Instrumentation & Measurement Magazine 24-9 - 6

much larger than 1 for the frequencies that constitute the input
signal, that for very thin sensors are as high as 10 GHz . For
this reason, one of the key aspects of the MONOLITH project
[2] described below is the integration of the sensor in a technology
that contains a transistor with transition frequency
ft
100 GHz.
Electronics Noise
Once the geometry and the electric field are defined and the
capacitance is matched, the main contribution to the detector
time jitter is given by the electronics noise, which is equivalent
to an input noise on the induced signal current. If the condition
expressed in the previous point is satisfied, the time resolution
σt
  
V
t
ENC rise time

dV vd
dt D qi i
S
N
This formula expresses the requirement to have low noise
while having a fast signal rise time. If the pixel capacitance is
properly matched, the noise performance of the amplifier ultimately
depends on the noise figure of the transistor used. For
a fast charge integration, in particular, the dominating term
in the transistor noise figure is its series noise. Starting from
this consideration, we favored the use of bipolar transistors
to build fast charge amplifiers. The SiGe BiCMOS SG13S and
SG13G2 technologies by IHP, in particular, have proven to provide
extraordinary results in terms of low noise, fast response
and low power consumption on large (~1 pF) detector capacitance
[4]. For lower pixel capacitance, the matching with the
amplifier input is more effective and the noise performance
improves significantly. Fig. 1 shows the CADENCE Spectre
simulation of the ultra-fast amplifier that we developed
and produced for the TT-PET project [5]. An ENC of 90 electrons
RMS was recently measured for a pixel capacitance of
70 fF [6]. The equation above shows that, for a saturated carrier
drift velocity of 100 μm/ns and a charge deposition of
~60 e−
/μm, without an increase of the S/N ratio the electronics
contribution would limit the time resolution to ~15 ps. Therefore,
even in the presence of an ultra-fast SiGe HBT amplifier,
an electronic contribution to the time resolution down to the
.
(3)
Present Status of Timing with Silicon
Sensors
LGAD Sensors
Up to present, the approach to increase the signal-to-noise ratio
of silicon sensors, and consequently the time resolution, has
been to structure the diode junction to generate an avalanche
multiplication region underneath the pixel, with a gain in the
range of 10÷50. This approach is implemented in the Low Gain
Avalanche Detectors (LGAD) [9], which obtained the excellent
results to bring down to ~30 ps the time resolution of silicon.
Despite offering excellent time resolution, LGAD sensors have
two major limiting factors: first, the absence of a gain layer in
the inter-pixel region limits the LGAD sensors to have large
pixel areas (~1mm2
), in order to avoid that the degraded time
resolution of the inter-pixel zones becomes dominant; therefore,
LGADs cannot be used for precise tracking. An attempt
is being made to realize full-fill factor and small pitch resistive
AC-coupled silicon sensors [10]. Second, the intrinsic time
jitter introduced by the Landau fluctuations of the spatial density
of the primary charge limits the time resolution of this type
of detector to ~30 ps RMS [7].
Fig. 1. CADENCE Spectre simulation of the ENC vs. sensor capacitance for
the ultra-fast amplifier produced in the SG13G2 process by IHP.
6
PIN Sensors
Typical silicon pixel detectors are made by PIN diodes operated
in reverse polarization. The PIN diode has a great
advantage compared to present sensors with internal gain: it
can fully exploit the performance of the front-end electronics
thanks to the possibility to operate on very low pixel capacitance
and be immune from the excess noise generated by
the dark current multiplication in the sensor. It also has relatively
low Landau noise. Despite its intrinsic fast response,
when targeting picosecond time resolution, the performance
of the PIN diode is limited by the small signal-to-noise ratio
that introduces a time jitter at the output of the front-end
electronics. The best time resolutions achieved for this type
of sensors are the 150 ps of the hybrids of the NA62 GigaTracker
and the 50 ps measured with MAPS by the authors
and colleagues [6].
IEEE Instrumentation & Measurement Magazine
December 2021
picosecond level can be achieved only by the introduction of a
gain mechanism internal to the sensor.
can be expressed as a function of the amplifier Equivalent
Noise Charge (ENC) [3] as:
Landau Noise
Another noise source affecting the induced signal current
comes from the fluctuation of the primary charge deposition
inside the sensor. This term, called Landau noise, is presently
the limiting factor to the time resolution of the silicon detectors
with internal avalanche gain mechanisms [7]. Since the onset
of the current signal is barely sensitive to the Landau noise, a
sensor able to integrate a charge 5 times the ENC over the first
~20 ps of the signal waveform could provide picosecond resolution.
This condition can be obtained in a small-capacitance
detector with internal gain that enhances the charge deposited
in a very thin (~1 μm) layer: the patented Picosecond Avalanche
Detector (PicoAD) [8].
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