Transient response of silicon devices at 4.2 K. I. Theory

A semi-empirical analytical expression for the shallow-level impact ionization rate coefficient A ii and the thermal capture rate coefficient B T is derived, which gives a good qualitative agreement with the reported data and can be used for engineering purposes, in particular for the simulation of the operation of Si devices at liquid helium temperatures. In the calculations, the hot carrier distribution is approximated by a Maxwellian distribution with an effective carrier temperature T e . The results obtained in this way are used to simulate the forced depletion layer formation (FDLF) in a silicon resistor at liquid helium temperatures. As will be shown, a space charge is injected with a time constant which is maximum at the edge of the depletion region and corresponds with the minimum in A ii +B T . These results will be applied to the transient behaviour of a metal-oxide-semiconductor transistor (MOST) in part II.