## THREE-DIMENSIONAL MASTER EQUATION SIMULATIONS OF CHARGE-CARRIER TRANSPORT AND RECOMBINATIO Nl IN ORGANIC SEMICONDUCTOR MATERIALS AND DEVICES 

## FIELD OF THE INVENTION 

This invention relates to simulation of semiconductor devices 

## BACKGROUND 

Organic semiconductors are used in various types of electronic and opto-electronic devices, such as organic light-emitting diodes (OLEDs), organic photovoltaic (OPV) devices and organic transistors. The materials used are often structurally disordered (amorphous). The electrical conductivity is a result of ’’hopping” of the electrical charges between the molecules. Due to the disorder, the energy of the charges in the molecules varies quite randomly, and the distribution of ’’hopping-rates” between each pair of molecules is quite wide. As a result, the current density is not uniform, but hlamentary. And if there are charges with opposite polarities (+ and -), as in OLEDs, the molecules at which they recombine (followed by light emission) after a mutual attraction process are not uniformly distributed. 

The ’’gold standard” for predictively describing these complex processes is three- dimensional kinetic Monte Carlo (3D-KMC) simulation. Within 3D-KMC simula tions, the actual positions of all charges are followed in time, taking the molecular energies, electric held and temperature into account. A disadvantage of this approach is the long simulation time. For OLEDs, obtaining a statistically correct result is at low voltages too computer-time consuming. A commonly used alternative approach, 

