Ionisation waves in solids

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Abstract
It is shown that ionisation waves, familiar in connection with the positive column of a gaseous plasma, can occur in solids. This is demonstrated with a simple model in which a single type of carrier (electrons) impact ionise a deep-level trap in an insulator. Impact ionisation is described by lucky-drift theory taking into account the non-local nature of the process. An analytic theory is presented for linear waves and conditions for the existence and stability of ionisation waves are derived. It is shown that stationary, forward-travelling and backward-travelling waves are all possible, and they occur as a consequence of the non-local nature of the impact ionisation process. It is also shown that the presence of stationary waves in a finite length of sample leads to a current-controlled negative differential resistance (NDR). The end point of the growth of stationary waves in time is shown to be saw tooth waves of unchanged wavelength with an amplitude determined by the occupation of the trap at electrical neutrality; being zero for completely full or completely empty traps and being a maximum when the traps are half filled. The theory is applicable to semiconductors as well as insulators.

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