Depleted region

Fig. 5. Device model for an MIS photodiode, the basic building block of the CCD photodetector. The depletion region is generated by the battery...

When electrons are injected as minority carriers into a -type semiconductor they may diffuse, drift, or disappear. That is, their electrical behavior is determined by diffusion in concentration gradients, drift in electric fields (potential gradients), or disappearance through recombination with majority carrier holes. Thus, the transport behavior of minority carriers can be described by a continuity equation. To derive the p—n junction equation, steady-state is assumed, so that = 0, and a neutral region outside the depletion region is assumed, so that the electric field is zero. Under these circumstances,... 

Lp Pi 50 pm. and the reverse saturation current would be 17 x 10 = 17 pA for a square centimeter of junction area. Typical reverse saturation currents are about one thousand times greater as a result of generation—recombination currents in the depletion region (9). As the reverse voltage bias increases, the field increases in the depletion region until avalanche breakdown occurs, resulting in the characteristic shown in Figure 7. 

Eig. 10. The n—p—n transistor biased ia its active region, where 7 = current, (------) indicate depletion regions at the p—n junctions, and S is the electric field ... 

The frequency response or switching speed of the bipolar transistor is governed by the same processes which control the speed of thep—n junction, the capacitance associated with the movement of charge into and out of the depletion regions. To achieve high frequencies the dimensions of the active areas and parasitic circuit elements must be reduced. The two critical dimensions are the width of the emitter contact and the base thickness, W. The cutoff frequency,, is the frequency at which = 57 / - b /t > where is the emitter-to-coUector delay time and is the sum of the emitter... 

Although Eqs. (14.2) and (14.4) can be solved analytically (as will be shown in the next section), here it is sufficient to use the renowned depletion, or Schott-ky approximation, in which it is assumed that the effective density of chaige is constant and equal to qNd in the depletion region, and zero outside this region. In this case, a double integration of Eq. (14.2) directly gives... 

Finally, the total charge per unit area due to the uncompensated donors in the depletion region is given by... 

The silicon diode (photodiode) detector consists of a strip of p-type silicon on the surface of a silicon chip (n-type silicon). By application of a biasing potential with the silicon chip connected to the positive pole of the biasing source, electrons and holes are caused to move away from the p-n junction. This creates a depletion region in the neighbourhood of the junction which in effect becomes a capacitor. When light strikes the surface of the chip, free... 

Relation (18) for the potential-dependent PMC signal is a reasonably good approximation only for the depletion region, where the space charge layer is controlled by the presence of fixed electron donors (Afo). It would become even more complicated if bimolecular or even more complicated kinetic reaction steps were considered. 

Relation (18) for the PMC signal in the depletion region is sufficiently complicated to require a more detailed analysis, but is already sufficiently simple to allow the discussion of limiting cases. 

In the depletion region for a band bending U - Ujb> 100 mV, where a reasonably low surface recombination velocity is found, the PMC signal can consequently be approached by... 

Figure 13. Numerically calculated PMC potential curves from transport equations (14)—(17) without simplifications for different interfacial reaction rate constants for minority carriers (holes in n-type semiconductor) (a) PMC peak in depletion region. Bulk lifetime 10" s, combined interfacial rate constants (sr = sr + kr) inserted in drawing. Dark points, calculation from analytical formula (18). (b) PMC peak in accumulation region. Bulk lifetime 10 5s. The combined interfacial charge-transfer and recombination rate ranges from 10 (1), 100 (2), 103 (3), 3 x 103 (4), 104 (5), 3 x 104 (6) to 106 (7) cm s"1. The flatband potential is indicated.

These same features of the PMC signal can be reproduced by plotting the calculated analytical formula for the depletion region [relation (18)]. This is shown for the positive PMC peak in Fig. 14. By inserting the same parameters into both the numerical and analytical computation procedures, it is found that the analytical solution coincides with the numerical one... 

Figure 16 shows such PMC peaks in the depletion region for electrodes of Si,9 WSez8 and ZnO.12 They all appear near the onset of anodic photocurrents. They have different shapes, which, however, can easily be explained with the assumption of potential-dependent interfacial charge-transfer and charge recombination rates. 

Figured 16. PMC peaks in the depletion region near the onset of anodic photocurrents for Si,9 WSe2,8 and Zn0.iaThe clearly reduced width of the ZnO peak can be seen.

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