Ballistic transport in a semiconductor with collisions

At low temperature in a high mobility semiconductor such as GaAs the transit time of electrons across a short device may become comparable or even less than the time between collisions. Under such conditions electrons may move almost ballistically accelerating in the electric field. Such a situation is analyzed in the frame of a simple model assuming a single energy independent relaxation time. This model allows solving a problem in an analytical form. The model predicts that at high injection level (voltages larger than a punchthrough voltage) the characteristics change from the case described by the Child-Langmuir law for a short device and/or a large time between collisions to the case described by the Mott-Gurney law in the collision-dominated case. At low injection level the space oscillations of the electric field with the wavelength may appear (ωpis the plasma frequency and is the electron velocity) and the characteristic may become multivalued (S-type) due to the influence of the positive donor charge leading to the space overshoot of electrons.