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Absorption coefficient for interband transition

calculation of absorption coefficient for bulk and quantum well for interband transition

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Absorption coefficient for interband transition

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  1. Course: Quantum Electronics Arpan Deyasi Quantum Electronics Absorption Coefficient of Bulk Semiconductor and Quantum Well for Interband Transition Arpan Deyasi Arpan Deyasi, RCCIIT 5/11/2021 1

  2. Optical Absorption in Semiconductor Arpan Deyasi E.M wave incident on a solid material undergoes Quantum 1. partially reflection at vacuum 2. partially absorbed by the solid itself Electronics 5/11/2021 Arpan Deyasi, RCCIIT 2

  3. Absorption process in bulk semiconductor Arpan Deyasi Band-to-Band: Electron in V.B band absorbs a photon with enough energy to be excited to the C.B, leaving a hole behind Quantum Electronics 5/11/2021 Arpan Deyasi, RCCIIT 3

  4. Absorption process in bulk semiconductor Arpan Deyasi Band-to-Exciton: Electron in V.B absorbs almost enough energy to be excited to the C.B. The electron and hole it leaves behind remain electrically "bound" together, much like the electron and proton of a hydrogen atom. Quantum Electronics 5/11/2021 Arpan Deyasi, RCCIIT 4

  5. Absorption process in bulk semiconductor Arpan Deyasi Band-to-Impurity/Impurity to Band: Electron absorbs a photon that excites it from the V.B to an empty impurity atom, or from an occupied impurity atom to the C.B. Quantum Electronics 5/11/2021 Arpan Deyasi, RCCIIT 5

  6. Absorption process in bulk semiconductor Arpan Deyasi Free carrier: Electron in C.B., or hole in V. B., absorbs a photon and is excited to a higher energy level within the same set of bands (i.e, conduction or valence) Quantum Electronics 5/11/2021 Arpan Deyasi, RCCIIT 6

  7. Absorption process in quantum well Arpan Deyasi Intra-band: Transitions can occur only between even and odd index levels and are only operative for light polarized parallel to the direction of quantization. Quantum Electronics 5/11/2021 Arpan Deyasi, RCCIIT 7

  8. Absorption process in quantum well Arpan Deyasi Inter-band: conduction and valence bands, or between different valence bands (light-hole, heavy-hole,and spin-off). Quantum Inter-band transitions can occur between Electronics 5/11/2021 Arpan Deyasi, RCCIIT 8

  9. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi In bulk semiconductor, Quantum ( ) dz dI z Electronics = − ( ) ( ) I z   absorption coefficient 5/11/2021 Arpan Deyasi, RCCIIT 9

  10. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi Rate of energy absorption Quantum = − d dt d dt . ( ) AdI z Electronics  =   . ( ). . ( ) AI z dz A: cross-section of the semiconductor 5/11/2021 Arpan Deyasi, RCCIIT 10

  11. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi Energy absorption is also defined as Quantum  d dt Electronics =  t . T → v c total transition probability from valence to conduction band 5/11/2021 Arpan Deyasi, RCCIIT 11

  12. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi . ( ). . ( ) AI z dz Quantum   =  t . T → v c Electronics  t . T   = → ( ) v c . ( ). AI z dz 5/11/2021 Arpan Deyasi, RCCIIT 12

  13. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi For propagation of sinusoidal electromagnetic wave Quantum   2 . ( ) 2  rn Electronics 2 =  ( ) I z 0 c 0 Λ0: amplitude of e.m wave nr: real part of refractive index 5/11/2021 Arpan Deyasi, RCCIIT 13

  14. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi    t 2 . . . ( ). r n  . c T Quantum   = → ( ) 0 v c 2  2 . . Adz 0 Electronics   t 2 .  . . . ( ). r n  . c T   = → ( ) 0 2 v  c 2 V 0 2 t 2 . T   = → ( ) v c 2 . . . . ( ). cn    V 0 0 r 5/11/2021 Arpan Deyasi, RCCIIT 14

  15. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi Transition probability of an electron from valence band to conduction band Quantum  2 2 c Electronics →=   . (  − −  ) T k H k E E v c v k k c v After calculating Hamiltonian  2 q m 2 →=  . (  − −  2 ) T M E E 0 v c k k * 2 c v 0 5/11/2021 Arpan Deyasi, RCCIIT 15

  16. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi M: transfer of momentum from valence band to conduction band Quantum Total transition probability Electronics  →= − t kv FD kc FD 2 (1 ) T f f v c c v Factor ‘2’ included for Pauli’s spin degeneracy 5/11/2021 Arpan Deyasi, RCCIIT 16

  17. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi Quantum 2 q V   2 →=   − −  2 3 t ( ) T M E E d k 0 v c k k 2 2 8 m c v 0 Electronics 3/2       * 2 2 q V  m 2 =    − 2 t .2 T M E r → 0 v c g 2 2 2 8 m 0 5/11/2021 Arpan Deyasi, RCCIIT 17

  18. Absorption Coefficient in Bulk Semiconductor for Interband Transition Arpan Deyasi 3/2       *  Quantum 2 2 1  q m 2   =   − 2 ( ) . M E r 0 g 2 2 2 . . . cn m 0 0 r Electronics α E 5/11/2021 Arpan Deyasi, RCCIIT 18

  19. Absorption Coefficient in Quantum Well for Interband Transition Arpan Deyasi For 2D system, reduced DoS has to be considered Quantum 3/2    Electronics    * 1  2 m  − E r g 2 2 2 * m  r m n  −  ( ) g g E v c nm  2 L , m n 5/11/2021 Arpan Deyasi, RCCIIT 19

  20. Absorption Coefficient in Quantum Well for Interband Transition Arpan Deyasi Quantum n m = + + E E E E nm g c v <gvm|gcn>: overlap integral between envelope functions of C.B and V.B Electronics L: width of quantum well 5/11/2021 Arpan Deyasi, RCCIIT 20

  21. Absorption Coefficient in Quantum Well for Interband Transition Arpan Deyasi ( ) Quantum * 2 2 . . q N m M   Electronics =  −   ( ) E r nm  2 2 . . . . . cn  Lm 0 0 r Nω: no. of quantum well 5/11/2021 Arpan Deyasi, RCCIIT 21

  22. Absorption Coefficient in Quantum Well for Interband Transition Arpan Deyasi Define oscillator strength Quantum 2 2 m  M = f vc 0 Electronics * 2 . . q N m    =  −   ( ) ( ) f E r vc nm 4 . . . . . cn  Lm , m n 0 0 r 5/11/2021 Arpan Deyasi, RCCIIT 22

  23. References Arpan Deyasi O.Manaresh, “Semiconductor Heterojunctions and Nanostructures”, MH Quantum https://ocw.mit.edu/courses/electrical-engineering-and-computer- science/6-772-compound-semiconductor-devices-spring-2003/lecture- notes/Lecture15.pdf Electronics 5/11/2021 Arpan Deyasi, RCCIIT 23

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