# Chapter 5a

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### Chapter 5a

1. 1. Chapter 5: Semiconductor Laser
2. 2. General Principles of Laser
3. 3. Resonant Cavity • A radio-frequency oscillator consists of an amplifier, a tuned circuit and a feedback mechanism. – The feedback connects the amplifier output to its input, causing the signal to increase as it periodically passes through the amplifier. – A steady state is reached when the system losses are exactly made up by the gain through the amplifier. – System losses constitute of power extracted from the oscillator as useful output & heating loss. – The tuned circuit determines the oscillation frequency.
4. 4. Optical resonant cavity • A laser is a Very-High-Frequency oscillator – Also refer to an optic oscillator • The laser consists of a cylindrically shaped medium with mirrors attached at each end. – The medium provides the amplification – Properties of the medium determine the output frequency and spectral width of the laser • Mirrors provide feedback for the light oscillator, reflecting the light back & forth through the amplification medium. • Power exits the laser through one of the mirrors, which is partially transmitting.
5. 5. Fig.A: A laser cavity consists of an amplifying medium and optical cavity
6. 6. Fabry-Perot resonator • The two mirrors form a cavity called Fabry-Perot resonator – In which two wave exist, one moving to the right and one moving to the left – The total field in the cavity is the sum of the two moving waves. – This results in the standing-wave pattern • To produce standing-wave pattern, the cavity must be an integral number of half wavelength long, that is L = ml/2. – where l is the wavelength as measured in the material within the cavity and m is a positive integer.
7. 7. Fig. B: Stationary Standing-wave pattern L = l/2 L = 2l/2 L = 3l/2 L = 4l/2 L = 4l/2
8. 8. Cavity resonant frequencies • Only wavelengths satisfying l=2L/m can exist inside the cavity in a steady state. – Any wave of another length interferes destructively with itself & attenuates very quickly – We say that the cavity is resonant at wavelength satisfying l=2L/m. • The resonant frequencies are found as f = mc/2nL • The longitudinal modes of the cavity is shown in Fig. C – The spacing between adjacent cavity longitudinal mode is D f = c/2nL
9. 9. Fig. C: Allowed modes and their frequency due to stationary EM waves within the optical cavity. f Allowed Oscillations (Cavity Modes) L Stationary EM oscillations MirrorMirror Dfc =c/2nL fm–1 fm fm+1 fm+2 …… fm+3
10. 10. Stimulated emission and photon amplification • An electron in an atom can be excited from an energy level E1 to a higher energy level E2 by the absorption of a photon energy hu= E2 – E1 • When an electron at a higher energy level transits down in energy to an unoccupied energy level, it emit a photon • There are two possibilities for the emission process 1. The electron undergo the downward transition by itself spontaneously 2. It can be induced to do so by another photon
11. 11. Spontaneous emission • The electron falls down in energy from level E2 to E1 – emits a photon of energy hu = E2–E1 in a random direction as shown in Fig.1 – A random photon is emitted • The transition is spontaneous provided that the state with energy E1 is not occupied • The emission process during the transition of electron from E2 to E1 can be thought of as if the electron is oscillating with a frequency u.
12. 12. E1 E2 hu (a) Absorption hu (b) Spontaneous emission hu (c) Stimulated emission In hu Out hu E2 E2 E1 E1 Absorption, spontaneous (random photon) emission and stimulated emission. © 1999 S.O. Kasap,Optoelectronics(Prentice Hall) Fig.1 : Stimulated emission and photon amplification
13. 13. Stimulated emission • An incoming photon of energy hu = E2 – E1 stimulates the whole emission process by inducing the electron at E2 to transit down to E1 as shown in Fig.1 – The emitted photon is in phase with the incoming photon – It is in the same direction, it has the same polarization and it has the same energy since hu = E2–E1
14. 14. Stimulated emission, cont • During stimulate emission, the E-field of incoming photon couples to the electron and drives it with the same frequency as the photon – The forced oscillation of the electron at a frequency u = (E2–E1)/h causes it to emit EM radiation whose E-field is in total phase with that of stimulating photon. – When the incoming photon leaves the site, the electron return to E1because it has emitted a photon of energy hu = E2–E1
15. 15. Population Inversion • Stimulated emission is the basis for obtaining photon amplification – since one incoming photon results in two outgoing photons which are in phase. – The incoming photon should not be absorbed by another atom at E1. • When we are considering a collection of atoms to amplify the light, we must have the majority of the atoms at the energy level E2 – When there are more atoms at E2 than at E1, we then have what is called a population inversion
16. 16. Optical pumping and stimulated emission • For three energy level system – An external excitation causes the atoms in this system to be excited to E3, which is called optical pumping – From E3, the atoms decay rapidly to an energy level E2 • The state E2 is a long-lived state – Since the atoms cannot decay rapidly from E2 to E1, they accumulate at this energy level causing a population inversion between E2 and E1 – When one atom at E2 decays spontaneously, it emits a photon which can go on to a neighboring atom and cause that to execute stimulated emission – The photons from the latter can go on to the next atom at E2 and cause that to emit by stimulated emission & so on. – The result is an avalanche effect of stimulated emission processes with all the photons in phase.
17. 17. E1 hu13 E2 Metastable state E1 E3 E2 hu32 E1 E3 E2 E1 E3 E2 hu21 hu21 Coherent photons OUT (a) (b) (c) (d) E3 The principle of the LASER. (a) Atoms in the ground state are pumped up to the energy levelE3 by incoming photons of energyhu13 = E3–E1. (b) Atoms at E3 rapidly decay to the metastable state at energy level E2 by emitting photons or emitting lattice vibrations;hu32 = E3–E2. (c) As the states atE2 are long-lived, they quickly become populated and there is a population inversion betweenE2 and E1. (d) A randomphoton (from a spontaneous decay) of energyhu21 = E2–E1 can initiate stimulated emission. Photons fromthis stimulated emission can themselves further stimulate emissions leading to an avalanche of stimulated emissions and coherent photons being emitted. © 1999 S.O. Kasap, Optoelectronics(Prentice Hall) IN Fig.2 : Principle of the LASER
18. 18. Light Amplification by Stimulated Emission of Radiation • At the end of the avalanche of stimulated emission processes, the atoms at E2 would have dropped to E1 – It can be pumped again to repeat the stimulated emission cycle again • The emission from E2 to E1 is called the lasing emission – The system we have just described for photon amplification is a LASER, an acronym for “Light Amplification by Stimulated Emission of Radiation”
19. 19. Fig 42-27, p.1386
20. 20. Upward transition rate • Consider a medium as in Fig 1 – N1 atoms per unit volume with energy E1 – N2 atoms per unit volume with energy E2 • The rate of upward transition from E1 to E2by photon absorption will be proportional to – The number of atoms N1 – The number of photon per unit volume with energy hu = E2–E1. Upward transition rate: R12 = B12 N1 r (hu) (1) where B12 is a proportionality constant (Einstein coefficient) r (hu) is the photon energy density per unit frequency which represents the number of photon per unit volume with an energy hu
21. 21. E1 E2 hu (a) Absorption hu (b) Spontaneous emission hu (c) Stimulated emission In hu Out hu E2 E2 E1 E1 Absorption, spontaneous (random photon) emission and stimulated emission. © 1999 S.O. Kasap,Optoelectronics(Prentice Hall) Fig.1 : Stimulated emission and photon amplification
22. 22. Downward transition rate • The rate of downward transitions from E2 to E1 involved spontaneous and stimulated emission depends on – The concentration of N2 of atoms at E2 – Both N2 and the photon concentration r (hu) with energy hu (= E2–E1) Downward transition rate: R21 = A21 N2 + B21 N2 r (hu) (2) – First term is due to spontaneous emission (no need photon to drive it) – Second term is due to stimulated emission which requires photons to drive it. where A21 & B12 are the Einstein coefficients for spontaneous and stimulated emission respectively
23. 23. Thermal Equilibrium • To find the coefficients A21 , B12 , B21 , we consider the medium in thermal equilibrium • There is no net change with time in the populations at E1 and E2 which means R12 = R21 (3) • In thermal equilibrium, Boltzmann statistics demands that (4) where kB is the Boltzmann constant & T is the absolute temperature • In thermal equilibrium, radiation from the atom must give rise to an equilibrium photon energy density that is given by Planck’s black body radiation distribution law, ( )         Tk EE N N B 12 1 2 exp ( ) )5( 1exp 8 3 3              Tk h c h h B eq u u ur
24. 24. Stimulated & spontaneous ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 12 21 3 3 21 21 221 221 21 21 33 21212112 absorp stim isabsorptionoemission tstimulatedofratiotheaddition,In 8spon stim emissionsspontaneoutostimulatedofratioheconsider tNow /8/and thatshowsit(5),toeqn(1)Fromlarger.muchisitfactineqn(5);by describednotiscourse,ofoperation,lasertheDuringts.coefficien Einsteinthedeterminetoconditionthisusingarewem;equilibriuin thermal onlyapplieseqn(5)inLawsPlanck'that theemphasizetoimportantisIt N N R R h h c A hB NA hNB R R chBABB h    ur u urur u ur
25. 25. Conclusion: stimulated emission • There are two important conclusion 1. For stimulated photon emission to exceed photon absorption, we need to achieve population inversion, that is N2 > N1. • According to Boltzmann statistics, N2 > N1 implies a negative absolute temperature • The laser principle is based on non-thermal equilibrium 2. For stimulated emission far exceed spontaneous emission, we must have a large photon concentration, which is achieved by building an optical cavity to contain the photons
26. 26. Fig 42-27, p.1386
27. 27. Principle of Laser Diode
28. 28. Principle of the Laser Diode • Consider a degenerately doped direct band gap semiconductor pn-junction whose band diagram is shown in Fig.3 – Degenerate doping means that the Fermi level EFp in the p-side is in the valence band (VB) and that EFn in the n-side is in the conduction band (CB) – All energy levels up to the Fermi level are occupied by electrons • Without applied voltage, the Fermi level is continuous across the diode, EFp= EFn. – The depletion region is very narrow – High potential energy barrier eVo (Vo is built-in voltage) that prevents electrons in the n+-side diffusing into the p+-side – Similar potential barrier also stop hole diffusion.
29. 29. p+ n+ EFn (a) Eg Ev Ec Ev Holes in VB Electrons in CB Junction Electrons Ec p+ Eg V n+ (b) EFn eV EFp The energy band diagramof a degenerately doped p-n with no bias. (b) Band diagramwith a sufficiently large forward bias to cause populationinversion and hence stimulated emission. Inversion region EFp Ec Ec eVo © 1999 S.O. Kasap,Optoelectronics(Prentice Hall) Fig.3 : Energy Band Diagram
30. 30. Forward bias • When a voltage is applied, the separation between EFp and EFn is due to electrical work done by the applied voltage, DEF=eV. • The applied voltage diminishes the built-in potential barrier to almost zero – Electrons flow into the Space Charge Layer (SCL) and flow over to p+-side to constitute diode current. – Holes flow from p+-side to n+-side.
31. 31. Active region: population inversion • From the energy band diagram with EFp – EFn = eV >Eg as shown in Fig.3, – there are more electrons in the CB at energies near Ec than electrons in the VB near Ev. – In other words, there is a population inversion between energies near Ec and those near Ev around the junction. • This population inversion region is a layer along the junction – It is called the inversion layer or the active region
32. 32. Stimulated emission & optical gain • An incoming photon with an energy of (Ec – Ev) cannot excite an electron from Ev to Ec as there are almost none near Ev – However, it stimulate an electron to fall down from Ec to Ev – The incoming photon stimulates direct recombination • The region where there is population inversion and hence more stimulated emission than absorption – The active region has an optical gain • The optical gain depends on – The photon energy as apparent by the energy distributions of electrons and holes in the CB and VB in the active layer.
33. 33. hu Eg Optical gain EFn  EFp Optical absorption 0 Energy Ec Ev CB VB (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 EFn  EFp > Eg. Holes in the VB are empty states. (b) Gain vs. photon energy. Density of states Electrons in CB Holes in VB = Empty states EFn EFp eV At T > 0 At T = 0 (a) (b) © 1999 S.O. Kasap,Optoelectronics(Prentice Hall) Fig.4: Density of state & optical gain
34. 34. Optical Gain for T=0K & T>0K • At T 0K, the states between Ec and EFn are filled with electrons and those between EFp and Ev are empty. – Photon with energy (Eg < hu < EFn – EFp) cause stimulated emission – whereas those photon with energy (EFn–EFp< hu) become absorbed • As T > 0K, the Fermi-Dirac function spreads the energy distribution of electrons in the CB to above EFn and holes below EFp in the VB – The result is a reduction in optical gain as shown in Fig.4 – The optical gain depends on EFn–EFp (which depends on the applied voltage and hence on the diode current)
35. 35. Injection Pumping • It is apparent that population inversion between energies near Ec and those near Ev is achieved – by the injection of carriers across the junction under a sufficiently large forward bias. • The pumping mechanism is therefore the forward diode current • The pumping energy is supplied by the external battery • This type of pumping is called injection pumping
36. 36. Optical Cavity • Optical cavity is also needed to implement a laser oscillator – to build up the intensity of stimulated emissions by means of an optical resonator – This would provide a continuous coherent radiation as output • Fig.5 shows schematically the structure of a homojunction laser diode – pn-junction with direct bandgap material like GaAs – The ends of the crystal are cleaved to be flat and optically polished to provide reflection and hence form optical cavity
37. 37. L Electrode Current GaAs GaAsn+ p+ Cleaved surface mirror Electrode Active region (stimulated emission region) A schematic illustration of a GaAs homojunction laser diode. The cleaved surfaces act as reflecting mirrors. L © 1999 S.O. Kasap,Optoelectronics(Prentice Hall) Fig.5 : Homojunction laser diode
38. 38. Mode of cavity • The photons are reflected from the cleaved surface stimulate more photons of the same frequency – This process builds up the intensity of the radiation in the cavity – The wavelength of the radiation is determined by the cavity length L because only multiple of the half-wavelength can exists m (l/2n) = L where m is an integer, n is the refractive index of the semiconductor and l is free space wavelength
39. 39. Resonant frequency m (l/2n) = L where l  c/u (u is laser frequency) • Each radiation satisfying the above relationship is essentially a resonant frequency of the cavity – that is a mode of the cavity – The separation between possible modes (allowed wavelength) of the cavity Dlm.
40. 40. Output spectrum of laser diode • The exact output spectrum from the laser diode depends on 1. The nature of optical cavity 2. The optical gain vs wavelength characteristic • dependant on the energy distribution of electrons in the CB and holes in the VB around the junction
41. 41. Diode current • Two critical diode current 1. Transparency current Itrans: • provides just sufficient injection to lead to stimulated emission just balancing absorption • Above Itrans, there is optical gain in the medium but output is not yet a continuous wave coherent radiation 2. Threshold current Ith: • the optical gain in the medium has overcome the photon losses from the cavity • Lasing radiation is only obtained above Ith
42. 42. Threshold current • Fig.6 shows the output light intensity as a function of diode current – Above Ith, the light intensity becomes coherent radiation consisting of cavity wavelength (or mode) and increases steeply with current – The number of modes in the output spectrum and their relative strengths depends on the diode current
43. 43. Typical output opticalpower vs. diode current ( I) characteristics and the corresponding output spectrum of a laser diode. l Laser l LaserOptical Power Optical Power I 0 l LEDOptical Power Ith Spontaneous emission Stimulated emission Optical Power © 1999 S.O. Kasap,Optoelectronics(Prentice Hall) Fig.6: Characteristics of laser output
44. 44. Threshold current of homojunction • The main problem of the homojunction laser diode is that the threshold current density Jth is too high for practical uses – For GaAs at room temperature, Jth the order of 500 Amm-2 – GaAs laser can only operates continuously at very low temperature. • The reduction of Ith to a practical value requires – Improvement in the rate of stimulated emission – Improving the efficiency of the optical cavity
45. 45. Reduction of the threshold current 1. Carrier confinement – Confine the injected electrons and holes to a narrow region around the junction – Less current is needed to establish the necessary concentration of carriers for population inversion 2. Photon confinement – Build a dielectric waveguide around the optical gain region to increase the photon concentration and the probability of stimulated emission – Can reduce the loss of photons traveling off the cavity axis