Photonic Devices. Light absorption and emission. Transitions between discrete states
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1 Light absorption and emission Photonic Devices Transitions between discrete states Transition rate determined by the two states: Fermi s golden rule Absorption and emission of a semiconductor Vertical transition (momentum conservation). Why? (Why the photon s momentum is negligible? See next page) Can we make decent light emitters (LEDs) based on band-to-band transitions from an indirect gap semiconductor (e.g. Si)? Can we make decent light detectors (photodiodes) from an indirect gap semiconductor? Why?
2
3 Compare the k of a photon to the dimension of the Brillouin zone:
4 (linear scale) (What if you just plot n & p on log scale for all x? See your (not equilibrium) Homework 2 results.) Strong field in depletion region sweeps electrons to n side, holes to p side. When dark, no photo-generation. p n (x n ) < equilibrium value (i.e. excess concentration < 0) because holes swept by increased field.
5 Forward biased Like an npn BJT with BC junction forward biased
6 I s qv kt I ( e 1) I p b V b
7 Is there band bending in the i region? Why?
8 (log scale)
9 Semiconductor optical amplifiers and lasers What do you already know about lasers? (How are lasers different from other light sources?)
10 For discrete levels Spontaneous emission Absorption Stimulated emission Spontaneous emission: Into all possible photon modes. How LEDs work. Stimulated emission: Duplicate the incoming photon. Amplification. Amplification + positive feedback oscillation The positive feedback and frequency selection mechanism: Optical cavity c 2L n n c n 2 L
11 2 2 2 E g = (h = 2 ) 1 1 1
12 E 2 and E 1 are related by the photon energy m r : the reduced effective mass of the e-h pair Density of states of conduction band e s; see Note #7 Joint density of states
13 E 2, E 1 E C E Fn Weak injection Probability of emission (e at E 2, and there s a hole at E 2 for it to fall into): E Fp E V Probability of absorption: Probability of net gain in number of photons:
14 The LED works by spontaneous emission. Spontaneous emission rate: (Emissions per time per volume per frequency interval) At equilibrium, Radiative recombination lifetime Joint density of states (per volume per frequency interval) Peak at E g + ½ k B T You can calculate the optical power emitted by a slab of semiconductor. At room temperature, a 2 micron layer of GaAs emits W/cm 2. You have to either heat it up (incandescence) or pump e-h pairs into it (electroluminescence). This and many other figures are adapted from Saleh & Teich, Fundamentals of Photonics
15 We are not interested in making incandescent light bulbs from semiconductors. Let s look at LEDs. T E 2, E 1 E Fn E Fp Compare to the equilibrium case: 0
16 LED weak injection: Equilibrium: 0 Peak at E g + ½ k B T Same peak, same width, enhanced by an exponential factor Compare with incandescence Photons can escape before getting absorbed. Therefore we consider f e, instead of net f e f a. Photons are emitted into all modes.
17 Now let s talk about semiconductor optical amplifiers and lasers Stimulated emission rate: (Emissions per time per volume per frequency interval) Absorption rate: (Photons absorbed per time per volume per frequency interval) Compare with the spontaneous emission rate: Incoming photon flux (photons per time per area per frequency interval) The origin of the 2 dependence: density of modes The photon density of modes is similar to the electron density of states D(E). The difference: E = 2 k 2 /(2m * ) for e s, E = h = c k for photons. Simply put, the larger the E, the more k states in an interval de. See Note #7 (Slide 25).
18 For spontaneous emission, photons are emitted into all modes. For stimulated emission, photons are emitted into the one mode of the incoming photon. For absorption, the absorbed photon is of a specific mode. Thus the modal density should be in the denominator Thus the 2 dependence.
19 A medium absorbs at equilibrium. If pumped, net gain is possible:
20 Notations used in figures: E fc E Fn E fv E Fp
21 A digression: net absorption at equilibrium Calculated absorption of GaAs
22 Notations used in figures: E fc E Fn E fv E Fp Net gain: amplification. To have net gain (for some frequencies), you must have E Fn E Fp > E g. (the population inversion in semiconductors) Amplification with positive feedback: oscillation
23
24 E fc E Fn E fv E Fp
25 The positive feedback and frequency selection mechanism: Optical cavity c 2L n n c n 2 L To have oscillation, you must have net gain (of the cavity, not just the medium). There are losses in the medium other than band-toband absorption, which is already accounted for in net medium gain ( ), or 0 ( ) in the right figure. Other losses include scattering and free carrier absorption in the medium, as well as transmission at cavity ends (reflection R < 1). You can prorate the transmission loss to the medium: Loss other than ab. ln(r R ) ( 1 2 ) loss L
26 You can prorate the transmission loss to the medium: ln(r R ) ( 1 2 ) loss L Loss other than bandto-band absorption L c n 2 The concept of hole burning. No spectral hole burning in semiconductors due to fast intra-band processes. But there s spatial hole burning.
27 Example: spectrum of an InGaAsP laser
28 Threshold behavior
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