Optical transitions Handout

Optical transitions Handout - University of California,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor Optical transitions Handout.fm Optical Transitions (reading in supplementary references: Singh, Pankove) Fermi’s Golden Rule For the interaction of an electron with the electromagnetic field, the perturbation Hamilto- nian is given by the electric dipole operator: We are interested in inter-band transitions in semiconductors. The wavefunctions are Bloch functions: For the electromagnetic field, we take a uniform plane wave: (Note that k is the wavevector for the electron and k r is the wavevector for the electromag- netic field.) For transitions from valence conduction band: f i h ω fi optical absorption if S 2 π h ------ H 2 δ E f E i h ω () = H efr E i ⟨⟩ = Ψ k r 1 N ------- U k r e ik r = H cv e N --- U c r e ik c r rE 1 e r r U v r e v r r 3 d crystal = eU c r 1 U v r r 3 d cell 1 N e v k c k r + R
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
- 150 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor where is a lattice vector in the crystal. This expression leads to conservation of momen- tum: . However, note the difference in magnitude between the photon and electron wavevectors: We see that the photon momentum is negligible so we will neglect it. Then the conservation of momentum rule becomes: We refer to such a transition as a “direct transition”. Such a transition is vertical in a reduced zone picture.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/01/2008 for the course EE 230 taught by Professor Bokor during the Spring '08 term at University of California, Berkeley.

Page1 / 8

Optical transitions Handout - University of California,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online