54 



PHOTOCHEMICAL PRINCIPLES 



levels will be completely occupied by electrons, whereas the upper 

 bands will be vacant. Absorption of a quantum of light will raise an 

 electron from the lowest, ground state, band into the upper, singlet 

 state, band. Inasmuch as the levels in this upper band are very closely 

 spaced, at most temperatures the thermal energy will be sufficient to 

 allow the electron to move from any one level in the band to any other 

 level. Thus, the excited state cannot be considered as belonging to any 

 one molecule in the crystal, but rather must be considered as belong- 

 ing to the crystal as a whole. We thus arrive at a concept of an excited 

 state free to migrate throughout an ordered array of molecules. Such 

 an excited state can be visualized as consisting of a negatively charged 

 electron in the upper, or excited, band and a positively charged hole 

 (the vacancy left by the electron when it is raised into the upper band) 

 in the lower, or valence, band. This is shown schematically in Fig. 3. 



® GROUND 

 STATE 



(2) EXCITON 

 formation: 

 BOUND BY 

 COULOMB 

 FORCES 



(D IONIZATION: ® TRAPPING : 



ELECTRON a ELECTRON a HOLE 



HOLE FREE TO IMMOBILIZED AT 



MIGRATE IMPERFECTION 



INDEPENDENTLY IN LATTICE 



CON DUCTION BAN D 



^fn^^" =EXCITON 

 ^ J LEVELS 



^ ^7777 ^ 





TT7~^ 



7"W 



*u ^^ZS^ 



eea/eee 

 HOLE TRAP 



VALENCE BAND 



^u ' ' ' ' \J' \J' 



eaeeee /ese'e.^, 

 \j TJ ' ' ' ' w 



Fig. 3. Schematic representation of conduction bands and trapping 

 levels in an ordered array of molecules. 



This electron-hole pair will attract each other through ordinary 

 Coulomb forces and will migrate as a unit throughout the crystal. Such 

 a state of the crystal is called an exciton, inasmuch as it is formally 

 equivalent to a neutral, massless particle with spin zero traveling 

 through the crystal. It is apparent that it is possible to have triplet 

 excitons as well as singlet excitons. 



In an ideal crystal, such an exciton would migrate throughout the 

 crystal until either it recombined with the emission of a quantum of 

 radiation or its energy became degraded into the lattice vibrations of 



