Semiconductor laser fundamentals

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1 Semiconductor laser fundamentals Major disadvantages of LEDs: Too broad output beam r/rmax Energy, ev Too broad spectrum P opt time Too slow pulse response

2 Semiconductor laser fundamentals Laser definition involves two fundamental processes: light amplification and light emission In lasers, light amplification is achieved via stimulated emission. Stimulated emission had been proposed by Albert Einstein in 1915 but has been forgotten until 1950s

3 Absorption, Emission and Stimulated Emission In atoms or in semiconductor crystals, absorption of a photon will occur only when the quantum energy of the photon precisely matches the energy gap between the initial and final states. If there is no pair of energy states such that the photon energy can excite the electron from the lower to the upper state, then the matter will be transparent to that radiation.

4 Stimulated Emission As formulated by A. Einstein, if an electron is already in an excited state (an upper energy level, in contrast to its lowest possible level or "ground state"), then an incoming photon can "stimulate" a transition to that lower level, producing a second photon of the same energy.

5 Absorption Stimulated emission competition The rate of absorption = Number of electrons in the state 1 the probability to absorb the photon: AR = N 1 W ABS The rate of Stimulated emission = Number of electrons in the state 2 the probability to emit the photon: SER = N 2 W SE Normally, in solid states and in semiconductors, in equilibrium, N 1 > N 2 because E 1 < E 2 According to Einstein, W ABS = W SE It follows that in equilibrium or close to equilibrium, AR > SER; i.e. absorption dominates.

6 Population Inversion (PI): N 2 > N 1 is the key condition for the stimulated emission and the laser action Electrons will normally reside in the lowest available energy state. They can be elevated to excited states by absorption, but no significant collection of electrons can be accumulated by absorption alone since both spontaneous emission and stimulated emission will bring them back down. E 2, N 2 E 2 - E 1 = ω ω ω ω E 1, N 1 Rate a 12 ω ω Rate b 12 Absorption Spontaneous Emission Stimulated Emission The total emission rate is always greater than the absorption rate. Hence, the population inversion can never be achieved by absorbing the photons (with the same energy that the one to be emitted).

7 Population Inversion (PI) in Semiconductors E Conduction band Very few electrons E C No electrons (forbidden band) Majority of electrons Valence band E V n(e C ) << n(e V ) No PI

8 Electron energy distribution in semiconductors. The probability to find an electron with the energy E: f(e) 1/2 f ( E) = 1+ 1 E exp E kt F f(e F ) = ½ E v E F E c Fermi Energy Example: E C E F = 1 ev; kt = ev; f(e C ) = Under normal (quasi-equilibrium conditions) the free electron concentration must be increased by around 17 orders of magnitude to reach the PI condition

9 Electron and hole concentrations requirements for population inversion in semiconductors f n (E) f p (E) 1/2 f n (E C ) The PI condition: n(e C ) > n(e V ) N C f n (E C ) > N V f n (E V ) N C,, N V are the numbers of energy positions available. Assume N C = N V. f p (E C ) Then the PI condition is: f n (E C ) > f n (E V ) E v E F E c In the valence band, the absence of electron means the presence of the hole: f n (E V ) + f p (E V ) =1; f n (E V ) =1 - f p (E V ); Then the PI condition is: f n (E C ) > 1 - f p (E V ), or: f n (E C ) + f p (E V ) > 1

10 Electron and hole concentrations requirements for population inversion in semiconductors The Fermi energies for both electrons and holes must be positioned inside the conductance and valence bands correspondingly. In other words, both electron and hole concentrations must be very high simultaneously 1 fp ( E) = 1 EFp E fn ( E) = 1+ exp E E 1 exp Fn kt + kt f p (E V ) f p =1/2 E Fp f n (E C ) f n =1/2 E Fn E v E c The PI condition can be reformulated as E Fn E Fp > (E C -E V )

11 p Forward biased p-n junction is one way to approach the PI condition E F n P-n junction in equilibrium, n p = n i2 ; f n (E C ) + f p (E V ) <1 E F E Fn E Fp E F Forward biased p-n junction, n p >> n i2 ; f n (E C ) + f p (E V ) <1 E Fn Forward biased heavily doped p-n junction, n p >> n i2 ; f n (E C ) + f p (E V ) >1 E Fp In the first semiconductor lasers, the PI has been achieved in a heavily doped forward biased p-n junctions. The pumping current was too high to operate at room temperature in CW-mode

12 Quantum well heterostructure laser allows to achieving the PI at much lower pumping currents Zero bias Forward bias

13 Quantum well heterostructure laser

14 Laser gain If the PI condition is met, the intensity of stimulated emission I(x) increases the the optical beam propagates along the p-n junction plane: I( x) = I( 0) e γ x x=0 is the coordinate corresponding to one of the sample facets and x is the position inside the sample along the junction plane. γ is the laser gain

15 I(x) Laser gain and loss I( x) = I( 0) e α x Regular semiconductor material α is the absorption coefficient I(x) I( x) = I( 0) e γ x Laser γ is the gain In practical lasers, the are regions with the gain (PI) and with absorption. We can say that the gain can be positive (the actual gain) or negative (the absorption) The net laser gain is the difference between the gain in the PI region and the absorption in the rest of the laser

16 Self-sustainable laser emission The stimulated emission must be initiated by the incoming photon. After all the photons have passed through the semiconductor sample the emission is over. Laser Feedback output Amplifier Lasing can be achieved by redirecting a portion of the out coming photons back to the input

17 Cleaved facets as a Fabri-Perot etalon in heterolasers The power reflection coefficient for the mirror is R Wave amplitude reflection coefficient is R 1/2

18 Waveguide structure of hetero-lasers

19 Laser Fabri-Perot resonator

20 Laser Fabri-Perot resonator amplitude balance L Light output (5):R P 1 2 R 1 P 1 e 2γL RP 1 (1): P 1 (4): R 2 R 1 P 1 e γl R 1 RP (2): 1 (3:) P 1 (R 1 P 1 )e γl R 1 P 1 R 2 Light output The mirror power reflection factor R = n n where n is the refraction index. In GaAs, n 3.5 and R Optical power change after a full roundtrip is R 1 R 2 exp(2γl) (γ is the net gain of the entire laser structure). The condition for continuous emission is: R 1 R 2 exp(2γl)= 1, or: 1 1 γ L= ln 2 R 1 R 2 lasing condition (Fabri-Perot laser equation) α m 1 1 = ln 2L γ = α R1R2 is called the mirror loss. Then, the lasing condition: m

21 Laser Fabri-Perot resonator phase balance Under the equilibrium lasing condition, the electromagnetic wave phase should remain unaltered after a round trip (the path is 2L). Otherwise the wave superposition will decrease the beam intensity. n λ = 2L n r n r is the semiconductor refractive index; n is any integer

22 Example Find the value of the integer n for operation at 1.4 µm, assuming n r =3.5, L=250 µm. n 1250 Laser mode separation: Find λ for the above example. λ ~ 1 nm.

23 Carrier and light intensity distribution in the transverse direction 2 Loss Gain Loss Light confinement n-type Active GaAs region Al 0.3 Ga 0.7 As p-type Al 0.3 Ga 0.7 As Distance (µm)

24 Electrical and optical confinement in heterostructure lasers GaAs/AlGaAs QWs

25 Optical gain as a function of injected carrier concentration Pumping current Gain > Loss; lasing Loss Gain < Loss; no lasing The Gain must be greater or equal to the total loss in the cavity for the lasing. The loss comes from the cavity loss outside the QW and from the leak through the mirrors

26 Laser threshold current Loss Threshold current density: j = q d n /τ th th e Threshold current: I = q L W d n /τ th th e d - the active layer thickness, L and W - the resonator length and width n th - the threshold electron-hole density corresponding to Gain = Loss τ e - the electron-hole recombination time.

27 Steady-state Photon Number The net photon population is controlled by three processes : (a) the generation by stimulated emission, (b) the absorption through various other processes, e.g., free-carrier absorption, interface scattering, inter-valence band absorption and (d) the spontaneous emission. The laser rate equation shows the photon balance N t Ph = GN α N + R Ph Ph sp where N ph is the total number of photons in the cavity. GN ph is the rate of photon generation through stimulated emission αn ph is the rate of photon decay through absorption and end-surface loss, R sp is the rate of spontaneous emission. In the absence of spontaneous recombination (R sp = 0), the lasing will not initiate: for N Ph (0)=0 YdN/dt = 0 R sp N The steady-state number of photons Ph = G α

28 Output Optical Power When the laser current exceeds the threshold, all the additionally supplied e-h pairs convert their energy into stimulated emission. Therefore, the internal optical power (no light is leaking through the mirrors) is: P = η E int i ph where η i is the internal quantum efficiency and E ph is the photon energy A fraction of the power is coupled out through the mirrors (cleaved facets). The OUTPUT power for identical mirrors: P I I E th α = η m q α + α out i ph r I m q I th where α r is the loss in the resonator and α m is the mirror loss; for R 1 = R 2 : α m 1 1 = ln L R

29 Photon life time and laser modulation speed The photon lifetime in lasers τ p, is the time the photon spends in the resonator before being emitted or absorbed. Typically, τ p 4 10 single-path travel times (2..5 roundtrip times). Photon life time estimate: t tr1 = L / v 0 ; L = 100 µm = 1E-4 m; v 0 = 3E8/n r m/s; n r 2.5 Single path travel time: t tr1 = 0.75 E-12 s = 0.75 ps; t ph = 4 10 t tr1 = ps => very fast modulation is possible

30 Laser emission spectrum Just below the threshold Above the threshold 5mW)

31 Laser LED spectrum comparison Power density Wavelength, um 1.52 um LED Above the threshold (@ 5mW)