Gate-tunable semiconductor nanosystems are getting more and more important in the realization of quantum circuits. While such
devices are typically cooled to operation temperature with zero bias applied to the gate, biased cooling corresponds to a non-zero
gate voltage being applied before reaching the operation temperature. We systematically study the effect of biased cooling on different
undoped SiGe/Si/SiGe quantum well field-effect stacks designed to accumulate and density-tune two-dimensional electron gases
(2DEGs). In an empirical model, we show that biased cooling of the undoped FES induces a static electric field, which is constant at
operation temperature and superimposes onto the field exerted by the top gate onto the 2DEG. We show that the voltage operation
window of the field-effect-tuned 2DEG can be chosen in a wide range of voltages via the choice of the biased cooling voltage. Importantly,
quality features of the 2DEG such as the mobility or the temporal stability of the 2DEG density remain unaltered under biased
cooling.