Introduction

Since I started my PhD I have been testing several LGAD devices, and variations such as TI-LGAD and others. All these devices are samples intended for research purposes, i.e. with relatively small number of pixels and literally hundreds of different flavors with different characteristics. To test these samples I was using the so called Santa Cruz board  or a variation of it called the Chubut board (or Chubut 1) . These are single channel readout boards with a built in single stage amplifier in which the sample is stick onto a high voltage pad, and then wire bonded to the board itself.

Though these boards can get the job done, they present some inconveniences when the number of samples to be tested grows, as each time a new sample has to be tested, the old sample has to be removed thus destroying the wire bondings. As the number of times a sample can be wire bonded is finite, this makes it not only tedious but in some cases impossible to repeat a test on a sample that has previously been tested. Additionally, after some number of tested sensors the board as well wears and it cannot be further wire bondedI have experienced this with several boards, that when new the wires stick perfectly to the bonding pads but after some number of usages it becomes impossible to wire bond them again. In some cases this number of usages was relatively large (say about ten) but in some other cases it was as low as only one usage. I believe this is related to some effect related to moisture with the cooling and warming cycles required for each test. But I still don't know it for sure., having to be replaced with a new one. In doing this we are discarding a whole board which completely operational except that the wires do not stick, which is not just pity but it also complicates the logistics because I found myself sometimes without useful boards and still with sensors to be tested. Furthermore the amplification provided by these boards is usually not enough to go straight into a digitizer (or an oscilloscope) and a 20 dB second stage amplifier has to be used.

To overcome these issues I decided to develop a new board from scratch, which is the Chubut 2 board. It incorporates a design with a carrier board + a main board. The main board hosts all the circuitry and connectors while the carrier board is a super-cheap board which only hosts the DUT. In this way the main board can be reused up to infinite timesWell, it probably has a limit but for sure it is more than 1e3 times according to the specifications of the components. with different carriers. The fact that the carrier only hosts the DUT makes it very cheap (when compared with the main board, or with one of the other readout boards) and thus it is feasible to produce one carrier for each DUT, and even with different designs to adapt the wire bondings to the DUT's layout. The current design possesses 4 independent (and identical) channels, and each channel has two amplification stages leading to a total of ~40 dB voltage gain (on 50 Ω input and output).

In this document I present the reader (i.e. probably me in the future) with some information about this board.

Board design and details

In pictures of the Chubut 2 board are shown. Here it can be seen the main board with the electronic components and connectors as well as an example of a carrier board with a DUT mounted. The blue 3D printed piece is there to hold in position the carrier board. This piece can be easily re manufactured (or even omitted) depending on how the board is going to be mounted on the rest of the setup. As can be seen the main board hosts all the electronic components and comprises the "expensive half" of the setup, while the carrier board (the smaller one) requires no assembly at all other than mounting the DUT, thus making it very cheap in comparison.

Pictures of the Chubut 2 board.

All the connectors are of type MMCX, a kind of miniature RF connectors, even those for the high voltage and the power supply. These connectors were chosen in order to reduce the layout of the board and leaving the door open to further versions of this board with a larger number of channels with a similar layout size. For the high voltage and power input the choice for coaxial connectors was done in order to make it easier to avoid EMI in setups where the length of the cables is large, which can easily happen in my experience.

The amplifiers are implemented with the PSA4-5043+ by Mini-Circuits. This is a low noise integrated amplifier with a bandwidth spanning from 50 MHz to 4 GHz and with an input and output impedance of 50 Ω . It can be powered with any voltage between 3 V and 5 V with a relatively constant performance. Each channel has two of such amplifiers in series leading to a total voltage gain of ~40 dB (on 50 Ω), which is roughly what we get with the Chubut 1 (or Santa Cruz) board and a second stage 20 dB amplifier. Thus, the outputs of the Chubut 2 board can be connected straight into the input of an oscilloscope or a digitizer. For further details on the circuit please consult the source files on reference .

The most challenging part in the design of the Chubut 2 board was the interface between the main and the carrier boards. The reason is that I was looking for an interface that can handle high frequencies but at the same time minimizes the cost and assembly effort on the carrier board. The high frequency constraint basically implied keeping the distance from the DUT to the input of the amplifiers as low as possible. After several iterations and visits to the design table, I ended up with a very simple yet amazingYes, I am proud of it 😀. It is simple, functional, cheap and elegant. All the principles of engineering accomplished. design which is based on pogo pins. This design, which can be seen in the pictures in and in , uses one pogo pin per channel plus a few additional pins for ground and high voltage. The pogo pins are mounted on the main board. On the carrier board, instead, contact with the pogo pins is made simply with exposed pads on the bottom side of the board. When the carrier is put on top of the main board, the contacts are established. These contacts turn out to be super reliableMaybe you have seen the amazing MagSafe magnetic connector by Apple. It uses pogo pins. and to my surprise work very well at high frequencies. The type of pogo pin was carefully chosen to match the thickness of the board, and is installed in a non conventional way going from one side to the other. This guarantees that a small amount of pin is exposed on the carrier side just enough for contacting, thus minimizing the distance from the DUT to the input of the amplifiers, which at high frequencies is crucial. Additionally this design is super flexible in the sense that the pins can be arranged in any way on the surface so if the number of channels is increased in the future it is just a matter of distributing additional pins. According to the datasheet the number of "mating" cycles of the pogos ranges from 1e5 to 1e6 , which seems to be enough.

Detail of the pogo pins and the carrier board.

As one important test that is usually performed with LGADs are beta scans, a hole in the middle of the board is included in the design. This makes it possible for the beta particles to make it through the board. The carrier boards also have a hole, however the size of this hole can vary for different samples layouts.

The design of the board is open source. The source files can be found on reference . For quick reference the layout of the board with some dimensions is shown in .

Layout of the Chubut 2 board.

In the electrical schematic of each channel is shown. As seen each channel has two amplifying stages and there is a 3 dB resistive pi attenuator in betweenAs suggestion from the electronics workshop at our institute, to avoid undesired oscillations.. Each of the pads is DC-grounded via a 10 kΩ resistor hanging from the input.

Electrical schematic of one channel of the Chubut 2.

As a final comment, the number of components and size of each amplifying stage can probably be reduced. The current version (230202) has extra filtering stages on the power supply, and soldering pads for RF shields (which seem to be not necessary), etc. This can probably be simplified for a higher integration density with more channels.

Characterization

In this section I present some results of the first tests I performed with the board.

Time resolution

In the context of my PhD it is probably the time resolution the most important parameter to be measured. So here I am presenting results of time resolution measured with the newer Chubut 2 board and comparing it with measurements done in similar conditions using the older readout board Chubut 1 . The results are shown in . To perform the measurement a TI-LGAD from the RD50 production (wafer 16, 1 trench, pixel border V3, contact type dot) was used. In blue the results from the Chubut 1 board, in red the result using the Chubut 2. As seen, the results are in agreement. This data was obtained in our beta setup at UZH .

Transimpedance

The transimpedance is an important parameter of the readout board as it allows the conversion of charge measurements to Coulomb. In general, for any circuit, the transimpedance is defined (in the frequency domain) as $$\text{transimpedance}\overset{\text{def}}{=}\frac{V_{\text{out}}}{I_{\text{in}}}$$ and characterizes the current-to-voltage gain of an amplifier. Since we are interested in measure the current flowing through a DUT we can also define an effective transimpedance as $$\text{effective transimpedance}\overset{\text{def}}{=}\frac{V_{\text{out}}}{I_{\text{DUT}}}$$ which measures the relation between the output voltage of the circuit and the current in our DUT. An ideal transimpedance amplifier is a circuit with zero input impedance and zero output impedance, so no matter what the source and load impedances are (as long as they are finite and non-zero) the effective transimpedance will coincide with the transimpedance. This is the kind of amplifier we would like to have, so that all the charge from the DUT makes it to the input of the amplifier and is converted into a voltage signal that can be digitized without loss.

can be expanded into $$\text{effective transimpedance}=\frac{V_{\text{out}}}{I_{\text{in}}\frac{Z_{\text{DUT}}+Z_{\text{in}}}{Z_{\text{DUT}}}}$$ where $Z_{\text{DUT}}$ is the impedance of the DUT and $Z_{\text{in}}$ the input impedance of the amplifier. If we assume that we are within the ideal transimpedance amplifier regime, i.e. we assume that $Z_{\text{DUT}}\gg Z_{\text{in}}$, then this becomesNote that this assumption also implies, as stated before, that $I_{\text{in}}=I_{\text{DUT}}$. $$\text{effective transimpedance ideal}=Z_{\text{in}}\frac{V_{\text{out}}}{V_{\text{in}}}$$ We can find the parameters of the amplifier in the datasheet , where an input impedance of 50 Ω and a voltage gain of 20 dB are specified. Since the board has two stages, this is a total voltage gain of 40 dB which is equivalent to 100. There is a 3 dB pi attenuator in between the two stages. Thus, $$\text{effective transimpedance ideal} \approx 3540~\Omega$$ is the expected value as per design assuming things work as intended.

In order to validate the previous analysis I also want to measure the effective transimpedance. First of all, if we assume that the effective transimpedance is flatI.e. independent of frequency. This implies that in the time domain $$ \begin{align*} V_{\text{out}}\left(t\right) & =\intop V_{\text{in}}\left(\tau\right)\text{effective transimpedance}\left(t-\tau\right)\text{d}\tau\\ & =\text{effective transimpedance}\intop V_{\text{in}}\left(\tau\right)\delta\left(t-\tau\right)\text{d}\tau\\ & =\text{effective transimpedance}V_{\text{in}}\left(t\right) \end{align*} $$ where $\delta$ is the Dirac delta function. within the bandwidth of our signals then from we can go to $$\text{effective transimpedance}=\frac{\int V_{\text{out}}\ \text{d}t}{\int I_{\text{DUT}}\ \text{d}t}$$ The denominator here is nothing more than the total charge produced in the DUT while the numerator can be measured by recording the waveform at the output (e.g. with an oscilloscope) and integrating it. Thus, $$\text{effective transimpedance}=\frac{\int V_{\text{out}}\ \text{d}t}{Q_{\text{DUT}}}$$ If for a DUT we use a PIN diode, i.e. an "LGAD with no gain layer" then we know what to expect for the charge $Q_{\text{DUT}}$ when a MIP impinges on it. The charge will follow a Landau distribution with a known MPV  that can be calculated. Thus, the transimpedance can be measured with $$\text{effective transimpedance measured}=\frac{\text{MPV of time integral of voltage}}{Q_{\text{MPV for fully depleted PIN from theory}}}$$

To proceed with the measurement I mounted a PIN from the RD50 FBK TI-LGAD production which has a 2×2 layout with a pad size of 1200×1200 µm and a thickness of 45 µm, so the MPV for the charge, when fully depleted, is 0.48 fC . I wire bonded the four pads of the PIN to each of the channels of the Chubut 2. Then I placed the board in the climate chamber in the usual configuration for beta scans, i.e. on top of our MCP-PMT, as illustrated in . The climate chamber was set at -20 °C. Each of the channels of the board were connected to each input of the oscilloscope, a LeCroy WaveRunner 9254M, while the signal from the MCP-PMT was connected to the external trigger input, and it was used to trigger the oscilloscopeThe fact of triggering with the MCP-PMT not only ensures that no bias is introduced by setting a threshold on the DUT but at the same time the MCP-PMT somehow filters out the low energy tail of the spectrum of the beta source and keeps only the MIPs, which is desired.. I powered the board with 3 V as it reduces the power consumption and, in my experience, the performance is not altered.

Schematic diagram of the setup used to measure the effective transimpedance with a PIN.

I performed several beta scans at different bias voltages. At each voltage I measured the most probable value of the integral of the signal, as explained in In reference  I explain using the amplitude of the signal, but exactly the same procedure can be followed with the integral under the peak of the signal.. In an example of the charge distribution is shown for one of the voltages that were measured. In this plot the x axis is the integral in time, under the peak, of the waveforms reported by the oscilloscope. From these fits, the MPV of the distribution for the signal was obtained, denoted as x_mpv in the legend of the plot.

From a series of fits like those shown in the numerator from was obtained. Dividing each of these values by the (known and constant) value for the denominator, the plot in was obtained. In this plot we can appreciate that the measured effective transimpedance is a function of the bias voltage, although in principle it should not. The reason is that for low voltages the PIN is not yet fully depleted, and thus the collected charge is lower than expected. For voltages higher than ~30 V we see that this quantity reaches a plateau which indicates that the PIN is fully depleted so this is the region in which to look for. The average of the measured effective transimpedance both voltage- and channel-wise in region where the bias voltage is higher than 30 V is $$\text{measured effective transimpedance} = 5050\pm250\ \Omega$$ There is a disagreement with respect to the design value from . The reason for this disagreement is still not clear to me, but it is probably related to the falling edge of the signals, as discussed in .

Since in this kind of setup with LGADs the charge is, to the best of my knowledge, proportional to the amplitude of the signalsSee ., I performed the same kind of data analysis as shown in but instead of using the integral under the peak using the amplitude of the signals. The results are shwon in . From this measurement: $$\text{charge in Coulomb}\approx\frac{\text{amplitude}}{\left(5.67\pm0.25\right)\times10^{12}}$$

About the conversion to Coulomb

In order to obtain the collected charge in Coulomb units it is possible either to divide the integral of the signal by the effective transimpedance from or to divide the amplitude of the signal by the factor from . In doing so for the LGAD signal in (the one measured with the Chubut 2 board) we obtain 30±1 fC using the integral under the peakI.e. the Collected charge (V s). and 16±0.7 fC when using the amplitude which is clearly in disagreement. I believe that this disagreement is related to the "falling edge issue" discussed in more detail in , which for some reason is less noticeable with the small signals from a PIN diode while the large signals from an LGAD are more affected.

For the time being I will use the amplitude ofreason the signals and in order to obtain the charge in Coulomb. The reason I find it more reliable than the integral-under-the-peak is that if the issue is related to the falling edge, as discussed in , then this should have a much stronger influence in the integral than in the amplitude itself.

Waveforms

The critical aspect of the board in terms of prformance is the fact that it behaves well as a broadband amplifier for use in the time domain. The waveforms thus yield valuable information. In two waveforms can be seen. The two waveforms were obtained in our beta setup at UZH using two identical TI-LGADs. The first signal is using the Chubut 1 readout board while the second signal is with a Chubut 2 board.

When looking at the signals in it is possible to notice that the rising edge is similar but the falling edge in the Chubut 2 case is slower. I observed this not only in the example signal shown but in all cases, and this probably accounts for the non agreement in the effective transimpedance discussed in . The reason for this is still unknown to me.

To perform timing measurements (in the way we usually do it) the most critical part of the waveforms is the rising edge. Despite the good looking rising edge from , a little bit more quantitative comparison is shown in where the rise time distribution for two measurements performed with each board, both in similar conditions, is compared. Here we see that the rising edge is slightly slower in the Chubut 2, but in practical terms this should not introduce any inconvenience.

Signal to noise ratio

A comparison of the SNR is shown in . Here the SNR is defined as the ratio between the amplitude of the signal and the noise measured in the region before the peak in the waveform. In this plot the ECDF for a single voltage measured with each board is shown. As seen the results are in essence the same.

Conclusions

A multichannel readout board for LGADs was developed with a novel interconnection mechanism that allows for an easy interchange between different samples. The produced version of the board has four channels, but it can easily be modified. Each channel has two amplifying stages implemented with integrated RF amplifiers thus providing enough amplification to connect the board straight into a digitizer or an oscilloscope. A time resolution measurement with an LGAD mounted in the new board was performed and the results show it is good. There is a disagreement between the expected transimpedance and the measured transimpedance which is still to be studied.

Additional stuff