Semiconductor lasers and LEDs read Agrawal pp

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1 Semiconductor lasers and LEDs read Agrawal pp Objectives, understand the following: Stimulated emission, spontaneous emission, and absorption in semiconductors Design of an LED and laser diode: injection mechanism, optical cavity, waveguide, electron & hole confinement, and materials Efficiency and modulation response of LEDs Efficiency, threshold, modulation response and relative intensity noise of laser diodes important semiconductor laser cavity designs for narrow linewidth or tuning (WDM sources)

2 Fundamental emission and absorption processes in a 2-level system. Where does optical gain come from? E 2 E 2 E 2 In Out E 1 E 1 E 1 (a) Absorption (b) Spontaneous emission (c) Stimulated emission Absorption, spontaneous (random photon) emission and stimulated emission. Uses in semiconductor optoelectronic devices: Absorption: detectors and modulators Spon. Emis.: light emitting diode (LED), incoherent light Stim. Emis. (source of optical gain): laser diode (LD, coherent light), semiconductor optical amplifier (SOA), and superluminescent diode (SLD)

3 What does the energy level system look like in a semiconductor? Many levels: energy bands called the conduction (CB) and valence bands (VB). Energy CB Optical gain E Fn E Fp E Fn Electrons in CB ev 0 E Fp VB Holes in VB = Empty states E g Optical absorption At T > 0 At T = 0 Density of states (a) (a) The density of states and energy distribution of electrons and holes in the conduction and valence bands respectively at T 0 in the SCL under forward bias such that E Fn E Fp > E g. Holes in the VB are empty states. (b) Gain vs. photon energy. (b)

4 Equations for spontaneous emission, stimulated emission and (stimulated) absorption rates in semiconductors (Agrawal, pp ) R spon ω ()= AE 1,E 2 ( )f c ( E 2 )1 [ f v ( E 1 )]ρ cv de 2 AE ( 1,E 2 )= Einstein spontaneous emission coefficient f c ( E 2 )= probability of an electron in the CB at E2 [ 1 f v ( E 1 )]= probability of a hole in the VB at E1 ρ cv = joint density of (electronic) states R stim ω ()= BE 1, E 2 ( )f c ( E 2 )1 [ f v ( E 1 )]ρ cv ρ em de 2 BE ( 1, E 2 )= Einstein stimulated emission coefficient f c ( E 2 )= probability of an electron in the CB at E2 [ 1 f v ( E 1 )]= probability of a hole in the VB at E1 R abs ω ρ cv = joint density of (electronic) states ρ em = the spectral density (Planck's blackbody formula) ()= BE 1, E 2 ( )f v ( E 1 )1 [ f c ( E 2 )]ρ cv ρ em de 2 BE ( 1, E 2 )= Einstein stimulated emission coefficient ( ρ cv = 2m r) 32 ( h ω E g ) 2π 2 h 3 m r = m c m v /( m c + m v )= reduced mass m c = electron effective mass in the CB m v = hole effective mass in the VB Fermi - Dirac Distribution function (probabilities) { [( ) k B T] } 1 [( ) k B T] f c ( E 2 )= 1+ exp E 2 E fc { } 1 f v ( E 1 )= 1+ exp E 1 E fv E fc = quasi Fermi level in the CB E fv = quasi Fermi leve in the VB ρ em = 8πhν 3 c 3 exp( hν k B T) 1 f v ( E 1 )= probability of an electron in the VB at E1 [ 1 f c ( E 2 )]= probability of a hole (empty state) in the CB at E2 ρ cv = joint density of (electronic) states ρ em = the spectral density (Planck's blackbody formula)

5 The population inversion condition in semiconductors Energy CB Optical gain R stim > R abs (this yields optical gain) E Fn E Fp ev E Fn Electrons in CB 0 results in : E Fp VB Holes in VB = Empty states E g At T > 0 E fc E fv > E 2 E At T 1 > E = 0 g Optical absorption Density of states (a) (a) The density of states and energy distribution of electrons and holes in the conduction and valence bands respectively at T 0 in the SCL under forward bias such that E Fn E Fp > E g. Holes in the VB are empty states. (b) Gain vs. photon energy. Note that at equilibrium in a semiconductor that E fc = E fv. We need to pump energy into the semiconductor from an external source. The most compact and efficient way of doing this is to inject current from a forward biased p-n junction. (b)

6 The p-n homojunction: injection mechanism for sustaining population inversion (we ve got gain) p + Junction n + E Fp E g Holes in VB Electrons ev o Electrons in CB E Fn E g p + Inversion region n + ev E Fn E Fp (a) (b) The energy band diagram of a degenerately doped p-n with no bias. (b) Band diagram with a sufficiently large forward bias to cause population inversion and hence stimulated emission. Next, we need Degenerate doping in GaAs is N I > mid cm -3 The diode equation: I = I S [exp(qv/nk B T)-1] V feedback and an optical waveguide to construct the LD

7 To convert an amplifier to an oscillator feedback is needed The Fabry-Perot Resonator Optical Gain Relative intensity (a) Doppler broadening (c ) ο δ m Allowed Oscillations (Cavity Modes) m(/2) = L L (b) δ m Mirror Stationary EM oscillations Mirror (a) Optical gain vs. wavelength characteristics (called the optical gain curve) of the lasing medium. (b) Allowed modes and their wavelengths due to stationary EM waves within the optical cavity. (c) The output spectrum (relative intensity vs. wavelength) is determined by satisfying (a) and (b) simultaneously, assuming no cavity losses.

8 Cleaved crystal facets for mirrors! Cleaved surface mirror p + n + Current L L GaAs GaAs Electrode Electrode Active region (stimulated emission region) This is a vintage 1970 s LD with cleaved mirrors forming a Fabry Perot Resonator and a p-n homojunction for injection. However, there is a problem with this optical and electrical confinement in this cavity design. A schematic illustration of a GaAs homojunction laser diode. The cleaved surfaces act as reflecting mirrors.

9 The separate confinement heterostructure (SCH) improved electron, hole, and optical confinement Refractive index Photon density (a) (b) (c ) (d) Electrons in CB 2 ev n AlGaAs p GaAs (~0.1 µm) Active region 1.4 ev Holes in VB p AlGaAs n ~ 5% 2 ev (a) A double heterostructure diode has two junctions which are between two different bandgap semiconductors (GaAs and AlGaAs). (b) Simplified energy band diagram under a large forward bias. Lasing recombination takes place in the p- GaAs layer, the active layer (c) Higher bandgap materials have a lower refractive index (d) AlGaAs layers provide lateral optical confinement.

10 Light-Current Curve and Spectrum of an LD Optical Power Optical Power Laser Optical Power LED Stimulated emission Spontaneous emission Optical Power Laser 0 I th I Typical output optical power vs. diode current (I) characteristics and the corresponding output spectrum of a laser diode.

11 Material Choices for LEDs and LDs 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 Infrared 1.7 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 nm is dominated by InGaAsP/InP materials 850 nm is based on the GaAs/AlGaAs system

12 E g (ev) GaP Quaternary alloys with indirect bandgap GaAs In 1-x Ga x As In Ga As InP Direct bandgap Indirect bandgap Quaternary alloys with direct bandgap InAs Lattice constant, a (nm) X It is very desirable that the various materials used to fabricate an LD be lattice-matched. That is have the same lattice constant. Bandgap energy E g and lattice constant a for various III-V alloys of GaP, GaAs, InP and InAs. A line represents a ternary alloy formed with compounds from the end points of the line. Solid lines are for direct bandgap alloys whereas dashed lines for indirect bandgap alloys. Regions between lines represent quaternary alloys. The line from X to InP represents quaternary alloys In 1-x Ga x As 1-y P y made from In Ga As and InP which are lattice matched to InP.

13 Indirect vs. direct bandgap semiconductors E E E Direct Bandgap E g CB Photon CB Indirect Bandgap, E g k cb E r CB Phonon k VB k k VB k vb k k VB k (a) GaAs (b) Si (c) Si with a recombination center (a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs is therefore a direct bandgap semiconductor. (b) In Si, the minimum of the CB is displaced from the maximum of the VB and Si is an indirect bandgap semiconductor. (c) Recombination of an electron and a hole in Si involves a recombination center. Direct bandgap semiconductors have much stronger optical transitions (stimulated emission) than indirect gap materials

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