Time resolution and power consumption of a monolithic silicon pixel prototype in SiGe BiCMOS technology

SiGe BiCMOS technology can be used to produce ultra-fast, low-power silicon pixel sensors that provide state-of-the-art time resolution even without an internal gain mechanism. The development of such sensors requires the identification of the main factors that may degrade the timing performance and the characterisation of the dependance of the sensor time resolution on the amplifier power consumption. Measurements with a $ \mathrm{^{90}Sr} $ source of a prototype sensor produced in SG13G2 technology from IHP Microelectronics, shows a time resolution of 140 ps at an amplifier current of 7 $ \mathrm{\mu} $A and 45 ps at higher power consumption. A full simulation shows that the resolution on the measurement of the signal time-over-threshold, used to correct for time walk, is the main factor affecting the timing performance.


A
: SiGe BiCMOS technology can be used to produce ultra-fast, low-power silicon pixel sensors that provide state-of-the-art time resolution even without an internal gain mechanism. The development of such sensors requires the identification of the main factors that may degrade the timing performance and the characterisation of the dependance of the sensor time resolution on the amplifier power consumption. Measurements with a 90 Sr source of a prototype sensor produced in SG13G2 technology from IHP Microelectronics, shows a time resolution of 140 ps at an amplifier current of 7 µA and 45 ps at higher power consumption. A full simulation shows that the resolution on the measurement of the signal time-over-threshold, used to correct for time walk, is the main factor affecting the timing performance.
1 Low-power performance of SiGe HBT-based amplifiers 1

.1 Time jitter comparison at low power operation of HBT and CMOS amplifiers
The integration of pixelated sensors in a microelectronic process has opened to the possibility of producing sensors with small pixels for particle-physics experiments [1] [2] without incurring in a complex hybridization process. An evolution of this approach is to combine a 100 ps or better time resolution to develop low-cost, easy to fabricate 4D sensors that can be produced in large volumes. One of the main challenges for the development of such a detector is to reduce the power consumption of the front-end electronics while maintaining excellent timing performance, in a trade-off where the limits are set by the characteristics of the transistor.
The selection of the technology for the signal amplification and the read-out is also primordial. The most direct approach to achieve excellent timing resolution with low power consumption is to use small-size transistors from the most advanced microelectronic technologies. However the cost of an engineering run in these technologies is often too high for high-energy physics experiments and the improvement in transistor speed is limited by its vulnerability to the circuit parasitic capacitances. One alternative approach [3] to maximize the timing performance without scaling down the process node is to use SiGe BiCMOS technologies, which offer a standard silicon CMOS process with the addition of a high-performance SiGe Hetero-junction Bipolar Transistor (HBT). SiGe HBTs feature a transconductance and a transition frequency that can exceed those of most advanced CMOS nodes [4]. Moreover, they exhibit low noise for fast signal integration typical of BJT technologies [5] and robustness to parasitic capacitance [4] that make them suitable for a pixel detector.

The SiGe BiCMOS monolithic pixel prototype
To evaluate the analogue behavior of a pixel detector with 4D tracking capability, we designed a small-size monolithic silicon pixel prototype [3] in the IHP SG13G2 process [6] (Figure 1). The sensor was produced on a standard substrate resistivity of 50 Ω cm. It has matrices of large and small hexagonal pixels, with hexagon sides of 130 µm and 65 µm, respectively. Each pixel is connected to the front-end circuit, which is placed in an independent deep-nwell to insulate it from the high-voltage substrate. A study of the timing performance at high power consumption of the prototype is described in [3]. In this paper we focus on the contribution to the time resolution of the amplifier power consumption and of the time-walk correction method.

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L5 L1 L4 L6 S1 S0 S2 S3 Figure 1: The prototype in IHP SG13G2 technology used for the measurements. The pixel and front-end electronics are inside deep-nwells operated at positive low-voltage, while the pdoped substrate is operated at negative high-voltage. The output of the discriminators is sent to a differential driver and directly readout by an oscilloscope.
The prototype integrates a front-end electronic circuit consisting of a HBT-based amplifier and a CMOS-based discriminator originally developed to read large pixels of a silicon sensor for medical applications [7], which was not designed to operate at very low current. For this reason in this study the CMOS-based discriminator was kept at the original design current of 40 µA. The HBT-based amplifier, on the other hand, has programmable bias components and it was operated with a supply current in the range between 7 µA and 150 µA. The output of the discriminator was sent out from the chip using a differential CML driver, allowing the measurement of the signal Time of Arrival (ToA) and Time over Threshold (ToT). In this prototype, the measurement of the amplitude of the signal at the output of the amplifier was not possible.

Experimental setup with radioactive sources
An experimental setup with radioactive sources (Figure 2) was built to measure the gain, noise and time resolution of the prototype chip while operating the amplifier at a collector current of 7, 20 and 50 µA and the sensor at a bias voltage between 100 and 180 V. The expected depletion depth at a bias voltage of 140 V for a bulk resistivity of 50 Ω cm is 26 µm, making the intrinsic sensor contribution to time resolution from the charge deposition profile and the sensor uniformity of response below 30 ps [8]. The measurement of the gain of the amplifier at the different working points was performed using a 109 Cd source, which generates 22 and 25 keV photons.
The time resolution was measured as the difference between the signal time of arrival for the pixel under test and a reference Low Gain Avalanche Diode (LGAD) using a 90 Sr source. The LGAD was glued on a dedicated amplifier board, which had a 1 mm-wide hole to allow for the passage of the 90 Sr electrons and enable Time-of-Flight (ToF) measurement (see Figure 2). The reference LGAD used for this test had a time resolution of 50 ps RMS [3,9]. The board with the monolithic SiGe prototype under test was mounted so to have the hole in the LGAD board aligned with the small pixel called "S0", as indicated in Figure 1.

Amplifier noise and gain
The measurement of the noise hit rate as a function of the discriminator threshold is reported in Figure 3, for thresholds above and below the baseline and for different amplifier currents. Although the noise hit rates show a compression for values larger than 500 kHz due to a saturation of the counting-rate capability of the data-acquisition system, these measurements allow estimating the RMS voltage noise as seen at the output of the discriminator.
The CMOS-based discriminator acts as a filter for the amplifier noise. The ratio between the noise at the output of the amplifier (σ V ) and the one measured after the discriminator was estimated using a Cadence Spectre1 simulation. The simulation shows that, in order to estimate the voltage noise at the output of the amplifier that we need to calculate the Equivalent Noise Charge (ENC), the standard deviation of the voltage noise obtained by the measurement of the noise hit rate at the output of the discriminator should be increased by 20% for an amplifier current of 7 µA, 50% for a current of 20 µA and 60% for a current of 50 µA. The resulting values after the scaling factor obtained from the simulation are reported in Table 1. The charge gain A Q of the amplifier was estimated by measuring the photon count rate as a function of the discriminator threshold using a 109 Cd source. The results for the three amplifier currents considered are reported in Figure 4; the data were fitted with the sum of two error functions, to account for the two main photon energies, and a constant, to account for the low-probability emission of 88 keV photons. A second degree polynomial was added to describe the low threshold region. The mean value of the error functions estimated by the fit was used to extract the amplifier gain values reported in Table 1. Then, the noise and gain measurements were used to estimate the Equivalent Noise Charge (ENC) values, also reported in Table 1. Table 1: Voltage noise at the output of the amplifier, charge gain and ENC for the different amplifier currents. The results for an amplifier current of 150 µA are those from [3]. : Photon count rate as a function of the discriminator threshold for the three values of the amplifier collector current with the sensor exposed to a 109 Cd source. The lines represent the fit done with a composition of two error functions, a constant and a second degree polynomial function (the latter being limited to the low-threshold region).

Time resolution
Electrons emitted by the 90 Sr source were used to measure the jitter on the ToF between pixel "S0" and the reference LGAD detector. The output of the discriminator of the pixel under test was read by an oscilloscope with a sampling rate of 40 GSa/s and an analogue bandwidth of 3 GHz. The output signal of the LGAD was amplified using a discrete components amplifier based on SiGe HBTs [10] and sent to a channel of the oscilloscope. Pixels "S1" and "S2" were operated at the lowest possible threshold clean from noise. They were attenuated and read by one channel of the oscilloscope to generate a tag signal for events with charge shared between the pixel "S0" under test and the neighbouring ones. Pixel "S3" was not used and its discriminator threshold was set to the highest possible value to prevent it from firing.
The oscilloscope trigger was configured to require a pulse from the pixel under test followed by a pulse from the reference LGAD within a 50 ns time window. At each trigger, the waveforms from all channels were recorded, allowing the calculation of the ToA of all pulses, the ToT of the pixel "S0" under test and the amplitude of the LGAD signal.
During data analysis, each waveform was split in a signal region and a background region. The signal region was defined as the time interval in a window of ±15 ns around the trigger time, containing all the pulses from the LGAD and the Device Under Test (DUT). The part of the waveform before and after the signal region was treated as background region. The latter was used to estimate the baseline and remove noisy events: if one of the waveforms exceeded a given threshold in the background region, the event was considered to be noisy and removed from the analysis. The fraction on noisy events was typically within 0.1% of the total events.
Coincidences between the reference LGAD and the DUT were acquired at several thresholds and bias voltages for different amplifier currents. To keep the data analysis as simple as possible, the same correction function was applied to the entire ToT range, although it was noticed that a slightly improved time resolution could be obtained by a special treatment of events at the edge of the TOT distribution. For the same reason, the only event selection applied was to remove noisy events and define an interval for the LGAD pulse amplitude where the time resolution was measured to be 50 ps [3]. Figure 5 shows the distribution of the ToT for the three amplifier-current working points after the simple data analysis described. The increase of the average value of the ToT at lower currents is an indication of the reduction of the amplifier bandwidth that is in part attributed to the increase of the output impedance and in part to a reduction of the gain-bandwidth product of the transistor. The charge thresholds are obtained dividing the discriminator threshold voltage by the amplifier gain.  Once fixed the thresholds, the ToF was measured with the oscilloscope as the difference of the ToA values of the signals from the prototype under test and the reference LGAD. The time-walk can be partly corrected by the distribution of the correlation between the ToF and the prototype-signal ToT, as the one showed in Figure 6 for an amplifier current of 50 µA and a threshold of 1046 electrons. The range of the time-walk correction depends on the discriminator threshold and on the amplifier current, as shown in Figure 7, with values ranging from 250 ps to 2.5 ns. Figure 8 shows the ToF distribution after time-walk correction for the same amplifier current and discriminator threshold of Figure 6. The mean value of the distribution was set close to zero by the time-walk correction. The time jitter of the distribution was estimated by a gaussian fit that excluded part of the tail at positive values of ToF that is caused by a systematic error in the time walk correction [3]. Due to its non-linear transfer function, the discriminator produced an asymmetrical jitter of the ToT, sometimes overestimating its value. In the latter case, the events are   under-compensated for time walk, producing a tail in the ToF distribution. In all cases, the full width at half maximum (FWHM) of the distribution was found to be compatible with the σ T oF obtained from the Gaussian fit. The fraction of events in the tails exceeding the Gaussian distribution is typically below 5% of the total number of events. The time resolution of the prototype under test with ToT-based time walk correction was finally estimated by subtracting in quadrature 50 ps (the time resolution of the LGAD) from the σ ToF value obtained from the fit. Figure 9 shows the time resolution for the different amplifier currents as a function of the discriminator threshold. In all cases the measured time resolution is below 180 ps and improves at larger thresholds. Cadence Spectre simulations suggest that the dependence on the discriminator threshold indicates that the poor ToT resolution, which limits the accuracy of the time-walk correction, is the dominating factor for the sensor time resolution. The reduction of the amplifier current enhances this effect, increasing both the range of the time walk and the signal fall time, with consequent deterioration of the ToT resolution at the lower thresholds. Therefore, we conclude that the intrinsic jitter of the amplifier is negligible in this prototype with respect to the resolution of the time walk correction. Figure 10 shows that the time resolution improves at higher sensor bias voltages. A large improvement is observed at the lowest amplifier current, where the resolution is approximately 140 ps at the highest voltage. This improvement cannot be explained only by an increase of the average charge drift velocity inside the sensor, because the sensor intrinsic contribution to the time resolution is expected to be small compared to the resolution measured at low amplifier current. The improvement of the timing performance at a higher bias voltage can be attributed to an increase of the signal charge (up to 13% at the highest voltage) and a small reduction of the pixel capacitance.

Conclusions
The first small-size monolithic pixel prototype shows in ToF measurement with a 90 Sr source that a time resolution of 140 ps is achievable for an amplifier current as low as 7 µA, while the best achievable performance is 45 ps. These measurements indicate that some design characteristics of this prototype are affecting the time resolution: 1. The timing performance improves for higher thresholds. A study of the sensor response with a Cadence Spectre simulation suggests that this behavior is indicative of a time resolution limited by the use of the ToT to compensate for the signal time walk.
2. The better timing performance at higher sensor bias indicates that an increase of the depletion layer width is especially beneficial at very low power consumption.
The understanding of these effects is fundamental to drive the development of fast monolithic silicon pixel sensors, to exploit the full potential offered by the SiGe technology.

Discussion
Thanks to their low-noise and high transition frequency, SiGe HBTs can be used to produce amplifiers for silicon pixel detectors with low time jitter at very low power consumption. A singletransistor amplifier in common source (emitter) configuration was simulated using CADENCE Spectre. The simulation investigates the trade-off between the intrinsic timing jitter and the power consumption for a minimum-size CMOS transistor and a SiGe HBT in the SG13G2 130nm BiCMOS process of IHP Microelectronics. Figure 11 shows the result of the simulation for two scenarios: 1. A noiseless, ideal polarization of the transistors with a parasitic capacitive load of 2.5 fF.

2.
A realistic CMOS-based polarization circuit with the same capacitive load.
In both cases a pixel capacitance of 80 fF is considered. BJT -without polarization circuit MOS -without polarization circuit BJT -with polarization circuit MOS -with polarization circuit Figure 11: Cadence Spectre simulation. Time jitter as a function of the supply current for an amplifier based on a CMOS transistor in common source configuration (blue) and for a SiGe HBT in common emitter configuration (orange). Input capacitance: 80 fF, input charge: 1600 electrons. The time jitter is defined as the ratio between voltage noise at the output of the amplifier and the maximum slope of the pulse rising edge. Dashed lines: biasing circuit made of ideal, noiseless resistors. Full lines: Realistic CMOS-based biasing circuit.
The simulation shows that the HBT has a lower intrinsic jitter than the CMOS transistor by more than a factor of two, despite the extra capacitance that was added to the standard HBT in the insulation process. This superior performance is further enhanced when the robustness to parasitic capacitance of the HBT is taken into account.