DOI: 10.48577/jpl.2kljle
title: Characterization of self-heating in cryogenic high electron mobility transistors using Schottky thermometry

description: Abstract: 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, and the physical mechanisms governing the microwave noise figure are therefore of practical interest. In particular, 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 a Schottky thermometry method. At temperatures ∼ 20 K, we observe a nonlinear trend of thermal resistance versus 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. Introduction: I. INTRODUCTIONMicrowave 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 1-100 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 hot electron noise added in the channel and thermal noise in the gate, parameterized by equivalent temperatures Td and Tg, respectively. The gate noise tempera- ture is typically assumed to be the cryostat base temperature Tg = T while the drain temperature is fit to measured data. For a constant drain current, the hot electron contribution is taken to be constant and the minimum noise figure then scales as T 1/2 [2].Although the noise temperature does decrease with base temperature over a range of tempera- tures as predicted, at liquid helium temperatures the noise temperature is observed to plateau to a value several times the quantum noise limit [15–17]. This noise temperature plateau has been attributed to a variety of mechanisms, including drain shot noise [18], gate leakage current [9], and self-heating [15, 19]. 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 under bias at cryogenic temperatures would provide more direct evidence that self-heating is the origin of the noise temperature plateau. This measurement is challenging for conventional thermometery techniques such as IR microscopy [20, 21], micro- Raman spectroscopy [22–24], or liquid crystal thermography [25] due to geometrical constraints like the sub-micron gate lengths and the buried structure of modern HEMTs. Consequently, self- heating in FETs is usually characterized with measurements of 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 [26–29]. However, these approaches neglected a number of mechanisms relevant to the drain current in sub-micron 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 temperature2grise. Later studies of self-heating in MOSFETs incorporated some of these effects and reported measurements of temperature rise and thermal time constants [30]. Recent work in SOI MOSFETs reported that the dominant thermal resistance is due to the buried oxide layer [31]. Self-heating studies in HEMTs have largely focused on GaN power FETs at room temperature, where device lifetime is limited by channel heating [32]. Typically, the temperature rise is extracted from pulsed current measurements on the gate [33, 34], but this technique is generally unsuitable for cryogenic HEMTs where the thermal time constants are on the same order as the pulse duration [35]. As a result, self-heating in cryogenic III-V HEMTs remains poorly characterized.Here, we present measurements of the junction temperature and thermal resistance of the metallic gate in low-noise GaAs HEMTs using Schottky thermometry. At cryogenic temperatures, we observe a nonlinear trend of the thermal resistance on dissipated power that is consistent with heat transport by phonon radiation. We analyze the implications of this finding at the low-noise bias in which the drain and gate are forward and reverse biased, respectively, using a radiative circuit model. The model predicts that the gate self-heats to a value comparable to the physical temperature of the drain, 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.