Characterization of self-heating in cryogenic high electron mobility transistors using Schottky thermometry

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.

摘要：基于高电子迁移率晶体管（High Electron Mobility Transistors, HEMTs）的低温低噪声放大器（Cryogenic Low Noise Amplifiers）已广泛应用于射电天文、深空通信以及量子计算等领域，因此调控微波噪声系数的物理机制具有重要的实际研究价值。尤其在低温环境下，由于缺乏对应条件下热阻的实验测量数据，栅极热噪声的贡献机制仍不明确。本文采用肖特基测温法（Schottky Thermometry），对低温及室温环境下高电子迁移率晶体管的栅极结温与热阻进行了测量。在约20 K的温度条件下，我们观测到热阻随耗散功率变化呈现非线性趋势，这与声子辐射（Phonon Radiation）的散热机制相符。基于这一发现，我们针对低噪声偏置与液氦温度下的声子辐射热输运过程进行了分析，并估算得出：由于自热效应（Self-Heating），栅极热噪声的强度比此前假设的数值高出数倍。我们最终得出结论：若不改进热管理（Thermal Management）手段，自热效应将为低温环境下高电子迁移率晶体管的微波噪声系数设定实际下限。

一、引言
微波低噪声放大器（Microwave Low Noise Amplifiers, LNAs）作为高电子迁移率晶体管（HEMTs）的经典应用，已成为射电天文[1,2]、深空通信[3]以及量子计算[4-8]等领域科学仪器的核心组件。经过数十年的发展[9-13]，高电子迁移率晶体管低噪声放大器已在1~100 GHz的频段范围内实现了约为量子极限5~10倍的低温噪声温度[1]。尽管取得了上述进展，实际应用仍推动着放大器朝着更低噪声系数的方向持续迭代。
高电子迁移率晶体管放大器的噪声特性通常采用波皮耶夏尔斯基模型（Pospieszalski Model）进行解释。该模型将噪声分解为沟道内产生的热电子噪声与栅极热噪声，分别以等效温度Td与Tg进行参数化表征。常规研究中通常假设栅极温度等于低温恒温器的基底温度Tg=T，而漏极温度则通过拟合实测数据得到。在漏极电流恒定的情况下，热电子噪声贡献为定值，此时最小噪声系数随T^(1/2)缩放变化[2]。
尽管在一定温度范围内，噪声温度确实如预测般随基底温度降低而下降，但在液氦温度下，噪声温度会趋于平稳，其数值可达量子噪声极限的数倍[15-17]。这种噪声温度平台现象被归因于多种机制，包括漏极散粒噪声（Shot Noise）、栅极泄漏电流（Gate Leakage Current）以及自热效应[9,15,19]。其中，文献[15]通过微波噪声测量得出结论：与声子辐射相关的热阻会在低温环境下引发不可忽视的自热效应。然而，该结论仅通过噪声模型间接估算栅极结温得到，缺乏直接实验证据。
若能实现低温偏置条件下栅极温度的直接测量，将为自热效应是噪声温度平台现象的成因提供更直接的佐证。但由于现代高电子迁移率晶体管存在亚微米栅长与埋入式结构等几何限制，传统测温技术如红外显微镜（Infrared Microscopy）[20,21]、显微拉曼光谱（Micro-Raman Spectroscopy）[22-24]以及液晶热成像（Liquid Crystal Thermography）[25]均难以适用。因此，场效应晶体管（Field-Effect Transistors, FETs）的自热效应通常通过温度敏感电参数的测量进行表征。
早期针对互补金属氧化物半导体（Complementary Metal-Oxide Semiconductor, CMOS）自热效应的半定量研究，通过漏极电流的温度依赖性估算了偏置下的器件温度[26-29]。但这类方法忽略了亚微米器件漏极电流相关的多种机制，例如阈值电压的偏置依赖性、串联电阻以及非稳态输运效应（Non-Stationary Transport Effects）——这些效应在现代高电子迁移率晶体管中被证实至关重要，且可能影响提取的温度结果[2grise]。后续针对金属-氧化物-半导体场效应晶体管（Metal-Oxide-Semiconductor Field-Effect Transistors, MOSFETs）的自热效应研究纳入了部分此类效应，并报道了温升与热时间常数（Thermal Time Constants）的测量结果[30]。近期针对绝缘体上硅金属-氧化物-半导体场效应晶体管（Silicon-On-Insulator Metal-Oxide-Semiconductor Field-Effect Transistors, SOI MOSFETs）的研究表明，其主导热阻来源于埋氧层（Buried Oxide Layer）[31]。
针对高电子迁移率晶体管的自热效应研究大多聚焦于室温环境下的氮化镓功率场效应晶体管（Gallium Nitride Power Field-Effect Transistors, GaN Power FETs），这类器件的寿命受沟道发热限制[32]。通常通过对栅极开展脉冲电流测量（Pulsed Current Measurements）提取温升[33,34]，但该技术并不适用于低温高电子迁移率晶体管——这类器件的热时间常数与脉冲持续时间处于同一量级[35]。因此，低温III-V族高电子迁移率晶体管（III-V Group High Electron Mobility Transistors, III-V HEMTs）的自热效应仍缺乏充分表征。
本文采用肖特基测温法，对低噪声砷化镓高电子迁移率晶体管（Gallium Arsenide High Electron Mobility Transistors, GaAs HEMTs）的金属栅极结温与热阻进行了测量。在低温环境下，我们观测到热阻随耗散功率变化呈现非线性趋势，这与声子辐射主导的热输运机制相符。我们结合辐射电路模型（Radiative Circuit Model），分析了漏极正向偏置、栅极反向偏置的低噪声偏置条件下该发现的潜在影响。模型预测栅极自热后的温度可与漏极物理温度相当，这与“栅极与基底温度保持等温”的常规假设相悖。因此，本研究表明：若不改进器件热管理手段以移除栅极热量，自热效应将为低温环境下高电子迁移率晶体管的微波噪声系数设定实际下限。