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A Simple Method to Extract the Thermal Resistance of GaN HEMTs From De-Trapping Characteristics
从去捕获特性提取 GaN HEMT 热阻的简单方法

Benito González ⊕ ⊕ ^(o+){ }^{\oplus}, Luís C. Nunes ⊕ ⊕ ^(o+){ }^{\oplus}, Member, IEEE, João L. Gomes ⊕ ⊕ ^(o+){ }^{\oplus}, Graduate Student Member, IEEE,
贝尼托·冈萨雷斯 ⊕ ⊕ ^(o+){ }^{\oplus} ，路易斯·C·努内斯 ⊕ ⊕ ^(o+){ }^{\oplus} ，IEEE 会员，若昂·L·戈麦斯 ⊕ ⊕ ^(o+){ }^{\oplus} ，研究生会员，IEEE，Joana C. Mendes ⊕ ⊕ ^(o+){ }^{\oplus}, Member, IEEE, and Jose L. Jimenez, Member, IEEE
乔安娜·C·门德斯 ⊕ ⊕ ^(o+){ }^{\oplus} ，IEEE 会员，和何塞·L·希门尼斯，IEEE 会员

Abstract 摘要

This letter proposes a new method for extracting the thermal resistance of GaN-based HEMTs using pulse recovery data. After the device temperature and trapping state are established from different quiescent power dissipations for several base-plate temperatures, the recovery profile of the drain current is measured. The recovery time is then used as a temperature-sensitive electrical parameter to extract the thermal resistance of the device. The proposed method has been applied to a Schottky-gate HEMT on SiC, for which a thermal resistance of 15.7 ∘ C − mm / W 15.7 ∘ C − mm / W 15.7^(@)C-mm//W15.7^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} was extracted, a value in good agreement with others reported for similar devices. Comparison with the one obtained from a step response is also done. Finally, the uncertainties of the proposed method related to the pulse width, temperature, percentage of the drain current recovery time, and averaging procedure are discussed.
这封信提出了一种使用脉冲恢复数据提取基于 GaN 的 HEMT 热阻的新方法。在为几个基板温度建立设备温度和捕获状态后，测量漏电流的恢复曲线。然后，将恢复时间用作温度敏感电气参数，以提取设备的热阻。该方法已应用于 SiC 上的肖特基栅 HEMT，提取的热阻为 15.7 ∘ C − mm / W 15.7 ∘ C − mm / W 15.7^(@)C-mm//W15.7^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} ，与其他类似设备报告的值相符。还与从阶跃响应获得的值进行了比较。最后，讨论了与脉冲宽度、温度、漏电流恢复时间百分比和平均过程相关的提议方法的不确定性。

Index Terms-Pulse recovery data, electrothermal characterization, trapping, gallium nitride, high-electronmobility transistors (HEMTs), thermal resistance.
索引词-脉冲恢复数据，电热特性，捕获，氮化镓，高电子迁移率晶体管（HEMTs），热阻。

I. INTRODUCTION 一. 引言

THERE are several techniques for measuring the thermal resistance, R th R th R_(th)R_{\mathrm{th}}, of GaN high-electron mobility transistors (HEMTs), such as pulsed characteristics [1], [2], step response [3], infrared and Raman thermography [4], [5], and AC conductance method [6]. Temperature-sensitive electrical parameters (TSEPs), such as the forward voltage drop between the gate and source [7], the channel ON-resistance [7], [8], the saturation drain current [9], and the gate metal resistance
测量氮化镓高电子迁移率晶体管（HEMTs）热阻 R th R th R_(th)R_{\mathrm{th}} 的几种技术包括脉冲特性[1]，[2]，阶跃响应[3]，红外和拉曼热成像[4]，[5]，以及交流导电法[6]。温度敏感电气参数（TSEPs），如栅极与源极之间的正向电压降[7]，通道导通电阻[7]，[8]，饱和漏电流[9]，以及栅极金属电阻。
Fig. 1. Illustration of the pulse response method: the excitation waveforms and the drain current with the de-trapping recovery phenomenon and the respective channel temperature variation, together with R t h R t h R_(th)R_{t h} vs. φ φ varphi\varphi, and the extraction of R th R th  R_("th ")\mathrm{R}_{\text {th }} with the VFM.
图 1. 脉冲响应方法的示意图：激励波形和漏电流与去捕获恢复现象及相应的通道温度变化，以及 R t h R t h R_(th)R_{t h} 与 φ φ varphi\varphi 的关系，以及使用 VFM 提取 R th R th  R_("th ")\mathrm{R}_{\text {th }} 。
[10], [11], have also been used to extract the R th R th  R_("th ")R_{\text {th }} of HEMTs. Limitations of all these techniques are addressed in [6].
[10]，[11] 也被用来提取 HEMT 的 R th R th  R_("th ")R_{\text {th }} 。所有这些技术的局限性在 [6] 中得到了讨论。
Knowing that the de-trapping time is very sensitive to temperature (one order of magnitude for a 40 ∘ C 40 ∘ C 40^(@)C40{ }^{\circ} \mathrm{C} swing) [12]- [17], the main objective of this work is to take advantage of this feature and develop a simple and fast but precise thermo-electrical method, using easily accessible equipment in most RF laboratories, to extract the thermal resistance of HEMTs from pulse recovery data. Moreover, contrary to other simpler methodologies [1], [2], [3], [6], [8], [9], the proposed method does not require any separation of thermal and trapping effects. It can be applied to extract the thermal resistance of packaged devices, by simply mounting them on thermal stages and automatically repeating the procedure.
知道去捕获时间对温度非常敏感（对于 40 ∘ C 40 ∘ C 40^(@)C40{ }^{\circ} \mathrm{C} 的摆动变化一个数量级）[12]- [17]，本工作的主要目标是利用这一特性，开发一种简单、快速但精确的热电方法，使用大多数射频实验室中易于获取的设备，从脉冲恢复数据中提取 HEMT 的热阻。此外，与其他更简单的方法论[1]，[2]，[3]，[6]，[8]，[9]相反，所提出的方法不需要分离热效应和捕获效应。它可以通过简单地将封装设备安装在热台上并自动重复该过程来提取封装设备的热阻。
The method is described in Section II. The experimental setup and the characteristics of the tested device are detailed in Section III. The results and experimental validation are presented in Section IV. Conclusions are given in Section V.
该方法在第二节中描述。实验设置和测试设备的特性在第三节中详细说明。结果和实验验证在第四节中呈现。结论在第五节中给出。

II. PROPOSED TECHNIQUE II. 提议的技术

The new method to extract the R th R th R_(th)R_{\mathrm{th}} of GaN HEMTs is based on the dependence of the de-trapping time constant on the channel temperature, T ch T ch  T_("ch ")T_{\text {ch }}. As shown in Fig. 1, after setting the base-plate temperature, T bp T bp T_(bp)T_{\mathrm{bp}}, the measurement sequence starts by setting different quiescent gate- and drain-source voltages, V GQ V GQ V_(GQ)V_{\mathrm{GQ}} and V DQ V DQ V_(DQ)V_{\mathrm{DQ}}, respectively, to generate a quiescent drain current, I DQ I DQ I_(DQ)I_{\mathrm{DQ}}, and to consequently increase T ch T ch T_(ch)T_{\mathrm{ch}}. The initial biasing period should be sufficiently long (around 5 min ) to ensure a steady-state condition, with T ch = T ch , Q T ch = T ch , Q T_(ch)=T_(ch,Q)T_{\mathrm{ch}}=T_{\mathrm{ch}, \mathrm{Q}}. A high drain voltage, V D V D V_(D)V_{\mathrm{D}}, is then applied to induce charge trapping,
提取 GaN HEMT 的 R th R th R_(th)R_{\mathrm{th}} 的新方法基于去捕获时间常数对通道温度的依赖性 T ch T ch  T_("ch ")T_{\text {ch }} 。如图 1 所示，在设置基板温度 T bp T bp T_(bp)T_{\mathrm{bp}} 后，测量序列通过设置不同的静态栅极和漏源电压 V GQ V GQ V_(GQ)V_{\mathrm{GQ}} 和 V DQ V DQ V_(DQ)V_{\mathrm{DQ}} 开始，以生成静态漏电流 I DQ I DQ I_(DQ)I_{\mathrm{DQ}} ，并因此增加 T ch T ch T_(ch)T_{\mathrm{ch}} 。初始偏置周期应足够长（约 5 分钟），以确保稳态条件， T ch = T ch , Q T ch = T ch , Q T_(ch)=T_(ch,Q)T_{\mathrm{ch}}=T_{\mathrm{ch}, \mathrm{Q}} 。然后施加高漏电压 V D V D V_(D)V_{\mathrm{D}} 以诱导电荷捕获，
while the gate voltage, V G V G V_(G)V_{\mathrm{G}}, is simultaneously pulsed down to avoid temperature spikes. These pulses must be narrow enough ( 1 μ s ) ( 1 μ s ) (1mus)(1 \mu \mathrm{s}) to prevent a significant decrease of T ch T ch T_(ch)T_{\mathrm{ch}}, while, at the same time, ensuring considerable trapping. With this, we can assume that, immediately after the pulse is stepped down, right when the de-trapping process is about to start, T ch ≈ T ch , Q T ch ≈ T ch , Q T_(ch)~~T_(ch,Q)T_{\mathrm{ch}} \approx T_{\mathrm{ch}, \mathrm{Q}}.
在此期间，栅电压 V G V G V_(G)V_{\mathrm{G}} 同时被脉冲降低，以避免温度峰值。这些脉冲必须足够窄 ( 1 μ s ) ( 1 μ s ) (1mus)(1 \mu \mathrm{s}) ，以防止 T ch T ch T_(ch)T_{\mathrm{ch}} 的显著下降，同时确保相当的捕获。这样，我们可以假设，在脉冲降低后立即，正当去捕获过程即将开始时， T ch ≈ T ch , Q T ch ≈ T ch , Q T_(ch)~~T_(ch,Q)T_{\mathrm{ch}} \approx T_{\mathrm{ch}, \mathrm{Q}} 。
During the de-trapping process, the drain current, I D I D I_(D)I_{\mathrm{D}}, recovers from an initial value, I Do I Do I_(Do)I_{\mathrm{Do}}, to I DQ I DQ I_(DQ)I_{\mathrm{DQ}}, where the channel temperature is again T ch , Q T ch , Q T_(ch,Q)T_{\mathrm{ch}, \mathrm{Q}}. Thus, with a percentage of I DQ − I o I DQ − I o I_(DQ)-I_(o)I_{\mathrm{DQ}}-I_{\mathrm{o}}, φ φ varphi\varphi, as a criterion, the drain current recovery time, τ φ τ φ tau_(varphi)\tau_{\varphi}, given by:
在去捕获过程中，漏电流 I D I D I_(D)I_{\mathrm{D}} 从初始值 I Do I Do I_(Do)I_{\mathrm{Do}} 恢复到 I DQ I DQ I_(DQ)I_{\mathrm{DQ}} ，此时通道温度再次为 T ch , Q T ch , Q T_(ch,Q)T_{\mathrm{ch}, \mathrm{Q}} 。因此，以 I DQ − I o I DQ − I o I_(DQ)-I_(o)I_{\mathrm{DQ}}-I_{\mathrm{o}} 的百分比 φ φ varphi\varphi 作为标准，漏电流恢复时间 τ φ τ φ tau_(varphi)\tau_{\varphi} 为：
τ φ ( T ch , Q ) = Δ t | Δ I D Δ I DQ = φ 100 = Δ t | I D − I Do I DQ − I Do = φ 100 τ φ T ch , Q = Δ t Δ I D Δ I DQ = φ 100 = Δ t I D − I Do I DQ − I Do = φ 100 tau_(varphi)(T_(ch,Q))= Delta t|_((DeltaI_(D))/(DeltaI_(DQ))=(varphi)/(100))= Delta t|_((I_(D)-I_(Do))/(I_(DQ)-I_(Do)))=(varphi)/(100)\tau_{\varphi}\left(T_{\mathrm{ch}, \mathrm{Q}}\right)=\left.\Delta t\right|_{\frac{\Delta I_{\mathrm{D}}}{\Delta I_{\mathrm{DQ}}}=\frac{\varphi}{100}}=\left.\Delta t\right|_{\frac{I_{\mathrm{D}}-I_{\mathrm{Do}}}{I_{\mathrm{DQ}}-I_{\mathrm{Do}}}}=\frac{\varphi}{100}
could be used as a TSEP with T ch , Q T ch , Q T_(ch,Q)T_{\mathrm{ch}, \mathrm{Q}} (see Fig. 1).
可以用作 TSEP 与 T ch , Q T ch , Q T_(ch,Q)T_{\mathrm{ch}, \mathrm{Q}} （见图 1）。
The de-trapping process can be physically described by the Shockley-Read-Hall model, where the emission time constant, τ e τ e tau_(e)\tau_{\mathrm{e}}, is given by A − 1 T ch − 2 exp ⁡ ( E A / ( K B T ch ) ) A − 1 T ch − 2 exp ⁡ E A / K B T ch A^(-1)T_(ch)^(-2)exp(E_(A)//(K_(B)T_(ch)))A^{-1} T_{\mathrm{ch}}^{-2} \exp \left(E_{\mathrm{A}} /\left(K_{\mathrm{B}} T_{\mathrm{ch}}\right)\right), with E A E A E_(A)E_{\mathrm{A}} and K B K B K_(B)K_{\mathrm{B}} being the trap activation energy and Boltzmann constant, respectively, and A A AA incorporates the remaining temperature independent parameters [18]. In a steady-state regime, τ φ τ φ tau_(varphi)\tau_{\varphi} in (1) is directly proportional to τ e τ e tau_(e)\tau_{\mathrm{e}}. Then, considering a small range of channel temperature variation (typically 40 ∘ C 40 ∘ C 40^(@)C40^{\circ} \mathrm{C} of variation), δ T ch = δ T bp + R th × δ P DQ δ T ch = δ T bp + R th × δ P DQ deltaT_(ch)=deltaT_(bp)+R_(th)xx deltaP_(DQ)\delta T_{\mathrm{ch}}=\delta T_{\mathrm{bp}}+R_{\mathrm{th}} \times \delta P_{\mathrm{DQ}}, with P DQ = I DQ V DQ P DQ = I DQ V DQ P_(DQ)=I_(DQ)V_(DQ)P_{\mathrm{DQ}}=I_{\mathrm{DQ}} V_{\mathrm{DQ}} being the quiescent power dissipation, ln ⁡ τ φ ln ⁡ τ φ ln tau_(varphi)\ln \tau_{\varphi} can be easily linearized without significantly increasing the error. That is,
去捕获过程可以通过肖克利-里德-霍尔模型进行物理描述，其中发射时间常数 τ e τ e tau_(e)\tau_{\mathrm{e}} 由 A − 1 T ch − 2 exp ⁡ ( E A / ( K B T ch ) ) A − 1 T ch − 2 exp ⁡ E A / K B T ch A^(-1)T_(ch)^(-2)exp(E_(A)//(K_(B)T_(ch)))A^{-1} T_{\mathrm{ch}}^{-2} \exp \left(E_{\mathrm{A}} /\left(K_{\mathrm{B}} T_{\mathrm{ch}}\right)\right) 给出， E A E A E_(A)E_{\mathrm{A}} 和 K B K B K_(B)K_{\mathrm{B}} 分别是陷阱激活能和玻尔兹曼常数，而 A A AA 包含剩余的温度无关参数[18]。在稳态条件下，(1)中的 τ φ τ φ tau_(varphi)\tau_{\varphi} 与 τ e τ e tau_(e)\tau_{\mathrm{e}} 成正比。然后，考虑到通道温度变化的小范围（通常为 40 ∘ C 40 ∘ C 40^(@)C40^{\circ} \mathrm{C} 的变化）， δ T ch = δ T bp + R th × δ P DQ δ T ch = δ T bp + R th × δ P DQ deltaT_(ch)=deltaT_(bp)+R_(th)xx deltaP_(DQ)\delta T_{\mathrm{ch}}=\delta T_{\mathrm{bp}}+R_{\mathrm{th}} \times \delta P_{\mathrm{DQ}} ，其中 P DQ = I DQ V DQ P DQ = I DQ V DQ P_(DQ)=I_(DQ)V_(DQ)P_{\mathrm{DQ}}=I_{\mathrm{DQ}} V_{\mathrm{DQ}} 是静态功耗， ln ⁡ τ φ ln ⁡ τ φ ln tau_(varphi)\ln \tau_{\varphi} 可以很容易地线性化，而不会显著增加误差。也就是说，
ln ⁡ τ φ ≈ a o − a 1 × T chQ ≈ a o − a 1 × ( T bp + R th × P DQ ) ln ⁡ τ φ ≈ a o − a 1 × T chQ ≈ a o − a 1 × T bp + R th × P DQ ln tau_(varphi)~~a_(o)-a_(1)xxT_(chQ)~~a_(o)-a_(1)xx(T_(bp)+R_(th)xxP_(DQ))\ln \tau_{\varphi} \approx a_{\mathrm{o}}-a_{1} \times T_{\mathrm{chQ}} \approx a_{\mathrm{o}}-a_{1} \times\left(T_{\mathrm{bp}}+R_{\mathrm{th}} \times P_{\mathrm{DQ}}\right)
where a 0 a 0 a_(0)a_{0} and a 1 a 1 a_(1)a_{1} are fitting parameters that can be extracted using least squares to minimize the mean quadratic error with respect to the measured data. The accuracy of this method lies in the use of multiple base-plate temperatures and power dissipations, resulting in an average R th R th R_(th)R_{\mathrm{th}}. Additionally, R th R th R_(th)R_{\mathrm{th}} could be extracted for a wide range of T ch T ch T_(ch)T_{\mathrm{ch}} (varying T bp T bp T_(bp)T_{\mathrm{bp}} and P DQ ) P DQ {:P_(DQ))\left.P_{\mathrm{DQ}}\right), by dividing it into small consecutive ranges for which ln ⁡ τ φ ln ⁡ τ φ ln tau_(varphi)\ln \tau_{\varphi} can be linearized.
其中 a 0 a 0 a_(0)a_{0} 和 a 1 a 1 a_(1)a_{1} 是可以通过最小二乘法提取的拟合参数，以最小化与测量数据的均方误差。该方法的准确性在于使用多个基板温度和功率耗散，从而得到平均值 R th R th R_(th)R_{\mathrm{th}} 。此外， R th R th R_(th)R_{\mathrm{th}} 可以在广泛的 T ch T ch T_(ch)T_{\mathrm{ch}} 范围内提取（变化的 T bp T bp T_(bp)T_{\mathrm{bp}} 和 P DQ ) P DQ {:P_(DQ))\left.P_{\mathrm{DQ}}\right) ），通过将其划分为小的连续范围，使得 ln ⁡ τ φ ln ⁡ τ φ ln tau_(varphi)\ln \tau_{\varphi} 可以线性化。
In our case, during the pulse, and certainly during the de-trapping process, some thermal dynamics can be excited, which leads the slight decrease of T ch T ch T_(ch)T_{\mathrm{ch}}, as it is illustrated in Fig. 1. Nevertheless, for high percentages of the drain current recovery time, T ch T ch  T_("ch ")T_{\text {ch }} tends to the original value, T chQ T chQ  T_("chQ ")T_{\text {chQ }}, imposed by T bp + R th × P DQ T bp + R th × P DQ T_(bp)+R_(th)xxP_(DQ)T_{\mathrm{bp}}+R_{\mathrm{th}} \times P_{\mathrm{DQ}}, when (2) is valid. As Fig. 1 shows, where the dependence of the extracted thermal resistance on φ φ varphi\varphi is represented (measured data with solid squares and their trend with a dashed line), a percentage of between 90 − 95 % 90 − 95 % 90-95%90-95 \% turns out to be reasonable. For φ < 90 % φ < 90 % varphi < 90%\varphi<90 \%, an unrealistic overestimated R th R th R_(th)R_{\mathrm{th}} would be obtained due to excited de-trapping and thermal dynamics and, for φ φ varphi\varphi at nearly 100 % , I D 100 % , I D 100%,I_(D)100 \%, I_{\mathrm{D}} tends to plateau and the uncertainty in the extracted recovery time increases.
在我们的案例中，在脉冲期间，尤其是在去捕获过程中，一些热动力学可以被激发，这导致 T ch T ch T_(ch)T_{\mathrm{ch}} 的轻微下降，如图 1 所示。然而，对于高比例的漏电流恢复时间， T ch T ch  T_("ch ")T_{\text {ch }} 趋向于由 T bp + R th × P DQ T bp + R th × P DQ T_(bp)+R_(th)xxP_(DQ)T_{\mathrm{bp}}+R_{\mathrm{th}} \times P_{\mathrm{DQ}} 施加的原始值 T chQ T chQ  T_("chQ ")T_{\text {chQ }} ，当(2)有效时。如图 1 所示，提取的热阻与 φ φ varphi\varphi 的依赖关系（用实心方块表示的测量数据及其趋势用虚线表示），在 90 − 95 % 90 − 95 % 90-95%90-95 \% 之间的百分比被认为是合理的。对于 φ < 90 % φ < 90 % varphi < 90%\varphi<90 \% ，由于激发的去捕获和热动力学，将获得不切实际的高估 R th R th R_(th)R_{\mathrm{th}} ，而对于 φ φ varphi\varphi 在接近 100 % , I D 100 % , I D 100%,I_(D)100 \%, I_{\mathrm{D}} 时趋于平稳，提取的恢复时间的不确定性增加。
In [19] a simple thermally activated trapping model based on SRH model was proposed. In this model, the trapping dynamics induces a threshold voltage shift modeled by the charging (for capture) and discharging (for emission) of a capacitor through the corresponding R-C linear system. By incorporating self-heating effects using a first-order thermal network, as in [13] and [19], the proposed method could be reproduced without a significant deviation of the extracted R th R th  R_("th ")R_{\text {th }} from the thermal network, showing its consistency.
在[19]中，提出了一种基于 SRH 模型的简单热激活捕获模型。在该模型中，捕获动态引起的阈值电压偏移通过相应的 R-C 线性系统中电容器的充电（用于捕获）和放电（用于发射）进行建模。通过使用一阶热网络结合自加热效应，如[13]和[19]所示，所提出的方法可以在提取的 R th R th  R_("th ")R_{\text {th }} 与热网络之间没有显著偏差的情况下重现，显示出其一致性。
Alternatively, as Fig. 1 shows, a linear relationship, F F FF, between ln ⁡ τ 90 % ln ⁡ τ 90 % ln tau_(90%)\ln \tau_{90 \%} and P DQ P DQ P_(DQ)P_{\mathrm{DQ}} can be extracted for a base-plate temperature T bp − a T bp − a T_(bp-a)T_{\mathrm{bp}-\mathrm{a}} (with, at least, three quiescent power dissipations). Then, for a given pair of [ T bp − b , P DQ − b ] T bp − b , P DQ − b [T_(bp-b),P_(DQ-b)]\left[T_{\mathrm{bp}-\mathrm{b}}, P_{\mathrm{DQ}-\mathrm{b}}\right] with τ 90 % − b τ 90 % − b tau_(90%-b)\tau_{90 \%-\mathrm{b}}, the necessary quiescent power dissipation for producing the same channel temperature at T bp − a T bp − a T_(bp-a)T_{\mathrm{bp}-\mathrm{a}} results in
或者，如图 1 所示，可以提取出基板温度 T bp − a T bp − a T_(bp-a)T_{\mathrm{bp}-\mathrm{a}} 下 ln ⁡ τ 90 % ln ⁡ τ 90 % ln tau_(90%)\ln \tau_{90 \%} 和 P DQ P DQ P_(DQ)P_{\mathrm{DQ}} 之间的线性关系 F F FF （至少需要三个静态功耗）。然后，对于给定的 [ T bp − b , P DQ − b ] T bp − b , P DQ − b [T_(bp-b),P_(DQ-b)]\left[T_{\mathrm{bp}-\mathrm{b}}, P_{\mathrm{DQ}-\mathrm{b}}\right] 和 τ 90 % − b τ 90 % − b tau_(90%-b)\tau_{90 \%-\mathrm{b}} ，在 T bp − a T bp − a T_(bp-a)T_{\mathrm{bp}-\mathrm{a}} 下产生相同通道温度所需的静态功耗为
Fig. 2. Diagram of the experimental setup.
图 2. 实验装置示意图。
Fig. 3. Percentage of the recovered drain current (lines) vs. recovery time, for different P D Q P D Q P_(DQ)P_{D Q} and T b p = 25 ∘ C T b p = 25 ∘ C T_(bp)=25^(@)CT_{b p}=25^{\circ} \mathrm{C}. The inset shows analogously the same dependency for different T bp T bp T_(bp)\mathrm{T}_{\mathrm{bp}} with V GQ = − 2 V V GQ = − 2 V V_(GQ)=-2V\mathrm{V}_{\mathrm{GQ}}=-2 \mathrm{~V}. In both cases, the 90 % 90 % 90%90 \% criterion for the drain current recovery time is indicated with horizontal and vertical lines.
图 3. 不同 P D Q P D Q P_(DQ)P_{D Q} 和 T b p = 25 ∘ C T b p = 25 ∘ C T_(bp)=25^(@)CT_{b p}=25^{\circ} \mathrm{C} 的恢复漏电流百分比（线）与恢复时间的关系。插图同样显示了不同 T bp T bp T_(bp)\mathrm{T}_{\mathrm{bp}} 与 V GQ = − 2 V V GQ = − 2 V V_(GQ)=-2V\mathrm{V}_{\mathrm{GQ}}=-2 \mathrm{~V} 的相同依赖关系。在这两种情况下，漏电流恢复时间的 90 % 90 % 90%90 \% 标准用水平和垂直线表示。
P DQ − a = F − 1 ( ln ⁡ τ 90 % − b ) P DQ − a = F − 1 ln ⁡ τ 90 % − b P_(DQ-a)=F^(-1)(ln tau_(90%-b))P_{\mathrm{DQ}-\mathrm{a}}=F^{-1}\left(\ln \tau_{90 \%-\mathrm{b}}\right). Since [ T bp − a , P DQ − a ] T bp − a , P DQ − a [T_(bp-a),P_(DQ-a)]\left[T_{\mathrm{bp}-\mathrm{a}}, P_{\mathrm{DQ}-\mathrm{a}}\right] and [ T bp − b , P DQ − b ] T bp − b , P DQ − b [T_(bp-b),P_(DQ-b)]\left[T_{\mathrm{bp}-\mathrm{b}}, P_{\mathrm{DQ}-\mathrm{b}}\right] follow (2) with τ 90 % − b , R th τ 90 % − b , R th tau_(90%-b),R_(th)\tau_{90 \%-\mathrm{b}}, R_{\mathrm{th}} results ( T bp − a − T bp − a − T_(bp-a)-T_{\mathrm{bp}-\mathrm{a}}- T bp − b ) / ( P DQ − b − P DQ − a ) = Δ T bp / Δ P DQ T bp − b / P DQ − b − P DQ − a = Δ T bp / Δ P DQ {:T_(bp-b))//(P_(DQ-b)-P_(DQ-a))=DeltaT_(bp)//DeltaP_(DQ)\left.T_{\mathrm{bp}-\mathrm{b}}\right) /\left(P_{\mathrm{DQ}-\mathrm{b}}-P_{\mathrm{DQ}-\mathrm{a}}\right)=\Delta T_{\mathrm{bp}} / \Delta P_{\mathrm{DQ}}. This will be named a very fast method (VFM).
P DQ − a = F − 1 ( ln ⁡ τ 90 % − b ) P DQ − a = F − 1 ln ⁡ τ 90 % − b P_(DQ-a)=F^(-1)(ln tau_(90%-b))P_{\mathrm{DQ}-\mathrm{a}}=F^{-1}\left(\ln \tau_{90 \%-\mathrm{b}}\right) 。由于 [ T bp − a , P DQ − a ] T bp − a , P DQ − a [T_(bp-a),P_(DQ-a)]\left[T_{\mathrm{bp}-\mathrm{a}}, P_{\mathrm{DQ}-\mathrm{a}}\right] 和 [ T bp − b , P DQ − b ] T bp − b , P DQ − b [T_(bp-b),P_(DQ-b)]\left[T_{\mathrm{bp}-\mathrm{b}}, P_{\mathrm{DQ}-\mathrm{b}}\right] 在(2)后跟随 τ 90 % − b , R th τ 90 % − b , R th tau_(90%-b),R_(th)\tau_{90 \%-\mathrm{b}}, R_{\mathrm{th}} 结果（ T bp − a − T bp − a − T_(bp-a)-T_{\mathrm{bp}-\mathrm{a}}- T bp − b ) / ( P DQ − b − P DQ − a ) = Δ T bp / Δ P DQ T bp − b / P DQ − b − P DQ − a = Δ T bp / Δ P DQ {:T_(bp-b))//(P_(DQ-b)-P_(DQ-a))=DeltaT_(bp)//DeltaP_(DQ)\left.T_{\mathrm{bp}-\mathrm{b}}\right) /\left(P_{\mathrm{DQ}-\mathrm{b}}-P_{\mathrm{DQ}-\mathrm{a}}\right)=\Delta T_{\mathrm{bp}} / \Delta P_{\mathrm{DQ}} 。这将被称为一种非常快速的方法（VFM）。

III. EXPERIMENTAL SETUP III. 实验设置

A diagram of the experimental setup is shown in Fig. 2, with an arbitrary waveform generator (Tektronix AWG5012C) generating the gate and drain voltage pulses, which were then amplified using two pulser heads and bias-tees (Keysight 11612 A ) 11612 A ) 11612A)11612 \mathrm{~A}) to prevent possible oscillations at high frequencies. The drain current was obtained through a 120 − MHz 120 − MHz 120-MHz120-\mathrm{MHz} bandwidth Hall-effect current sensor (TCP0030A) connected to a high-speed digital oscilloscope (Tektronix DPO3052) [18], and the bare die was placed directly on a hotplate to maintain T bp T bp T_(bp)T_{\mathrm{bp}} in the range 25 − 50 ∘ C 25 − 50 ∘ C 25-50^(@)C25-50^{\circ} \mathrm{C}, with steps of 5 ∘ C 5 ∘ C 5^(@)C5^{\circ} \mathrm{C}.
实验设置的示意图如图 2 所示，任意波形发生器（Tektronix AWG5012C）生成栅极和漏极电压脉冲，然后通过两个脉冲头和偏置接头（Keysight 11612 A ) 11612 A ) 11612A)11612 \mathrm{~A}) ）进行放大，以防止在高频下可能出现的振荡。漏电流通过连接到高速数字示波器（Tektronix DPO3052）的 120 − MHz 120 − MHz 120-MHz120-\mathrm{MHz} 带宽霍尔效应电流传感器（TCP0030A）获得[18]，裸芯片直接放置在热板上，以保持 T bp T bp T_(bp)T_{\mathrm{bp}} 在范围 25 − 50 ∘ C 25 − 50 ∘ C 25-50^(@)C25-50^{\circ} \mathrm{C} 内，步长为 5 ∘ C 5 ∘ C 5^(@)C5^{\circ} \mathrm{C} 。
A GaN Schottky-gate HEMT on SiC with a threshold voltage of -3 V , a gate length of 0.25 μ m 0.25 μ m 0.25 mum0.25 \mu \mathrm{m}, and a gate width of 400 μ m ( 2 × 200 μ m ) 400 μ m ( 2 × 200 μ m ) 400 mum(2xx200 mum)400 \mu \mathrm{m}(2 \times 200 \mu \mathrm{m}) was used to validate the method.
一种在 SiC 上具有-3 V 阈值电压、 0.25 μ m 0.25 μ m 0.25 mum0.25 \mu \mathrm{m} 的栅长和 400 μ m ( 2 × 200 μ m ) 400 μ m ( 2 × 200 μ m ) 400 mum(2xx200 mum)400 \mu \mathrm{m}(2 \times 200 \mu \mathrm{m}) 的栅宽的 GaN 肖特基栅 HEMT 被用来验证该方法。
Since the gate-lag phenomenon is nowadays solved [20], [21], [22], to generate different P DQ P DQ P_(DQ)P_{\mathrm{DQ}} without changing the trapping state, only the quiescent gate voltage, V GQ V GQ V_(GQ)V_{\mathrm{GQ}}, is changed from -2.5 to -2 V in steps of 0.1 V and the V DQ V DQ V_(DQ)V_{\mathrm{DQ}} if fixed at 6 V . Short-pulsed voltages of 40 and -5 V for the drain and gate terminals, respectively, induced the current collapse.
由于门延迟现象如今已得到解决[20]，[21]，[22]，为了在不改变捕获状态的情况下生成不同的 P DQ P DQ P_(DQ)P_{\mathrm{DQ}} ，仅将静态门电压 V GQ V GQ V_(GQ)V_{\mathrm{GQ}} 从-2.5 V 以 0.1 V 的步长调整到-2 V，而 V DQ V DQ V_(DQ)V_{\mathrm{DQ}} 固定在 6 V。分别为漏极和门极施加 40 V 和-5 V 的短脉冲电压，导致电流崩溃。

IV. RESULTS AND VALIDATION
IV. 结果与验证

Fig. 3 shows the percentage of the recovered I D I D I_(D)I_{\mathrm{D}} (with lines) after the pulsed OFF-state stress for a base-plate temperature of 25 ∘ C 25 ∘ C 25^(@)C25{ }^{\circ} \mathrm{C} at different quiescent power dissipations.
图 3 显示了在不同静态功耗下，基板温度为 25 ∘ C 25 ∘ C 25^(@)C25{ }^{\circ} \mathrm{C} 时，脉冲关断状态应力后恢复的 I D I D I_(D)I_{\mathrm{D}} 百分比（带线）。
Fig. 4. 90 % 90 % 90%90 \% of the drain current recovery time vs. power dissipation, at different base-plate temperatures. The inset shows the linear temperature dependence of R th R th  R_("th ")R_{\text {th }} with the VFM. Measured and modeled data are represented by symbols and lines, respectively.
图 4. 90 % 90 % 90%90 \% 排水电流恢复时间与功耗的关系，基板温度不同。插图显示了 R th R th  R_("th ")R_{\text {th }} 与 VFM 的线性温度依赖性。测量和建模数据分别用符号和线条表示。
Fig. 5. Drain current response to a positive drain voltage step of 50 V with V GQ = − 2.3 V V GQ = − 2.3 V V_(GQ)=-2.3V\mathrm{V}_{\mathrm{GQ}}=-2.3 \mathrm{~V} and T bp = 25 ∘ C T bp = 25 ∘ C T_(bp)=25^(@)C\mathrm{T}_{\mathrm{bp}}=25^{\circ} \mathrm{C}. The inset shows the linear baseplate temperature dependence of the peak drain current, I D P I D P I_(DP)I_{D P}.
图 5. 在 V GQ = − 2.3 V V GQ = − 2.3 V V_(GQ)=-2.3V\mathrm{V}_{\mathrm{GQ}}=-2.3 \mathrm{~V} 和 T bp = 25 ∘ C T bp = 25 ∘ C T_(bp)=25^(@)C\mathrm{T}_{\mathrm{bp}}=25^{\circ} \mathrm{C} 下，50 V 正排电压阶跃对漏电流的响应。插图显示了峰值漏电流的线性基板温度依赖性， I D P I D P I_(DP)I_{D P} 。
The corresponding 90 % 90 % 90%90 \% of the drain current recovery time, τ 90 % τ 90 % tau_(90)%\tau_{90} \%, is indicated with vertical lines. As expected from (2), the higher the quiescent power dissipation, the sooner the drain current recovers due to enhanced self-heating effects. The inset in Fig. 3 shows similarly the recovery dynamics of the drain current and τ 90 τ 90 tau_(90)\tau_{90} at different base-plate temperatures for a representative quiescent gate voltage of V GQ = − 2 V V GQ = − 2 V V_(GQ)=-2VV_{\mathrm{GQ}}=-2 \mathrm{~V}. Naturally, a faster recovery is observed when the base-plate temperature is increased as described by (2).
相应的 90 % 90 % 90%90 \% 漏电流恢复时间 τ 90 % τ 90 % tau_(90)%\tau_{90} \% 用垂直线表示。正如（2）所预期的，静态功耗越高，漏电流恢复得越快，这是由于增强的自加热效应。图 3 中的插图同样显示了在代表性的静态栅压 V GQ = − 2 V V GQ = − 2 V V_(GQ)=-2VV_{\mathrm{GQ}}=-2 \mathrm{~V} 下，不同基板温度下漏电流和 τ 90 τ 90 tau_(90)\tau_{90} 的恢复动态。自然，当基板温度升高时，恢复速度会更快，如（2）所述。
The resulting quiescent power dissipation dependence of the 90 % 90 % 90%90 \% of the normalized drain current recovery time, ln ⁡ τ 90 % ln ⁡ τ 90 % ln tau_(90%)\ln \tau_{90 \%}, is shown in Fig. 4 with symbols for each base-plate temperature. By applying (2) and considering all base-plate temperatures and power dissipations, the extracted values for a o , a 1 a o , a 1 a_(o),a_(1)a_{\mathrm{o}}, a_{1}, and R th R th R_(th)R_{\mathrm{th}} are − 1.25 , 0.08 ∘ C − 1 − 1.25 , 0.08 ∘ C − 1 -1.25,0.08^(@)C^(-1)-1.25,0.08^{\circ} \mathrm{C}^{-1}, and 15.7 ∘ C − mm / W 15.7 ∘ C − mm / W 15.7^(@)C-mm//W15.7^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W}, respectively. The resulting modeled data for ln ⁡ τ 90 % ln ⁡ τ 90 % ln tau_(90)%\ln \tau_{90} \% are shown in Fig. 4 with lines, showing a good agreement with the measurements with an average relative error of 6.3 % 6.3 % 6.3%6.3 \%.
所得到的静态功耗依赖于归一化漏电流恢复时间 ln ⁡ τ 90 % ln ⁡ τ 90 % ln tau_(90%)\ln \tau_{90 \%} 的 90 % 90 % 90%90 \% 如图 4 所示，图中用符号表示每个基板温度。通过应用(2)并考虑所有基板温度和功耗，提取的 a o , a 1 a o , a 1 a_(o),a_(1)a_{\mathrm{o}}, a_{1} 和 R th R th R_(th)R_{\mathrm{th}} 的值分别为 − 1.25 , 0.08 ∘ C − 1 − 1.25 , 0.08 ∘ C − 1 -1.25,0.08^(@)C^(-1)-1.25,0.08^{\circ} \mathrm{C}^{-1} 和 15.7 ∘ C − mm / W 15.7 ∘ C − mm / W 15.7^(@)C-mm//W15.7^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} 。所得到的 ln ⁡ τ 90 % ln ⁡ τ 90 % ln tau_(90)%\ln \tau_{90} \% 的模型数据如图 4 所示，线条显示与测量结果良好一致，平均相对误差为 6.3 % 6.3 % 6.3%6.3 \% 。
Because the R th R th R_(th)R_{\mathrm{th}} of HEMTs depends on the gate length [2], [6], our result ( 15.7 ∘ C − mm / W ) 15.7 ∘ C − mm / W {:15.7^(@)C-mm//W)\left.15.7^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W}\right) has been compared with data reported for 0.25 μ m GaN 0.25 μ m GaN 0.25 mumGaN0.25 \mu \mathrm{m} \mathrm{GaN}-based HEMTs on SiC : 18.3 and 12.6 ∘ C − mm / W 12.6 ∘ C − mm / W 12.6^(@)C-mm//W12.6^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} in [2] and [8], respectively, using pulse response measurements and the channel ON -resistance as TSEP, and 15.5 ∘ C − mm / W 15.5 ∘ C − mm / W 15.5^(@)C-mm//W15.5^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} in [3] using a step response, which shows that our result is in same range. A more specific comparison would require the use of the same power densities and even transistors with similar gate-to-drain extension [23].
由于 HEMT 的 R th R th R_(th)R_{\mathrm{th}} 依赖于栅长[2]，[6]，我们的结果（ 15.7 ∘ C − mm / W ) 15.7 ∘ C − mm / W {:15.7^(@)C-mm//W)\left.15.7^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W}\right) ）已与在 SiC 上报告的基于 0.25 μ m GaN 0.25 μ m GaN 0.25 mumGaN0.25 \mu \mathrm{m} \mathrm{GaN} 的 HEMT 数据进行了比较：在[2]和[8]中分别为 18.3 和 12.6 ∘ C − mm / W 12.6 ∘ C − mm / W 12.6^(@)C-mm//W12.6^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} ，使用脉冲响应测量和通道导通电阻作为 TSEP，以及在[3]中使用阶跃响应，这表明我们的结果在相同范围内。更具体的比较需要使用相同的功率密度，甚至是具有相似栅极到漏极扩展的晶体管[23]。
The R th R th  R_("th ")R_{\text {th }} in our device was also measured by making use of the step response technique [3]. Fig. 5 shows the resulting drain current transient response affected only by self-heating and measured for a V D V D V_(D)V_{\mathrm{D}} step of 50 V with a fixed V GQ = V GQ = V_(GQ)=V_{\mathrm{GQ}}= -2.3 V and T bp = 25 ∘ C T bp = 25 ∘ C T_(bp)=25^(@)CT_{\mathrm{bp}}=25^{\circ} \mathrm{C}; it can be seen that I D I D I_(D)I_{\mathrm{D}} decreases with a thermal time constant, τ th τ th  tau_("th ")\tau_{\text {th }}, of ∼ 100 μ s ∼ 100 μ s ∼100 mus\sim 100 \mu \mathrm{s}. The inset shows the linear base-plate temperature dependence of the peak drain current, without self-heating, I DP I DP I_(DP)I_{\mathrm{DP}}. So R th = ( I DS − I DP ) / ( P DS × R th = I DS − I DP / P DS × R_(th)=(I_(DS)-I_(DP))//(P_(DS)xx:}R_{\mathrm{th}}=\left(I_{\mathrm{DS}}-\mathrm{I}_{\mathrm{DP}}\right) /\left(P_{\mathrm{DS}} \times\right. ∂ I DP / ∂ T bp ) ∂ I DP / ∂ T bp {: delI_(DP)//delT_(bp))\left.\partial I_{\mathrm{DP}} / \partial T_{\mathrm{bp}}\right), using the stationary power dissipation P DS = V D P DS = V D P_(DS)=V_(D)P_{\mathrm{DS}}=V_{\mathrm{D}}. I DS I DS I_(DS)I_{\mathrm{DS}}, resulting in 13.1 ∘ C − mm / W 13.1 ∘ C − mm / W 13.1^(@)C-mm//W13.1^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W}, which is in good agreement with that obtained with the new method.
我们设备中的 R th R th  R_("th ")R_{\text {th }} 也通过使用阶跃响应技术[3]进行了测量。图 5 显示了仅受自加热影响的排流电流瞬态响应，测量了 50 V 的 V D V D V_(D)V_{\mathrm{D}} 阶跃，固定 V GQ = V GQ = V_(GQ)=V_{\mathrm{GQ}}= 为-2.3 V 和 T bp = 25 ∘ C T bp = 25 ∘ C T_(bp)=25^(@)CT_{\mathrm{bp}}=25^{\circ} \mathrm{C} ；可以看出， I D I D I_(D)I_{\mathrm{D}} 随着热时间常数 τ th τ th  tau_("th ")\tau_{\text {th }} 的变化而减小， ∼ 100 μ s ∼ 100 μ s ∼100 mus\sim 100 \mu \mathrm{s} 。插图显示了峰值排流电流的线性基板温度依赖性，没有自加热， I DP I DP I_(DP)I_{\mathrm{DP}} 。因此 R th = ( I DS − I DP ) / ( P DS × R th = I DS − I DP / P DS × R_(th)=(I_(DS)-I_(DP))//(P_(DS)xx:}R_{\mathrm{th}}=\left(I_{\mathrm{DS}}-\mathrm{I}_{\mathrm{DP}}\right) /\left(P_{\mathrm{DS}} \times\right. ∂ I DP / ∂ T bp ) ∂ I DP / ∂ T bp {: delI_(DP)//delT_(bp))\left.\partial I_{\mathrm{DP}} / \partial T_{\mathrm{bp}}\right) ，使用稳态功率耗散 P DS = V D P DS = V D P_(DS)=V_(D)P_{\mathrm{DS}}=V_{\mathrm{D}} 。 I DS I DS I_(DS)I_{\mathrm{DS}} ，导致 13.1 ∘ C − mm / W 13.1 ∘ C − mm / W 13.1^(@)C-mm//W13.1^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} ，与新方法获得的结果非常一致。
For the new method, with a pulse width, P W P W PWP W, of 1 μ s 1 μ s 1mus1 \mu \mathrm{s}, the normalized temperature rise, Δ T ch / Δ T chQ Δ T ch / Δ T chQ DeltaT_(ch)//DeltaT_(chQ)\Delta T_{\mathrm{ch}} / \Delta T_{\mathrm{chQ}}, with Δ T ch = T ch − Δ T ch = T ch − DeltaT_(ch)=T_(ch)-\Delta T_{\mathrm{ch}}=T_{\mathrm{ch}}- T bp T bp T_(bp)T_{\mathrm{bp}}, results in exp ⁡ ( − P W / τ th ) > 0.99 exp ⁡ − P W / τ th > 0.99 exp(-PW//tau_(th)) > 0.99\exp \left(-P W / \tau_{\mathrm{th}}\right)>0.99 at the end of the pulse. Thus, the initial and final T ch T ch T_(ch)T_{\mathrm{ch}} of the de-trapping process match. Otherwise, the method is not valid since τ 90 % τ 90 % tau_(90%)\tau_{90 \%} is overvalued and R th R th R_(th)R_{\mathrm{th}} is undervalued. So the smaller the τ th τ th tau_(th)\tau_{\mathrm{th}} the narrower the required P W P W PWP W, particularly when 3-D heat spreading creates a broad time constant spectrum [24]. Once a valid P W P W PWP W is set for a significant P DQ P DQ P_(DQ)P_{\mathrm{DQ}} and T bp T bp T_(bp)T_{\mathrm{bp}} pair, the P W P W PWP W would remain valid at higher P DQ P DQ P_(DQ)P_{\mathrm{DQ}} and T bp T bp T_(bp)T_{\mathrm{bp}} values since τ th τ th tau_(th)\tau_{\mathrm{th}} would increase [25].
对于新方法，脉冲宽度为 P W P W PWP W ，为 1 μ s 1 μ s 1mus1 \mu \mathrm{s} ，归一化温度升高为 Δ T ch / Δ T chQ Δ T ch / Δ T chQ DeltaT_(ch)//DeltaT_(chQ)\Delta T_{\mathrm{ch}} / \Delta T_{\mathrm{chQ}} ，与 Δ T ch = T ch − Δ T ch = T ch − DeltaT_(ch)=T_(ch)-\Delta T_{\mathrm{ch}}=T_{\mathrm{ch}}- T bp T bp T_(bp)T_{\mathrm{bp}} 一起，导致在脉冲结束时结果为 exp ⁡ ( − P W / τ th ) > 0.99 exp ⁡ − P W / τ th > 0.99 exp(-PW//tau_(th)) > 0.99\exp \left(-P W / \tau_{\mathrm{th}}\right)>0.99 。因此，去捕获过程的初始和最终 T ch T ch T_(ch)T_{\mathrm{ch}} 匹配。否则，该方法无效，因为 τ 90 % τ 90 % tau_(90%)\tau_{90 \%} 被高估，而 R th R th R_(th)R_{\mathrm{th}} 被低估。因此， τ th τ th tau_(th)\tau_{\mathrm{th}} 越小，所需的 P W P W PWP W 就越窄，特别是在三维热扩散产生广泛时间常数谱时[24]。一旦为显著的 P DQ P DQ P_(DQ)P_{\mathrm{DQ}} 和 T bp T bp T_(bp)T_{\mathrm{bp}} 对设置了有效的 P W P W PWP W ，则在更高的 P DQ P DQ P_(DQ)P_{\mathrm{DQ}} 和 T bp T bp T_(bp)T_{\mathrm{bp}} 值下， P W P W PWP W 将保持有效，因为 τ th τ th tau_(th)\tau_{\mathrm{th}} 将增加[25]。
The difference between the R th R th R_(th)R_{\mathrm{th}} values extracted by the two methods could relate to where the temperature is being perceived [17]. For both electrothermal methods, the temperature is averaged in the device channel, with the proposed one also perceiving where traps are located. Thus, R th R th R_(th)R_{\mathrm{th}} values extracted with the proposed method might be overvalued or undervalued if τ 90 % τ 90 % tau_(90%)\tau_{90 \%} refers to a trap located close to the hot spot in the device or far away from it, respectively.
通过这两种方法提取的 R th R th R_(th)R_{\mathrm{th}} 值之间的差异可能与温度的感知位置有关[17]。对于这两种电热方法，温度在设备通道中取平均，而所提议的方法还感知了陷阱的位置。因此，如果 τ 90 % τ 90 % tau_(90%)\tau_{90 \%} 指的是位于设备热点附近或远离热点的陷阱，则使用所提议的方法提取的 R th R th R_(th)R_{\mathrm{th}} 值可能被高估或低估。
Finally, assuming a linear temperature dependence for the thermal resistance, R th ≈ R th − 25 ∘ C [ 1 + α ( T bp − 25 ) ] R th ≈ R th − 25 ∘ C 1 + α T bp − 25 R_(th)~~R_(th-25^(@)C)[1+alpha(T_(bp)-25)]R_{\mathrm{th}} \approx R_{\mathrm{th}-25^{\circ} \mathrm{C}}\left[1+\alpha\left(T_{\mathrm{bp}}-25\right)\right], by applying the VFM with T bp − a = 25 ∘ C T bp − a = 25 ∘ C T_(bp-a)=25^(@)CT_{\mathrm{bp}-\mathrm{a}}=25{ }^{\circ} \mathrm{C} and P DQ − b =< P DQ − a > P DQ − b =< P DQ − a > P_(DQ-b)=<P_(DQ-a) >P_{\mathrm{DQ}-\mathrm{b}}=<P_{\mathrm{DQ}-\mathrm{a}}> ( ∼ 0.25 W ∼ 0.25 W ∼0.25W\sim 0.25 \mathrm{~W} ), varying T bp − b , R th − 25 ∘ C T bp − b , R th − 25 ∘ C T_(bp-b),R_(th-25^(@)C)T_{\mathrm{bp}-\mathrm{b}}, R_{\mathrm{th}-25^{\circ} \mathrm{C}} results 14.1 ∘ C − mm / W 14.1 ∘ C − mm / W 14.1^(@)C-mm//W14.1^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} and a temperature coefficient α α alpha\alpha of 0.009 ∘ C − 1 0.009 ∘ C − 1 0.009^(@)C^(-1)0.009^{\circ} \mathrm{C}^{-1} is predicted, in agreement with [3]. The inset in Fig. 4 shows the modeled data for R th R th R_(th)R_{\mathrm{th}} with a line. However, by using the VFM with the role of T bp T bp T_(bp)T_{\mathrm{bp}} and P DQ P DQ P_(DQ)P_{\mathrm{DQ}} swapped, no linear dependence of R th R th R_(th)R_{\mathrm{th}} on P DQ P DQ P_(DQ)P_{\mathrm{DQ}} is achieved [26], which is attributed to the low power densities used [27].
最后，假设热阻具有线性温度依赖性， R th ≈ R th − 25 ∘ C [ 1 + α ( T bp − 25 ) ] R th ≈ R th − 25 ∘ C 1 + α T bp − 25 R_(th)~~R_(th-25^(@)C)[1+alpha(T_(bp)-25)]R_{\mathrm{th}} \approx R_{\mathrm{th}-25^{\circ} \mathrm{C}}\left[1+\alpha\left(T_{\mathrm{bp}}-25\right)\right] ，通过应用 VFM 与 T bp − a = 25 ∘ C T bp − a = 25 ∘ C T_(bp-a)=25^(@)CT_{\mathrm{bp}-\mathrm{a}}=25{ }^{\circ} \mathrm{C} 和 P DQ − b =< P DQ − a > P DQ − b =< P DQ − a > P_(DQ-b)=<P_(DQ-a) >P_{\mathrm{DQ}-\mathrm{b}}=<P_{\mathrm{DQ}-\mathrm{a}}> （ ∼ 0.25 W ∼ 0.25 W ∼0.25W\sim 0.25 \mathrm{~W} ），变化 T bp − b , R th − 25 ∘ C T bp − b , R th − 25 ∘ C T_(bp-b),R_(th-25^(@)C)T_{\mathrm{bp}-\mathrm{b}}, R_{\mathrm{th}-25^{\circ} \mathrm{C}} 导致结果 14.1 ∘ C − mm / W 14.1 ∘ C − mm / W 14.1^(@)C-mm//W14.1^{\circ} \mathrm{C}-\mathrm{mm} / \mathrm{W} ，并预测温度系数 α α alpha\alpha 为 0.009 ∘ C − 1 0.009 ∘ C − 1 0.009^(@)C^(-1)0.009^{\circ} \mathrm{C}^{-1} ，与[3]一致。图 4 中的插图显示了 R th R th R_(th)R_{\mathrm{th}} 的建模数据及其线性关系。然而，通过使用 VFM 并交换 T bp T bp T_(bp)T_{\mathrm{bp}} 和 P DQ P DQ P_(DQ)P_{\mathrm{DQ}} 的角色，未能实现 R th R th R_(th)R_{\mathrm{th}} 对 P DQ P DQ P_(DQ)P_{\mathrm{DQ}} 的线性依赖[26]，这归因于所使用的低功率密度[27]。

V. CONCLUSION V. 结论

A fast, highly sensitive and simple thermo-electrical method for any standard testing laboratory, to extract the thermal resistance of GaN-based HEMTs (even packaged devices), has been presented in detail. By obtaining the drain current recovery time for a Schottky-gate HEMT on SiC induced by de-trapping for different power dissipations and base-plate temperatures, the thermal resistance of the device, including the temperature dependence, has been determined. A good agreement with other reported data and the thermal resistance measured with the step response technique has been achieved.
一种快速、高灵敏度且简单的热电方法已详细介绍，适用于任何标准测试实验室，以提取基于 GaN 的 HEMT（甚至封装设备）的热阻。通过获取在不同功耗和基板温度下，由去捕获引起的 SiC 上肖特基栅 HEMT 的漏电流恢复时间，确定了该设备的热阻，包括温度依赖性。与其他报告的数据以及使用阶跃响应技术测量的热阻达成了良好的一致。

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  1. Manuscript received 17 February 2023; revised 28 March 2023; accepted 5 April 2023. Date of publication 10 April 2023; date of current version 23 May 2023. This work was supported in part by MCIN/AEI/10.13039/501100011033 under Grant PID2021-127712OBC21 and in part by the Foundation for Science and Technology (FCT) and the Portuguese Ministry of Science, Technology, and Higher Education (MCTES) through national funds and when applicable cofunded by European Union (EU) funds under Project UIDB/50008/2020UIDP/50008/2020. The review of this letter was arranged by Editor V. Moroz. (Corresponding author: Benito González.)
    手稿于 2023 年 2 月 17 日收到；2023 年 3 月 28 日修订；2023 年 4 月 5 日接受。出版日期为 2023 年 4 月 10 日；当前版本日期为 2023 年 5 月 23 日。本研究部分得到了 MCIN/AEI/10.13039/501100011033 的资助，资助编号为 PID2021-127712OBC21，部分得到了科学与技术基金会（FCT）和葡萄牙科学、技术与高等教育部（MCTES）的支持，通过国家资金，并在适用时由欧盟（EU）资金共同资助，项目编号为 UIDB/50008/2020UIDP/50008/2020。此信件的审阅由编辑 V. Moroz 安排。（通讯作者：Benito González。）
    Benito González is with the Institute for Applied Microelectronics, Universidad de Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas, Spain (e-mail: benito@iuma.ulpgc.es).
    贝尼托·冈萨雷斯在西班牙拉斯帕尔马斯大学应用微电子研究所工作，地址为：35017 拉斯帕尔马斯，塔菲拉大学校园（电子邮件：benito@iuma.ulpgc.es）。
    Luís C. Nunes, João L. Gomes, and Joana C. Mendes are with the Departamento de Eletrónica, Telecomunicações e Informática (DETI), Instituto de Telecomunicações, Universidade de Aveiro, 3810-193 Aveiro, Portugal.
    路易斯·C·努涅斯、若昂·L·戈麦斯和乔安娜·C·门德斯均来自葡萄牙阿维罗大学电气、通信与计算机系（DETI），阿维罗电信研究所，邮政编码 3810-193。
    Jose L. Jimenez is with Qorvo Inc., Richardson, TX 75080 USA.
    何塞·L·希门尼斯在美国德克萨斯州理查森市的 Qorvo 公司工作，邮政编码 75080。
    Color versions of one or more figures in this letter are available at https://doi.org/10.1109/LED.2023.3265766.
    此信中的一个或多个图的彩色版本可在 https://doi.org/10.1109/LED.2023.3265766 获取。
    Digital Object Identifier 10.1109/LED.2023.3265766
    数字对象标识符 10.1109/LED.2023.3265766