2. Quantum Well Lasers Christopher P. Heagney Jason Yoo

3. Objectives What exactly is a LASER? Three types of electron/photon interactions Background information Basic Physics of Lasing Active Region Quantum Effects Quantum Cascade Lasers Threshold Current Calculations

4. “LASER”L ight A mplification by the S timulated E mission of R adiation

5. Electron/Photon Interactions Absorption Spontaneous Emission Stimulated Emission

6. Laser Animation

7. History 1958 - Arthur L. Schalow and Charles H. Townes invent the laser and publish a paper title “Infared and Optical Masers” 1961 - First continuous operation of an optically pumped solid state laser 1963 - Quantum well laser first suggested by H.Kroemer from the U.S. and Kazrinov and Alferov from the Soviet Union. 1975 - First quantum well laser operation made by J.P. Van der Ziel, R, Dingle, R.C Miller, W. Wiegmann, and W.A. Nordland, Jr. 1977 - R.D. Dupuis, P.D. Dapkus, N. Holonyak submitted paper demonstrating first quantum well injection laser 1994 - Quantum cascade lasers first developed

8. Main requirements for Lasing Initial Photons Population Inversion Threshold Current

9. Semiconductor Laser

10. Interband Lasing Concept

11. Intersubband Lasing Concept

12. Threshold Gain Concept Гg th ≡ mode gain required for lasing α i ≡ internal mode loss Г o e (Г g th -α i )L * Г b e (Г g th -α i )L = I g th = (Г -1 )[α i + (2L) -1 * ln (R o R b ) -1 ]

13. Quantum Cascade Laser

15. Spikes shown are the energy levels that correspond to tunneling phenomena. Illustrates Transmission Probability as Electron Energy increases. Clearly visible are the valence and conduction bands as well as a vivid drop in transmission through the energy gap.

16. Quantized Electron and Hole States in a quantum box. k x and k y are in-plave wave vectors

17. Problem J th (QC) = [e/  21 ][d z /(N p  z )][(  m +  I )/(  in  -  1 )] + [e/(  in  -  1 )  BG exp(-  /(kT))  =  2 +  1 + (  2  1 )/  ’ 21  21 = ( 2 /4  2  r 2 )(A 21 /  v)

18. Problem e = electron charge  21 = stimulated emission cross section d z = first active well width N p = number of cascade stages  z = transverse optical confinement factor  m = mirror loss  i = internal mode loss  in = injection efficiency into upper laser level  1 = lifetime of C1 state  ’ 21 = total relaxation time between C2 and C1  BG = doping sheet density in the Bragg mirror  = thermal activation energy  r = mode-refractive index A 21 = Einstein’s coefficient for spontaneous emission from level E 2 to E 1

19. Assumptions d z = 4.5 nm N p = 25 cascade stages  z = 2.1 x 10 -3  m = 5.6 cm -1  i = 10 cm -1  1 = 0.6 ps  2 = 1.43 ps  ’ 21 = 1.8 ps  BG = 1.2 x 10 11 cm -2  r = 3.22 Electron Injection Efficency =.8 Problem And the answer is….

20. The Answer: 1