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1 234 BRIDGING THE PRICE/PERFORMANCE GAP BETWEEN SILICON DRIFT AND SILICON PIN DIODE DETECTORS Derek Hullinger, Keith Decker, Jerry Smith, Chris Carter Moxtek, Inc. ABSTRACT Use of silicon drift detectors continues to increase as new XRF applications drive performance improvements beyond existing silicon PIN detector capabilities. Increasing the thickness of PIN diodes (and, correspondingly, the thickness of the depletion region within the diode) significantly reduces the diode capacitance and results in improved performance. For example, the new Moxtek XPIN-6 detector (which uses a diode with a 6mm 2 area and 625-µm thickness) has a typical improvement in resolution of 20 ev over the Moxtek XE600 detector (with a 400-µm diode), at a peaking time of 5 µs and an energy of 5.9 kev. It also has a 50% higher absorption efficiency at energies above 20 kev. Further improvements, including thicker diodes, are expected to further bridge the gap between existing PIN detectors and SDDs. These improvements result in detectors that, in some applications, offer an attractive alternative to silicon drift detectors at a reduced cost. SILICON PIN VS. SDD DETECTORS Figure 1 shows the resolution of a typical Moxtek XE600 detector and a typical high-end silicon drift detector (SDD) at an energy of 5.9 kev at different peaking times. Both sets of measurements are made at -25 C. The resolution performance of an SDD is much better, but the cost is also much higher typically by about 3 times. Figure 1: Typical Resolutions of an XE600 PIN Diode Detector and an SDD

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3 235 PEAKING TIME AND COUNT RATE Whenever the resolution of a detector is cited, a particular peaking time is assumed. Therefore, it is helpful to discuss the meaning of peaking time and how it relates to the attainable count rate. When the voltage signal produced by an x-ray photon detection passes through a shaping amplifier, the result is a voltage pulse with a particular shape (commonly, a triangle). A set of consecutive photon events result in a series of pulses each pulse representing a detected photon, with the pulse height proportional to the photon energy (or, more properly, to the energy absorbed in the detector). The peaking time of the shaping function is the time between the beginning of the voltage pulse and its peak (see Figure 2). Pulse Height Peaking Time Time Figure 2: Voltage Pulses Resulting from Consecutive Photon Detections If one uses a shaping function with shorter peaking time, one can collect more photons in a given amount of time without the pulses substantially overlapping one another. Thus, there s a one-toone relationship between the count rate a detector can handle and the peaking time used. If one were to decrease the peaking time by a factor of ten, one could accommodate a factor of 10 higher count rate. For example, if we assume a 50% dead time and no losses to pile-up, a 10 µs peaking time would result in approximately 25,000 counts per second, whereas a 1 µs peaking time would result in ten times that count rate (see Figure 3). Figure 3: Peaking Time vs. Count Rate

4 236 CONTRIBUTIONS TO DETECTOR RESOLUTION The various noise sources which contribute to the resolution of a detector result in resolution components that have different dependences on the peaking time of the shaping amplifier (Gatti and Manfredi 1986) (see Figure 4). The series thermal noise component (due substantially to the JFET) is inversely proportional to peaking time, so that as peaking time increases, thermal noise decreases. On the other hand, parallel shot noise (which largely depends on the leakage current of the diode) is directly proportional to peaking time, so that as peaking time increases, shot noise increases. There is also a significant series flicker (or 1/f ) noise component that is independent of peaking time. The statistical noise, which represents the fluctuation in the actual number of electron-hole pairs resulting from a photon, is also independent of peaking time. Figure 4: Resolution contributions typical of an XE600 detector at -25 C To illustrate how leakage current affects the overall resolution at different peaking times, Figure 5 shows the shot noise contribution (green) and total resolution (blue) that would result from an XE600 detector with three different leakage currents. The solid lines indicate the resolution due to shot noise and total resolution typical of 10 pa of leakage current, the dashed lines show resolutions typical of 1 pa, and the dotted lines show resolutions typical of 0.1 pa. With 10 pa of leakage current, the contribution of shot noise becomes significant above a peaking time of about 5 µs. With a leakage current of 1 pa, shot noise is significant above about 20 µs. With a leakage current of 0.1 pa, shot noise isn t significant except at very long peaking times of 100 µs or more.

5 pa 1 pa 0.1 pa Figure 5: Resolution for Different Leakage Currents Referring again to Figure 4, we note that at short peaking times (where shot noise has little impact on the resolution), the two dominant noise sources (thermal noise and 1/f noise) depend strongly on the total capacitance between the anode and any grounded or fixed-voltage conductors. Thus, reducing the anode capacitance has an enormous impact on resolution. This is the reason that silicon drift detectors have excellent resolution performance the anode capacitance of the chip itself is so small as to be negligible compared to other capacitance sources, such as the JFET. REDUCING DIODE CAPACITANCE In considering ways to reduce the total capacitance of a PIN diode detector, one possibility that presents itself is to increase the thickness of the diode. Making use of the parallel-plate approximation, (which is a good approximation for the anode-to-backside capacitance), a 6 mm 2 diode that is 400 µm thick (like the XE600) has an anode-to-backside capacitance of 1.6 pf, whereas a fully-depleted 625-µm diode of comparable area has a capacitance of only 1.0 pf. One obstacle to this approach is that the anode-to-backside capacitance depends upon the thickness of the depletion region within the diode, rather than on the thickness of the diode itself. Thus, the maximum possible reduction in capacitance is realized only if the diode is fully depleted. Full depletion of a thicker diode requires either a higher bias (V in Equation 1) or a

6 238 substrate with higher resistivity (corresponding to a lower doping concentration N d in Equation 1) (Sze 1981). (1) å: Permittivity of silicon ( F/m) V: Reverse bias applied to the diode q: Charge of an electron ( C) N d : Doping concentration of the diode s intrinsic region A second obstacle involves leakage current. The leakage current scales roughly with the volume of the depletion region (Sze 1981). Therefore, either a very low leakage current process or else a very low operating temperature is necessary. PERFORMANCE OF NEW XPIN-6 DETECTOR Moxtek has just introduced a new PIN diode detector called the XPIN-6 which uses a 625-µm diode. Figure 6 shows typical 5.9 kev resolutions of this detector alongside those of a typical XE600 (with a 400-µm diode) and a high-end SDD. All measurements are made at -25 C, and the XPIN-6 and XE600 are both biased to 130 V (at which both are fully depleted). As can be seen in the figure, the lower capacitance of the XPIN-6 results in significant improvement at short peaking times. For example, at a peaking time of 5 µs, the XPIN-6 has a resolution that is 20 ev lower than that of the XE600.

7 239 Figure 6: Resolution of XPIN-6 Another advantage of a thicker diode is that it is able to absorb higher energy photons more efficiently. This is equivalent, in terms of count rate, to a larger active area, but without the disadvantage of increased capacitance and correspondingly poorer resolution. Figure 7 shows the absorption curve of the XPIN-6 compared to the XE600. Above 20 kev, where the average depth of interaction in silicon is much larger than the thickness of the diode, the XPIN-6 has about a 50% greater absorption efficiency than the XE600.

8 240 Figure 7: Absorption Efficiency of XE600 and XPIN-6 NEXT GENERATION PIN DIODES Modeling suggests that additional improvements (including a further increase in thickness of the diode) should result in resolutions that further bridge the gap between the XE600 and high-end SDDs. Figure 8, for example, shows the expected resolution from a 6-mm µm diode that is in development. An 875-µm diode would also offer improved absorption, as shown in Figure 9. Such PIN diode detectors may offer resolutions that are adequate for some applications and at a much lower cost than typical SDDs.

9 241 Figure 8: Resolution from an 875-µm, 6mm 2 diode in development Next Gen PIN (875 µm) Figure 9: Absorption Efficiency of 875-µm-thick silicon

10 242 Larger area diodes are desirable for some applications for example, when a much higher count rate is needed. Modeling suggests that the same types of improvements we ve described could result in significant gains in resolution performance over Moxtek s current 13mm 2 diode the XE1300 (see Figure 10). Even 25mm 2 diodes should be possible with resolutions that aren t too far from the resolutions of typical 6mm 2 diodes of just a few years ago. Figure 10: Theoretical resolutions of larger-area pin diodes SUMMARY In conclusion, an increase in diode thickness permits a larger depletion thickness, which in turn leads to better resolution performance due to its lower anode capacitance, as long as acceptable leakage current is maintained. This performance begins to approach the performance of silicon drift detectors and at a much lower cost than SDDs. As an added benefit, thicker diodes also result in improved x-ray absorption. Bibliography Gatti, E., and Manfredi P.F. (1986). Processing the Signals from Solid-State Detectors in Elementary- Particle Physics, Rivista Del Nuovo Cimento. 9, Sze, S. M. (1981). Physics of Semiconductor Devices (Wiley, New York).