IEEE Solid-States Circuits Magazine - Spring 2021 - 42

and threshold increase is through
systematic creation of dedicated timing
models for the digital library.
Cryogenic Circuit Design
Low-Power, Low-Noise
Analog Front End
HEP detectors commonly employ
capacitive sensors, from approach1010
109
108
107
106
105
104
103
102
101
100
10-1
10-2
10-3
10-4
10-5
0.1
0.2
ing
200 pF of the wire capacitance in
LAr TPC [13] to lower than 1 pF of the
point-contact germanium detector
[31]. A typical low-power, low-noise
analog front end includes a charge
amplifier (also referred as preamp) for
low-noise amplification of the charge
pulses from the sensor electrodes,
followed by a filter to limit the bandwidth
and maximize SNR, as shown in
1.8 V1.7 V
Lifetime ~3,200 yrs at Vds = 1.8 V, 77 K
300 K
Figure 7 [32]. In the time domain, the
filter " shapes " the charge pulses and
is often referred as " shaper " for HEP
detectors. Semi-Gaussian shapers
are most practical to implement in
analog front ends and achieve close
to optimal SNR. Shapers can also be
digitally synthesized to implement
weighting functions beyond semiGaussian,
e.g., trapezoidal or triangular,
to reduce the equivalent noise
charge (ENC) at the input of the front
end. The gain of the charge amplifier
needs to be large enough to keep the
ENC contribution from the shaper
lower than 10% of the total ENC, while
not exceeding the required dynamic
range. The shaper stages are synthesized
to operate rail-to-rail for maximum
dynamic range [32].
The ENC of this front end is given
77 K
by [31], [33]
2
ENCENC f
=+ +
=
1
2
2rAK
Vds<1.8 V
3.2, 3.1, 3, 2.8 V
0.3
0.4
1/Vds (1/V)
(a)
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12
10-13
10-14
Stressed Lifetime = 8,506 s at Vds = 3.2 V, 300 K
Stressed Lifetime = 798 s at Vds = 3.2 V, 77 K
Lifetime ~5,500 yrs at Vds = 1.8 V, 77 K
0.5
0.6
+ Aw
where A /f1
1 ff
2
/ ENCENC
/
2
w
eC C 2
ng
xp
det
+
+ qA I x
lk lk p
()
()
,
CC
det + g
Cg
2
2
lk
(3)
, Aw, and Alk are shaper
noise coefficients corresponding to
1/f noise, white series noise, and
detector leakage current Ilk, respectively.
Cdet is the detector electrode
capacitance. For the input transistor,
Cg is the gate capacitance, Kf is the 1/f
noise coefficient, and en
is the thermal
noise, which can be lowered by
increasing power. px is the shaper
peaking time. The general behavior
of ENC versus shaper peaking time
x p
x p
can be found in [33], where, as
increases, 1/f noise contribution
300 K
77 K
ASIC Design: Vds<1.5 V
01 2
Vds = 1.8 V
1/Vds (1/V)
(b)
FIGURE 5: (a) The projected lifetime versus 1/Vds extracted from a conventional stress test. (b) The
measured substrate current versus 1/Vds, which derived a lifetime at normal core voltage [27].
42
SPRING 2021
IEEE SOLID-STATE CIRCUITS MAGAZINE
does not change, the white noise contribution
decreases, and the detector
leakage noise increases. Given the
detector capacitance and leakage current,
the optimal shaper peaking time
is where the 1/f noise contribution
equals the leakage noise contribution.
Comparing the noise coefficients of
different shaper weighting functions,
triangular has the lowest A /f1
and Alk,
while semi-Gaussian has the lowest
Aw, as shown in Table 1 [31]. Depending
on the dominant noise sources,
Isub/W (A/µm)
τ∗/ds/W (s∗A/µm)
IEEE Solid-States Circuits Magazine - Spring 2021

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