Modeling of NIR free carrier absorption in aluminum-doped zinc oxide layers using the simulation system RIG-VM

RIG-VM is a simulation system developed at Fraunhofer IST which simplifies the use of numeric models by embedding them as C++ classes within a comfortable scripting language of C style syntax. Variables in RIG-VM can be bound to arithmetic expressions enabling automatic actualization of their values for changing input parameters. This allows the connection of multiple models for e. g. simulation of controlling cycles or optimizing certain model parameters by fit algorithms. In this work we use the multilayer optic module within RIG-VM for the modeling of NIR free carrier absorption in aluminum-doped ZnO films using varible angle ellipsometry, reflection and transmission spectroscopy. For free carriers the simplified Drude approximation is compared with the more sophisticated semi quantum mechanical model by Hamberg using a Lindhard expression for the frequency and wave vector dependent dielectric function. RIG-VM allows the Hamberg model to be directly written as complex formula and combined with further expressions e. g. for the band gap absorption. We show that the Hamberg model is more appropriate for the description of free carrier behavior and leads to more consistent predictions of sheet resistance, while the Drude model is only a poor approximation. Consequently the extracted sheet resistances show better correlation with experimentally obtained four probe measurements, when the Hamberg model instead of a Drude approximation is used.