The theory of physical doping in organic semiconductor

A theory for carrier concentration in physically doped organic semiconductors has been presented based on Gaussian energy distribution of the lowest unoccupied molecular orbitals （LUMOs） and the highest occupied molecular orbitals （HOMOs） as well as the Fermi - Dirac distribution of carriers in allowed quantum states. The dependence of carrier concentration on doping concentration, ambient temperature and energy gap of organic semiconductors were numerically investigated. It is shown that carrier concentration will increase with the ambient temperature in doped or undoped organic semiconductors, and the carrier concentration decreases exponentially with the reciprocal of temperature. For intrinsic organic semiconductor, carrier concentration will decrease exponentially with the energy gap （the difference between the average energy levels of HOMO and LUMO ）and increase exponentially with the square of the width of Gaussian distribution. We then discussed the effect of doping concentration on carrier concentration for different HOMO and LUMO positions of the dopant relative to that of the host.