Branch : Computer Science and Engineering
Subject : Fundamental of Electronic Devices
Unit : Basic Electronics
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 dc 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 Q_{0}, the instantaneous charge is
where t_{d} = 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 Ωcm 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 velocityfield diagram for ntype 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.