# Operation and Calibration of a
Highly Granular Hadron Calorimeter
with SiPM-on-Tile Read-out

O. Pinto for the CALICE Collaboration  Manuscript received December 13, 2019.
This project has received funding from the European Union Horizon 2020
Research and Innovation programme under Grant Agreement no. 654168. O. Pinto
is with the Deutsches Elektronen-Synchrotron (DESY), Germany (e-mail:
<EMAIL_ADDRESS>
###### Abstract

The Analogue Hadron Calorimeter (AHCAL) is being developed within the CALICE
collaboration for experiments at a future lepton collider. It is a sampling
calorimeter with alternating layers of steel absorber plates and plastic
scintillator tiles as active material. In the SiPM on tile design, the tiles
are directly coupled to silicon photomultipliers (SiPMs). The front-end
electronics are integrated into the active layers of the calorimeter. They are
designed for low power consumption by rapidly power cycling according to the
beam structure of a linear accelerator. In 2017 and 2018, a new large
prototype with 38 active layers of 72x72 cm2 size has been built. Each active
layer consists of four readout boards with four 36 channel SPIROC2E readout
ASIC each, resulting in 576 channels per layer. The prototype has been
designed for mass production and assembly techniques: It uses injection-
moulded tiles which were wrapped semi-automatically in reflector foil, tiles
and electronics components were assembled using pick-and-place machines and
all detector parts were tested during assembly. The prototype with
$\text{\,}\sim$22,000 channels was commissioned at DESY and took muon,
electron and pion data at the CERN SPS to demonstrate the capabilities of a
SiPM-on-tile calorimeter concept with scalable detector design and the
reliable operation of a large prototype. This proceedings gives an overview of
the calibration results of the large CALICE AHCAL technological prototype.

##  I Introduction

The physics at future high-energy lepton colliders demands a jet energy
reconstruction with unprecedented precision. It can be reached by employing
Particle Flow Algorithms (PFA)[1], which are capable of achieving this by
measuring each particle in the detector component with the best energy
resolution. These algorithms require highly granular calorimeters to deliver
optimal performance in jet energy resolution of the order of
$3\text{\,}\mathrm{-}$$4\text{\,}\mathrm{\char 37\relax}$ for jet energies
between 45 GeV and several 100 GeV. Within the CALICE collaboration several
highly granular technologies for electromagnetic and hadronic calorimeters are
developed. One of these technologies is the Analog Hadron Calorimeter
(AHCAL)[2].

##  II The CALICE SiPM-on-Tile Hadron Calorimeter technological Prototype

Figure 1: Top view of AHCAL technological prototype fully assembled with 38
active layers Figure 2: HCAL Base Unit.

The AHCAL technological prototype consists of a non-magnetic stainless steel
absorber structure with approximately 17.2 mm thick plates and 38 active
layers which are placed in the absorber structure as shown in Fig.1. It has
21,888 channels read out on an individual basis by SiPMs. The basic unit of
the active elements is the HCAL Base Unit (HBU)[3], which has a size of 36x36
cm2. It is equipped with 144 SiPMs which are read out by four SPIROC2E
ASICs[4]. The key features of the electronics are its integration into the
active volume and its capability to operate in power-pulsed mode which reduces
the power consumption and eliminate the need for active cooling by exploiting
the beam structure of linear colliders. The SPIROC2E ASIC also provides a
cell-by-cell auto trigger and individual hit time with a precision of a few ns
in test beam operations. In linear collider operation conditions with shorter
data-taking windows, sub-ns time resolution is expected. The prototype is
constructed with injection-moulded polystyrene scintillator tiles[5] with a
dimple at the centre optimised for best light collection[6]. They are read out
by Hamamatsu MPPC S13360-1325PE photon sensors. The technological prototype
has a layout scalable to full a ILC detector.

##  III CALIBRATION

The calibration procedure of the AHCAL prototype has several goals:

  * •

The conversion of the hit energy and time from electronics to physical units

  * •

if necessary, the equalisation of the cell response to allow an efficient
auto-triggering in all channels

  * •

the monitoring of the stability of the detector

A global calibration chain is necessary to properly calibrate the calorimeter
channels. Every channel has to be calibrated separately due to non-
uniformities such as unequal tile wrapping, glueing or SiPM and ASIC specific
effects. Two calibration chains are needed, one for energy calibration and the
other for time calibration. The hit energy or SiPM charge is read-out as ADC
(Analogue to Digital Converter) and needs to be calibrated in units of minimum
ionising particles (MIPs). The time is stored as a charge TDC (Time to Digital
Converter) and is calibrated into values of nanoseconds.
The calibrated hit energy $E_{i}$ in units of MIP can be determined by eq. 1:

$E_{i}\hskip 4.26773pt[MIP]=f_{desat}\hskip
4.26773pt(pixels)\frac{(A_{i}[ADC]-Pedestal)/IC}{MIP}$ (1)

where

$pixels=\frac{(A_{i}[ADC]-Pedestal)/IC}{Gain}$ (2)

the function fdesat is the inverse of the SiPM response function, describing
the SiPM output signal as a function of the incoming light intensity. At small
amplitudes fdesat is close to one and increases strongly for large signals. IC
is the inter-gain calibration.
As a final step in calibration, cluster energies will be converted to the GeV
scale using electron testbeam data of known energies.

###  III-A Gain Calibration

The gain calibration allows the possibility of monitoring the detector
performance and stability. The gain calibration is performed using dedicated
LED runs. For all the AHCAL channels, single photon spectra are taken at low
intensity LED light, and are fitted with a multi-Gaussian function. The gain
value is extracted as the distance between the first and the second single
photon-electron peaks. An example of a typical single photon spectrum is shown
in Fig 3. The distance between two neighbouring peaks is left as a single free
parameter in the multi-Gaussian fit. The width of the peaks is dominated by
electronic noise. The statistical uncertainty on the gain determination is
less than $1\text{\,}\mathrm{\char 37\relax}$ for fits which pass quality
criteria.
During testbeam operation LED runs were taken approximately once per day. Gain
extraction was achieved for $95\text{\,}\mathrm{\char 37\relax}$ of the
channels. The gain values for the remaining $5\text{\,}\mathrm{\char
37\relax}$ of channels were taken as the average of the channels of the
corresponding chip. Combining several gain runs, more than
$99.9\text{\,}\mathrm{\char 37\relax}$ of all channels can be calibrated
individually. The mean gain is ${\sim}$16.6 ADC/pixel with a spread of 1.0
ADC/pixel which is about $6\text{\,}\mathrm{\char 37\relax}$ as shown in Fig
4. For channels on the same ASIC the spread is only $2.5\text{\,}\mathrm{\char
37\relax}$, showing that the gain variation between ASICs contributes
significantly to the overall spread. The gain is consistent between the May
2018 run and the June 2018 run (both without power pulsing). For the October
2018 run (with power pulsing) a small shift in gain is observed which was
caused by electronic effects.

Figure 3: SiPM single photoelectron spectrum of a single channel. Figure 4:
Gain constant extracted for all AHCAL channels.

###  III-B MIP Calibration

Minimum-ionising particles (MIPs) are used to perform a cell to cell
equalization. For each channel the measured hit energy spectrum for muons is
analysed. Its most probable value is derived from a fit with a Landau function
convoluted with a Gaussian. An example of a single channel is shown in Fig 5.
The fit function takes into account not only the energy loss of muons within
the scintillator tiles, but also contributions from photon counting statistics
and electronic noise. The MIP calibration efficiency, i.e. the amount of
successful fits of muon hit energy spectra, is about
$99.92\text{\,}\mathrm{\char 37\relax}$. As shown in Fig 6 the mean MIP
calibration constant is 217 ADC with an RMS spread of 30 ADC which corresponds
to $\text{\,}\sim$$14\text{\,}\mathrm{\char 37\relax}$. For channels on the
same ASIC, the spread is $8\text{\,}\mathrm{\char 37\relax}$, which is good
enough for autotrigger operation with the same threshold for all channels.

Figure 5: Energy deposited by a muon in one AHCAL cell. The red solid line is
obtained by fitting a Landau convoluted to a Gaussian function to the data.
The dotted red line is the function extrapolated outside the fitting range.
Figure 6: MIP constant extracted for all AHCAL channels.

###  III-C Inter-Gain Calibration

The SPIROC2E chip can store the ADC either in low gain (LG) or in high gain
(HG) mode. The inter-gain calibration factor of the channel is the ratio of HG
to LG and is required for smooth transition between HG and LG hit energies.
This constant depends on ratio of capacitors because of the circuit design.
The extraction of the inter-gain calibration coefficients from LED runs is
possible because the range of linear response of the chip in both modes
overlaps. The amplitude of the signal is varied within the linear range of HG
and LG by varying the LED light intensity. The inter-calibration coefficient
for each channel is taken as the slope of a linear fit as shown in Fig 7. The
inter-calibration factor ranges between 17 and 21 with a mean of 19.4 and a
RMS spread of 0.66 which is $\text{\,}\sim$ $3\text{\,}\mathrm{\char
37\relax}$. For the remaining channels the inter calibration values were taken
as the average of the channels of the corresponding chip.

Figure 7: Response of one AHCAL channel in the two amplifier gain modes (Low
Gain and High Gain) for increasing LED light intensity. Figure 8: Inter-gain
calibration values extracted for all calibrated channels.

###  III-D SiPM Saturation

Due to the limited number of pixels and the finite pixel recovery time, the
SiPM is an intrinsically a non-linear device and limited by response
saturation at high amplitudes. The response function of a SiPM describes the
number of fired pixels as a function of the number of incoming photons (see
figure 9). It can be approximated by

$N_{fired}^{sat}=N_{eff}\hskip 7.11317pt(1-e^{N_{fired}^{unsat}/N_{eff}}),$
(3)

where $N_{fired}^{sat}$ is the number of fired pixels and $N^{eff}$ is the
effective number of pixel in the SiPM. For studies of saturation behaviour
bare SiPMs were used. A dedicated set-up was used to ensure that all the
pixels were illuminated in a homogeneous way. The $N_{eff}$ for MPPC
S13360-1325PE is found to be consistent with the real number of pixels of
2668[7]. Alternatively, $N_{eff}$ has been extracted using the AHCAL
measurements with the SiPM mounted on a tile, showing consistent results. In
this case, also saturation effects in the ASIC can play a role. For the
reconstruction of hit energies from the SiPM signals the inverse of the
saturation function is used.

Figure 9: Describing the response of SiPM.

###  III-E Time Calibration

Figure 10: TDC vs. time reference plot.

The time calibration is performed using muon runs. The time information is
stored in TDC values and needs to be calibrated to nanoseconds to have a
common time reference in each event. To record time, TDC voltage is ramped up
and down in intervals of 4000 ns. For this purpose the SPIROC2E chip has two
TDC ramps for even and odd bunch crossings (bx) that form together a combined
up and down ramping. Once a hit occurs the bxID as well as the current TDC
value is recorded. From the slope of the TDC ramp and its pedestal the time in
nanoseconds is calculated for both channel wise and memory cell-wise as shown
in Fig 10. A detailed description on how the time calibration is performed can
be found in [8]. A 1 ns time resolution of the AHCAL is one of the design goal
for testbeam mode. In practice the time resolution is limited by the front-end
electronics.

##  IV CONCLUSION

The CALICE AHCAL is a SiPM-on-tile steel sampling calorimeter prototype which
handles large number of SiPMs ($\text{\,}\sim$22000 channels in total). It has
been calibrated with an integrated LED system for SiPM gain, using minimum
ionising particles (muons) for energy scale and corrected for the non-
linearity of the SiPM response curves. The detector has been successfully
operated in test beams from May to October 2018 at the CERN SPS and was stable
with more than $99.9\text{\,}\mathrm{\char 37\relax}$ channels working. With
the calibrated prototype, shapes and structures of hadronic showers as well as
the separation of two close-by showers can be studied in great detail, thus
testing directly an important ingredient to the performance of particle flow
algorithms.

## Acknowledgment

I would like to thank my colleagues from AHCAL group for allowing me to
present material and results from their research and colleagues from the
CALICE collaboration for their help.

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