Ultra-low noise HEMTs for high-impedance and low-frequency deep
cryogenic readout electronics
Q. Dong,1 Y. X. Liang,1 D. Ferry,1 A. Cavanna,1 U. Gennser,1 L. Couraud,1 and Y. Jin1, a)
CNRS, Laboratoire de Photonique et de Nanostructures (LPN), Route de Nozay, 91460 Marcoussis,
France
(Dated: 20 March 2014)
We report on the results obtained from specially designed HEMTs at 4.2 K: the gate leakage current can
be limited lower than 1 aA, and the equivalent input noise-voltage and noise-current at 1 Hz can reach
6.3 nV/Hz1/2 and 20 aA/Hz1/2 , respectively. These results open the way to realize high performance lowfrequency readout electronics under very low-temperature conditions.
a) Electronic
mail: yong.jin@LPN.cnrs.fr
(a)
en
(b)
g d
9.0
s
8.5
in
g s d
8.0
300 K
g d
6.5
6.0
source battery
Av
at 4.2 K
7.0
analyzer
amp.
Av-amp.
s
Rinput
4 mF
Av
fit
7.5
Av
drain battery
RL
4.2 K
5.5
0
4 mF
2
10
4
10
10
f (Hz)
(c)
(d)
6
6
1/2
4
edrain
simulat.
2
10
at 4.2 K
-8
8
6
en
simulat.
2
1/2
en (V/Hz )
edrian (V/Hz )
4
10
at 4.2 K
-9
4
8
6
4
2
2
0
2
10
10
f (Hz)
10
4
0
2
10
10
f (Hz)
10
4
ξ
FIG. 1. (a) Fabricated HEMT, equivalent input noise sources
and experimental setup of the common-source voltage ampli(a)
(b)
(c)
(d)
-2
fier at 4.2 K (in the frame with black dashed
drain battery line) based on
8x10
RL 300 K
drain battery
output
C
input
gd
4.2
K
Rinput
with “s” the source,
4.2 K, RL and the under test HEMT4mF
6
en
d
analyze
300
K the drain,
“g” theg gate,
“d”
noise-voltage source
amp.
g d en the input
4
1
i
n
A
v-amp.
s
VS
and in , the
noise-current
source.
(b) Measured voltage
gaingd RL
s
Cinput
2
δ
I
C
ds
gs
Cinput
source battery
RS
Cinput
Av of the
HEMT
as a function
of frequency f . (c) NoiseAv
4mF
0
voltage spectrum at the drain edrain . (f) Input noise-voltage
spectrum at the gate en in which the thermal noise due to 50
(f)
(e) removed.
(g)
Ω has been
-7
4
4
Input
10 pF
50 pF
100 pF
300 pF
1 nF
50 Ω
4
Input
10 pF
50 pF
100 pF2
300 pF
1 nF
50 Ω
2
10
-8
2
6
4
1/2
1/2
2
-8
8
6
ent (V/Hz )
the HEMT with a large gate surface of 6.4×104 µm in
order10to decrease its low frequency noise,11 and to meet
10
the need for ionization channel readout
of deep cryogenic
4.2 K
4.2 K
germanium detectors atfor
dark matter searching.at1,2
The
working
point is chosen and fixed with a drain voltage
10
10
Vds = 100
mV10and
a 10drain
current
I10
1 10mA10for10all
ds =
10
10
10
10
10
10
measurements at
4.2 K. The corresponded f transconduc(Hz)
f (Hz)
tance gm and output conductance gd are 35 and 0.75 mS,
respectively.
For low-frequency noise characterization, a commonsource amplifier based on the transistor to be tested is
used as shown in Fig. 1(a). A real FET can be considered as a noiseless transistor with two noise sources in
its input, i.e., the noise-voltage source en , which is the
4
2
-9
6
4
2
10
-8
6
4
1/2
8
6
eni (V/Hz )
10
edrain (V/Hz )
High impedance ultra sensitive sensors, such as for
searching for dark matter, operate at few tens of mK.
In order to achieve the lowest possible noise level at
low-frequency range for ionization readout channels, high
performance electronics have been based for decades on
Si JFETs.1,2 However, their operating temperature is
limited to above about 100 K because of the charge
freeze-out. Consequently, a long cable is required between readout electronics and sensors, which degrades
the sensors intrinsic performance and the readout rate.
From the intrinsic point of view, there are only two types
of FETs available to operate at very low-temperature:
MOSFETs and HEMTs. However, the MOSFET suffers
an extremely high low-frequency noise due to the oxide
layer between the metal gate and the active conducting
channel.3 The HEMT is based on a 2DEG (Two Dimensional Electron Gas) which is realized in a heterostructure with a high purity material interface. In particular
at cryogenic conditions, high electron mobility can be
obtained and it has been widely used for mesoscopique
field-effect devices operating at tens of mK for quantum
coherent electron transport investigations,4 as well as for
the demonstration of a fully ballistic FET.5 However, for
cryogenic readout electronics, most HEMTs are used in
a frequency range above few hundreds of kHz, and suffer
a relative high noise current and especially a large lowfrequency noise.6–10 In this work, we show that specially
designed HEMTs can reach unprecedented low noise levels at low frequencies and deep cryogenic conditions.
The investigated HEMTs are based on an AlGaAs/GaAs heterostructure grown by MBE (Molecular
Beam Epitaxy). It consists of a GaAs buffer layer, a 20
nm AlGaAs spacer layer which is much thicker than that
- between 2 to 5 nm - employed in commercial HEMTs,
a Si δ-doping layer, then a 15 nm undoped AlGaAs barrier layer, and finally a 6 nm undoped GaAs cap layer.
At 4.2K, the 2DEG carrier concentration and mobility
are 3.7×1015 m-2 and 29 m2 V-1 s-1 , respectively. HEMTs
with various gate lengths and gate widths are fabricated
and individually packaged in a ceramic SOT23 as shown
in Fig. 1(a). In this paper, experimental results are from
2
10
-9
6
4
2
-9
8
-10
0
1
2
3
4
5
0
1
2
3
4
5
2
-10
10
10
0
1
10
10
10
f (Hz)
10
10
10
f (Hz)
10
2
(b)
drain battery
4.2 K
d
g
g d
VS
Cinput
RL 300 K
4.2 K
300 K
s
(c)
RS
Cinput
-2
en
analyze
Cinput
source battery
Av
Cgd
input
4mF
amp.
Av-amp.
s
(d)
drain battery
8x10
output
ξ
fit.
6
in
Cgs δIds
ξ
(a)
1
gd RL
4
at 4.2 K
2
4mF
0
300
600
900
Cinput(pF)
-8
8
6
10
4
Input
10 pF
50 pF
100 pF
300 pF
1 nF
50 Ω
2
-8
10
6
4
1/2
ent (V/Hz )
1/2
edrain (V/Hz )
2
(g)
4
2
-9
10
at 4.2 K
2
6
4
10
6
4
2
10
0
10
1
10
2
3
10
10
f (Hz)
4
10
5
10
-9
10
at 4.2 K
2
-9
8
10
Input
10 pF
50 pF
100 pF
300 pF
1 nF
2
-8
1/2
Input
10 pF
50 pF
100 pF
300 pF
1 nF
50 Ω
4
(f)
4
eni (V/Hz )
(e)
-7
8
6
10
at 4.2 K
6
4
2
-10
10
0
10
1
10
2
3
10
10
f (Hz)
4
10
5
10
-10
0
10
1
10
2
3
10
10
f (Hz)
4
10
5
10
FIG. 2. (a) Experimental setup for the gate leakage current measurement. (b) Experimental setup of a HEMT based capacitorinput common-source voltage amplifier. (c) Equivalent circuit for the HEMT based amplifier in the frame with dashed line in
(b). (d) Determination of Cgs and Cgd by fitting the experimental feedback parameter ξ. (e) edrain with different Cinput and a
50 Ω inputs. (f) Total input noise voltage ent with different Cinput and a 50 Ω inputs. (g) Input noise current induced noise
voltage eni with different Cinput inputs, deduced from (f) according to Eq. (1).
lowest noise level of a FET, and noise-current source in .
With the input impedance z, in induces a noise voltage
eni , i.e., in × |z|. In practice, only the total equivalent
input noise voltage ent can be measured. By supposing
that eni and in are uncorrelated, ent can be written as:
q
ent = e2n + e2ni .
(1)
en can be obtained by grounding the gate, e.g., with a
sufficient small input resistor Rinput ; in is thus shorted,
and consequently eni en , and ent = en . The determination of in is more laborious.12 |z| must be large enough
to have ent > en and then in can be deduced from:
q
in = e2nt − e2n / |z| = eni / |z| .
(2)
For en measurement, the common source amplifier, with
the HEMT to be tested, the input resistance of Rinput =
50 Ω and the load resistance of RL = 300 Ω, is mounted
in a cryogenic insert as illustrated in Fig. 1(a). Using a
lock-in amplifier, the measured voltage gain13 Av remains
constant = 8.68 for f > 10 Hz, and decreases with decreasing f < 10 Hz as shown in Fig. 1(b). This is due to
insufficient filtering by the source bypass capacitor. The
measured output impedance14 Re remains at a constant
value of 246 Ω for f > 10 Hz and increases for lower f .
The signal at the drain of the HEMT is amplified once
more by a low-noise amplifier with a voltage gain Av-amp .
The output voltage noise spectrum emeasured is recorded
by a vector signal analyzer. In Fig. 1(c), the noise voltage spectrum at the drain edrain is deduced directly by
emeasured /Av-amp ; in the same figure the simulated curve
is composed by a 1/f noise and a white noise. A discrepancy between the experimental values and the simulation is clearly seen below 10 Hz. This gap is due to
the frequency dependence of Av . en shown in Fig. 1(d)
is obtained from edrain /Av . Indeed, for en , the simulation fits very well the experimental values, i.e., the low
frequency noise of the HEMT at 4.2 K demonstrates a
nearly perfect 1/f noise feature given by:
p
ent = 4.0 × 10-17 /f 0.95 + 4.8 × 10-20 .
(3)
This implies that the low frequency or 1/f noise originates from the gate region. Using Eq. (3) the corner frequency fc , at which the 1/f noise value is equal to that
of the white noise, can be found to be 1.2 kHz. From Fig.
1(d), en can reach as low values as 6.3 nV/Hz1/2 at 1 Hz
and 0.32 nV/Hz1/2 at 1 kHz. For f > 10 kHz, en is dominated by white noise which, from Eq. (3), is only 0.22
nV/Hz1/2 . It should be mentioned that for our HEMTs
at 4.2 K, in contrast to usual FETs at high temperature,3
the white noise is dominated by the channel current noise
which can be expressed by a reduced shot noise:
e2n-white ≈
F 2eIds
.
2
gm
(4)
where F is the so-called Fano factor. For a fixed large
3
gate length, F is almost a constant with the variation of
Vgs and Vds .15
The circuit used for measuring the leakage current is
shown in Fig. 2(a): with an input capacitor Cinput =
100 pF, the drain is biased with a constant value by a
stable voltage source, and the source is connected with
an appropriate resistance Rs to fit the working point as
chosen above. The evolution of Vs is recorded during a
time δt. Since δVs = δVg , the variation of charges in
Cinput can be read as δVg × Cinput , and the gate leakage
current Igs is therefore δVg ×Cinput /δt. For the measured
HEMT, δVg = 0.10 mV and δt = 1.6 × 104 s, we have
thus a Igs value as low as 0.62 aA. Such a low value can
also suppress Igs induced low-frequency noise.16
For in characterization, we use a capacitor-input
common-source voltage amplifier as shown in Fig. 2(b),
with Cinput varying from 10, 50, 100, 300 pF to 1 nF.
The feedback parameter ξ is defined as:
ξ=
Cgd
,
Cgd + Cgs + Cinput
(5)
where Cgs and Cgd are gate-source and gate-drain capacitances, respectively. By neglecting the gate-source
conductance and using the equivalent circuit in Fig.
2(c), the corresponding voltage gain Av-capa and output
impedance Re-capa due to the capacitance feedback, can
be expressed as:
Av-capa =
Av
,
1 + Av ξ
(6)
Re-capa =
Re
.
1 + Av ξ
(7)
and
Re-capa can be measured by a lock-in amplifier and used
to deduce ξ with the help of the Eq. (7), and together
with Eq. (6) this gives us Av-capa ; using Eq. (5), along
with the fit shown in Fig. 2(d), Cgs and Cgd can be
extracted as 92 and 7.8 pF, respectively; we summarize
all parameters in Tab. 1 including Ctotal , the total input
capacitance with the Miller effect for Cgd :
Ctotal = Cinput + Cgs + (1 + Av-capa )Cgd
(8)
We plot in Fig. 2(e) measured edrain for different Cinput
inputs, as well as for a 50 Ω input (as the reference spectrum). In the 1/f noise region (f at lower than few
kHz), all edrain curves are of the same order of magnitude.
By contrast, in the white noise region (f higher than 10
kHz), the observed variation of edrain can be explained
as follows: with the decrease of Cinput , Re-capa decreases
while the channel white noise
current is a constant at a
√
given working point, i.e., F 2eIds , thus, edrain decreases.
We draw the corresponding ent in Fig. 2(f). Interestingly,
in the white noise region ent is almost the same for all
Cinput and 50 Ω inputs. This result shows that the white
noise is independent of the input impedance as described
TABLE I. Used input capacitance Cinput and measured
output resistance Re-capa , deduced feedback parameter ξ,
capacitor-input voltage gain Av-capa , and total input capacitance including the Miller effect Ctotal .
Cinput
10 pF
50 pF
100 pF
300 pF
1 nF
Re-capa
152 Ω
170 Ω
184 Ω
210 Ω
230 Ω
7.12
5.15
3.88
1.97
8.02
ξ
×10−2
×10−2
×10−2
×10−2
×10−3
Av-capa
5.63
6.00
6.49
7.41
8.11
Ctotal
152 pF
197 pF
250 pF
458 pF
1.16 nF
by Eq. (4). In the 1/f noise region, for Cinput from 10
to 100 pF, the ent are nearly the same, and this is due
to that the total input capacitance is close to that of
the HEMT. With a further increase of Cinput , ent starts
to decrease, and at a sufficient large Cinput of 1 nF, ent
reaches the noise-voltage limit en . Indeed, the component eni as defined by Eq. (1) can also be suppressed by
a sufficiently large Cinput . Deduced eni spectra according
to Eq. (1) are shown in Fig. 2(g), where the upper limit
of eni can be distinguished with Cinput from 10 to 100 pF.
Based on Eq. (2), the highest input impedance is found
with Cinput = 10 pF, at 1 Hz eni is of about 20 nV/Hz1/2
and the impedance of Ctotal = 152 pF is around 1 GΩ,
and we have thus an unprecedented ultra-low in ≈ 20
aA/Hz1/2 .
As concluding remarks, firstly, from the intrinsic point
of view, charge carriers consisting of the degenerate
electrons of the 2DEG in HEMTs are located in the
pure GaAs material near the AlGaAs/GaAs interface,
where impurity densities can be efficiently reduced by
the MBE growth, and therefore associated generationrecombination process can be greatly reduced. In addition, low-frequency noise due to the sequential tunnelling
can almost be suppressed by eliminating the gate leakage current. Indeed, with the improvement of the material quality and an appropriately designed heterostructure and gate configuration, extremely low noise voltage,
and especially low noise current, can be obtained with
HEMTs under very low-temperature conditions. Secondly, the results from this work make an important step
the search for other 1/f noise mechanisms and their limits
in FETs. And finally, one type of our HEMTs has been
used to realize an ultra low noise cryogenic preamplifier
for measuring the quantum limit of heat flow across a
single electronic channel;17 other deep cryogenic readout
electronics, with appropriate design, can be expected for
e.g., low-temperature STM (Scanning Tunnelling Microscope) and different wavelength photons detection.18,19
ACKNOWLEDGMENTS
This work was supported in part by the French RENATECH network, le RTRA Triangle de la Physique
4
grants No. 2008-015T and No. 2009-004T, European
FP7 space project CESAR grant No. 263455 and DEFI
Instrumentation aux limites CryoHEMTs 2013. Q. D. is
funded by the BDI CNRS/CEA. We thank Drs. A. Juillard, B. Sadoulet, A. Anthore, F. Pierre, F. Parmentier
and E. Cambril for stimulating discussions and help.
1 D.
S. Akerib, P. D. Barnes, P. L. Brink, B. Cabrera, R. M. Clarke,
R. J. Gaitskell, S. R. Golwala, M. E. Huber, M. Kurylowicz,
V. Mandic, J. M. Martinis, P. Meunier, N. Mirabolfathi, S. W.
Nam, M. Perillo-Isaac, T. Saab, B. Sadoulet, R. W. Schnee, D. N.
Seitz, T. Shutt, G. W. Smith, W. K. Stockwell, K. M. Sundqvist,
and S. White, Nucl. Instr. Meth. A 591, 476 (2008).
2 B. Censier, A. Benoit, G. Bres, F. Charlieu, J. Gascon, J. Gironnet, M. Grollier, R. Guichardaz, A. Juillard, L. Lauro, J. Minet,
B. Paul, and L. Vagneron, J. Low Temp. Phys. 167, 645 (2012).
3 A. V. der Ziel, Noise in solid state devices and circuits (Wiley,
New York, 1986).
4 E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni,
B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, Science 339, 1054
(2013).
5 E. Gremion, D. Niepce, A. Cavanna, U. Gennser, and Y. Jin,
Appl. Phys. Lett. 97, 233505 (2010).
6 L. DiCarlo, Y. Zhang, D. T. McClure, C. M. Marcus, L. N. Pfeiffer, and K. W. West, Rev. Sci. Instrum. 77, 073906 (2006).
7 N. Oukhanski and E. Hoenig, Appl. Phys. Lett. 85, 2956 (2004).
8 S.
Urazhdin, S. Tessmer, and R. Ashoori, Rev. Sci. Instrum. 73,
310 (2002).
9 A. M. Robinson and V. I. Talyanskii, Rev. Sci. Instrum. 75, 3169
(2004).
10 R. Plana, L. Escotte, O. Llopis, H. Amine, T. Parra, M. Gayral,
and J. Graffeuil, IEEE Trans. Electron. Dev. 40, 852 (1993).
11 Q. Dong, Y. X. Liang, U. Gennser, A. Cavanna, and Y. Jin, J.
Low Temp. Phys. 167, 626 (2012).
12 F. Ayela, J. L. Bret, and J. Chaussy, Rev. Sci. Instrum. 62, 2816
(1991).
13 The no-feedback voltage gain A of a common source amplifier
v
based on a FET can be expressed by gm × RL /(1 + gd × RL ) in
the frequency range where Av is independant of f .
14 The no-feedback output impedance R of a common source ame
plifier based on a FET can be expressed by RL /(1 + gd × RL )
in the frequency range where Re is independant of f , and consequently Av = gm × Re .
15 The detail of the white noise in these HEMTs is out of the scope
of this paper, we will publish elsewhere.
16 Y. X. Liang, Q. Dong, M. C. Cheng, U. Gennser, A. Cavanna,
and Y. Jin, Appl. Phys. Lett. 99, 113505 (2011).
17 S. Jezouin, F. D. Parmentier, A. Anthore, U. Gennser, A. Cavanna, Y. Jin, and F. Pierre, Science 342, 601 (2013).
18 E. R. Fossum and B. Pain, in Infrared Technology XIX: Proceedings of SPIE, Vol. 2020, edited by B. F. Andresen and F. D.
Shepherdl (1993) pp. 262–285.
19 M. Huber, A. Pauluhn, J. Culhane, J. Timothy, K. Wilhelm,
and A. Zehnder, eds., Observing Photons in Space, ISSI Scientific
Reports Series, Vol. 9 (2010).