Chapter 4 Optical Source - Outline 4.1 Semiconductor physics - Energy band - Intrinsic and Extrinsic Material - pn Junctions - Direct and Indirect Band Gaps 4. Light Emitting Diodes (LED) - LED structure - Light source materials -Quantum Efficiency and power - Modulation of LED 4.3 Laser Diodes - Laser diodes modes and thershold - Rate Equations - External Quantum Efficiency - Resonant Frequencies - Single mode lasers - Laser modulation
4.1 Semiconductor physics - Energy band Semiconductor: Conduction properties lies somewhere between those of conductor (metal) and insulator Intrinsic Semiconductor: Pure crystal (such as Si, Ge) group IV I II IIIb IVb Vb VIb VIIb VIIIb Ib IIb III IV V VI VII 0 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16 17 18 H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La* Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac** Rf Db Sg Bh Hs Mt Uun Uuu Uub Uuq Uuh Uuo Lanthanides * Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Actinides ** Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
4.1 Semiconductor physics - Energy band Energy-band diagram: - conduction band E C - valence band E V - band gap Eg= E C -E V Carrier: electrons / holes Concentration : - free electron concentration n - hole concentration p - intrinsic carrier concentration n i Eg n = p = n = i Kexp( ) (4.1) K = ( πk / ) 3/ ( ) 3/4 BT h mm e h kt B
4.1 Semiconductor physics - Energy band Doping: Conduction can be greatly increased by adding traces of impurities from Group V or Group III Doping Group V donor impurity (P, As, Sb; 5 electrons) free-electrons n-type material Doping Group III acceptor impurity ( Al, Ga, In, Boron ) free-holes p-type material
Semiconductor physics - Intrinsic and Extrinsic Material Intrinsic material : A perfect material containing no impurities is called ~. Extrinsic material : Doped semiconductor is called ~. Thermal generation produce electron-hole pairs ( for intrinsic material: equal concentration n = p = n i ) Recombination : a free electron releases its energy and drops into a free hole in the valence band. For extrinsic material: concentration of p and n is different, and follow the mass-action law: pn = n i n i : intrinsic carrier concentration Majority carriers : refers to electrons in n-type material, and holes in p-type material. Minority carriers: refers to holes in n-type material, and electrons in p-type material
Semiconductor physics - Intrinsic and Extrinsic Material Example 4- Consider an n-type semiconductor which has been doped with a net concentration of N D donor impurities. Find electron and hole concentrations (n N, p N ). Let n N and p N be the electron and hole concentrations, respectively, where the subscript N is used to denote n-type semiconductor characteristics. Total hole concentration p N (only from thermal excitation): Total electron concentration n N (from doped and thermal excitation): p N nn = ND + pn Mass-action law: n p = n N N i ( n + p ) p = n D N N i ND + ND 4ni N D pn = = ( 1+ 1 4 ni / ND ) ni nd p n n n N i / D N n D
Semiconductor physics - pn Junction Doped n- or p-type semiconductor material by itself serves only as a conductor. Only pn junction is responsible for the useful electrical characteristics of a semiconductor device Barrier potential : prevents further movement of charges Depletion region : External battery can be connected to the pn junction, by reverse-bias or forward bias. Reverse biased for application in photodiode Forward biased for application in laser diode
Semiconductor physics - pn Junction Forward-biased pn junction: Creates barrier potential, which prevent holes and electrons to move to junction region, but when pn junction is applied forward voltage, if ev >= W g, the electrons and holes will move into junction region, and recombine, which will create Photons. Reverse-biased pn junction: The width of the depletion region will increase on both the n side and p side. (will talk in next chapter for photodiode) Operating Wavelength: hf = W, λ = hc/ W g Note: for direct bandgap material g
Semiconductor physics - Direct and Indirect Band Gaps Direct band gap material: no change of wavevector efficient For example: GaAs Indirect band gap material with change of wavevector
Light-Emitting Diodes - LED Structure To achieve high radiance, high quantum efficiency, carrier confinement and optical confinement are necessary. Structure: - homojunctions: same material (W g ) - single and double heterojunctions : difference bandgap materials Put fig. 4-8 here The most effective structure: Double heterojunction (it could provide carrier and optical confinements.) Carrier (electron or hole ) confinement - bandgap difference of adjacent layer Optical confinement - index difference of adjacent layer Two basic LED configuration - Surface emitters - Edge emitters
Surface emitters /lambertian pattern Edge emitters unsymmetric radiation Parallel plane: Lambertian pattern Perpendicular plane: there is beam confinement (better coupling)
Light-Emitting Diodes - Laser Source Materials III-V materials (Al, Ga, In III group; P, As, Sb V group Ternary and quaternary combinations - Ternary alloy Ga 1-x Al x As, spectrum at 800 900 nm - Quaternary alloy In 1-x Ga x As y P 1-y, spectrum at 1.0 1.7 μm -x, y Lattice constant Spectrum, full-width-half-maximum (FWHM)
Light-Emitting Diodes - Laser Source Materials Relationship between energy E and frequency ν : hc E = hν = λ 1.40 λ( μm) = E ( ev ) g Relationship between lattice constant (x, y) and band-gap - For Ga 1-x Al x As : E = + x+ x g 1.44 1.66 0.66 (4 4) - For In 1-x Ga x As y P 1-y : E = y + y g 1.35 0.7 0.1 (4 5) Example 4-3 Consider a Ga 1-x Al x As laser with x=0.07. Find the diode emission wavelength. Example 4-4 Consider the alloy In 1-x Ga x As y P 1-y (i.e., x = 0.6 and y =0.57), find diode emission wavelength.
η int r Light-Emitting Diodes When carrier injection stops, carrier density t /τ decays: n = n0e For constant current flow into LED, an equilibrium condition will be established. Internal Quantum efficiency η int : = r R r τ = n / R Rr + R 1 1 1 = + τ τ τ r nr nr τ 1 = 1+ τ / τ nr r = n / R nr nr = τ τ r R r : radiative recombination rate - Internal quantum efficiency τ r : radiative recombination lifetime R nr : nonradiative recombination rate τ nr nonradiative recombination lifetime dn dt = rate equation J qd Current injection n τ Thermal generation J current density in A/cm q electron charge d thickness of recombination region equilibrium condition n = Jτ qd P int : internal optical power I Pint = ηint hν = η q int hci qλ
Light-Emitting Diodes - Internal quantum efficiency Example 4-5 A double-heterojunction InGaAsP LED emitting at a peak wavelength of 1310 nm has radiative and nonradiative recombination times of 30 and 100 ns, respectively. The drive current is 40 ma. Compute internal quantum efficiency and internal optical power.
Light-Emitting Diodes n - External quantum efficiency External quantum efficiency 1 φc η ext = T( φ)(π sin φ) dφ 4π 0 Incidental angle φ critical angle c Fresnel transmissivity for normal incidence T (0) = 4n1n ( n + n 1 1 φ = π / θ = sin ( n / n ) c ) 1 Example 4-6 Assuming a typical value of n=3.5 for refractive index of an LED material, calculate the η ext. Emitted power For n 1 =n, n =1 1 η ext nn ( + 1) Pint Pext = η ext Pint = n( n + 1)
Light-Emitting Diodes - Modulation Modulated output power P 0 ( ) = (4.18) 1 + ( ωτ i ) P ω P 0 ω τ i power emitted at DC modulation frequency carrier lifetime Optical 3-dB modulation bandwidth : P( ω3 db ) = P(0) Detected current is linearly proportional to optical power : Detected electric power : p( ω) = I ( ω) R 1 P( ω) I( ω) = P(0) I(0) Therefore, 3-dB electrical loss corresponds to 1.5-dB optical loss; in other words, 3-dB optical loss corresponds to 6-dB electrical loss. 1 f3 db ( electrical) = f3 db ( optical) = 0.707 f3 db ( optical)
Laser Diodes - Principles Types of Laser : lasing medium gas, liquid, solid state (crystal), semiconductor. Laser action is the result of 3 key process: photon absorption, spontaneous emission, and stimulated emission. Photon absorption: When a photon of energy hν 1 impinges on the system, an electron in ground state E 1 can absorb the photon energy and be excited to state E. Spontaneous emission : The electron in state E falls down to state E 1 by itself quite spontaneously, and emits a photon of energy hν 1 in random direction. Stimulated emission : The electron in state E falls down to state E 1, induced by a coming photon of energy of hν 1, and emits a photon of energy hν 1 in the same direction.
Laser Diodes - Principles In thermal equilibrium : The density of exited electron is very small Population inversion : Population of excited states > that of the ground state stimulated emission will exceed absorption Pumping techniques : obtain population inversion For a semiconductor laser, population inversion can be achieved by injecting electrons, or another pumping laser for solid state laser (crystal)
Laser Diodes - Modes Laser cavity : to convert the device into an oscillator and provide optical feedback to compensate the optical loss in the cavity - Fabry-Perot (FP) laser: mirrors, cleaved facets - Distributed feedback (DFB) laser : Bragg reflector Modes: Longitudinal mode; Lateral mode; Transverse mode - spectral characteristics (resonant frequencies) / longitudinal modes - spatial characterisitics depend on / lateral and transverse modes
Laser Diodes - Threshold conditions -1 Optical field intensity in longitudinal direction I( z, t) = I( z) e j ωt β z ( ) I(z) optical field intensity ω optical radian frequency β propagation constant with I( z) = I(0) e [ Γg( hν) α( hν)] z Γ optical confinement factor g gain coefficient depended on optical frequency α effective material absorption coefficient R a Γg Amplitude condition I (L) = R th b e cavity threshold gain I (0) L( Γg ( hν ) α ( hν )) = α + = 1 1 1 ln( L R R a b ) = α + α cavity Material loss end cavi mirr loss Fabry-Perot laser cavity Reflecting mirror Phase condition e jβ L = 1 Decided by laser cavity dimension! Amplitude condition Phase condition R a R b n Gain medium 1 n z 0 L Amplitude during one round trip I (L) = I (0) R a R R a R b mirror Fresnel reflection coefficients n n R = ( n 1 b e 1 ) + n L( Γg ( hν ) α ( hν )) Laser condition: Laser occurs when the gain is sufficient to exceed the optical loss during one round trip
I ( L) = I (0) Laser Diodes - Threshold conditions - Example 4-7 For GaAs, R 1 =R =0.3 for uncoated facets (i.e. 3% of the radiation is 1 1 reflected at a facet) and α 10cm. This yields Γ g th = 33cm for a laser diode of length L = 500μm. Optical power vs. drive current Threshold current density J th g th g = β th J th Threshold current density Threshold gain β constant depended on device construction - spontaneous radiation below threshold - threshold current J = I / A th th I th Threshold current A Area
Laser Diodes - Rate equation -1 Relationship between optical power and drive current can be determined by two rate equations: For photon density Φ ; For electron density n rate equation for photon density dφ Φ = CnΦ+ Rsp dt τ stimulated emission ph spontaneous emission photon loss Φ : photon density C coefficient for optical absorption and emission interactions R sp rate of spontaneous emission into lasing mode τ ph photon lifetime dφ 0 dt with R sp 0 Cn 1 0 τ ph Photon density should be in increasing mode towards lasing with negligible spontaneous emission n n th = C 1 τ ph Electron density must exceed a threshold value in order for photon density to increase rate equation for electron density dn J n = CnΦ dt qd τ sp dn = 0 dt with Φ = 0 n = n th n τ th = sp J th qd injection spontaneous recombination stimulated emission J injection current density τ sp spontaneous recombination lifetime If electron density is at threshold level, injected electrons are just fully consumed by spontaneous recombination without light emission
Laser Diodes - Rate equation - Steady-state solution for rate equations d Φ Φ = s Cn Φ + th s R = sp 0 dt τ ph dn J n = th Cn thφ s = 0 dt qd τ Φ s sp steady-state photon density + n τ th = sp J th qd τ ph Φ s = ( J J th ) + τ qd Photons resulting from stimulated emission ph R sp Spontaneously generated photons
Laser Diodes - External quantum efficiency External quantum efficiency η ext is defined as the number of photons emitted per radiative electron-hole pair recombination above threshold. External quantum efficiency η ext α = η (1 ) (4.37) i g th Achieved experimentally q dp η ext = = E di g 0.8065λ( μm) dp( mw ) di ( ma) η i internal quantum efficiency ~ 0.6-0.7 at room temperature Ε g band-gap energy λ emitted wavlength g th gain coefficient at threshold
Laser Diodes - Resonant frequencies e jβ L Phase condition for lasing = 1 ν = m c nl 1 πν βl = nl 1 = mπ c Optical resonant frequencies (or longitudinal modes) c λ Δ ν = or Δ λ = nl nl 1 1 Frequency or wavelength spacing between modes (or free spectral range FSR) These modes describe the possible resonant optical frequency, if lasing really happen at these frequencies or not, still depends on the laser gain profile. If many modes are allowed for lasing under the gain spectral profile, it is a multi-mode laser e.g. Fabry-Perot laser
Laser Diodes - Resonant frequencies Laser spectral gain profile g ( λ λ0 ) σ ( λ) = g(0) e g(0) maximum gain proportional to population inversion λ 0 wavelength at the spectrum center σ spectral width of the gain Example, 4-1 A GaAs laser operating at 850 nm has a 500 μ m length and a refractive index n=3.7. What are the frequency and wavelength spacings. If, at the half-power point, λ λ 0 = nm, what is the spectral width σ of the gain?
Laser Diodes - Single mode lasers - reduce cavity length L to increase frequency interval (FSR) between modes until there is only one mode falls within the laser gain bandwidth (not practical due to its dimension and low optical power) - distributed-feedback (DFB) laser - two 0-order modes will be degenerated to single mode due to imperfect AR coating DFB laser cavity λb λ = λb ± ( m + n L e e 1 ) λ B n e Λ = k n 1 n Anti-reflection coating k order of the grating n e effective refrative index of the mode Λ period of corrugation
Laser Diodes - Modulation Internal (direct, current) modulation ; External modulation Modulate the laser above the threshold - Spontaneous radiative lifetime τ sp ~ 1 ns - Stimulated carrier lifetime τ st ~ 10 ps - photon lifetime τ ph ~ ps sets the upper limit to the direct modulation capacity Modulation frequency also can not be larger than the frequency of the relaxation of laser field f P Laser injection current f = 1 1 I 1 π τ τ I sp ph th Laser output power I B I p +I B I t d Laser carrier density Fig. 4-30 Example of the relaxationoscillation peak o a laser diode
P195, 4-9 a) A GaAlAs laser diode has a 500 μ m cavity length which has an effective absorption coefficient of 10 cm -1. For uncoated facets the reflectivities are 0.3 at each end. What is the optical gain at the lasing threshold? b) If one end of the laser is coated with a dielectric reflector so that its reflectivity is now 90 percent, what is the optical gain at the lasing threshold? c) If the internal quantum efficiency is 0.65, what is the external quantum efficiency in cases of (a) and (b)? P196, 4-1 A GaAs laser emitting at 800 nm has a 400 μ m cavity length with a refractive index n=3.6. If the gain g exceeds the total loss α throughout t the range 750 nm < λ < 850 nm, how many modes will exist in the laser?
P195, 4-15 For laser structures that have strong carrier confinement, the threshold current density of stimulated emission J th can to a good approximation be related to the lasing-threshold optical gain g th by g th = β J th, where β is a constant that depends on the specific device construction. Consider a GaAs laser with an optical cavity of length 50 μ m and width 100 μ m. At the normal operating temperature, the gain factor β = 1x10-3 cm/a and the effective absorption coefficient α =10 cm 1. a) If the refractive index is 3.6, find the threshold current density and the threshold current I th. Assume the laser end facets are uncoated and the current is restricted to the optical cavity. b) What is the threshold current if the laser cavity width is reduced to 10 μ m?