Formation and Drift of Space Charge Domains
If a sample of GaAs is biased such that the field falls in the negative conductivity region, space charge instabilities result, and the device cannot be maintained in a d-c stable condition.
Formation and Drift of Space Charge Domains:
To understand the formation of these instabilities, let us consider first the dissipation of space charge in the usual semiconductor. It can be shown from treatment of the continuity equation that a localized space charge dies out exponentially with time in a homogeneous sample with positive resistances. If the initial space charge is Q0, the instantaneous charge is
where td = ζ/σ is called the dielectric relaxation time.
- Because of this process, random fluctuations in carrier concentration are quickly neutralized and space charge neutrality is a good approximation for most semiconductors in the usual range of conductivities.
- For example, the dielectric relaxation time for a 1.0 Ω-cm Si or GaAs sample is approximately 10-12 s.
- The above Equation gives a rather remarkable result for cases in which the conductivity is negative.
- For these cases, rd is negative also and space charge fluctuations build up exponentially in time rather than dying out.
- This means that normal random fluctuations in the carrier distribution can grow into large space charge regions in the sample.
- Let us see how this occurs in a GaAs sample biased in the negative conductivity regime.
- The velocity-field diagram for n-type GaAs is illustrated in Fig.a.
- If we assume a small shift of electron concentration in some region of the device, a dipole layer can form as shown in Fig.b.
Under normal conditions, this dipole would die out quickly.
- However, under conditions of negative conductivity, the charge within the dipole, and therefore the local electric field, builds up as shown in Fig.c.
Of course, this buildup takes place in a stream of electrons drifting from the cathode to the anode, and the dipole (now called a domain) drifts along with the
stream as it grows.
- Eventually, the drifting domain will reach the anode, where it gives up its energy as a pulse of current in the external circuit.