We report on three-dimensional numerical optical simulations of the emission extraction efficiency in light emitting devices with field effect carrier transport. The finite difference time domain (FDTD) method is applied for organic thin film structures on silicon substrates with metal and metal oxide electrodes. Simulations are performed for Au, Ag and indium tin oxide electrodes in bottom gate, bottom contact geometries. Special attention is paid on the dependence on electrode thickness and contact shape. It is demonstrated that in unipolar driven devices with Si gate, silicon dioxide insulator and 40 nm-thick organic films the maximum out-coupling efficiency is below 10%. This value can be doubled by an implementation of metal reflecting layers on the Si substrate. Furthermore, the emission efficiency in the ambipolar regime is investigated. The results present the dependence of light extraction on the distance between light source and electrode. Additionally, the influence of the contact edge shape is investigated for two different designs with rectangular and wedge electrodes. Interference effects cause an oscillation in the distance dependence.