I. Introduction

In the recent years, the power cycling test (PCT) has been attracting attention to evaluate the robustness of the chip and package assembly ^[1]. This applies thermal stress to a device under test (DUT) by continuously turning it on/off as shown in Fig. 1. During this process, temperature changes occur as the DUT is turned on/off, which creates thermal stress that can lead to major failure mechanisms such as cracking and delamination of wire and chip bonding ^[2-6].

In the PCT, the mean temperature and the temperature swing of the power devices are well known as the key parameters to make much impact on their lifetime ^[7]. To estimate the junction temperature (T$_{\mathrm{j}}$) of power device, the PCT utilizes a Temperature Sensitive Electrical Parameter (TSEP) such as threshold voltage, on-resistance, forward voltage drop of diode, and various transient-state parameters ^[8-11]. Among these TSEPs, the forward voltage drop of body diode (sensing voltage, V$_{\mathrm{SENS}}$) has been widely used for SiC MOSFET due to superior stability in relationship between temperature and TSEP over long-term aging ^[5]. This means the forward voltage drop of body diode enables a consistent junction temperature measurement over the lifetime of SiC MOSFET.

Fig. 2 shows the current flows in the SiC MOSFET during the PCT that employs the forward voltage drop of the body diode as TSEP. The drain-source electrode is biased with high constant current (heating current) in the turn-on time (powering cycle) and is reverse-biased with a low constant current (sensing current, I$_{\mathrm{SENS}}$) in turn-off time (sensing cycle). To guarantee an accurate measurement of T$_{\mathrm{j}}$ against the aging throughout the whole lifetime of SiC MOSFET, the sensing current must flow through only body diode in the sensing cycle. However, the leakage current through the channel beneath the gate oxide is known to be added and to affect the current-voltage characteristic of the body diode of SiC MOSFET, which determines the temperature sensitivity.

In the previous literatures that dealt with the forward voltage drop of body diode as TSEP to precisely estimate T$_{\mathrm{j}}$, the sensing current is found to affect the temperature sensitivity and linearity ^[12,13]. It is also found that the dynamic behavior of TSEP (TSEP drift over time) influences accuracy of T$_{\mathrm{j}}$ because a long drift time makes over- or under-estimation of T$_{\mathrm{j}}$ ^[6]. Therefore, an accurate estimation of T$_{\mathrm{j}}$ requires a thorough investigation of the sensitivity of sensing voltage to temperature (or the sensitivity) and of the sensing voltage drift over time with various sensing parameters.

In this paper, we will investigate the sensitivity and sensing voltage drift of commercial SiC power MOSFET and develop a methodology to accurately estimate the temperature of the MOSFET.

Fig. 1. Basic operation of power cycling test.

Fig. 2. Measuring junction temperature with a body diode in a SiC power MOSFET.

II. Experiment

Fig. 3 shows an in-house test setup used in this experiment. This setup is composed of three components:

(a) an oven that adjusts the temperature of ambient surrounding DUT (T$_{\mathrm{a}}$). In this work, it is assumed that DUT is in thermal equilibrium where T$_{\mathrm{j}}$ = T$_{\mathrm{a}}$ after another 3 minutes of the oven reaching target T$_{\mathrm{a}}$.

(b) a semiconductor parameter analyzer (Agilent 4156B) that measures the current-voltage (I-V) curves and the voltage-time (V-t) curves of DUT.

(c) a PC that controls the oven and the Agilent 4156B and that acquires I-V and V-t data.

To obtain the sensing voltage drift (${\Delta}$V$_{\mathrm{SENS}}$) and temperature sensitivity ($S_{{T_{j}}}$), the experimental flow is as the follows. The V-t curves were firstly measured at different I$_{\mathrm{SENS}}$ (80 ${\mu}$A, 40 mA, 80 mA) and V$_{\mathrm{GS}}$ (0 V, $-$5~V, $-$10 V) to examine the effect of I$_{\mathrm{SENS}}$ and V$_{\mathrm{GS}}$ on V$_{\mathrm{SENS}}$ drift. Note that the reason why this step is firstly executed is to determine a delay time for thermal equilibrium where V$_{\mathrm{SENS}}$ is supposed to remain constant. Based on the V-t curves, the delay time was determined. For the next step, the I-V curves of body diode were measured at different V$_{\mathrm{GS}}$ from 0 V to $-$10 V with a step of $-$1 V after additive delay time of the oven reaching a target temperature. This step was repeated at different oven temperatures from 10$^{\circ}$C to 150$^{\circ}$C with a step of 20$^{\circ}$C. Finally, the temperature sensitivity as a function of V$_{\mathrm{GS}}$ and I$_{\mathrm{SENS}}$ was calculated from the I-V curves of body diode. In this experiment, a commercially available SiC MOSFET (C2M0080120D) was used as DUT.

Fig. 3. Setup for measuring I-V curves at various junction temperatures.

III. Results and Discussion

Aforementioned, the forward voltage drop of body diode was used as TSEP to estimate the junction temperature in this work. In this case, the junction temperature can be calculated from the forward voltage drop of body diode (V$_{\mathrm{DS}}$) or the sensing voltage (V$_{\mathrm{SENS}}$) and the sensing current (I$_{\mathrm{SENS}}$) based on the well-known diode equation ^[12,14]:

where k$_{\mathrm{B}}$ is the Boltzmann constant, q is the electron charge, I$_{\mathrm{SD0}}$ is the saturation current, a is a slope of T$_{\mathrm{j}}$-V$_{\mathrm{SENS}}$ curve, and b is constant. Note that Eq. (1) is valid only within the range of sensing current where the log value of I$_{\mathrm{SENS}}$ is a linear function of V$_{\mathrm{SENS}}$. Otherwise, the estimation of T$_{\mathrm{j}}$ becomes inaccurate. This may be caused by (1) a resistance of diode that grows dominant when the diode operates in high-injection level (I$_{\mathrm{S}}$> 10~mA) and (2) a leaky current path not through the body diode at higher gate voltage ^[15].

Fig. 4 shows the source current (I$_{\mathrm{S}}$) versus drain-source voltage (V$_{\mathrm{DS}}$) curves, which is the log-linear diode current of the DUT measured at room temperature for V$_{\mathrm{GS}}$ from 0 V to -10 V. In Fig. 4, at higher gate bias (V$_{\mathrm{GS}}$ > -5 V), it is difficult to find a linear region in the log-linear I-V curves. This is due to the persistence of leakage current paths at higher gate biases (V$_{\mathrm{GS}}$ > -5 V). On the contrary, the log-linear I-V curves for V$_{\mathrm{GS}}$ $\leq $ -5~V show a linear region in the range of I$_{\mathrm{SENS}}$ from 10~nA to 1 mA and negligible change with respect to the gate bias. The linearity with respect to gate bias, as discussed, can be examined in greater detail in Table 1. To check the linearity, coefficient of determination (R$^{2}$) is used. R$^{2}$ is a statistical measure of the proportion of variance in the dependent variable that is explained by the independent variables in a regression model. It has a value between 0 and 1. The closer it is to 1, the better the independent variable explains the dependent variable ^[16]. As the gate bias decreases, it can be observed that R$^{2}$ approaches closer to 1. This indicates that the relationship becomes more linear. This means that the leakage current path through the channel beneath the gate oxide is effectively quenched ^[17].

Fig. 5 and Table 2 show the sensing voltage over time and the sensing voltage drift at different sensing currents and gate biases. The sensing voltage drift is defined as a difference between sensing voltage at a measurement start and a sensing voltage at the moment of the V-t curves showing no change, e.g., 3 minutes. The sensing voltage drift increases with the sensing current for V$_{\mathrm{GS}}$ ${\leq}$ -5~V. Although a relatively low I$_{\mathrm{SENS}}$ (80 mA) flows through DUT compared to the heating current of 10 A, the sensing voltage decreased with the elapsed measurement time as shown in Fig. 5. This means that the junction temperature also decreased with the elapsed measurement time based on Eq. (1) and suggests that a self-heating generated by the sensing current still occurs, leading to an inaccuracy of T$_{\mathrm{j}}$. For example, T$_{\mathrm{j}}$ error of 7.6$^{\circ}$C is calculated if T$_{\mathrm{j}}$ is estimated for DUT biased at V$_{\mathrm{GS}}$ = -10~V and I$_{\mathrm{SENS}}$ = 80 mA. However, the change in ${\Delta}$V$_{\mathrm{SENS}}$ for different I$_{\mathrm{SENS}}$ and V$_{\mathrm{GS}}$ = 0 V (1.16 mV) is smaller than those for V$_{\mathrm{GS}}$ = -5 V and -10 V (13.16~mV and 17.36 mV). This means that the self-heating effect is reduced for V$_{\mathrm{GS}}$ = 0 V.

Fig. 6 shows investigation of the effect of the gate bias and the sensing current on the linearity of T$_{\mathrm{j}}$-V$_{\mathrm{SENS}}$ curve and the sensitivity to T$_{\mathrm{j}}$, the linear regression was carried out for sensing voltages measured at different junction temperature from 10$^{\circ}$C to 150$^{\circ}$C.

In Fig. 6, R$^{2}$value extracted for higher gate voltage (0~V) and low sensing current (80 ${\mu}$A) is so low that much error may occur if this condition is used to predict T$_{\mathrm{j}}$. However, at higher sensing current (I$_{\mathrm{SENS}}$ > several tens of mA), the influence of leakage current through the channel is negligible, resulting in a high R$^{2}$value. This high R$^{2}$value indicates that a prediction model agrees well with the experimental T$_{\mathrm{j}}$. Nevertheless, errors can occur at high sensing currents due to self-heating, as discussed earlier. Therefore, it is noteworthy that, unlike V$_{\mathrm{GS}}$ = 0 V, R$^{2}$ values extracted for I$_{\mathrm{SENS}}$ = 80 ${\mu}$A and 80~mA are nearly 1 for V$_{\mathrm{GS}}$ = -5 V. Therefore, the channel of DUT must be quenched to achieve good linearity of T$_{\mathrm{j}}$-V$_{\mathrm{SENS}}$ curve that enhances an accuracy of T$_{\mathrm{j}}$.

Fig. 7 shows the dependency of the temperature sensitivity on the sensing current for different gate biases. The temperature sensitivity ($S_{{T_{j}}}$) of is mathematically defined by the following equation:

The temperature sensitivity at V$_{\mathrm{GS}}$ = 0 V increases with I$_{\mathrm{SENS}}$, while these at lower V$_{\mathrm{GS}}$ (e.g. -5 V and -10~V) decreases with increasing I$_{\mathrm{SENS}}$. Unfortunately, the origin of this opposing behavior has not been identified. However, an increase in $S_{{T_{j}}}$ with I$_{\mathrm{SENS}}$ may be related to a complex effect of self-heating and carrier detrapping in the channel of SiC MOSFET with relatively higher interface trap density than Si MOSFET ^[18]. In this case, for V$_{\mathrm{GS}}$ = 0 V where the channel is still leaky, the carrier (electron) trapped in the SiO$_{2}$/SiC interface can be released to promote the conduction even for a small increase in junction temperature caused by self-heating. Although sensitivity for higher V$_{\mathrm{GS}}$ are high, it is difficult to use this bias condition (e.g. V$_{\mathrm{GS}}$ = 0 or near 0 V) to estimate the junction temperature. This is because the conduction channel under the gate is still leaky at higher V$_{\mathrm{GS}}$ ( > -5 V) for SiC MOSFET, leading to a degradation of SiO$_{2}$/SiC interface and the I-V characteristics of body diode and therefore to a change in T$_{\mathrm{j}}$-V$_{\mathrm{SENS}}$ characteristics.

Fig. 4. I-V curves of body diode of DUT measured at various gate biases (V_GS).

Fig. 5. Sensing voltage over time at different sensing currents and gate biases: (a) V_GS = 0 V; (b) V_GS = -5 V; (c) V_GS = -10 V.

Fig. 6. Junction temperature versus sensing voltage along with a linear-fit curve (red dotted line) and the coefficient of determination (R²) as a function of V_GS and I_SENS.

Fig. 7. Temperature sensitivity versus sensing current graph for V_GS = 0 V, -5 V, and -10 V.

IV. Conclusions

To accurately estimate the junction temperature of the power device, an experimental methodology was developed by investigating the temperature sensitivity and sensing voltage drift of the body diode of SiC power MOSFETs for different gate biases. The sensing voltage drift increases with the sensing current for V$_{\mathrm{GS}}$ ${\leq}$ -5 V, while its change is small for V$_{\mathrm{GS}}$ = 0 V. The sensitivities and the linearities of T$_{\mathrm{j}}$-V$_{\mathrm{SENS}}$ curve were improved for lower sensing current and V$_{\mathrm{GS}}$ ${\leq}$ -5. This is attributed to reduction in leaky current path through the channel of SiC MOSFET. Finally, it is concluded that a precise Tj estimation requires a lower gate bias enough to close the channel and a lower sensing current that must be in the linear region of I-V curve to enhance sensitivity and accuracy.