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Sensors and Materials, Vol. 30, No. 7 (2018) 1611–1616
MYU Tokyo
S & M 1618

Study of an X-ray/Gamma Ray Photon Counting Circuit
Based on Charge Injection
Katsuyuki Takagi,1,2* Tsuyoshi Terao,1 Akifumi Koike,2 and Toru Aoki1,2
1Graduate School of Science and Technology, Shizuoka University,
3-5-1 Johoku, Naka-ku, Hamamatsu-shi, Shizuoka 432-8011, Japan
2ANSeeN Inc., 3-5-1 Johoku, Naka-ku, Hamamatsu-shi, Shizuoka 432-8011, Japan(Received January 22, 2018; accepted April 11, 2018)

Keywords: X-ray/gamma ray detector, photon counting, charge-to-digital converter

A direct charge-to-digital converter (QDC) based on charge injection for an X-ray/gamma ray
photon counting detector is introduced in this paper. The proposed circuit is a direct conversion
circuit unlike conventional indirect circuits. Direct charge signal processing does not lose time
because it accomplishes conversion and resets simultaneously and starts the conversion without
waiting for all the photon energy to be converted into charge. This conversion behavior wasverified by simulating a direct QDC circuit. Moreover, in the simulation, the effect of the darkcurrent in the detector was taken into consideration and an appropriate compensation method
for this was proposed. An experimental circuit was built and tested with discrete components
to confirm coincidence with the simulated results. Direct conversion is simpler than indirectconversion, and the resultant circuit contains fewer electronic components than an indirectconverter. This circuit is suitable for high-density imaging sensor design. In addition, thisarchitecture ideally counts generated charges individually, which is valuable for the analysis ofcharge drift inside the detector.

1.

Introduction

Various types of detectors exist for X-ray/gamma ray and they are categorized as either
direct or indirect conversion. Direct detectors directly convert X-ray/gamma ray photons into
electron–hole pairs that drift towards the electrode as a result of a reverse bias applied to thedetector. An advantage of direct detectors is that they can achieve higher efficiency in thedetection of absorbed photons and higher spatial resolution than indirect detectors because thiseliminates intermediate conversions.(1,2) However, conventional read-out circuits for directdetectors do not perform direct conversion in pulse processing. The read-out circuit is required
to detect charge and quantitatively measure it. The output charge from one photon is inadequate
to be considered as current without amplification; therefore, charge-sensitive amplifiers (CSAs)
are used in many photon counting applications.(1,3,4) A CSA collects and converts charge
to voltage, and the voltage is converted to a digitized code by an analog-to-digital converter*

Corresponding author: e-mail: takagi.katsuyuki.16@shizuoka.ac.jp
http://dx.doi.org/10.18494/SAM.2018.1925
ISSN 0914-4935 © MYU K.K.
http://myukk.org/

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Sensors and Materials, Vol. 30, No. 7 (2018)(ADC). Furthermore, resetting the circuit is essential for CSA to avoid saturation because it
stores the charge and the charge is unipolar. To continue the stepwise process, the charge must
be returned rapidly to zero; this reset causes dead time and limits conversion over that period oftime.(3)The conventional sensing system of direct X-ray/gamma ray detectors is not strictly a directconverter because of voltage pulse processing. Charge and voltage pulse processings havetheir own advantages and disadvantages, but direct conversion can further minimize losses
due to intermediate conversion. The main inevitable disadvantages of voltage pulse processing
are wider pulse, ballistic deficit due to fast shaping,(5) and dead time caused by reset; all thesefactors add up to significant losses in time. Conversely, charge pulse processing does not suffer
loss of time because conversion and reset can be achieved simultaneously. Consequently, an
additional reset circuit is not required, and the transient response of the pulse disappears (describedin Sect. 2). Therefore, a charge read-out circuit that performs charge pulse processing appears
promising for X-ray/gamma ray photon counting circuits for direct conversion.

2.

Ideal Charge Read-out Circuit

An easy way to build a charge read-out circuit is to eliminate the voltage-to-current
converter from the voltage ADC. However, if a sample-and-hold circuit precedes the ADC,
the circuit causes dead time and timing complications during sampling because of the random
nature of the input signal. The circuit shown in Fig. 1(a) can be used for charge read-out withoutsample-and-hold. The main components of this circuit are a detector with capacitance Cdet anda charge injection circuit (CIC). The charge generated in the detector is stored in Cdet and thenthe CIC counts the amount of charge as the rate e/Ts [C/s], where e is the elementary charge
and Ts is unit time. Counting and reset are carried out at the same time; however, the circuitcannot realize when it should start and stop counting. Consequently, an additional comparator
and switch are required in the circuit. The comparator should detect e as a unit charge and turn(a)Fig. 1.

(b)(Color online) An ideal charge read-out circuit: (a) architecture and (b) conversion results.

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its output to high, so the threshold voltage Vth should then be equal to e/Cdet [V]. The switch
is closed and CIC functions while Cdet has at least the unit charge e. The output of this circuitis the time-modulated output of the comparator similar to pulse width modulation. The timeof a comparator’s high output corresponds to the amount of generated charge. Therefore, noadditional multibit voltage ADC is required. Figure 1(b) shows an example of the time diagram
for a single conversion. The top graph of Fig. 1(b) shows the input of charge by a single photon,
the middle graph shows the voltage of the read-out node, and the bottom graph shows the outputof the comparator. In the given example, the time of the comparator’s high output is 4 × Ts,
which corresponds to the amount of the input charge, i.e., 4 × e.
This charge-to-time concept has been used in the Wilkinson ADC(3) and also in the recentLSIs.(6) By removing the sample-and-hold and voltage-to-current converters from the system,
the new circuit does not require an extra reset circuit and has no dead time since the stored
charge in Cdet is automatically discharged during conversion. In addition, each conversion
requires only a unit charge e and not the accumulated charge as a whole. Therefore, conversion
can initiate before the complete charge transfer from the detector is concluded. Conversion iscarried out in parallel with the charge drift and finishes simultaneously with the drift time of
the charge by using a faster Ts.

3.

Materials and Methods

It is difficult to build such an ideal read-out circuit with real electronic components. Figure
2 shows a realistic circuit diagram of the ideal circuit that is implemented as a direct chargeto-digital converter (QDC). The CSA block is added to the ideal circuit, and this circuit injects
charge to the feedback capacitor Cfb instead of to the detector capacitance Cdet. The CIC isimplemented by a switched capacitor network, CIC’s unit charge is scaled up by the factor N for
proportionate scaling in both the simulation and the experiment, and the clock frequency usedin both the comparator and CIC represents the unit time Ts.
This architecture is similar to a first-order delta-sigma modulator. However, this QDC isdesigned in the time domain, while the delta-sigma modulator is designed in the frequency
domain. Thereby, the main difference between the two is the unit charge of the CIC. The QDC
uses a small charge corresponding to the least significant bit (LSB) as a single charge injection

Fig. 2.

QDC based on charge injection as utilized in this study.

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Sensors and Materials, Vol. 30, No. 7 (2018)

for charge read-out. On the other hand, the delta-sigma uses a large charge corresponding to
the most significant bit (MSB) because it expects a frequency signal as the input; therefore, theformat of the output digital code is also different compared with that of a QDC. The decoder ofthe delta-sigma is a decimator circuit, whereas the decoder of the QDC is a conditional counter.
The simulation is executed by a circuit simulator, LTspice.(7) The detector is replaced by apulsed current source instead of a charge generated in the detector. An op-amp, a comparator,switches, and capacitors are implemented using ideal standard components in the LTspicelibrary. An extra current source is added to the read-out node to represent the dark current of
the detector, and the clock frequency for the simulation is set to 10 MHz.
The experimental circuit is built using discrete components. For the real physical circuit, acombination of 1 nF and 200 mV is used; therefore, the scaling factor N is equal to 4.0 × 106,and Vth is set to 200 mV according to the matching N. The clock frequency is set to 10 kHz
to control nanofarad-order capacitance. The relationship between capacitance and voltage togenerate charge is 10 fF and 5 mV, respectively, which corresponds to a photon energy of 1 keVwith a germanium detector. The circuit is designed for a larger charge because the discrete
component is much larger than the required charge scale.

4.

Results and Discussion

4.1

Simulation results

Figure 3(a) shows the results of the simulation of a single conversion by the direct QDCcircuit. The top graph shows a test input charge similar to the charge generated in the detector.
The middle graph shows the output of the CSA, and the bottom graph shows the output of thecomparator, i.e., high for 1 V and low for 0 V. This conversion process works in the same way
as the ideal circuit.

(a)
(b)
(c)
Fig. 3. (Color online) Simulation results: (a) single conversion results, (b) continuous conversion results, and (c)conversion with dark current.

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Figure 3(b) shows the results of the simulation with continuous test pulses. The top andmiddle graphs show the test input charge and the output of the CSA, respectively, and thebottom graph shows the decoder’s output instead of the comparator’s output. The decoder
counts the number of continuous high outputs of the comparator. The output of the CSA showsthat fractions of the charge remain in Cfb at the end of conversions because a voltage of thefraction of charge that is less than N × e does not exceed Vth. This is a quantization error of thissystem and causes an offset in the subsequent conversion. In the special case when the scale
factor N = 1, the quantization error disappears because there is no remaining fraction of charge
in Cfb.
Figure 3(c) shows the effect of the dark current. The dark current has the same polarity
as the input charge because they are in the same electric field. Consequently, the comparator
reacts to the dark current and has a high output when the charge is accumulated up to thethreshold charge by this current. On the other hand, the accumulated dark current in Cfb isdischarged by the CIC. The comparator outputs periodic highs as a result. Although the chargein Cfb is affected by the dark current, it is similar to the effect of the quantization error forconversions. Therefore, the effects can be removed by cutting off the LSB from the output ofthe decoder. This simulated circuit shown in Fig. 2 works even for an actual X-ray/gamma ray
detector that generates the dark current.
4.2

Experimental results

Figure 4 shows the experimental results from the circuit described in Sect. 3. The probe
channel 1 (blue) shows the output of the CSA that stores a test charge prior to clock initiation,
channel 2 (cyan) shows the output of the comparator, and channel 3 (magenta) shows theclock applied to the CIC, which is initiated at 0 s on the oscilloscope. This result confirms
the expected functionality of the proposed architecture to build a CIC with real electronic
components, namely, a main block for charge read-out different from the delta-sigma modulator.
The output of the CSA is stepped down by 200 mV, which is set by the combination of thespecific capacitance and voltage described in Sect. 3. The charge injection is triggered byFig. 4.

(Color online) Experimental results of charge injection.

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Sensors and Materials, Vol. 30, No. 7 (2018)the output of the comparator because the comparator and the charge injection only work after
initiation by the clock even if the charge stored in the CSA is more than the threshold charge.
Moreover, the charge injection is synchronized with the clock, and this enables Ts to controlthe rate of the charge injection. Therefore, the circuit shown in Fig. 2 is appropriate to builda real physical circuit for a direct QDC for X-ray/gamma ray photon counting. Although
the 1 nF capacitor used in the experimental circuit is relatively large for sensing the charge
corresponding to the energy of X-ray/gamma ray photons, a 10-fF-order capacitor is required
and it can be fabricated by current CMOS technology.(4)5.

Conclusions

We introduced an ideal charge read-out circuit for X-ray/gamma ray photon counting basedon charge injection and proposed a realistic implementation. This circuit reduces the loss due
to conversion time by eliminating intermediate conversions because it is a direct conversion
circuit unlike conventional circuits. The conversion behavior has been verified by simulatinga direct QDC circuit. Moreover, the effect of the detector’s dark current has been taken into
consideration and a method for its compensation has been proposed. An experimental circuit
has been built and tested with discrete components, and the possibility of a CIC block withreal electronic components has been confirmed. Although the experimental circuit has been
designed for a charge larger than the output charge of an actual X-ray/gamma ray detector,
a QDC based on a CIC will work with an actual detector if the circuit is built with a smallcapacitor (10 fF) and smaller transistors constructed using CMOS technology.
From the proposed direct conversion, the circuit is simpler than an indirect conversion circuitand can be made smaller in size, which leads to lower power consumption. This circuit is suitedfor use in designing high-density imaging sensors. In addition, this architecture is valuable forthe analysis of charge drift inside a detector because it ideally counts generated charges individually.

Acknowledgments
This research is a part of the Cooperative Research Project of the Research Center for
Biomedical Engineering/Research Institute of Electronics, Shizuoka University, and is
supported by AMED under Grant Number 17hm0102034.

References
1234Semiconductor Radiation Detection Systems, K. Iniewski, Ed. (CRC Press, Boca Raton, 2010).
Y. Eisen, A. Shor, and I. Mardor: IEEE Trans. Nucl. Sci. 51 (2004) 1191.
G. R. Gilmore: Practical Gamma-Ray Spectrometry (Wiley, West Sussex, 2008) 2nd ed.
R. Ballabriga, G. Blaj, M. Campbell, M. Fiederl, D. Greiffenberg, E. H. M. Heijne, X. Llopart, R. Plackett, S.
Procz, L. Tlustos, D. Turecek, and W. Wong: J. Instrum. 6 (2011) C01052.
5 F. S. Goulding and D. A. Landis: IEEE Trans. Nucl. Sci. 35 (1988) 119.
6 S. Ahmad, P. Barrillon, S. Blin-Bondil, S. Dagoret-Campagne, C. de La Taille, F. Dulucq, G. Martin-Chassard, Y.
Kawasaki, H. Miyamoto, H. Ikeda, T. Iguchi, and F. Kajino: J. Instrum. 8 (2013) C01006.
7 LTspice: http://www.linear-tech.co.jp/designtools/software/#LTspice (accessed January 2018).