page_title: Quantum-confined Stark effect
section_title: Absorption coefficient
hierarchical_section_title: Quantum-confined Stark effect / Theoretical description / Absorption coefficient
caption_attribution_description: English: Stark effect absorption coefficient simulations Ge/SiGe QWs
context_page_description: The quantum-confined Stark effect describes the effect of an external electric field upon the light absorption spectrum or emission spectrum of a quantum well. In the absence of an external electric field, electrons and holes within the quantum well may only occupy states within a discrete set of energy subbands. Only a discrete set of frequencies of light may be absorbed or emitted by the system. When an external electric field is applied, the electron states shift to lower energies, while the hole states shift to higher energies. This reduces the permitted light absorption or emission frequencies. Additionally, the external electric field shifts electrons and holes to opposite sides of the well, decreasing the overlap integral, which in turn reduces the recombination efficiency of the system.
  The spatial separation between the electrons and holes is limited by the presence of the potential barriers around the quantum well, meaning that excitons are able to exist in the system even under the influence of an electric field. The quantum-confined Stark effect is used in QCSE optical modulators, which allow optical communications signals to be switched on and off rapidly.
context_section_description: Additionally to the redshift towards lower energies of the optical transitions, the DC electric field also induces a decrease in magnitude of the absorption coefficient, as it decreases the overlapping integrals of relating valence and conduction band wave functions. Given the approximations made so far and the absence of any applied electric field along z, the overlapping integral for  transitions will be: 
  .
  To calculate how this integral is modified by the quantum-confined Stark effect we once again employ time independent perturbation theory.
  The first order correction for the wave function is
  .
  Once again we look at the  energy level and consider only the perturbation from the level  (notice that the perturbation from  would be  due to symmetry). We obtain 
  for the conduction and valence band respectively, where  has been introduced as a normalization constant. For any applied electric field  we obtain
  .
  Thus, according to Fermi's golden rule, which says that transition probability depends on the above overlapping integral, optical transition strength is weakened.
caption: Numerical simulation of the absorption coefficient of Ge/Si
    
      
        
          
            
            
              0.18
            
          
        
      
      {\displaystyle _{0.18}}
    
  Ge
    
      
        
          
            
            
              0.82
            
          
        
      
      {\displaystyle _{0.82}}
    
   quantum wells
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