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Chapter 4 Optical Source 4.1 Semiconductor physics - Energy band - Intrinsic and Extrinsic Material - pn Junctions - Direct and Indirect Band Gaps 4.2 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 - Outline 4.1 Semiconductor physics - Energy band ¾ Semiconductor: Conduction properties lies somewhere between those of conductor (metal) and insulator ¾ Intrinsic Semiconductor: Pure crystal (such as Si, Ge) Æ group IV I II IIIb 1 H Li Na K Rb Cs Fr 2 3 Be Mg Ca Sc Sr Y Ba La* Ra Ac** Lanthanides * Actinides ** IVb Vb VIb VIIb 4 5 6 7 VIIIb 8 Ib IIb III IV V VI VII 9 0 10 11 12 13 14 15 16 17 18 He B C N O F Ne Al Si P S Cl Ar Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Uuq Uuh Uuo Rf Db Sg Bh Hs Mt Uun Uuu Uub Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 4.1 Semiconductor physics - Energy band ¾ Energy-band diagram: - conduction band EC - valence band EV - band gap Eg= EC - EV ¾ Carrier: electrons / holes ¾ Concentration : - free electron concentration n - hole concentration p - intrinsic carrier concentration ni n = p = ni = K exp(− Eg 2kBT ) (4.1) K = 2(2π kBT / h2 )3/ 2 (me mh )3/ 4 4.1 Semiconductor physics - Energy band ¾ Doping: Conduction can be greatly increased by adding traces of impurities from Group V or Group III ¾ Doping Group V Æ donor impurity (P, As, Sb; 5 electrons) Æ free-electrons Æ n-type material ¾ Doping Group III Æ acceptor impurity ( Al, Ga, In, Boron ) Æ free-holes Æ p-type material Semiconductor physics - Intrinsic and Extrinsic Material ¾ Intrinsic material : A perfect material containing no impurities is called ~. ¾ Extrinsic material : Doped semiconductor is called ~. ¾ Thermal generation Æ produce electron-hole pairs ( for intrinsic material: equal concentration Æ n = p = ni ) ¾ Recombination : a free electron releases its energy and drops into a free hole in the valence band. ¾ For extrinsic material: concentration of p and n is different, and follow the mass-action law: Æ pn = n 2 n : intrinsic carrier concentration i i ¾ Majority carriers : refers to electrons in n-type material, and holes in p-type material. ¾ Minority carriers: refers to holes in n-type material, and electrons in p-type material Semiconductor physics - Intrinsic and Extrinsic Material Example 4-2 Consider an n-type semiconductor which has been doped with a net concentration of ND donor impurities. Find electron and hole concentrations (nN, pN). ¾ Let nN and pN be the electron and hole concentrations, respectively, where the subscript N is used to denote n-type semiconductor characteristics. pN ¾ Total hole concentration pN (only from thermal excitation): ¾ Total electron concentration nN (from doped and thermal excitation): n N = N D + p N ¾ Mass-action law: pN = − N D + N D 2 − 4ni 2 2 n N ⋅ p N = ni2 N = D ( −1 + 1 − 4ni 2 / N D 2 ) 2 ( n D + p N ) p N = ni2 ni n D p N ni 2 / nD n N nD Semiconductor physics - pn Junction ¾ Doped n- or p-type semiconductor material by itself serves only as a conductor. ¾ Only pn junction is responsible for the useful electrical characteristics of a semiconductor device ¾ Barrier potential : prevents further movement of charges ¾ Depletion region : ¾ External battery can be connected to the pn junction, by reverse-bias or forward bias. ¾ Reverse–biased Æ for application in photodiode ¾ Forward–biased Æ for application in laser diode Semiconductor physics - pn Junction ¾ 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 >= Wg, the electrons and holes will move into junction region, and recombine, which will create Photons. ¾ 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 = Wg , λ = hc / Wg Note: for direct bandgap material Semiconductor physics ¾ Direct band gap material: no change of wavevector Æ efficient For example: GaAs ¾ Indirect band gap material with change of wavevector - Direct and Indirect Band Gaps Light-Emitting Diodes - LED Structure ¾ To achieve high radiance, high quantum efficiency, carrier confinement and optical confinement are necessary. ¾ Structure: - homojunctions: same material (Wg) - single and double heterojunctions : difference bandgap materials ¾ The most effective structure: Double heterojunction (it could provide carrier and optical confinements.) ¾ Carrier (electron or hole ) confinement - bandgap difference of adjacent layer ¾ Optical confinement - index difference of adjacent layer ¾ Two basic LED configuration - Surface emitters - Edge emitters Put fig. 4-8 here ¾ Surface emitters /lambertian pattern ¾ Edge emitters unsymmetric radiation Parallel plane: Lambertian pattern Perpendicular plane: there is beam confinement (better coupling) Light-Emitting Diodes - Laser Source Materials ¾ III-V materials (Al, Ga, In Æ III group; P, As, Sb Æ V group ¾ Ternary and quaternary combinations - Ternary alloy Æ Ga1-xAlxAs, spectrum at 800 – 900 nm - Quaternary alloy Æ In1-xGaxAsyP1-y , spectrum at 1.0 – 1.7 μm - x, y Æ Lattice constant ¾ Spectrum, Æ full-width-half-maximum (FWHM) Light-Emitting Diodes - Laser Source Materials ¾ Relationship between energy E and frequency ν : E = hν = hc λ ( μm) = 1.240 E g (eV ) λ ¾ Relationship between lattice constant (x, y) and band-gap - For Ga1-xAlxAs : E g = 1.424 + 1.266 x + 0.266 x 2 (4 − 4) E g = 1.35 − 0.72 y + 0.12 y 2 (4 − 5) - For In1-xGaxAsyP1-y : Example 4-3 Consider a Ga1-xAlxAs laser with x=0.07. Find the diode emission wavelength. Example 4-4 Consider the alloy In1-xGaxAsyP1-y (i.e., x = 0.26 and y =0.57), find diode emission wavelength. Light-Emitting Diodes - Internal quantum efficiency rate equation ¾ When carrier injection stops, carrier density n = n0e−t /τ decays: ¾ For constant current flow into LED, an equilibrium condition will be established. dn J n = − dt qd τ Current injection J current density in A/cm2 q electron charge d thickness of recombination region ¾ Internal Quantum efficiency ηint : η int = τ Rr 1 = = Rr + Rnr 1 + τ r / τ nr τ r τ r = n / Rr 1 τ = 1 τr + τ nr = n / Rnr 1 τ nr Rr : radiative recombination rate equilibrium condition τr : radiative recombination lifetime n= Rnr : nonradiative recombination rate τnr nonradiative recombination lifetime ¾ Pint : internal optical power Thermal generation Pint = η int I hcI hν = η int q qλ Jτ qd 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 - External quantum efficiency External quantum efficiency n η ext 1 = 4π Incidental angle critical angle ∫ φc 0 T (φ )(2π sin φ ) d φ φ −1 φc = π / 2 − θc = sin (n2 / n1 ) Fresnel transmissivity for normal incidence T (0) = 4 n1 n 2 ( n1 + n 2 ) 2 Emitted power Example 4-6 Assuming a typical value of n=3.5 for refractive index of an LED material, calculate the ηext . For n1=n, n2=1 η ext ≈ 1 n ( n + 1) 2 Pext = η ext Pint = Pint n ( n + 1) 2 Light-Emitting Diodes - Modulation Modulated output power P (ω ) = P0 1 + (ωτ i ) 2 (4.18) P0 power emitted at DC ω modulation frequency τi carrier lifetime P (ω3dB ) 1 = P ( 0) 2 • Optical 3-dB modulation bandwidth : • Detected current is linearly proportional to optical power : • Detected electric power : • 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. f 3− dB (electrical ) = p (ω ) = I 2 (ω ) R 1 f 3− dB (optical ) = 0.707 f 3− dB (optical ) 2 P (ω ) I (ω ) = P (0) I (0) Laser Diodes - Principles ¾ Types of Laser : lasing medium Æ gas, liquid, solid state (crystal), semiconductor. ¾ Laser action is the result of 3 key process: photon absorption, spontaneous emission, and stimulated emission. ¾ Photon absorption: When a photon of energy hν12 impinges on the system, an electron in ground state E1 can absorb the photon energy and be excited to state E2. ¾ Spontaneous emission : The electron in state E2 falls down to state E1 by itself quite spontaneously, and emits a photon of energy hν12 in random direction. ¾ Stimulated emission : The electron in state E2 falls down to state E1, induced by a coming photon of energy of hν12, and emits a photon of energy hν12 in the same direction. Laser Diodes - Principles ¾ In thermal equilibrium : The density of exited electron is very small ¾ Population inversion : Population of excited states > that of the ground state Æ stimulated emission will exceed absorption ¾ Pumping techniques : Æ 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 ¾ 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 ¾Modes: 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 Amplitude condition I ( z , t ) = I ( z )e j (ω t − β z ) I ( 2 L ) = I ( 0) Ra Rb e 2 L ( Γg ( hν ) −α ( hν )) = 1 I(z) optical field intensity ω optical radian frequency β propagation constant with Γg th = α + I ( z ) = I (0)e[ Γg ( hν ) −α ( hν )] z cavity threshold gain Γ optical confinement factor g gain coefficient depended on optical frequency α effective material absorption coefficient 1 1 ln( ) = α + α end Ra Rb 2L cavity cavi Material mirr loss loss Phase condition Fabry-Perot laser cavity Reflecting mirror e− j 2β L = 1 Decided by laser cavity dimension ! Ra Rb Amplitude during one round trip I ( 2 L ) = I (0) Ra Rb e Gain medium n1 n2 z 0 Amplitude condition Phase condition L 2 L ( Γg ( hν ) −α ( hν )) Ra Rb mirror Fresnel reflection n1 − n2 2 coefficients R=( n1 + n2 ) Laser condition: Laser occurs when the gain is sufficient to exceed the optical loss during one round trip I ( 2 L ) = I ( 0) Laser Diodes - Threshold conditions -2 Example 4-7 For GaAs, R1=R2=0.32 for uncoated facets (i.e. 32% of the radiation is −1 reflected at a facet) and α 10cm −1 . This yields Γg th = 33cm for a laser diode of length L = 500μm . Optical power vs. drive current Threshold current density g th = β J th Jth Threshold current density gth Threshold gain β constant depended on device construction J th = I th / A - spontaneous radiation below threshold - threshold current Ith Threshold current A Area Laser Diodes - Rate equation -1 ¾ Relationship between optical power and drive current can be determined by two rate equations: ¾ For photon density Φ ; For electron density n 1 1 rate equation for photon density ≥ = n n Cn − ≥0 th C τ ph τ ph dΦ Φ = CnΦ + Rsp − dΦ Electron density τ ph dt ≥0 stimulated emission spontaneous emission photon loss dt with Rsp → 0 Φ : photon density Photon density should be C coefficient for optical absorption and emission interactions in increasing mode towards lasing with negligible Rsp rate of spontaneous emission into lasing mode spontaneous emission τph photon lifetime rate equation for electron density dn J n = − − CnΦ dt qd τ sp injection spontaneous recombination stimulated emission injection current density τsp spontaneous recombination lifetime J dn =0 dt with Φ = 0 n = nth must exceed a threshold value in order for photon density to increase n th τ sp = J th qd If electron density is at threshold level, injected electrons are just fully consumed by spontaneous recombination without light emission Laser Diodes - Rate equation -2 Steady-state solution for rate equations Φ dΦ = Cnth Φ s + Rsp − s = 0 τ ph dt + dn J nth n th J th = − − Cnth Φ s = 0 = dt qd τ sp Φs steady-state photon density τ sp qd Φs = τ ph qd ( J − J th ) + τ ph Rsp Photons resulting from stimulated emission Spontaneously generated photons Laser Diodes - External quantum efficiency External quantum efficiency ηext is defined as the number of photons emitted per radiative electron-hole pair recombination above threshold. External quantum efficiency ηext = ηi (1 − α g th ) (4.37) ηi internal quantum efficiency ~ 0.6-0.7 at room temperature gth gain coefficient at threshold Achieved experimentally η ext = q dP dP ( mW ) = 0.8065λ ( μm) E g dI dI ( mA) Εg band-gap energy λ emitted wavlength Laser Diodes - Resonant frequencies Phase condition for lasing e − j 2β L =1 ν =m 2β L = c 2n1 L c Δν = 2n1 L 2πν n1L = 2mπ c Optical resonant frequencies (or longitudinal modes) or Δλ = λ2 2n1 L 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 ) = g ( 0) e − ( λ − λ0 ) 2 2σ 2 g(0) maximum gain proportional to population inversion λ0 wavelength at the spectrum center σ spectral width of the gain Example, 4-12 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 = 2 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 2 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 = 2ne Λ k n1 n2 Anti-reflection coating k ne Λ order of the grating effective refrative index of the mode period of corrugation λ = λB ± λB 1 (m + ) 2ne Le 2 Laser Diodes - Modulation ¾ Internal (direct, current) modulation ; External modulation ¾ Modulate the laser above the threshold - Spontaneous radiative lifetime τsp ~ 1 ns - Stimulated carrier lifetime τst ~ 10 ps - photon lifetime τph ~ 2 ps Æ sets the upper limit to the direct modulation capacity ¾ Modulation frequency also can not be larger than the frequency of the relaxation of laser field f f = Laser injection current P 1 2π 1 τ spτ ph I −1 I th Laser output power IB Ip+ IB 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 0.32 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, 4-12 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 t throughout 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 Jth can to a good approximation be related to the lasing-threshold optical gain gth by gth = β Jth, where β is a constant that depends on the specific device construction. Consider a GaAs laser with an optical cavity of length 250 μ m and width 100 μ m . At the normal operating temperature, the gain factor β = 21x10-3 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 Ith. 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 ?