In field effect transistor (FET) based biological sensors the presence of the specimen is detected via determination of changes of the electrical potential on the sensor surface. The resolution is limited by the accuracy of the transistor source to drain current measurement. Therefore a high ratio of transconductance to current noise is desired to maximize the signal to noise ratio (SNR). Schottky barrier FETs suffer from a high serial resistance which increases the noise level in transistor regimes beyond the subthreshold. Here, a study is presented reflecting the scaling of important device parameters like threshold voltage, transconductance, current noise and subthreshold slope with respect to the nanowire length. Regarding these dependancies a compromise of transistor size to SNR can be found matching the demands of the particular measurement.