flowing from the n region into the p region; - keeps the large concentration of holes from flowing from the p region into the n region; > The potential barrier maintains thermal equilibrium.

- the potential of the n region is positive with respect to the p region > the Fermi energy in the n region lower than the Fermi energy in the p region; - the total potential barrier larger than in the zero-bias case; - still essentially no charge flow and hence essentially no current;

-a positive voltage is applied to the p region with respect to the n region; - the Fermi energy level lower in the p region than in the n region; - the total potential barrier reduced > the electric field in the depletion region reduced; diffusion of holes from the p region across the depletion region into the n region; diffusion of electrons from the n region across the depletion region into the p region; - diffusion of carriers > diffusion currents;

-in thermal equilibrium : - the n region contains many more electrons in the conduction band than the p region; - the built-in potential barrier prevents the large density of electrons from flowing into the p region; V n bi p 0 ln N N a V t 2 n i n n0 exp qv kt bi d - the built-in potential barrier maintains equilibrium between the carrier distribution on either side of the junction;

- the electric field E app induced by V a in opposite direction to the electric field in depletion region for the thermal equilibrium; - the net electric field in the depletion region is reduced below the equilibrium value; - majority carrier electrons from the n side -> injected across the depletion region into the p region; - majority carrier holes from the p region -> injected across the depletion region into the n region; - Va applied > injection of carriers across the depletion regions-> a current is created in the pn junction;

1/2 max 1/2 max 1/2 2 ) 2( ) ( 2 ) ( 2 + >> + + + + + + d a d a s R bi R R bi d a d a s R bi d a d a R bi s p n N N N N ev E V V W V V N N N N V e V E N N N N e V V x x W ε ε ε 2 1 2 + + d a d a bi s n p N N N N e V x x W ε For zero bias For reverse biased W V E bi 2 max For reverse biased For zero bias

When there is no voltage applied across the pn junction the junction is in thermal equilibrium > the Fermi energy level constant throughout the entire system. Fp Fn bi V Φ + Φ p n n p i d a bi n n e kt p p e kt n N N e kt V ln ln 2 + + Φ + Φ i d i a Fi Fn Fp Fi n p bi n N e kt n N e kt e E E e E E V ln ln )/ ( )/ (

ρ(c/cm³) + en d x p _ + + x n x p E + x n E E en ε s en ε s a d ( x + ( x n x p ), x), x p x 0 0 x x n Poisson' s Equation d 2 φ( x) dx 2 en a x 0 ρ( x) ε s de( x) dx 1 x E ( x) ρ( x) dx ε xp s E max For Si Charge neutrality: N x a p N The peak electric field Is at x 0 E max end x ε s 14 ε s ε 0 ε r (11.7)(8.85 10 ) F / cm n d x n enax ε s p

+ n p n p n p s L n qd L p qd J 0 0 1 exp kt qv J J a s - ideal-diode equation;

The bipolar transistor: - tree separately doped regions - two pn junctions; The width of the base region small compared to the minority carrier diffusion length; The emitter largest doping concentration; The collector smallest doping concentration;

- the bipolar semiconductor not a symmetrical device; -the transistor may contain two n regions or two p regions -> the impurity doping concentrations in the emitter and collector different; -- the geometry of the two regions can be vastly different;

Electromagnetic Spectrum Three basic bands; infrared (wavelengths above 0.7μm), visible (wavelengths between 0.4-0.7μm), and ultraviolet light (wavelengths below 0.4μm). E hν hc/ λ ; c νλ An emitted light from a semiconductor optical device has a wavelength proportional to the semiconductor band-gap. Longer wavelengths for communication systems; Eg 1μm. (lower Fiber loss). Shorter wavelengths for printers, image processing, Eg > 1μm. Semiconductor materials used to fabricate optical devices depend on the wavelengths required for the operating systems.

Materials Almost all optoelectronic light source depend upon epitaxial crystal growth techniques where a thin film (a few microns) of semiconductor alloys are grown on single-crystal substrate; the film should have roughly the same crystalline quality. It is necessary to make strain-free heterojunction with good-quality substrate. The requirement of minimizing strain effects arises from a desire to avoid interface states and to encourage long-term device reliability, and this imposes a lattice-matching condition on the materials used.

Materials The constraints of bandgap and lattice match force that more complex compound must be chosen. These compounds include ternary (compounds that containing three elements) and quaternary (consisting of four elements) semiconductors of the form AxB1-xCyD1-y; variation of x and y are required by the need to adjust the band-gap energy (or desired wavelength) and for better lattice matching. Quaternary crystals have more flexibility in that the band gap can be widely varied while simultaneously keeping the lattice completely matched to a binary crystal substrate. The important substrates that are available for the laser diode technology are GaAs, InP and GaP. A few semiconductors and their alloys can match with these substrates. GaAs was the first material to emit laser radiation, and its related to III-V compound alloys, are the most extensively studied developed.

Materials III-V semiconductors Ternary Semiconductors; Mixture of binary-binary semiconductors; AxB1-xC; mole fraction, x, changes from 0 to 1. (x will be adjusted for specific required wavelength). GaxAl1-xAs ; In0.53Ga0.47As; In0.52Al0.48As - Vegard s Law: The lattice constant of AxB1-xC varies linearly from the lattice constant of the semiconductor AC to that of the semiconductor BC. - The bandgap energy changes as a quadratic function of x. E g a + bx + 2 cx - The index of refraction changes as x changes. The above parameters cannot vary independently (due to the only one degree of freedom). Quaternary Semiconductors; AxB1-xCyD1-y (x and y will be adjusted for specific wavelength and matching lattices). GaxIn1-xPyAs1-y ; (AlxGa1-x)yIn1-yP; AlxGa1-xAsySb1-y

Materials II-VI Semiconductors CdZnSe/ZnSe; visible blue lasers. Hard to dope p-type impurities at concentration larger than 2 10 18 cm -3 (due to self-compensation effect). Densities on this order are required for laser operation.

Materials IV-VI semiconductors PbSe; PbS; PbTe By changing the proportion of Pb atoms in these materials semiconductor changes from n- to p-type. Operate around 50 K o PbTe/Pb1-xEuxSeyTe1-y operates at 174 K o

Materials

Materials In the near infrared region, the most important and certainly the most extensively characterized semiconductors are GaAs, AlAs and their ternary derivatives AlxGa1-xAs. At longer wavelengths, the materials of importance are InP and ternary and quaternary semiconductors lattice matched to InP. The smaller band-gap materials are useful for application in the long wavelength range. The III- V compounds of interest here are antimony (Sb)- bearing compounds and InAs and their ternary and quaternary.

Energy Band Structure of Semiconductors

Basic Semiconductor Luminescent Diode Structures LEDs (Light Emitting Diode) Under forward biased when excess minority carriers diffuse into the neutral semiconductor regions where they recombine with majority carriers. If this recombination process is direct band-to-band process, photons are emitted. The output photon intensity will be proportional to the ideal diode diffusion current. In GaAs, electroluminescence originated primarily on the p-side of the junction because the efficiency for electron injection is higher than that for hole injection. The recombination is spontaneous and the spectral outputs have a relatively wide wavelength bandwidth of between 30 40 nm. λ hc/eg 1.24/ Eg

Basic Semiconductor Luminescent Diode Structures

Electron energy E c p n + p n + ev o (a) E F E g E c E F E g (b) E v hυ - E g ev o E v Distance into device Electron in CB Hole in VB V (a) The energy band diagram of a p-n + (heavily n-type doped) junction without any bias. Built-in potential V o prevents electrons from diffusing from n + to p side. (b) The applied bias reduces V o and thereby allows electrons to diffuse, be injected, into the p-side. Recombination around the junction and within the diffusion length of the electrons in the p-side leads to photon emission. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Light output Light output p n + Epitaxial layers p n + Insulator (oxide) Epitaxial layer n + Substrate n + Substrate (a) Metal electrode (b) 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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

(a) (b) (c) Light output Plastic dome Light Domed semiconductor p n + n + pn Junction 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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

E c E N E c E g E v E v E a (a) GaAs 1-y P y y < 0.45 (b) N doped GaP (c) Al doped SiC (a) Photon emission in a direct bandgap semiconductor. (b). GaP is an indirect bandgap semiconductor. When doped with nitrogen there is an electron trap at E N. Direct recombination between a trapped electron at E N and a hole emits a photon. (c) In Al doped SiC, EHP recombination is through an acceptor level like E a. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Indirect bandgap GaAs 1-y P y x 0.43 In 1-x Ga x As 1-y P y Al x Ga 1-x As In 0.49 Al x Ga 0.51-x P 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Infrared 1.7 λ Free space wavelength coverage by different LED materials from the visible spectrum to the infrared including wavelengths used in optical communications. Hatched region and dashed lines are indirect E g materials. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

n + p p (a) AlGaAs GaAs AlGaAs (b) Electrons in CB E F E c 2 ev ~ 0.2 μm ev o 1.4 ev ΔE c 2 ev E c E F E v No bias (a) A double heterostructure diode has two junctions which are between two different bandgap semiconductors (GaAs and AlGaAs) E v Holes in VB (b) A simplified energy band diagram with exaggerated features. E F must be uniform. (c) (d) n + p p With forward bias (c) Forward biased simplified energy band diagram. (d) Forward biased LED. Schematic illustration of photons escaping reabsorption in the AlGaAs layer and being emitted from the device. AlGaAs GaAs AlGaAs 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

(a) E (b) (c) (d) CB Electrons in CB 2k B T Relative intensity Relative intensity 1 E g + k B T /2 k E B T c 1 (2.5-3)k B T E g 1 1 2 3 Δhυ E v 0 hυ 0 VB Holes in VB hυ 1 hυ 2 hυ 3 λ 3 Δλ λ 2 λ 1 λ Carrier concentration per unit energy E g (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)k B T above E c. (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). 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Relative intensity (a) 655nm (b) Relative light intensity V (c) 1.0 2 0.5 Δλ 24 nm 1 0 600 650 700 λ 0 0 20 40 I (ma) 0 0 20 40 I (ma) (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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Light Double heterostructure Light (a) Surface emitting LED (b) Edge emitting LED 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Epoxy resin Fiber (multimode) Electrode Fiber Microlens (Ti 2 O 3 :SiO 2 glass) Etched well Double heterostructure SiO 2 (insulator) Electrode (a) Light is coupled from a surface emitting LED into a multimode fiber using an index matching epoxy. The fiber is bonded to the LED structure. (b) A microlens focuses diverging light from a surface emitting LED into a multimode optical fiber. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

60-70 μm Stripe electrode Insulation p + -InP (E g 1.35 ev, Cladding layer) p + -InGaAsP (E g 1 ev, Confining layer) n-ingaas (E g 0.83 ev, Active layer) n + -InGaAsP (E g 1 ev, Confining layer) 2 n + 1 3 -InP (E g 1.35 ev, Cladding/Substrate) Current Electrode paths Substrate L 200-300 μm Light beam Active region (emission region) Schematic illustration of the the structure of a double heterojunction stripe contact edge emitting LED 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

ELED Lens Multimode fiber ELED GRIN-rod lens Single mode fiber Active layer (a) Light from an edge emitting LED is coupled into a fiber typically by using a lens or a GRIN rod lens. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) (b)

Partially reflecting plates Transmitted light Input light Output light L λ Fabry-Perot etalon λ m - 1 λ m Transmitted light through a Fabry-Perot optical cavity. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) I max I 0 ( 1 R) 2 I I 2 ( 1 R) 2 ( 1 R) + 4Rsin ( kl) transmitted incident 2

M 1 M 2 m 1 A m 2 Relative intensity 1 υ f R ~ 0.8 R ~ 0.4 B L m 8 υ m - 1 υ m υ m + 1 δυ m υ (a) (b) (c) Schematic illustration of the Fabry-Perot optical cavity and its properties. (a) Reflected waves interfere. (b) Only standing EM waves, modes, of certain wavelengths are allowed in the cavity. (c) Intensity vs. frequency for various modes. R is mirror reflectance and lower R means higher loss from the cavity. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) λ m 2 L m1,2,3. 0 I cavity 2 I 2 ( 1 R) + 4Rsin ( KL)

LASERS The sensitivity of most photosensitive material is greatly increased at wave-length < 0.7 μm; thus, a laser with a short wave-length is desired for such applications as printers and image processing. The sensitivity of the human eye range between the wavelengths of 0.4 and 0.8μm and the highest sensitivity occur at 0.555μm or green so it is important to develop laser in this spectral regime for visual applications. Laser-quality crystals are obtained only with lattice mismatches <0.01% relative to the substrate. It is generally true that semiconductor materials with larger band gaps show a tendency to have small lattice constants.

LASERS The semiconductor laser diode is a forward bias p-n junction. The structure appears to be similar to the LED as far as the electron and holes are concerned, but it is quite different from the point of view of the photons. Electrons and holes are injected into an active region by forward biasing the laser diode. At low injection, these electrons and holes recombine (radiative) via the spontaneous process to emit photons. However, the laser structure is so designed that at higher injections the emission process occurs by stimulated emission. As we will discuss, the stimulated emission process provides spectral purity to the photon output, provides coherent photons, and offers highspeed performance. The exact output spectrum from the laser diode depends both on the nature of the optical cavity and the optical gain versus wavelength characteristics. Lasing radiation is only obtained when optical gain in the medium can overcome the photon loss from the cavity, which requires the diode current I to exceed a threshold value Ith and gop>gth

LASER Diode Modes of Threshold Conditions Lasing Conditions: Population Inversion Fabry-Perot cavity gain (of one or several modes) > optical loss I ( z ) I (0) e Γ g ( hv ) α ( hv ) z α I optical field intensity g gain coefficient in F.P. cavity - effective absorption coefficient Γ optical field confinement factor. (the fraction of optical power in the active layer) In one round trip i.e. z 2L gain should be > loss for lasing; During this round trip only R1 & R2 fractions of optical radiation are reflected from the two laser ends 1 & 2. R n n 1 1 + n n 2 2 2

LASER Diode Modes of Threshold Conditions From the laser conditions: ( 2L) I ( o) j 2 L I e 1 β ( 2 βl 2πm) I ( 2 L ) I ( 0 ) R _ 2 L Γ g α 1 R 2 e I ( 0 ) e _ 2 L Γ g α 1 R 1 R 2 Lasing threshold is the point at which the optical gain is equal to the total loss αt 2 L Γ g α _ 1 ln R 1 R 2 Thus the gain Γ g th t _ α α + α end Γ g th 1 1 α + ln α + 2 L R R 1 2 α end g g th β J β is constant and depends on the specific device construction. th

Laser Diode Rate Equations The relationship between optical output and the diode drive current: Rate Equations govern the interaction of photons and electrons in the active region. Variation of photon concentration: d φ dt dn dt φ τ Bn φ + R sp stimulated emission + spontaneous emission - photon loss ph J n qd τ sp Bn φ injection - spontaneous recombination - stimulated emission (shows variation of electron concentration n). d - is the depth of carrier-confinement region B - is a coefficient (Einstein s) describing the strength of the optical absorption and emission interactions,; Rsp - is rate of spontaneous emission into the lasing mode; τ ph is the photon lifetime; τ sp is the spontaneous recombination lifetime; J is the injection current density;

Laser Diode Rate Equations Solving the above Equations for a steady-state condition yields an expression for the output power. Steady-state > d φ dt 0 and dn dt 0 d φ If we neglect Rsp and noting > 0 > dt Bn 1 τ ph 0 Therefore, n must exceed a threshold value nth in order for Φ to increase. In other words J needs to exceed Jth in steady-state condition, when the number of photons Φ0. J qd th n th τ sp

Laser Diode Rate Equations This expression defines the current required to sustain an excess electron density in the laser when spontaneous emission is the only decay mechanism. Now, under steady-state condition at the lasing threshold: R Φ s sp Φ BN th Φ s + R sp τ n th BN th Φ s + τ sp R Φ τ s ph n τ th sp n + J qd th sp τ ph τ ph + τ sp s ph J qd Adding these two equations: J qd 0 0 τ 0 ph Фs is the steady-state photon density. Φ s but τ qd ph n τ th sp J qd ( J J th ) + R sp τ ph # of photon resulting from stimulated emission The power from the first term is generally concentrated in one or few modes; The second term generates many modes, in order of 108 modes.

Laser Diode Rate Equations To find the optical power P0: P 0 1 Φ 2 s ( volume)( hv)( 1 R) Δt nl t c Δ time for photons to cross cavity length L. 1 2 Φ s - is the part travels to right or left (toward output face) P 0 2 hc τ phw (1 2qnλ R) [ J J ] th R is part of the photons reflected and 1-R part will escape the facet

Laser Characteristics P 0 n th Threshold population inversion n P 0 lasing output power Ф s J J th

We had: Laser Characteristics Resonant Frequency αβl 2πm β 2πn / λ m L λ n 2 2πn 2 L λ m 2nL λ 2πm 2nLv c This states that the cavity resonates (i.e. a standing wave pattern exists within it) when an integer number m of λ/2 spans the region between the mirrors. Depending on the laser structures, any number of freq. can satisfy I (2L) I (0) & e j 2 βl 1 Thus some lasers are single - & some are multi-modes. The relationship between gain & freq. can be assumed to have Gaussian form: g ( λ λ ) 2σ ( λ ) g (0) e 0 2 2 where λ0 is the wavelength at the center of spectrum; σ is the spectrum width of gain & maximum g(0) is proportional to the population inversion.

Laser Characteristics Spacing between the modes: m 2Ln m λ v m L c 2n m 2Ln c 1 vm 1 2nL 2nL 2nL δλ m 2 m m + 1 m 2 λ 2nL 2Ln c 2Ln c ( v v ) Δv 1 m m 1 Δv c 2Ln c vλ v c v > Δv cδλ 2 λ cδλ 2 λ c 2Ln > Δλ 2 λ 2Ln

Laser Characteristics Internal & External Quantum Efficiency Quantum Efficiency (QE) # of photons generated for each EHP injected into the semiconductor junction a measure of the efficiency of the electron-to-photon conversion process. If photons are counted at the junction region, QE is called internal QE (η int ), which depends on the materials of the active junction and the neighboring regions. For GaAs η int 65% to 100%. If photons are counted outside the semiconductor diode QE is external QE(η ext ). Consider an optical cavity of length L, thickness W and width S. Defining a threshold gain gth as the optical gain needed to balance the total power loss, due to various losses in the cavity, and the power transmission through the mirrors.

Laser Characteristics Internal & External Quantum Efficiency The optical intensity due to the gain is equal to: I Io exp(2lgth), this will be lost due to the absorption and the reflections on both ends by R1R2 exp(-2lα) So: I Io exp(2lgth){ R1R2 exp(-2lα)} Io. Therefore: R R e 2L( g th α ) 1 2 where R1 and R2 are power reflection coefficients of the mirrors, α is attenuation constant. 1

Laser Characteristics Internal & External Quantum Efficiency g th α + 1 2L ln 1 R R 1 2 g is gain constant of the active region and is roughly proportional to current density (g βj). β is a constant. J th (1/ β) α + 1 2L 1 R R ( ln ) 1 2 By measuring Jth, α, L, Γ1 and Γ2 one can calculate β (dependent upon the materials and the junction structure). 1 1 ln 2L R1R2 1 1 α + ln 2L R R 1 2 P P ra total The ratio of the power radiated through mirrors to the total power generated by the semiconductor junction is

Laser Characteristics Internal & External Quantum Efficiency Therefore η ext η int (P ra /P total ) which can be determined experimentally from PI characteristic. For a given I a (in PI curve current at point a) the number of electrons injected into the active area/sec Ia /q and the number of photons emitted /second Pa /hν η ext P / hν a I a / q η ext P b I b / hν / q η ext q( P ( I a a Pb ) I ) hν b q ΔP hν ΔI i.e. ηext is equal to slope of IP curve in the region of I > I th. If we choose Ib Ith, Pb 0 and hν Eg and hν/q Eg /q gives voltage across the junction in volts. η ext q P h ν I I th

Laser Characteristics Power Efficiency At dc or low frequency the equivalent circuit to a LASER diode may be viewed as an ideal diode in series with rs. Therefore the power efficiency ηp (optical power output)/ (dc electrical power input) η p P I( E / q) + g I 2 r s P hν ( I q I th ) η ext ext( I η p η I( E g I th ) E / q) + I g 2 / q r s