With germanium gamma-ray detectors, the best time resolution can be achieved by deriving the timing signal from the output of the charge-sensitive preamplifier. This signal requires amplification before presentation to a timing discriminator, and a Timing Filter Amplifier is the optimum choice for the task. (See the Amplifier introduction.) The rise time of the Timing Filter Amplifier is typically selected to be similar to the preamplifier rise time⁶ (measured with a fast pulser applied to the preamplifier TEST input).

Two factors control the intrinsic time resolution of germanium detectors: (a) variations in the charge collection time, and (b) the noise/slope effect described by Equation (10). The former so overwhelms the latter that the timing technique must be focused on overcoming the charge collection time variations, with the resulting noise/slope contribution simply being tolerated. The top diagram in Fig. 8 depicts the variation in pulse shapes observed at the preamplifier output for a germanium detector. The longest charge collection times (illustrated by pulse C) are caused by gamma rays that produce electron-hole pairs in the detector at a location close to one of the electrodes. In this case, one of the charge carriers has to "drift" the entire distance between electrodes. The minimum charge collection time (pulses A and B) results when the gamma ray interacts in the detector at a position midway between the electrodes. In that situation, the holes and the electrons each drift to their respective electrodes through half of the inter-electrode distance. Consequently, the charge collection time for pulses A and B is about half the charge collection time of pulse C. Gamma rays interacting at other locations in the detector produce charge collection times that are between the limits set by pulses B and C. The longest charge collection time (pulse C) exhibited by a specific germanium detector ranges from 50 ns for the thinnest planar detectors to 600 ns for very large coaxial detectors.

When a leading edge discriminator is used for timing with germanium detectors, the time resolution is about equal to the charge collection time, because of the long and variable charge collection time. Application of a conventional constant-fraction discriminator, as analyzed in Fig. 8, eliminates the walk caused by the difference in A and B pulse heights, but it does not eliminate the timing uncertainty caused by the difference in charge collection times between pulses B and C. The constant-fraction zero-crossing signals for pulses B and C cross the baseline at different times, t₁ and t₂.

The Amplitude and Risetime Compensated timing technique (ARC timing) minimizes the effect of charge collection time variations from Ge detectors by an unconventional adjustment of a constant-fraction discriminator.^7,8 The fraction is left at its normal setting (0.2 to 0.3), but the constant-fraction shaping delay is significantly shortened. Instead of selecting the delay per Fig. 3, the rise times of detector pulses are measured at the preamplifier output, and the delay is set to approximately 30% of the minimum rise time. The result is illustrated in Fig. 9. With the shorter delay, the bipolar signals for all three pulses (A, B, and C) cross the baseline at the same time, in spite of different amplitudes or rise times. Thus, the zero-crossing trigger in the modified constant-fraction discriminator delivers amplitude and rise time compensated timing.

Theoretically, ARC timing generates a timing marker that is independent of amplitude and rise time, provided each pulse has a constant slope throughout its leading edge. Real pulses from planar Ge detectors exhibit constant slope only for the pulses with either minimum or maximum rise time. Pulses with intermediate rise times start with the maximum slope, but abruptly lower their slope by a factor of two when the charge carrier that experiences the shorter drift distance reaches its electrode. ARC timing will not completely compensate for the rise time if the slope changes before the time of zero crossing. The shaping delay is purposely kept short to minimize the sensitivity to abrupt slope changes.

Because of their coaxial structure, large Ge detectors produce pulse shapes that deviate somewhat from the linear rise depicted in Fig. 9. The shape of each pulse depends on where the hole-electron pairs were created in the detector.⁹ On a pulse-to-pulse basis, the shape of the leading edge varies from convex to concave, and many pulses are a mixture of these two shapes. As a result of this deviation from the ideal linear rise, ARC timing does not provide perfect compensation for the rise time variations on coaxial Ge detectors. Still, it is the most productive method for minimizing the dominant timing errors, which are caused by charge collection time variations and amplitude swings.

⁶T. D. Douglas and C. W. Williams, IEEE Trans. Nucl. Sci. NS-16 (1), 87 (1969).
⁷R. L Chase, Rev. Sci. Instrum. 39(9), 1318 (1968).
⁸Z. H. Cho and R. L. Chase, Nucl. Instrum. Methods 98, 335-347 (1972).
⁹E. Sakai, IEEE Trans. Nucl. Sci. NS-15 (3), 310 (1968).

Figure 8. Germanium Detector Signals Processed by a Conventional Constant-Fraction Discriminator.

Figure 9.  Signal Formation for ARC Timing.