Ballistic and collision dominated transport in a short semiconductor diode

Electron transport in a short semiconductor diode is analyzed in the frame of a simple model assuming a single energy independent relaxation time. The model predicts that at high injection levels the I-V 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 wave-length may appear (ωpis the plasma frequency and is the electron velocity) and the I-V characteristic may become multivalued (S-type) due to the influence of the positive donor Space charge leading to "the space overshoot" of electrons. This indicates a possibility of an instability in a short diode. High values of the Velocity lead to a large geometrical magnetoresistance which decreases with the increase of voltage in agreement with the experimental results.