Cryogenic low-noise amplifiers based on high electron mobility transistors (HEMTs) are widely used in applications such as radio astronomy, deep space communications, and quantum computing. Consequently, the physical mechanisms governing the microwave noise figure are of practical interest. In particular, the magnitude of the contribution of thermal noise from the gate at cryogenic temperatures remains unclear owing to a lack of experimental measurements of thermal resistance under these conditions. Here, we report measurements of gate junction temperature and thermal resistance in a HEMT at cryogenic and room temperatures using Schottky thermometry. At temperatures 20 K, we observe a nonlinear trend of thermal resistance vs power that is consistent with heat dissipation by phonon radiation. Based on this finding, we consider heat transport by phonon radiation at the low-noise bias and liquid helium temperatures and estimate that the thermal noise from the gate is several times larger than previously assumed owing to self-heating. We conclude that without improvements in thermal management, self-heating results in a practical lower limit for microwave noise figure of HEMTs at cryogenic temperatures.

Microwave low-noise amplifiers (LNAs) based on high electron mobility transistors (HEMTs) are widely used components of scientific instrumentation in fields such as radio astronomy,1,2 deep space communication,3 and quantum computing.4–8 After decades of development,9–13 HEMT LNAs have achieved cryogenic noise temperatures approximately 5–10 times the quantum limit over frequencies from 1 to 100 GHz.1 Despite this progress, applications drive the development of amplifiers with ever-lower noise figures.

Noise in HEMT amplifiers is typically interpreted using the Pospieszalski model.14 In this model, noise is decomposed into components associated with the drain and the gate, parameterized by equivalent temperatures Td and Tg, respectively. These components have been ascribed to hot-electron noise in the channel and thermal noise in the gate. The gate noise temperature Tg is typically assumed to be the cryostat base temperature, Tg=T, while the drain temperature is fit to measured noise data. For a constant drain current, the hot electron contribution is taken to be constant and the minimum noise figure then scales as Tg1/2.2 

Although the noise temperature does decrease with the base temperature over a range of temperatures as predicted, at liquid helium temperatures the noise temperature is observed to plateau to a value several times the quantum noise limit.15–18 This noise temperature plateau has been attributed to a variety of mechanisms, including drain shot noise,19 gate leakage current,9 and self-heating.15,20 In particular, Ref. 15 used measurements of microwave noise to conclude that the thermal resistance associated with phonon radiation leads to non-negligible self-heating at cryogenic temperatures. However, this conclusion is based on an indirect estimate of the gate junction temperature using a noise model.

Measurements of the gate temperature at the low-noise bias and cryogenic temperatures would provide more direct evidence that self-heating is the origin of the noise temperature plateau. This measurement is challenging for conventional thermometry techniques such as IR microscopy,21,22 micro-Raman spectroscopy,23–25 or liquid crystal thermography26 due to geometrical constraints like the sub-micrometer gate lengths and the buried structure of modern HEMTs. Other methods such as resistance thermometry of the gate require the fabrication of custom structures or the use of alternate metals,27 which can be difficult to incorporate into the HEMT process.28 Consequently, self-heating in FETs is usually characterized with measurements of other temperature-sensitive electrical parameters. Early semi-quantitative studies of self-heating in CMOS estimated the temperature under bias using the temperature dependence of drain current.29–31 However, these approaches neglected a number of mechanisms relevant to the drain current in sub-micrometer devices such as the bias dependence of threshold voltage, series resistances, and non-stationary transport effects, which are known to be important in modern HEMTs and could affect the extracted temperature rise. Later studies of self-heating in MOSFETs incorporated some of these effects and reported measurements of temperature rise and thermal time constants.32 Recent work in SOI MOSFETs reported that the dominant thermal resistance is due to the buried oxide layer.33 

Self-heating studies in HEMTs have largely focused on GaN power FETs operated at room temperature, where device lifetime is limited by channel heating.34 In one approach, the temperature rise is extracted from pulsed measurements on the gate,35,36 but this technique is generally unsuitable for low-noise cryogenic HEMTs, where the thermal time constants are on the same order as the pulse duration.37 Bautista and Long used calibrated measurements of gate leakage current for various drain biases to conclude that the gate temperature in cryogenic InP HEMTs was close to that of the base temperature.18 However, the magnitude of the thermal resistance was not reported, and the physical origin of the thermal resistance and the impact of self-heating on the noise performance at liquid helium temperatures were not discussed. As a result, self-heating in cryogenic III-V HEMTs and its impact on noise remains a topic of interest.

In this work, we report measurements of the junction temperature and thermal resistance of the gate in a low-noise metamorphic HEMT using a Schottky thermometry method based on the temperature-dependent forward diode characteristics of the gate. At cryogenic temperatures, we observe a nonlinear trend of the thermal resistance on dissipated power that is consistent with heat transport by phonon radiation. Although the measurements are not performed at the low-noise bias, this finding can be used to estimate the magnitude of self-heating at this bias. Using a radiation circuit model, we find that at the low-noise bias the gate self-heats to a value comparable to the physical temperature of the channel, contradicting the typical assumption that the gate is isothermal with the base temperature. Our study thus implies that without improvements to device thermal management to remove heat from the gate, self-heating results in a practical lower limit for HEMT microwave noise figure at cryogenic temperatures.

We measured the temperature of the gate–barrier junction of a discrete HEMT under DC bias using the Schottky thermometry method introduced in Ref. 38. In brief, the method exploits the temperature dependence of the electrical parameters of the Schottky junction to infer the temperature rise of the junction using DC IV characteristics and microwave S parameters. Under thermionic emission theory, the current in a Schottky diode is given by

I=ISexp(q(VIRS)ηkBTj),
(1)

where q is the elementary charge, kB is the Boltzmann constant, RS is the parasitic series resistance, IS is the saturation current, η is the ideality factor, and Tj is the intrinsic junction temperature.

To obtain Tj for a given bias, the temperature dependence of IS and η is extracted from DC IV characteristics by varying the cryostat base temperature at low bias where self-heating is negligible. Next, the small signal resistance about a DC bias is determined from the microwave S parameters. Equating expressions for the series resistance yields an equation including the measured Schottky and S parameters in which the only unknown is the junction temperature,

VIη(Tj)kBTjqIln(IIS(Tj))=rTη(Tj)kBTjqI.
(2)

Here, rT is the small signal resistance obtained from the S parameters. With the DC IV characteristics and S parameters for different biases known, we obtain the junction temperature at various base temperatures by numerically solving Eq. (2). Although this method was originally developed for THz Schottky diodes at room temperature, the physical basis for the measurement is general and can be applied to the gate Schottky diodes of HEMTs at cryogenic temperatures so long as the IV characteristics exhibit a dependence on temperature.

We used this method to characterize the thermal resistance of a metamorphic HEMT manufactured by OMMIC with 70 nm gate length and 200μm gate width consisting of an InGaAs–InAlAs–InGaAsInAlAs epitaxial stack on a semi-insulating GaAs substrate over base temperatures from 20 to 300 K. Further details of the device are specified in Chap. 5.1 of Ref. 39. All measurements were performed in a custom cryogenic probe station40 with the cryostat base temperature (denoted base temperature, T) controlled between 20 and 300 K by a LakeShore 336 temperature controller. The HEMT was biased using a Minicircuits ZX85-12G-S+ bias-tee. S-parameter measurements were performed with a Rohde & Schwarz ZVA50 vector network analyzer from 10 MHz to 18 GHz, calibrated with the through-reflect-match method. The DC measurements were corrected for the parasitic series resistance in the bias-tee and coaxial lines. The temperature dependence of the Schottky parameters Is and η was extracted in the log-linear region at low bias I100μA so that self-heating can be neglected but at sufficiently high bias so that the characteristic is still log-linear.41 The saturation current and ideality factor were fit to the expressions derived from thermionic emission theory [see Eqs. (2) and (3) in Ref. 38]. The saturation current expression was modified by adding a temperature-independent term to Eq. (3) in Ref. 38 to account for the tunneling gate leakage current that is known to dominate in Schottky diodes at low temperature.42 After extracting the junction temperature, we verified that the self-heating can be neglected in the fit range by confirming that the temperature rise induced by the dissipation in the fit range at the highest extracted thermal resistance satisfies TjTT. The junction temperature was extracted at biases ranging from 0.5 to 9 mA for which the capacitance of the channel depletion layer is negligible. In this current range, the frequency dependence of rT is negligible up to 1 GHz, and the influence of the parasitic capacitances is negligible. For the calculation of the thermal resistance, we took the area of the gate to be 14μm2=70nm×200μm.

Figure 1(a) shows the measured forward bias DC IV characteristics at different base temperatures. The form of the characteristic is qualitatively consistent with those from other low-noise HEMTs reported in the literature [see Fig. 3(c) in Ref. 7]. The gate current is larger than the typical HEMT leakage current because the gate is forward-biased in the present experiments. As the device is cooled, the characteristics shift to higher threshold voltages but still exhibit a clear dependence on temperature. The DC data were used to extract the temperature dependence of the saturation current and ideality factor as discussed in Sec. II. Figure 1(b) shows the measured reflection coefficient S11 at various bias points at 20 K from 1 to 10 GHz. The total small signal resistance is obtained from the reflection coefficient through rT=Re[(1+S11)/(1S11)Z0], where Z0=50Ω is the characteristic impedance of the system.

FIG. 1.

(a) Measured forward IV characteristics of the HEMT at different base temperatures (colored symbols). We fit the temperature dependence of the Schottky parameters for I100μA for which TjT and the diode characteristics are log-linear. The DC resistance is combined with S parameter measurements to extract the junction temperature at the 0.5–9 mA biases for which self-heating occurs. (b) Small signal reflection coefficient extracted from S-parameters at different bias points (colored markers) and T=20 K from 1 to 10 GHz. The small signal resistance is extracted by taking the real part of the input impedance.

FIG. 1.

(a) Measured forward IV characteristics of the HEMT at different base temperatures (colored symbols). We fit the temperature dependence of the Schottky parameters for I100μA for which TjT and the diode characteristics are log-linear. The DC resistance is combined with S parameter measurements to extract the junction temperature at the 0.5–9 mA biases for which self-heating occurs. (b) Small signal reflection coefficient extracted from S-parameters at different bias points (colored markers) and T=20 K from 1 to 10 GHz. The small signal resistance is extracted by taking the real part of the input impedance.

Close modal

Qualitative evidence of self-heating can be obtained by inspecting the IV characteristics. Ideal Schottky diodes exhibit log-linear IV characteristics, but, in practice, deviations are observed owing to self-heating and parasitic series resistance. Series resistance leads to a sublinear log IV, while self-heating causes a superlinear trend (see Fig. 3 in Ref. 38). These effects depend on bias as well as temperature, and their balance determines the trend of the measured IV characteristic.

Figure 2 compares the measured IV characteristics with those generated by an ideal Schottky model, a cold-diode model, and a model including self-heating with a constant thermal resistance Rth. The ideal Schottky model neglects series resistance and self-heating and consequently exhibits log-linear DC characteristics at all biases. The cold-diode model incorporates the measured diode series resistance but neglects self-heating so that the junction temperature equals the base temperature at all biases, Tj=T. Finally, the linear-heating model incorporates series resistance, temperature-dependent Schottky parameters, and assumes that the junction temperature increases linearly with the dissipated power, Tj=T+RthIV, with thermal resistance Rth taken as a fitting parameter. Through comparison to the measured DC IV, we can infer the relative magnitude and power dependence of the junction temperature Tj at different T.

FIG. 2.

Measured IV characteristics at (a) 300 and (b) 20 K (red markers) compared to the ideal diode (black dashed line), cold-diode (blue dashed–dotted line), and linear-heating model (orange solid line). A calculation assuming constant thermal resistance explains the measurements at 300 K but not at 20 K. See text for details. The curves for the cold-diode and linear-heating models coincide with the ideal diode model below 0.5 mA and are omitted for clarity.

FIG. 2.

Measured IV characteristics at (a) 300 and (b) 20 K (red markers) compared to the ideal diode (black dashed line), cold-diode (blue dashed–dotted line), and linear-heating model (orange solid line). A calculation assuming constant thermal resistance explains the measurements at 300 K but not at 20 K. See text for details. The curves for the cold-diode and linear-heating models coincide with the ideal diode model below 0.5 mA and are omitted for clarity.

Close modal

Figure 2(a) shows the model comparison to measurements at T=300 K. At low biases below 1 mA, the measured diode is nearly ideal and exhibits the expected log-linear trend (region A). At 1 mA, the cold-diode model, linear-heating model, and measured current agree to within 3%, indicating that the temperature rise at this bias is small compared to the base temperature. At high currents exceeding 1 mA, the series resistance leads to a sublinear trend (region B); however, the cold-diode model including only series resistance underpredicts the measured current at high biases (9 mA) by 25%. In contrast, the linear-heating model agrees with the measured IV characteristics in region B. From this comparison, we infer that at 300 K, self-heating is appreciable above 1 mA biases and that the thermal resistance is constant with power.

Figure 2(b) shows the model comparison at T=20 K. As at 300 K, below 100 μA, the diode is nearly ideal, but a superlinear trend associated with self-heating is evident at intermediate biases between 100 μA and 1 mA (region C), which is not observed in the room temperature characteristics. At 1 mA, the measured current exceeds that of the cold-diode model by over 15%, indicating that the temperature increase due to self-heating is substantially larger at this bias than at 300 K. Furthermore, above 1 mA (region B), the linear-heating model at 20 K markedly overpredicts the measured current, indicating that the thermal resistance must decrease as the bias increases at 20 K.

We now perform a quantitative analysis of the data by using the method in Sec. II to extract the junction temperature. Figure 3(a) shows the extracted junction temperature rise vs power for T=300, 60, 40, and 20 K. The features of the temperature rise are consistent with the qualitative expectations developed in Fig. 2. First, at T=300 K, the temperature rise is nearly linear with the dissipated power, indicating that a constant thermal resistance can account for the measurements. Second, at the low bias point of 1 mA and 40 μWμm2, the junction temperature rise is 3 K or 1% of the base temperature, confirming the qualitative prediction of small temperature rise at this power shown in Fig. 2(a). In contrast, at cryogenic temperatures, the temperature rise exhibits a nonlinear trend with power, with the temperature initially increasing rapidly but transitioning to a weaker increase at higher powers. This observation is consistent with Fig. 2(b) and suggests that the thermal resistance decreases as the bias is increased. At T=20 K and the same low bias point of 1 mA and 50 μWμm2, the temperature rise is 29 K, almost 10 times larger than the room temperature value of 3 K. This difference is on the same order as the difference in heat capacity between these temperatures, which decreases by over an order of magnitude from 300 K to 20 K.43 At T=40 K and 60 K, the temperature rise exhibits the same qualitative features as those seen at 20 K, but for the same power, the temperature rise is smaller at higher base temperatures.

FIG. 3.

(a) Junction temperature rise, TjT, vs dissipated power density at base temperatures 20 K (red circles), 40 K (yellow triangles), 60 K (blue triangles), and 300 K (black squares). The temperature rise is approximately linear with power at room temperature but nonlinear at cryogenic temperatures. Dashed black lines are added as guides to the eye. (b) Interpolated junction temperature Tj vs base temperature T at various power densities (colored lines). As the device is cooled, the junction temperature begins to plateau due to self-heating.

FIG. 3.

(a) Junction temperature rise, TjT, vs dissipated power density at base temperatures 20 K (red circles), 40 K (yellow triangles), 60 K (blue triangles), and 300 K (black squares). The temperature rise is approximately linear with power at room temperature but nonlinear at cryogenic temperatures. Dashed black lines are added as guides to the eye. (b) Interpolated junction temperature Tj vs base temperature T at various power densities (colored lines). As the device is cooled, the junction temperature begins to plateau due to self-heating.

Close modal

As described in Sec. II, the junction temperature is extracted for fixed gate current values. To extract the temperature dependence of the junction temperature at fixed power instead of current, we linearly interpolate the junction temperatures for each power density. This procedure is analogous to taking a vertical slice at fixed power in Fig. 3(a). Figure 3(b) shows the interpolated junction temperature vs the base temperature for various power densities applied to the gate. At base temperatures near 80 K and all powers, the junction temperature decreases with base temperature as ΔTj/ΔT0.9 K/K, meaning that at these temperatures, a change in base temperature is exhibited nearly completely in the junction temperature as well. As the cryostat is cooled to 20 K, the cooling coefficient ΔTj/ΔT drops to 0.45 K/K, indicating that while the bulk device continues to cool, the gate temperature cools less rapidly due to self-heating. The observed temperature plateau in Fig. 3(b) implies that the thermal resistance at all powers must increase nonlinearly as the junction temperature decreases below 50 K.

We now compute the thermal resistance Rth=ΔT/q as the ratio of the junction temperature rise in Fig. 3(a) and the power density. Figure 4 shows the thermal resistance vs power density. At room temperature, the thermal resistance is nearly constant with power, as expected from Figs. 2(a) and 3(a). As the device is cooled to cryogenic temperatures, the thermal resistance increases at all powers. At 1 mA and 40 μWμm2, the thermal resistance increases by almost an order of magnitude from 300 to 20 K. Furthermore, at cryogenic temperatures, the thermal resistance exhibits a nonlinear power dependence.

FIG. 4.

Thermal resistance of the junction vs power density at base temperatures of 20 K (red circles), 40 K (yellow triangles), 60 K (blue triangles), and 300 K (black squares). At room temperature, the thermal resistance is nearly independent of power and thus junction temperature. At cryogenic temperatures, the thermal resistance increases nonlinearly as the power and junction temperature decrease. These features are qualitatively consistent with the predictions of a model assuming the thermal resistance is dominated by phonon radiation through an interface (computed at 20 K, red solid line). Dashed black lines are added as guides to the eye.

FIG. 4.

Thermal resistance of the junction vs power density at base temperatures of 20 K (red circles), 40 K (yellow triangles), 60 K (blue triangles), and 300 K (black squares). At room temperature, the thermal resistance is nearly independent of power and thus junction temperature. At cryogenic temperatures, the thermal resistance increases nonlinearly as the power and junction temperature decrease. These features are qualitatively consistent with the predictions of a model assuming the thermal resistance is dominated by phonon radiation through an interface (computed at 20 K, red solid line). Dashed black lines are added as guides to the eye.

Close modal

The magnitude and trend of the thermal resistance with temperature are inconsistent with a conduction thermal resistance associated with the thermal conductivity of the epitaxial semiconductor materials. For example, the conduction thermal resistance based on the bulk thermal conductivity of GaAs at T=20 K is L/κ0.5Kμm2mW1 for κ=2000Wm1K143 and L=1μm, orders of magnitude smaller than the observed resistance. If this thermal resistance was the dominant contributor, the temperature rise at 20 K and 1 mW would be only 0.03 K, which is far smaller than the extracted temperature rise. Even with accounting for large thermal gradients by taking the value at an intermediate temperature of 100 K, κ=200Wm1K1, the estimated temperature rise is only 0.3 K. The lower thermal conductivity of the alloy is also unable to explain the discrepancy.

In addition to this magnitude discrepancy, bulk conduction cannot explain the temperature trend exhibited in the measurements. While the conduction thermal resistance is predicted to decrease by around an order of magnitude from 300 to 20 K based on the temperature dependence of the thermal conductivity (κ20K/κ300K4043), the opposite trend is observed in the measurements where the thermal resistance actually increases at lower temperatures. This analysis indicates that the measured thermal resistance is not associated with the thermal conductivity of the semiconductors.

Instead, the resistance can be attributed to the thermal boundary resistance of the gate–semiconductor interface. The HEMT gate is formed by depositing a metallic stack consisting of metals such as Pt, Ti, and Au on the InAlAs barrier layer that has been subjected to semiconductor processing steps such as wet etching. At 300 K, reported values of thermal boundary conductance for a soft metal such as gold on semiconductor are in the range of 30–40 MWm2K1.44 These studies utilize pristine interfaces for which the metal is evaporated directly onto a high-quality crystalline substrate. In contrast, the etching step in the fabrication of the gate leaves an amorphous region several nanometers thick at the gate–semiconductor junction [see Fig. 4.11(a) in Ref. 45]. Prior measurements report that crystalline disorder can increase thermal boundary resistance by factors of approximately 3–4 (see Fig. 7 in Ref. 46) as phonons with atomic-scale wavelengths are reflected at the interface.47 At 300 K, the average thermal resistance of the HEMT over all power levels is 60μm2mW1. This value corresponds to a conductance of 17MWm2K1, which is consistent with the above values for thermal conductance of a defective interface.

We next examine the origin of the nonlinear trend of thermal resistance vs power in Fig. 4. Assuming the total gate thermal resistance is dominated by the thermal boundary resistance, in principle, a microscopic model of thermal boundary resistance could be constructed from thermal resistance vs temperature and knowledge of the phonon density of states of the semiconductor and metal. However, in practice, the bake and passivation steps in the gate fabrication induce atomic diffusion and the formation of intermetallic compounds.45 As a result, knowledge of the atomic structure and vibrational modes of the interface required for such a model is lacking.

Considering these challenges, we instead construct a qualitative model for the thermal resistance in which the phonons are assumed to follow a Debye model and radiate from the gate through the interface. Assuming that the temperature is small compared to a Debye temperature associated with atomic vibrations at the interface, the heat flux through the interface obeys the Stefan–Boltzmann law q=ϵσp(Tj4T4),27 where ϵ is a temperature-independent transmission coefficient associated with phonons impinging on the interface48 and σp=π2kB4/403vave2600Wm2K4 is the Stefan–Boltzmann constant for phonons in GaAs. Here, vave3500ms1 is the Debye velocity in GaAs computed from the average sound velocities.43 In this phonon radiation regime, the thermal resistance can be defined as Rth1=ϵσp(Tj+T)(Tj2+T2).49 

Applying this model to the data measured at 20 K, we obtain the curve shown in Fig. 4. Despite the simplicity of the model, it qualitatively captures the nonlinear variation of thermal resistance with power with ϵ0.02 as the best fit parameter. The physical picture of heat dissipation from the gate that emerges is, therefore, the radiation of phonons from the gate with a heat flux that is smaller than the pure radiation value owing to phonon reflections at the gate–semiconductor interface.

We now discuss the implications of heat dissipation by phonon radiation on the self-heating and microwave noise figure of HEMTs. In the present experiments, the gate was forward-biased while the drain was grounded so that heat was generated by the emission of phonons by hot electrons in the gate metal. However, under the typical low-noise operating conditions for depletion-mode HEMTs, the gate and drain are reverse and forward biased, respectively, and heat is generated by the emission of phonons from hot electrons flowing through the channel. Despite these differences, the identification of the phonon radiation mechanism supported by the measurements in this study allows us to assess the magnitude of self-heating at the low-noise operating bias. Considering heat transport to occur by phonon radiation, at the low-noise bias, phonons generated in the channel radiate to the gate, which then radiates phonons to the substrate to balance the incoming heat flux. The steady-state temperature of the gate is set by the radiation space resistances between the gate, channel, and substrate.

An equivalent radiation circuit model can be used to predict the temperature rise in the gate from the radiative phonon flux originating at the drain [see Eq. (6.48) and Fig. 6.12 of Ref. 50]. In this model, the three nodes in the circuit are the channel (c), gate (g), and substrate (s) linked by space radiation resistances. We assume all surfaces are black for simplicity. The gate node is adiabatic to excellent approximation so that all absorbed radiation is re-emitted (see supplementary information in Ref. 15).

Under these assumptions, the gate emissive power Jg can be expressed as

Jg=JdRcg+JcRgsRcg+Rgs,
(3)

where Rij=AiFij is the space resistance between nodes i and j, Ai is the emitting line length, Fij is the view factor, and Ji=σpTi4 is the blackbody emissive power from node i at temperature Ti. For a specified substrate temperature Ts=T and power density from Joule heating at the channel Qc=(JcJg)/Rcg+(JdJs)/Rcs, Eq. (3) circuit can be solved for the gate temperature Tg. Based on typical HEMT geometry, we estimate emitting line lengths as Ag=Ac70 nm. The view factor is estimated from the intercept of the 2D solid angle of the gate from the emitter region in the channel. For a typical HEMT geometry, we obtain Fcg0.3.

At a typical low-noise bias, the dissipated power is 30mWmm1.15 Note that this dissipated power is that at the low-noise bias, which is distinct from the powers used in the experiments of Sec. II. For a base temperature T=20 K, numerical solution of Eq. (3) predicts a gate temperature 24 K, consistent with the finding of Ref. 18. However, taking T=4 K, the gate temperature is predicted to be 20 K.

The self-heating of the gate affects the microwave noise of HEMTs because the thermal noise associated with the gate resistance is added at the input. If the steady-state gate temperature exceeds the base temperature, the microwave noise will be larger than predicted based on the base temperature. The above analysis implies that the thermal noise contribution of the HEMT gate at liquid helium temperatures is several times larger than previously assumed. An incorrect gate temperature directly affects the extracted drain temperature and consequently the interpretation of the physical origin of noise in HEMTs. We note that previous work has interpreted noise saturation at liquid helium temperatures to the saturation of the drain noise added at the output [see Fig. 1(d) of Ref. 15]. Our measurements indicate that the observed noise saturation is, in fact, due to elevated thermal noise at the input as the gate temperature plateaus with base temperature, as seen in Fig. 3(b).

This analysis indicates that self-heating will limit the minimum noise figure of cryogenic HEMT amplifiers without decreases in power consumption or improvements in device thermal management that decrease the physical temperature of the gate. Recently, LNAs with power consumption of hundreds of μW were reported, a value that is several times lower than those of typical HEMTs.7 While these reductions can reduce gate heating, the quartic temperature dependence associated with phonon radiation means that even at 300 μW and T=4 K, the gate temperature is predicted to be 10 K. Therefore, additional considerations for thermal management are necessary to reduce the excess thermal noise resulting from self-heating. A possible strategy is to introduce an additional thermal path above the gate using direct immersion in normal or superfluid liquid helium, which is routinely done for thermal management of superconducting magnets in high-energy physics experiments.51 

We have presented measurements of the gate junction temperature and thermal resistance of a low-noise HEMT from cryogenic to room temperature obtained using Schottky thermometry. The magnitude and trend of the extracted thermal resistance vs power and base temperature are consistent with heat dissipation by phonon radiation through an interface. Considering phonon radiation as the dominant mechanism of heat transfer, we estimate the intrinsic temperature of the gate at the low-noise operating bias using a radiation circuit. The model predicts that at liquid helium temperatures, the gate will self-heat to a temperature several times that of the base temperature. Our measurements thus indicate that self-heating constitutes a practical lower limit for the minimum microwave noise figure of cryogenic HEMT amplifiers unless thermal management strategies to remove heat from the gate can be identified.

A.Y.C., B.G., and A.J.M. were supported by the National Science Foundation under Grant No. 1911220. I.E. was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1745301. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. J.K. and A.J.M. were supported by the Jet Propulsion Laboratory PDRDF under Grant No. 107614-20AW0099. Experimental work was performed at the Cahill Radio Astronomy Laboratory (CRAL) and the Jet Propulsion Laboratory at the California Institute of Technology, under a contract with the National Aeronautics and Space Administration (Grant No. 80NM0018D0004).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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