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Introduction to Charged-Particle Detectors

Depletion Depth and Capacitance

As stated in the section, Review of Detector Physics, silicon detectors are reverse-biased diodes with parallel, planar electrodes and therefore have the capacitance of the corresponding parallel-plate capacitor. The electric field in the detector, however, is not constant but decreases linearly from the contact at which the p-n junction is made to the end of the depletion region (Fig. 1).

The nomograph in Fig. 2 shows the depth W of the depletion region as a function of the bias voltage applied to the detector and the resistivity of the silicon material. For a given value of bias, the depletion depth increases with increasing resistivity, and correspondingly, the slope of the electric field in Fig. 1 decreases with increasing material resistivity, that is, as the silicon material behaves more and more like an insulator. If, as shown in Fig. 1, L is the overall thickness of the silicon slice, the detector is totally depleted when W = L.

The nomograph of Fig. 2 also shows the "specific capacitance" (capacitance per unit area) of silicon detectors for any given value of W. A detector's capacitance can be read directly from this nomograph once the active area has been determined.

The value of the capacitance is of interest because the effective electronic noise of preamplifiers used with silicon detectors increases with increasing capacitance values (Fig. 3). The electronic noise increase per unit capacitance increase is called the preamplifier's "slope."

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Fig. 1.   Representation of Electric Field E in Silicon Surface Barrier Detectors.

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Fig. 2.  Silicon Detector Parameters Nomograph. [Similar to Nomogram reported by J.L. Blankenship, IEEE Trans, Nucl. Sci. NS7 (2-3), 190-195 (1960).]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Fig. 3. Typical Noise Data for Model 142 Preamplifier. (Using ORTEC Shaping Amplifier with 0.5-µs shaping time constant.