Ultra-low noise high electron mobility transistors for

APPLIED PHYSICS LETTERS 105, 013504 (2014)

Ultra-low noise high electron mobility transistors for high-impedance and low-frequency deep cryogenic readout electronics Q. Dong, Y. X. Liang, D. Ferry, A. Cavanna, U. Gennser, L. Couraud, and Y. Jina) CNRS, Laboratoire de Photonique et de Nanostructures (LPN), Route de Nozay, 91460 Marcoussis, France

(Received 19 March 2014; accepted 25 June 2014; published online 7 July 2014) We report on the results obtained from specially designed high electron mobility transistors 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 low-frequency readout electronics under very low-temperature C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4887368] conditions. V

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 lowfrequency range for ionization readout channels, high performance electronics have been based for decades using Si junction field-effect transistors (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 high electron mobility transistors (HEMTs). However, the MOSFET suffers an extremely high lowfrequency 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 mesoscopic 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, commercially available HEMTs are used in a frequency range above a few hundreds of kHz and suffer a relative high noise current and especially a large low-frequency 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 employed in commercial HEMTs (between 2 and 5 nm), a Si d-doping layer, then a 15 nm undoped AlGaAs barrier layer, and finally a 6 nm undoped GaAs cap layer. At 4.2 K, the 2DEG carrier concentration and mobility are 4.5 1015 m2 and 29 m2 V1 s1, respectively. HEMTs with various gate lengths and gate widths are fabricated and individually packaged in a ceramic SOT23 as shown in Fig. 1(a). It has been found that the input 1/f noise voltage of our HEMTs at 4.2 K and a given frequency is approximately inversely proportional to the square a)

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root of the gate capacitance.11 In this paper, experimental results are based on the HEMT with a large gate surface of 6.4 104 lm2, in order to decrease its low frequency noise and to meet the need for ionization channel readout of deep cryogenic germanium detectors for dark matter searching.1,2 The working point is chosen and fixed with a drain voltage Vds ¼ 100 mV and a drain current Ids ¼ 1 mA for all measurements at 4.2 K. The corresponded transconductance 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 lowest noise level

FIG. 1. (a) Fabricated HEMT, equivalent input noise sources, and experimental setup of the common-source voltage amplifier at 4.2 K (in the frame with black dashed line) based on Rinput ¼ 50 X, RL ¼ 300 X and the under test HEMT with “s” being the source, “g” being the gate, “d” being the drain, en being the input noise-voltage source, and in being the noise-current source. (b) Measured voltage gain Av of the HEMT as a function of frequency f. (c) Noise-voltage spectrum at the drain edrain. (f) Input noisevoltage spectrum at the gate en in which the thermal noise due to 50 X has been removed.

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of a FET, and noise-current source in. With the input impedance z, in induces a noise voltage eni, i.e., in jzj. In practice, only the total equivalent input noise voltage ent can be measured. By supposing that en and in are uncorrelated, ent can be written as ent ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2n þ e2ni :

(1)

en can be obtained by grounding the gate, e.g., with a sufficiently small input resistor Rinput; in is thus shorted, and consequently eni en , and ent ¼ en. The determination of in is more laborious.12 jzj must be large enough to have ent > en and then in can be deduced from in ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2nt e2n =jzj ¼ eni =jzj:

(2)

For en measurement, the common source amplifier, with the HEMT to be tested, the input resistance of Rinput ¼ 50 X, and the load resistance of RL ¼ 300 X are mounted in a cryogenic insert as illustrated in Fig. 1(a). Using a lock-in amplifier, the measured voltage gain13 Av remains constant ¼ 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 X 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 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3) ent ¼ 4:0 1017 =f 0:95 þ 4:8 1020 : 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. Interestingly, at 1 Hz, compared to our early HEMTs based on a commercial heterostructure, with a gate surface of 3.7 104 lm2, the noise voltage can be estimated to be about 120 nV/Hz1=2;15 according to Ref. 11, whereas even with the same gate surface, the noise voltage in our early HEMTs would be 91 nV/Hz1=2, i.e., about 14 times higher than the value by this work. 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

F2eIds ; g2m

(4)

where F is the so-called Fano factor. For a fixed large gate length, F is almost a constant with the variation of Vgs and Vds.16 The circuit used for measuring the leakage current is shown in Fig. 2(a): with an input capacitor Cinput ¼ 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 dt. Since dVs ¼ dVg , the variation of charges in Cinput can be read as dVg Cinput , and the gate leakage current Igs is therefore dVg Cinput =dt. For the measured HEMT, dVg ¼ 0.10 mV and dt ¼ 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.17 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 n is defined as n¼

Cgd ; Cgd þ Cgs þ 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 ¼

Av ; 1 þ Av n

(6)

Re-capa ¼

Re : 1 þ Av n

(7)

and

Re-capa can be measured by a lock-in amplifier and used to deduce n with the help of 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 Table I including Ctotal, the total input capacitance with the Miller effect for Cgd Ctotal ¼ Cinput þ Cgs þ ð1 þ Av-capa ÞCgd :

(8)

We plot in Fig. 2(e) measured edrain for different Cinput inputs, as well as for a 50 X 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., pffiffiffiffiffiffiffiffiffiffiffiffi ffi F2eIds , 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 X inputs. This result shows that the white noise is independent of the input impedance as described by Eq. (4). In the 1/f noise region, for


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FIG. 2. (a) Experimental setup for the gate leakage current measurement. (b) Experimental setup of a HEMT based capacitor-input 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 n. (e) edrain with different Cinput and a 50 X inputs. (f) Total input noise voltage ent with different Cinput and a 50 X inputs. (g) Input noise current induced noise voltage eni with different Cinput inputs, deduced from (f) according to Eq. (1).

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 ¼ 10 pF, at 1 Hz eni is of about 20 nV/Hz1=2 and the impedance of Ctotal ¼ 152 pF is around 1 GX, and we have thus an unprecedented ultra-low in 20 aA=Hz1=2 . As concluding remarks, first, 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 the associated generation-recombination process can be greatly reduced. In addition, low-frequency noise due TABLE I. Used input capacitance Cinput and measured output resistance Re-capa, deduced feedback parameter n, capacitor-input voltage gain Av-capa, and total input capacitance including the Miller effect Ctotal. Cinput

Re-capa (X)

n

Av-capa

Ctotal

10 pF 50 pF 100 pF 300 pF 1 nF

152 170 184 210 230

7.12 102 5.15 102 3.88 102 1.97 102 8.02 103

5.63 6.00 6.49 7.41 8.11

152 pF 197 pF 250 pF 458 pF 1.16 nF

to 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. Second, the results from this work make an important step the search for other 1/f noise mechanisms and their limits in FETs. And finally, the result of this work has allowed us to design HEMTs with a smaller input capacitance of about 5 pF to meet the need of mesoscopic physics experiments. These HEMTs show an input noise voltage of 30 nV/Hz1=2 at 1 Hz and 1.4 nV/Hz1=2 at 1 kHz which are, compared to that obtained with a 92 pF HEMTs, in agreement with our early results.11 These HEMTs have been used to realize an ultra low noise cryogenic preamplifier for measuring the quantum limit of heat flow across a single electronic channel.18 Other deep cryogenic readout electronics, with appropriate gate capacitance, can be expected for e.g., lowtemperature STM (Scanning Tunnelling Microscope) and different wavelength photons detection.19,20 This work was supported in part by the French RENATECH network, le RTRA Triangle de la Physique Grant Nos. 2008-015T and 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 Dr. A. Juillard, Dr. B. Sadoulet, Dr. A. Anthore, Dr. F. Pierre, Dr. F. Parmentier, and Dr. E. Cambril for stimulating discussions and help.


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