Fig. 1

Computed density of states (DOS) in doped organic semiconductors. a DOS of doped organic semiconductors with zero intrinsic disorder on a logarithmic scale for three dopant molar ratios (DMR) (DMR = {10⁻³, 10⁻², 1.5 × 10⁻¹}). Relevant part of the DOS comprises energy distributions of the highest occupied and lowest unoccupied host orbitals, HOMO and LUMO⁺, respectively. HOMO⁽⁰⁾ and |V_C| is the mean HOMO of the corresponding undoped material, and the Coulomb interaction energy between the host cation and dopant anion at a distance a with a being the lattice constant. Feature “a” (“b”) in the top panel corresponds to neutral host molecules at a distance of a to host cations (dopant anions) and \(a/\sqrt 2\) to dopant anions (host cations). Features “c” and “d” correspond to host cations at distances of \(a/\sqrt 3\) and \(a/\sqrt 2\) to dopant anions, respectively. At low and moderate DMR (top and middle panels), novel LUMO⁺ distribution appears approximately at HOMO⁽⁰⁾ + |V_C|. b The same as a in a linear scale. Note the broadening of HOMO/LUMO⁺ distributions upon doping. c The same as b for high (σ_int = 0.2 eV) intrinsic disorder. In this case the mean LUMO⁺ is separated from HOMO⁽⁰⁾ by the energy significantly larger than |V_C| (cf. top panels of a and c) due to intrinsic disorder. The Fermi level position (denoted by E_F) determined from the DOS is always the crossing point of HOMO and LUMO⁺ distributions so that the density of states at E_F is low. The LUMO⁺ distribution in panels b and c has been multiplied by a factor of 100, 10, 1 from top to bottom to enhance visibility at low doping molar rates. The density of states in all panels is normalized so that the maximum DOS value is equal to 1