Fig. 3

Shift of the Fermi level and frontier orbitals energies upon doping. a The definition of the Fermi level shift with respect to the peak and the onset of the HOMO, \(\Delta E_{\mathrm{F}}^{{\mathrm{peak}}}\) and \(\Delta E_{\mathrm{F}}^{{\mathrm{onset}}}\), respectively shown in the material with DMR = 0.067 and zero intrinsic disorder (σ_int = 0). The total material disorder is denoted by σ_tot. b and c, Evolution of the density of states (DOS) upon doping (the grayscale shows the DOS in logarithmic scale) for organic materials with zero (σ_int = 0.0 eV) and high (σ_int = 0.2 eV) intrinsic disorder, respectively. The peaks of the HOMO and LUMO⁺ distributions are denoted as HOMO_peak and \({\mathrm{LUMO}}_{{\mathrm{peak}}}^ +\), respectively. HOMO_onset stands for the onset of the HOMO distribution, and E_F is the Fermi level. Panel a is a cut of Panel b at DMR = 0.067 as shown with a grey line