Towards Gotthard-II: Development of A Silicon Microstrip Detector for the European X-ray Free-Electron Laser
Jiaguo Zhang, Marie Andrä, Rebecca Barten, Anna Bergamaschi, Martin Brückner, Roberto Dinapoli, Erik Froejdh, Dominic Greiffenberg, Carlos Lopez-Cuenca, Davide Mezza, Aldo Mozzanica, Marco Ramilli, Sophie Redford, Marie Ruat, Christian Ruder, Bernd Schmitt, Xintian Shi, Dhanya Thattil, Gemma Tinti, Monica Turcato, Seraphin Vettera
aa r X i v : . [ phy s i c s . i n s - d e t ] N ov arXiv submission Towards Gotthard-II: Development of A Silicon MicrostripDetector for the European X-ray Free-Electron Laser
Jiaguo Zhang, a , Marie Andrä, a Rebecca Barten, a Anna Bergamaschi, a Martin Brückner, a Roberto Dinapoli, a Erik Froejdh, a Dominic Greiffenberg, a Carlos Lopez-Cuenca, a DavideMezza, a Aldo Mozzanica, a Marco Ramilli, b Sophie Redford, a Marie Ruat, a Christian Ruder, a Bernd Schmitt, a Xintian Shi, a Dhanya Thattil, a Gemma Tinti, a Monica Turcato, b SeraphinVetter a a Paul Scherrer Institut,5232 Villigen, Switzerland b European X-ray Free-Electron Laser Facility GmbH,Holzkoppel 4, 22869 Schenefeld, Germany
E-mail: [email protected]
Abstract:
Gotthard-II is a 1-D microstrip detector specifically developed for the European X-rayFree-Electron Laser. It will not only be used in energy dispersive experiments but also as a beamdiagnostic tool with additional logic to generate veto signals for the other 2-D detectors. Gotthard-II makes use of a silicon microstrip sensor with a pitch of either 50 µ m or 25 µ m and with 1280or 2560 channels wire-bonded to adaptive gain switching readout chips. Built-in analog-to-digitalconverters and digital memories will be implemented in the readout chip for a continuous conversionand storage of frames for all bunches in the bunch train. The performance of analogue front-endprototypes of Gotthard has been investigated in this work. The results in terms of noise, conversiongain, dynamic range, obtained by means of infrared laser and X-rays, will be shown. In particular,the effects of the strip-to-strip coupling are studied in detail and it is found that the reduction ofthe coupling effects is one of the key factors for the development of the analogue front-end ofGotthard-II. Keywords:
Radiation-hard detectors; Instrumentation for FEL; X-ray detectors Corresponding author. ontents
The European X-ray Free-Electron Laser (XFEL.EU) [1, 2] has been constructed in the Ham-burg/Schenefeld region and available for user experiments since the second half of 2017. It deliversextrashort, high intense X-ray pulses with a peak brilliance ∼ × and MID beamlines. The potential scientific applications include, but are not limitedto: X-ray emission/absorption spectroscopy, hard X-ray high resolution single-shot spectrometry(HiREX), energy dispersive experiments, beam diagnostics, as well as veto generation for the otherdetectors [11]. For more examples of potential scientific applications, refer to [12–14]. The Gotthard-II detector has less readout channels but similar complexity compared to the other 2-Ddetectors for experiments at the XFEL.EU. In addition, it is the only detector capable of measuringall the bunches in a train. To perform proper scientific experiments, Gotthard-II needs to achieve aframe rate of 4.5 MHz to match the particular bunch structure, a dynamic range up to 10 . A detailed specification can be found in table 1. Parameter Value Unit energy range 3 - 25 keVsensor thickness 450 | µ mquantum efficiency 83.5% | × | × pitch of strip 50 | µ mnumber of strips 1280 | ≥
100 nscooling air or liquidnoise ∼ e − r.m.s.signal-to-noise ratio (SNR) ≥
10 @12.4 keVphoton sensitivity (no gain switching) single photon @ >3.5 keV (SNR > 5)frame rate ≥ − - 10 − mbar Table 1 . Specification of Gotthard-II detector of 50 and 25 µ m pitches. 450 µ m and 320 µ m thick sensorswill be used for pitches of 50 and 25 µ m, respectively. Gotthard-II is equipped with on-chip Analog-to-Digital Converters (ADCs) and Static Random-Access Memories (SRAM, digital memory) capable of storing 2700 images for all X-ray pulses ina bunch train: The analogue signals, after passing through a charge sensitive pre-amplifier and a SPB: Single Particles, Clusters and Bio-molecules MID: Materials Imaging and Dynamics Radiation damage in Gotthard-II is not a problem, since the ASICs can be properly shielded and the silicon sensorwill see considerable less dose compared to 2-D detectors whose focal plane faces to the XFEL beam. – 2 –orrelated-Double Sampling (CDS) stage, are digitized by the ADCs immediately and the digitalvalues are stored in the SRAM. All the 2700 images are read out during the bunch train spacingof 99.4 ms. This approach has several advantages over the use of analogue memories to storesignals from the CDS output, as implemented in e.g.
AGIPD. The immediate digitization of thesignals removes the problem connected with the droop of charge in analogue memories and theconsequent need to cool the detector to a very low temperature in order to reduce such effects [15–17]. It moreover removes the complexity related to the analogue readout and off-chip digitization,which require great care and corresponding resources, to avoid signal degradation. The analoguememories would in addition be very large in size and suffer from an on-chip cross talk problem[18]. Another important function of Gotthard-II is the generation of veto signals for 2-D detectorsdepending on the interaction between an XFEL pulse and investigated sample. Since the 2-Ddetectors have limited memories and are not able to record all images from the 2700 pulses perbunch train, with the veto signals generated by Gotthard-II, useless images of 2-D detectors canbe discarded and the corresponding memories re-used. For this purpose, additional logic circuitryused to generate veto signals will be implemented into the final ASIC. This circuitry will provide aone-bit hit information per channel, not stored in the SRAM but read out immediately at a rate of4.5 MHz . This information will then be used by the FPGA on the readout board to generate theveto signal. The main building blocks of the Gotthard-II ASIC, namely the analogue front-end electronics in-cluding pre-amplifier and CDS, the ADC and the SRAM have been designed and implementedseparately in Multi-Project Wafer (MPW) runs. Therefore, each block can have its performanceassessed independently and is integrated in the full-size ASIC only in case of proven full function-ality. A first prototype version of a complete channel made out of blocks not yet rated as "finalgrade", has already been sent for production. This will provide information about the functionalityand the interactions of all the building blocks when interconnected to form a channel within themulti-channel prototype.The Gotthard-I and Jungfrau [19] readout ASICs have been used as a basis for the developmentof the Gotthard-II analogue front-end. The paper will focus on the performance of the existingfront-end prototypes of Gotthard fabricated in UMC-110 nm technology while the ADC and theSRAM will be discussed in a separate paper.
The architecture of the analogue front-end prototypes (version Gotthard-1.4 & -1.5) is shown infigure 1. It includes four main parts: 1) a dynamic gain switching pre-amplifier, 2) a CDS stage, 3)analogue and digital memory cells, and 4) a readout chain for all strip channels.The pre-amplifier is a charge-sensitive pre-amplifier with dynamic gain switching functionality,similar to AGIPD [4] and Jungfrau [19]. Its output is connected to a comparator and a dynamic The current design of Gotthard-I can achieve a frame rate of ≤ – 3 – igure 1 . The architecture of the analogue front-end prototypes. gain switching logic. There are four different feedback capacitors implemented in the pre-amplifier: C f , HG , C f , G , C f , G and C f , G . Initially, either C f , HG or C f , HG + C f , G can be selected asfeedback capacitance. During charge integration, if the output voltage moves above the thresholdof the comparator, V th , com , the dynamic gain switching logic will force the gain switching and thecapacitor C f , G will be added to the feedback loop of the pre-amplifier. This will cause a reductionof the pre-amplifier gain and, as a side effect, a charge redistribution and a consequent reduction ofthe output voltage of the pre-amplifier. If the output voltage of the pre-amplifer is still above V th , com ,a second gain switching occurs by adding another feedback capacitor, C f , G , to the feedback circuit. C f , G and C f , G can be pre-charged during the pre-amplifier reset phase. In this way, the outputvoltage range of the pre-amplifier after gain switching can be maximized, thus a larger dynamicrange can be achieved. For the convenience, in the following we will note the gain using C f , HG asHG0, with C f , G , C f , G and C f , G in addition as G0, G1 and G2, respectively.The CDS stage is connected to the output of the dynamic gain switching pre-amplifier. It isused to remove the low frequency noise and the pre-amplifier reset noise. The amplification factorof the CDS is 2.35 (also called "CDS gain"). If gain switching happens, the correlation of the initialsample, stored in the CDS circuitry, and the actual signal is lost, so that CDS is not beneficial anylonger. For this reason, the CDS stage is bypassed after gain switching. The signal is written intothe analogue memory cells through a resistor of 125 k Ω which, together with the capacitive load atthe CDS output, is used as an additional low-pass filter for noise reduction.The analogue signals from the CDS output are stored in analogue memory cells, while theinformation indicating the gain is stored, for each channel, in a 2-bit digital memory.During read-out, analogue and digital storage cells are driven by analogue and digital buffersseparately. The analogue signals are selected by a multiplexer (MUX) and converted to fullydifferential signals through an off-chip driver and finally digitized by 14-bit ADCs on the readoutboard; The digital signals are sampled by a Field Programmable Gate Array (FPGA) on the readoutboard directly.The investigated Gotthard-1.4 & -1.5 prototype ASICs are wire-bonded to 320 µ m thick siliconmicro-strip sensors with 128 strips of 50 µ m pitch and 8 mm length for testing. The only differencebetween Gotthard-1.4 and -1.5 ASICs is the size of the transistors used in the pre-amplifier, whichis supposed to influence the speed and the noise of the pre-amplifier. Since the speed of writing– 4 –harge into the analogue memory cell is limited by the serial resistor in the circuit, the difference inthe speed of the pre-amplifier between the two prototypes cannot be measured. Thus, only resultsfrom Gotthard-1.5 will be shown and discussed in Section 3. The performance of the front-end prototypes in terms of conversion gain, noise, dynamic range andstrip-to-strip coupling has been investigated experimentally. All measurements were performed atroom temperature and the prototype assemblies were cooled by a fan. The sensor was biased at240 V and the power supply voltage of the ASICs was 1.4 V.
In the following discussion, the conversion gain refers to the gain for HG0 and G0 and is expressedin ADU/keV. The conversion gain is determined using X-ray fluorescence of copper (Cu), whichwas placed as the target of an X-ray tube. The characteristic energy of the main k α line of thefluorescence, E k α , is 8.05 keV. In the measurement, an integration time of 10 µ s was used and 100kframes were collected.Figure 2(a) shows the histogram of the measured ADU values using HG0 for a specific channelas an example. The identified peaks in the figure refer to 0, 1, 2 and 3 photons. Good separationbetween different photon peaks can be seen, indicating good noise performance. The peak positionswere extracted from a Gaussian fit to each individual peak. Figure 2(b) shows the extracted peakposition in terms of ADU as function of energy, which is given by the energy of the k α X-rayfluorescence times number of photons. The slope of a linear fit gives the conversion gain. It shouldbe noted that the intensity of the k β -line at 8.90 keV of the cooper foil is much lower than the k α -line and cannot be resolved in the distribution due to the influence of noise as well as the chargediffusion, thus has been neglected in our case.Figure 2(c) shows the conversion gains of all channels for HG0 and G0, and figure 2(d)the histogram of the gain distributions. The conversion gains for HG0 and G0 are centered at35.2 ± ± ∼
2% channel to channel variations, whichshows very good uniformity over all channels of the ASIC.By means of the ratio of the conversion gain between HG0 and G0, the parasitic capacitancein the feedback loop of the pre-amplifier can be estimated to be 40.5 fF.
The noise measurement was performed in a light-tight box by measuring the integrated leakagecurrent of the sensor for 10 µ s multiple times. The histogram of ADU values was then fitted by aGaussian function and the standard deviation, σ , was extracted. The noise is obtained using: noise r . m . s . [ e − ] = σ [ ADU ] g ain [ ADU / keV ] · . [ eV ] (3.1)where 3.6[ eV ] is the mean energy needed to generate one electron-hole pair in silicon by ionizingradiation, and gain [ ADU/keV ] is the previously measured conversion gain.– 5 – igure 2 . The conversion gain of the prototypes measured with an integration time of 10 µ s. (a) Fittingto multiple peaks due to 0, 1, 2 and 3 photons for a single strip (strip-64) as an example; (b) Linear fit tothe peak positions to determine the conversion gain; (c) Conversion gain for all channels for HG0 and G0following the same procedure; (d) Histogram of conversion gain for HG0 and G0. The noises for HG0 and G0 are ± e − and ± e − for an integration time of 10 µ s,as shown in figure 3. In addition, the noise has been investigated for different integration times,from 20 µ s down to 50 ns. Figure 4 shows the extracted noise as function of integration time forall strip channels: The conversion gain obtained from the X-ray fluorescence measurement withan integration time of 10 µ s was applied to the extracted σ at different integration times usingformula 3.1. A reduction of σ below 500-600 ns has been observed which is due to the RC timeconstant in the circuit: The 125 k Ω resistor, that in Jungfrau helps to remove the high frequencynoise, limits the writing speed. When writing charge from the CDS output into analogue memories,at least 500-600 ns are needed for the signal to settle.– 6 – igure 3 . The noise of the prototypes measured with an integration time of 10 µ s for HG0 and G0. (a) Noisefor all channels; (b) Histogram of the noise distribution. Figure 4 . The noise, derived from the extracted σ from Gaussian fit, as function of integration time for allstrip channels. – 7 – igure 5 . Dynamic range scan with infrared laser using HG0 (in blue) and G0 (in green). (a) Dynamic rangescan; (b) Shot-to-shot laser fluctuation. The dynamic range was measured using a pulsed infrared laser with a wavelength of 1030 nm.The integration time was set to 5 µ s and the pulse duration was less than one nano second. Thedynamic range scan was done by varying the laser intensity. The laser intensities were calibratedby measuring the photo-current from a 320 µ m thick planar silicon diode and then converting toequivalent number of 12.4 keV photons per pulse. A detailed introduction to the experimental setupand conversion from laser intensity to photons can be found in [18, 20].Figure 5(a) shows the dynamic range for a specific channel using HG0 and G0. It can be seenthe dynamic range is up to . × σ as a good separation to resolve single photons,in HG0 and G0 single photon resolution can be achieved for X-ray photons with an energy above3.7 keV; in G1 and G2, it is possible to resolve 3 and 55 photons of 12.4 keV, respectively. Gain ratio
HG0/G1 HG0/G2 G0/G1 G0/G2
Measured value . ± .
08 346 . ± . . ± .
05 230 . ± . Table 2 . The ratio of gains in different gain stages using HG0 or G0.
Due to the capacitive coupling between strip channels, even if all charge carriers generated by X-rayphotons (no charge sharing effect) are collected by a strip, the neighbouring readout channels ofthe strip still measure a signal (also known as capacitive "charge division"). There are various– 8 –odels which describe this effect caused by the capacitive coupling between strip channels [21–27]. The charge measured by the strip channel collecting all carreries produced by X-ray photons, Q i , the charge measured by one of its first neighbouring channels, Q i + , by its second and thirdneighbouring channels, Q i + and Q i + , can be simplified as Q i = ( A + ) · ( C f + C par a )( A + ) · ( C f + C par a ) + C inp · Q tot (3.2) Q i + = C stc ( A + ) · ( C f + C par a ) + C inp · Q tot (3.3) Q i + = C ndc ( A + ) · ( C f + C par a ) + C inp · Q tot (3.4) Q i + = C r dc ( A + ) · ( C f + C par a ) + C inp · Q tot (3.5)with the assumption that C st , nd , r dc << ( A + )·( C f + C par a ) . A is the DC gain of the pre-amplifier,also known as open loop gain. C stc , C ndc and C r dc are the coupling capacitances between thestrip channel collecting all carriers and its first, second and third neighbours. The couplingcapacitance includes the contributions from the interstrip capacitance of the silicon sensor, thecoupling capacitances between bonding wires, as well as between bonding pads. C f is the feedbackcapacitance of the pre-amplifier of strip- i , C par a the parasitic capacitance adding to the samefeedback loop, Q tot the total charge, and C inp the total capacitance at the input node of strip- i . C inp is obtained by C inp = C strip + Õ i C ic (3.6)with C strip the bulk capacitance of an individual strip. If we only consider the capacitive couplingup to the third neighbouring channel, formula 3.6 can be written as: C inp = C strip + · ( C stc + C ndc + C r dc ) (3.7)Thus, the coupling factor k f actor , defined by the ratio of charge collected by the neighbouringchannel and the channel collecting the majority of the charge, is given by: k stf actor = Q i + Q i = C stc ( A + ) · ( C f + C par a ) (3.8) k ndf actor = Q i + Q i = C ndc ( A + ) · ( C f + C par a ) (3.9) k r df actor = Q i + Q i = C r dc ( A + ) · ( C f + C par a ) (3.10) Channel definition can be referred to figure 12 – 9 –ince C strip << · ( C stc + C ndc + C r dc ) , the charge lost to the strip capacitance coupled to thebackside is negligible [28, 29]. In this case, the fractional charge measured by each strip channelcan be calculated by Q if r ac = k if actor + Í i k if actor (3.11)after the coupling factors have been determined.The strip-to-strip coupling will be discussed in two cases: 1) Coupling before gain switching(all channels are in the same gain), and 2) coupling right after dynamic gain switching (channelsnot in the same gain). To determine the coupling factor before gain switching, low-rate X-ray measurements (only 0 or 1photon collected by each strip per frame) were performed. This can be done either by reducing thecurrent of the X-ray tube or by decreasing the integration time. Since the fractional charge in theneighbouring channels is of the same order as the noise charge, the determination has to be basedon a large statistic with enough photon entries.Figure 6 shows the relation between the energy measured by strip- i and its first, second andthird neighbouring channels on one side (noted as strip-( i + ), strip-( i + ) and strip-( i + )) in HG0 .The raw measurement in ADU values have been converted to energy based on the conversion gaindetermined from the X-ray fluorescence measurement.The region with maximal occurance appearing at (0,0) in the figure refers to the 0 photonpeak, and the other two regions to the single photons of 8.05 keV in strip- i and strip-( i + ) (orstrip-( i + ), strip-( i + )). Taking the single photon region of strip- i as the region of interest (ROI),and projecting it to the two axes, as seen in figure 7(a) and (b), the energy distributions for strip- i ,strip-( i + ), strip-( i + ) and strip-( i + ) for the same entry of X-ray photons onto strip- i areobtained. The mean energy/charge measured by each strip channel is obtained from Gaussian fitsto each individual distribution and thus the coupling factors determined according to formula 3.8,3.9, 3.10. The determined coupling factors, k stf actor , k ndf actor and k r df actor , as shown in figure 8, are6.2%, 2.3% and 1.0% in HG0, and 4.2%, 1.3% and 0.5% in G0. Using formula 3.11, the fractionalcharges have been calculated and shown in table 3. Strip channel Fractional charge in HG0 Fractional charge in G0 strip- i ( . ± . )% ( . ± . )%strip-( i + ) ( . ± . )% ( . ± . )%strip-( i + ) ( . ± . )% ( . ± . )%strip-( i + ) ( . ± . )% ( . ± . )% Table 3 . Fractional charge measured by strip- i , strip-( i + ), strip-( i + ) and strip-( i + ). Since the fraction of charge collected by neighbouring strips is not negligible (16.0% in HG0and 10.7% in G0), this effect has to be taken into account in the detector calibration. Thus, the Results in G0 have also been obtained but are not shown here. – 10 – igure 6 . 2D map of charge measured by strip- i vs. strip-( i + ), strip-( i + ) and strip-( i + ) in HG0. Inthis figure, strip- ( i = ) and its three neighbouring strips were used to generate the plot. – 11 – igure 7 . Projection of ROI onto the axes of strip- i , strip-( i + ), strip-( i + ) and strip-( i + ): (a) in HG0;(b) in G0. In this figure, strip- ( i = ) and its three neighbouring strips were used to generate the plot.The coupling to strip-( i + n ) are clearly visible as a peak shift. Figure 8 . Coupling factor for k stf actor , k ndf actor , k rdf actor in HG0 and G0. k k k C o u p li n g f a c t o r [ % ] HG0G0 conversion gain obtained in Section 3.1 should be corrected by dividing by a factor of 84.0% forHG0 and 89.3% for G0, and the noise in Section 3.2 multiplying a factor of 84.0% for HG0 and89.3% for G0, respectively.For a comprehensive understanding, the coupling factor has also been calculated theoretically.In the calculation, the DC gain of the pre-amplifer and the coupling capacitance have to be known.Since the DC gain of the pre-amplifier cannot be measured directly, it has been obtained fromsimulations using Cadence [30]. Figure 9(a) shows the simulated output voltage of the pre-amplifier, v pr ao , as function of the input voltage, v pr ai . The DC gain, A , is derived from A = − ∆ v pr ao / ∆ v pr ai and shown in figure 9(b). A is ∼
121 at the working voltage of the preamplifier ( v pr ao = v pr ai ). Thecoupling capacitance, C stc , C ndc and C r dc , is mainly attributed to: Interstrip capacitance of the– 12 –ilicon sensor, coupling capacitance between bonding wires as well as between bonding pads of thereadout channels. The interstrip capacitance is obtained from TCAD simulations [31]. Figure 10shows the simulated region of the strip sensor and the interstrip capacitance, C stint , C ndint and C r dint ,as function of bias voltage. The values at the operation voltage of 240 V are 287.1 fF, 65.2 fFand 25.8 fF, respectively. The simulated results agree with analytical calculations [32, 33]. Thecoupling capacitance between bonding wires, C stc , wire , C ndc , wire , and C r dc , wire , are 70.4, 46.9 and39.2 fF based on a theoretical calculation for pairs of parallel wires ; the coupling capacitancebetween bonding pads of strip- i and strip-( i + ) is found to be 35.4 fF, while the capacitancebetween strip- i and the others is negligible . Taking all the contributions into account, the couplingcapacitance, C stc , C ndc and C r dc , are approximately 105.8 fF, 46.9 fF and 39.2 fF, respectively.Giving the fact that the DC gain of the pre-amplifier, the feedback capacitance, and its parasitic, aswell as coupling capacitance have been obtained from previous determination, the coupling factor k stf actor , k ndf actor and k r df actor are 6.0%, 1.7% and 1.0% in HG0, and 3.7%, 1.1% and 0.6% in G0based on theoretical calculations using formula 3.11.Table 1 shows the comparison of the coupling factors obtained from measurements and theo-retical calculations, and the differences are within ∼ C st , nd , r dc << ( A + ) · ( C f + C par a ) , which neglects the charge divisionin-between the other channels without X-ray photons incoming, (2) the over-estimation of the DCgain of the pre-amplifier which depends on the input and output voltage of the pre-amplifier andmight be different in the measurement, (3) mismatch of the feedback capacitance of the pre-amplifierin ASICs fabrication, and (4) the rough estimation of coupling capacitance between bonding wires,under the assumptions that the coupling between different pair of wires is independent and the wiresare parallel and equal distance from one to another. Coupling factor Measurement Calculation k stf actor (in HG0) ( . ± . )% 6.0% k ndf actor (in HG0) ( . ± . )% 1.7% k r df actor (in HG0) ( . ± . )% 1.0% k stf actor (in G0) ( . ± . )% 3.7% k ndf actor (in G0) ( . ± . )% 1.1% k r df actor (in G0) ( . ± . )% 0.6% Table 4 . Comparison of coupling factors between measurement results and theoretical calculations in HG0and G0. The coupling capacitance between bonding wires is given by C c , wire = πǫ l / ln h d /( a ) + p d /( a ) − i [34]. ǫ is the permittivity of free space; d is the distance between two parallel bonding wires with a radius of a and a length of l . In the calculation, a = 12.5 µ m, l = 3.5 mm, and d = 50, 100 and 150 µ m were used, assuming independent couplingbetween each pair of wires. Thus, C st , nd , rdc , wire = 70.4 fF, 46.9 fF and 39.2 fF. The value is derived by measuring the coupling factor k stf actor between strip- i and strip-( i + ) after removing thebonding wires of strip-( i + ). – 13 – igure 9 . Simulation result for the inverting pre-amplifier. (a) Output voltage vs. input voltage; (b) DerivedDC gain. Figure 10 . Simulation results of interstrip capacitance using Synopsys TCAD for a strip sensor with 8 mmlong strips and pitch of 50 µ m. (a) Simulation region of the investigated sensor with a doping of × cm − and oxide charge density of × cm − ; (b) Interstrip capacitance as function of bias voltage. When dynamic gain switching happens in one strip channel, the charge stored on C f , G duringthe pre-charge phase (and C f , G if the second gain switching occurs) will be re-distributed to allcapacitors in the feedback loop of the pre-amplifier and to the neighbouring channels as well due tothe capacitive coupling. In this case, the charge division into neighbouring channels is also reduceddue to the equivalent capacitance of the pre-amplifer of the switched strip channel increases from ( A + ) · ( C f , HG + C par a ) to ( A + ) · ( C f , HG + C f , G + C par a ) , according to formula 3.3, 3.4,3.5. This causes: (a) an abrupt change of the charge in the neighbouring channels without gainswitching; (b) a delay of gain switching of the neighbouring channels.The first phenomena (a) is observed experimentally using fore-mentioned infrared laser inject-– 14 – igure 11 . Strip-to-strip coupling at the gain switching point using HG0. Infrared laser was injected into thecenter of strip- i . Measured ADU of strip- i , strip-( i + ), strip-( i + ) and strip-( i + ) as function of number of12.4 keV photons. strip- i switches at ∼
25 photons of 12.4 keV and its output decreases after gain switchingdue to the CDS stage has been by-passed. ing into the center of a strip (strip- i ) using HG0. Figure 11 shows the output of strip- i and its first,second and third neighbouring strip channels. The x -axis refers to the number of photons measuredby strip- i . Due to the diffusion of carriers in the silicon sensor and the size of the laser beam, afraction of the charge generated by the laser diffuses into strip-( i + ) and thus its outputs are higherthan 6.2% of the output of strip- i expected from pure capacitive coupling. When gain switching ofstrip- i occurs (at ∼
25 photons as seen in figure 11), a reduction in ADU is clearly visible in theneighbouring strip channels. The step corresponds to 3.3 × i + ), 1.1photons for strip-( i + ) and 0.5 photons for strip-( i + ). Considering up to the third neighbouringstrip channels, the total change is ∼ × i and the output of strip- i , strip-( i + ), strip-( i + ) and strip-( i + ) was simulated as function of thecurrent value. The injected current pulse was a triangle with a duration of 20 ns. The duration ofthe injected current pulse is longer than the pulse generated by photons in reality (usually a few nsif no "plasma effect" occurs [35–37]); however, this does not influence the results. The peak valuesof the injected current were ramped from 55 nA to 550 µ A, corresponding to 1 to 10 × i , the first gain switching occurs at ∼
25 photons. The– 15 – igure 12 . The SPICE model used for simulation including a RC network of different coupling sources,pre-amplifiers and CDS of seven strip channels. The injection current at the input node of the pre-amplifierof strip- i was a triangle shape of 10 ns for the rise and fall time. The injected current was ramped from 55 nAto 550 µ A, corresponding to 1 to 10 × switching point from simulation results is consistent with the measurements. Before the gainswitching of strip- i , the change of the CDS output for strip-( i + ), strip-( i + ) and strip-( i + )increases proportional to the output of strip- i with the ratios given by the coupling factors; afterthe gain switching of strip- i , the output node of strip- i , which is equal to the output voltage of thepre-amplifier as the CDS is by-passed, is brought to a voltage close to the pre-charge voltage. Itshould be noted that the output voltage of strip- i after the gain switching point is lower than thepre-charge voltage. This is mainly due to the fact that the charge pre-stored on C f , G (and C f , G )re-distributes to C f , HG and the neighbouring channels due to capacitive coupling and thus reducesthe output of the switched channel. The release of the pre-stored charge into the circuit is equivalentto writing a negative charge into the input node of the pre-amplifier of strip- i , and thus there isa negative charge division with the neighbouring strip channels, together with the increase of thecapacitive load in the feedback loop of the pre-amplifier of strip- i , which results in a reduction ofthe CDS output for strip-( i + ), strip-( i + ) and strip-( i + ). The SPICE simulation qualitativelyexplains the measured observation.The second phenomena (b) is observed through a measurement with laser injection into themiddle of the gap between two strips. Figure 14 shows the results when injecting the laser intothe middle of strip-( i − ) and strip- i . The results for strip-( i + ), strip-( i + ), strip-( i + ) arealso indicated in the figure. Due to the threshold dispersion of the channels, the gain switchingpoint differs channel by channel. In this measurement, strip- i and strip-( i − ) receive the sameamount of charge but switch at different number of photons: ∼
16 photons for strip- i and ∼
23– 16 – igure 13 . Simulation of the dynamic range scan showing the cross-talk after gain switching due to capacitivecoupling. CDS output of strip- i , strip-( i + ), strip-( i + ) and strip-( i + ) are shown. C D S o u t p u t [ V ] strip-istrip-(i + 1)strip-(i + 2)strip-(i + 3) photons for strip-( i + ). Immediately after the gain switching of strip- i , the cross-talk reduces thesignal in strip-( i − ) by ∼ × i − ). It has been noticed that after strip- i switched, the gain switching of strip-( i − ) requires3 photons more to switch gain, as shown in the open triangles in figure 14. The reason is that thecharge division to strip- i and strip-( i − ) is not identical any more due to the increase of capacitiveload from strip- i : After the gain switching of strip- i , its equivalent capacitance of the pre-amplifierincreases from ( A + ) · ( C f , HG + C par a ) to ( A + ) · ( C f , HG + C f , G + C par a ) . It means evenwith the same charge at the input of the pre-amplifier of strip- i and strip-( i − ), less charge flowsinto strip-( i − ) due to the non-equal charge division caused by different capacitive loads. Anotherevidence to support the explanation is that after the gain switching of strip- i , the slope of strip-( i − )decreases, which indicates less charge collected than expected even if the charge injected into thetwo strips is identical. Thus a careful calibration for each channel is necessary, which requires theknowledge of the gain status of the neighbouring channels.In addition, the cross-talk has also been investigated using different pre-charge voltages , V ref , prechr . Figure 15(a) shows the measured ADU value for strip- i , strip-( i + ), strip-( i + ) andstrip-( i + ) as function of V ref , prechr , when the gain of strip- i just switches from HG0 to G1. Theoutputs of all channels linearly depend on V ref , prechr . The intersection point between strip-( i + )and strip-( i + ) of ∼
580 mV is found to be the voltage when the reset switch of the pre-amplifieris just released. Above this voltage, the measured ADU values of strip-( i + ), strip-( i + ) andstrip-( i + ) are below their nominal pedestal values. Figure 15(b) is the measured cross-talk interms of the number of 12.4 keV photons at different pre-charge voltages. With increasing thepre-charge voltage, a larger negative cross-talk is observed, due to the fact that more negative chargeis pre-stored in C f , G and C f , G . The nominal pre-charge voltage used in the other measurements is 940 mV. – 17 – igure 14 . Cross-talk with infrared laser injected into the middle of the gap between two strips (strip-( i − )and strip- i ). Note that the threshold voltage of the comparator in this measurement is at a lower number ofphotons compared to figure 11. Figure 15 . (a) Measured ADU value of strip- i , strip-( i + ), strip-( i + ) and strip-( i + ) as function ofpre-charge voltage at the gain switching point of strip- i from HG0 to G1. (b) Cross-talk in terms of numberof 12.4 keV photons as function of pre-charge voltage. Note that the nominal pre-charge voltage is 940 mV. The measurements indicate two ways to reduce the cross-talk: 1) Reducing the voltage used topre-charge C f , G and C f , G ; 2) moving the working point of the pre-amplifier to a higher voltage.Both ways reduce the negative charge pre-stored in the medium and low gain capacitors, but haveunacceptable side consequences: The former reduces the dynamic range; the latter increases thepower of the ASIC and reduces the DC gain, which in turn increases the coupling factor before gainswitching as a further drawback.As a summary, the coupling effect can be calibrated easily before gain switching; however, aftergain switching, due to the negative charge from the pre-charged feedback capacitors and the larger– 18 –eedback capacitance, the charge redistributes in the readout network and a negative cross-talk isobserved making detector calibration complex. Thus, reducing the coupling effect is a key task forthe development of the Gotthard-II analogue front-end. Gotthard-II is currently being under development for the XFEL.EU. It makes use of silicon stripsensor as sensing material and a dynamic gain switching ASIC to cope with the high dynamic rangeup to × ∼ × w/p (width of the strip implant divided by the pitch) for the currentdesign is 11 µ m/50 µ m = 0.22. The width of the implantation of 11 µ m is close to the design limit;in addition, a further reduction of implant width cannot gain a factor of two in the reduction of thecoupling factor; the coupling capacitance due to bonding wires cannot be reduced too much as wellsince the length of the wires is limited by the guard ring region of the silicon sensor and by thereserved safe space between the ASIC and sensor edge with high voltage. For 2), an increase of thecapacitance in the feedback loop of the pre-amplifier will result in an increase of noise; in particular,since the coupling factor is inversely proportional to the feedback capacitance, a small increase inthe capacitance cannot improve the coupling effect too much whereas a significant increase canresult in a loss of single photon resolution due to the increase of noise. For 3), by optimizing thedesign of the pre-amplifier it is possible to achieve a high DC gain, and thus have the coupling– 19 –ffect reduced significantly. Thus, the design and optimization of a pre-amplifier with higher DCgain will be an important task in the development of the Gotthard-II analogue front-end. A List of parameters used in SPICE simulation
The SPICE simulation started in HG0 mode and the following parameters in table 5 were used.
Parameter Value Unit C stc C ndc C r dc C strip C par a Table 5 . Parameters used in the SPICE simulation.
The values for C stc , C ndc and C r dc are given by the sum of interstrip capacitance, couplingcapacitance between bonding wires, bonding pads, as well as the metal lines at the input of thepre-amplifiers. B Coupling factors derived from the dynamic range scan
According to the measured dynamic range scan when injecting charge with a laser into the middle oftwo strips, the slope ratio between strip-( i + ) and strip- i before gain switching, noted as Ratio i + , i ,the ratio between strip-( i + ) and strip- i , Ratio i + , i , as well as the ratio between strip-( i + ) andstrip- i , Ratio i + , i , have been calculated: Ratio i + , i = slope [ strip- ( i + )] slope [ strip- i ] = . [ ADU / ph ] . [ ADU / ph ] = . (B.1) Ratio i + , i = slope [ strip- ( i + )] slope [ strip- i ] = . [ ADU / ph ] . [ ADU / ph ] = . (B.2) Ratio i + , i = slope [ strip- ( i + )] slope [ strip- i ] = . [ ADU / ph ] . [ ADU / ph ] = . (B.3)Assuming the coupling between strip- i and strip-( i + ) is identical to the coupling betweenstrip- ( i − ) and strip- i , the coupling factor k stf actor for the first neighbouring strip can be calculatedby the difference of Ratio i + , i and Ratio i + , i : k stf actor = Ratio i + , i − Ratio i + , i = . (B.4)where the subtraction is made to remove the influence from strip-( i − ). And the coupling factor k ndf actor for the second neighbouring strip and k r df actor for the third neighbouring strip is given by: k ndf actor = k stf actor · Ratio i + , i Ratio i + , i = . · . . = . (B.5)– 20 – r df actor = k ndf actor · Ratio i + , i Ratio i + , i = . · . . = . (B.6)The derived coupling factors k stf actor , k ndf actor and k r df actor agree with the extraction fromlow-rate X-ray measurement quite well. References [1] XFEL.EU website: .[2] Altarelli, M. (2006).
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