Improved Scheme for Estimating the Embedded Gate Resistance to Reproduce SiC MOSFET Circuit Performance

The intrinsic gate resistance (<inline-formula> <tex-math notation="LaTeX">${R}_{\text {g}{\_}{\text {in}}}{)}$ </tex-math></inline-formula>, which is a novel resistance factor embedded in transistors, was determined for silicon carbide (SiC) metal–oxide–semiconductor field-effect transistors (MOSFETs). The study demonstrated that <inline-formula> <tex-math notation="LaTeX">${R}_{\text {g}{\_}{\text {in}}}$ </tex-math></inline-formula> is overestimated in the conventional measurement scheme due to the contact resistance <inline-formula> <tex-math notation="LaTeX">${R}_{\text {sp}}$ </tex-math></inline-formula> between p-type SiC and the source electrode. Here, 6.7 <inline-formula> <tex-math notation="LaTeX">$\text{m}\Omega \cdot $ </tex-math></inline-formula>cm2 was measured for <inline-formula> <tex-math notation="LaTeX">${R}_{\text {sp}}$ </tex-math></inline-formula> using the transfer length method (TLM), and <inline-formula> <tex-math notation="LaTeX">${R}_{\text {g}{\_}{\text {in}}}$ </tex-math></inline-formula> = <inline-formula> <tex-math notation="LaTeX">$9 \Omega $ </tex-math></inline-formula> was the revised value, unlike the conventional value of <inline-formula> <tex-math notation="LaTeX">$25 \Omega $ </tex-math></inline-formula>. This improved <inline-formula> <tex-math notation="LaTeX">${R}_{\text {g}{\_}{\text {in}}}$ </tex-math></inline-formula> provides better-simulated switching waveforms in a double-pulse test (DPT) with a SiC MOSFET; however, the method requires detailed knowledge of the target device. Accordingly, we developed another measurement scheme without such prerequisites. In this scheme, three types of impedance (<inline-formula> <tex-math notation="LaTeX">${Z}{)}$ </tex-math></inline-formula> were measured: <inline-formula> <tex-math notation="LaTeX">${Z}$ </tex-math></inline-formula> between the drain (D) and source terminal (S), and two <inline-formula> <tex-math notation="LaTeX">${Z}_{\text {s}}$ </tex-math></inline-formula> between the gate and S, with DS left open and short. From these results, <inline-formula> <tex-math notation="LaTeX">${R}_{\text {g}{\_}{\text {in}}}$ </tex-math></inline-formula> was determined to be <inline-formula> <tex-math notation="LaTeX">$8.8 \Omega $ </tex-math></inline-formula> with other device parasitic parameters simultaneously.


I. INTRODUCTION
S ILICON carbide (SiC) metal-oxide-semiconductor fieldeffect transistors (MOSFETs) are the most promising for next-generation power devices because of their excellent characteristics, including high breakdown voltage tolerance and high-speed switching [1], [2]. High-speed switching operations cause low power loss in switching power supplies; however, they simultaneously deteriorate the electromagnetic compatibility (EMC) of the supplies [3]. Accordingly, a reliable method for optimizing the switching processes of the transistors used in power applications is required.
The gate resistance (R g ) is a circuit element that is useful for adjusting transistor switching processes. R g comprises R g_ext and R g_in , which are the resistance elements existing outside the transistor and an intrinsic resistance factor embedded in a transistor chip, respectively. Power application engineers cannot adapt R g_in ; thus, device manufacturers should be responsible for providing an appropriate R g_in . R g_in is frequently provided on the device datasheet as the real part of the impedance, measured at 1 MHz between the gate (G) and source terminals (S), with an open drain terminal (D). The real part is calculated under the assumption that the input capacitances of the transistor and R g_in are serially connected [4]. This method is widely applied to SiC and Si MOSFETs [5], [6], [7].
However, R g_in of SiC MOSFETs reportedly differs from R g_cir , which denotes R g_in expected from the switching behavior of a transistor [8]. Fig. 1(a) shows the standard unit structure of a SiC MOSFET and the current flow path conventionally assumed in R g_in measurements [4], [5]. R g_in coincides with R g_cir if the path is valid. However, this is not the case for SiC MOSFETs because the contact resistance R sp between p-SiC and the source contact is not negligible.
According to [9] and [10], R sp in SiC MOSFETs is approximately 4.0 × 10 −3 ·cm −2 , and this value is larger by more than two orders of magnitude than the value of 1.0 × 10 −5 ·cm −2 for Si MOSFETs [11]. Thus, the current path, denoted by the red line in Fig. 1(b), competes impedance-wise with the conventional path. This indicates that the conventional methodology of measuring R g_in must be rebuilt.
In this article, the estimation of R sp using the transfer length method (TLM) is described in Section II. The measurement results for R sp are validated from multiple perspectives in Section III. In Section IV, the subtraction of R sp from R g_cir is  demonstrated. Circuit simulations using this newly determined R g_in reproduced the measured switching behaviors better than those using the conventional R g_in on device datasheets. Section V presents a revised measurement method to determine R g_in based on the impedance characteristics. Section VI concludes this article.
II. MEASUREMENT OF R SP R sh , i.e., the sheet resistance of a p-type SiC, and R sp were experimentally estimated. Fig. 2(a) and (b) shows the TLM patterns in the cross-and plane-sectional views, respectively [12]. These TLM structures were fabricated on an n-type 4H-SiC epitaxial layer implanted with aluminum ions (Al + ) and a distance between the metal pads, d, ranging from 20 to 60 µm in 10-µm steps. The acceptor ion densities of the p-SiC and p+-SiC regions were approximately 2 × 10 16 and 5 × 10 19 cm −3 , respectively. The TLM sample adopted for this measurement was manufactured for process-control monitoring of the product wafer of SiC MOSFETs (SCT2450KE, ROHM Company Ltd.). Fig. 3 shows the measured R TLM , i.e., the resistance between the pads, as a function of d. The slope of the observed linear correlation represents R sh , and R sp corresponds to the vertical intercept of the graph. The estimated R sh and R sp were 1.48 × 10 4 /sq. and 6.7 m ·cm 2 , respectively. Fig. 4(a) shows the TLM pattern to introduce R sh and R sp modeled in a TCAD simulation (Sentaurus Device, Synopsys Inc.), where we applied the incomplete ionization model for the implanted Al + [13] with an activation energy ( E A,0 ) of 0.38 eV [14]. R sp was considered to have a fixed resistance of 6.7 m ·cm 2 . Fig. 4(b) shows the current-voltage (I -V ) characteristics of the TLM samples and their simulated counterparts. The simulation setup conditions reproduced R sh and R sp . Accordingly, we used these setups in subsequent TCAD simulations.

III. VALIDATION OF THE EXPERIMENTAL R SP
The magnitude of R sp crucially influences R g_in estimation; thus, we examined its consistency using other methods. One of these was the drain current as a function of the drain voltage characteristics in the third quadrant, (I r -V r ), and the alternating  current (ac) characteristics between D and S. The TCAD model of the SiC MOSFET was the same as that reported previously [15]. Fig. 5(a) shows the wiring setup for I r -V r measurements; the circuit elements embedded in the SiC MOSFET are defined therein. Fig. 5(b) and (c) shows the equivalent circuits with and without R sp , respectively. According to [9], I r depends on V gs because of the current contribution of the MOS to I r if R sp is nonnegligible, as shown in Fig. 5(b) and (c). This trend depends on whether R sp can be ignored at high-V r values when V r is larger than the built-in potential ( p−n ) of the p-n junction between the drift layer and the p-body. A low V r means V r below p−n . According to [16], p−n is 2.7 V. Fig. 6(a) and (b) shows the measured (open circles) and simulated (solid lines) I r -V r characteristics under V gs = 0 V (in red) and −4 V (in blue). The simulation results for R sp = 0 and 6.7 m ·cm 2 are shown in Fig. 6(a) and (b), respectively. R sp = 0 ·cm 2 failed to reproduce the measured results, as shown in Fig. 6(a). In stark contrast, R sp = 6.7 m ·cm 2 accurately reflected the measurement results. This result was evidence that R sp = 6.7 m ·cm 2 is valid for SiC MOSFETs.
Furthermore, Z DS , i.e., the impedance between D and S, was analyzed. Fig. 7(a) shows the wiring setup for this, and the related circuitry elements embedded in the SiC MOSFET are also defined therein. Fig. 7(b) and (c) shows the equivalent circuits with and without R sp , respectively. As shown in Fig. 7(b), the ac signal flowed independently of the V ac frequency ( f ac ) without R sp because C ds always provides the lowest impedance path. However, in the presence of R sp , the   signal path varied with f ac [Fig. 7(c)] because a higher f ac increases the impedance of R sp and lowers that of C pn . Thus, the Z DS -f ac correlation depends on the magnitude of R sp , implying that this correlation can be used to estimate R sp . Fig. 8(a) and (b) shows the measured (open circles) and simulated (solid lines) results for R Z_DS = Re(Z DS ) and C Z_DS = |{Im(Z DS 2π f ac )} −1 | as a function of f ac . The simulations were performed for R sp = 0 and 6.7 m ·cm 2 . From Fig. 7(a) and (b), both of the simulated R Z_DS and C Z_DS for R sp = 6.7 m ·cm 2 reproduced the measured counterparts over f ac = 10 4 -10 7 Hz, whereas those for R sp = 0 ·cm 2 did not. In addition, the simulated R Z_DS and C Z_DS for R sp = 6.7 m ·cm 2 successfully followed the downward  trend experimentally observed at f ac ≥ 10 6 Hz. This decrease reflected the change in the signal path, as shown in Fig. 7(c).
The results in this section support the validity of R sp = 6.7 m ·cm 2 ; therefore, this R sp value was used in the simulation described in the following section. Fig. 9(a) shows the wiring setup for measuring and simulating the impedance between G and S (Z GS ). The circuitry elements embedded in the SiC MOSFET are also defined therein. Fig. 9(b) shows the equivalent circuit. As shown in Fig. 9(b), R g_in always lay along the current path and consequently functioned as a constant element in Z GS . Accordingly, R g_in could be determined as a fitting parameter for Z GS -f ac characteristics. Fig. 10(a) and (b) shows the simulation (red solid lines) and measurement (open circles) results for R Z_GS = Re(Z GS ) and C Z_GS = |{Im(Z GS ·2π f ac )} −1 | as a function of f ac , including the effects of R sp = 6.7 m ·cm 2 . R g_in = 9 provided the best fitting result, whereas R g_in on the datasheet of SCT2450KE was 25 .

IV. R G_in EXTRACTION AND ITS EFFECTS
The switching behavior of the transistors is important; hence, R g_in was verified using the extent to which it reproduces the switching behavior of the SiC MOSFET. Fig. 11 shows a schematic of the double-pulse test (DPT), where the device model of a SiC MOSFET and the circuit components were the same as those previously reported [17]. This device model reproduced the I d -V d and C-V d characteristics of the SiC MOSFET adopted in the DPT, as shown in Fig. 12(a) and (b), where I d and V d denote the drain current   Turn-on switching waveforms. Open circles and solid lines denote the experimental and simulated results, respectively, for (a) R g_in = 25 Ω and (b) R g_in = 9 Ω. and voltage, respectively. C denotes the input (C iss ), output (C oss ), and feedback capacitances (C rss ) of the device. These characteristics confirm the validity of the circuit simulations.
The measured turn-on waveforms are superimposed on the simulated counterparts in Fig. 13(a) and (b) for R g_in = 25 and R g_in = 9 , respectively. The quantitative index of the extent to which the simulated results agreed with their experimental counterparts was the relative root-mean-square (rRMS) error, as defined in [18]. Fig. 14(a) and (b) shows the measured and simulated turnon waveforms, respectively. Regarding R g_in = 25 , the simulated V d and I d altered with a lag behind the observed values. In stark contrast, R g_in = 9 provided better-quality  simulation results. This result was also the same for the turnoff behavior, as shown in Fig. 14(c) and (d). Table I lists the rRMS errors of V g (gate-to-source voltage), V d , and I d for the turn-on and turn-off waveforms. R g_in = 9 provided a better rRMS than R g_in = 25 . These results prove that the newly determined R g_in method better reflects R g_cir , implying that application engineers should use the proposed value.
V. R G_in DETERMINATION METHOD USING ONLY CIRCUITOUS MEASUREMENTS The aforementioned method for estimating R g_in requires that the structure of the target device is known; however, less prior knowledge is more useful. Therefore, we propose a measurement scheme to determine R g_in using only circuitous measurements. Fig. 15(a) shows all the decomposed circuitry elements embedded in the unit structure of the SiC MOSFET. In addition, the symbols for the elements are defined. Fig. 15(b) shows the equivalent circuit. There are ten parameters in total; however, R epi is more negligible than the other resistance factors because of its typical value of 1 m ·cm 2 [11]. In addition, from R sh , the resistance of the p-body region is also negligible because it is comparable to R epi . Thus, there are nine unknown parameters. C gd , C ds , and C gs are obtained from C − V d measurements. C gs is equal to C gsn + {(C gsp ) −1 + (C gsd ) −1 } −1 , and when two of C gsp , C gsn , and C gsd are known, the remaining one can be determined. R ch should be included because the magnitude of R ch is approximately 10 7 [10]. This value is not negligible compared to the impedances of other components. Consequently, the number of unknown parameters is reduced to six: R g_in , R sp , R ch , and C pn , and two from C gsp , C gsn , and C gsd . This implies that six mutually independent equations are required to determine these six parameters.
We adopt Z DS and Z GS to establish these six equations. Z ds is measured using the configuration shown in Fig. 7(a), i.e., the impedance between D and S with open G. Two types of Z GS are measured: open DS (Z GSO ) and short DS (Z GSS ). The ac signal flows for measuring Z GSO and Z GSS are shown in Fig. 16(a) and (b), respectively. The blue lines indicate the signal paths shared by Z GSO and Z GSS , and the red lines indicate the paths that are dependent on whether DS is open or short. This signal path difference leads to clear impedance differences between Z DS , Z GSO , and Z GSS , thereby creating six equations to determine the aforementioned unknown parameters. Z DS , Z GSO , and Z GSS can be expressed   (1)-(3), as shown at the top of the next page. The symbols used are listed in Table II. The real and imaginary parts of (1)-(3) provide six equations. Therefore, the unknown parameters can be uniquely determined by minimizing the rms error E r as given by the following equation: where i, x, c, and m denote the data point; DS, GSO, or GSS; calculated; and measured, respectively. Fig. 17(a)-(c) shows the measured Z DS , Z GSO , and Z GSS values of SCT2450KE, respectively. In addition, these figures show the curves determined to minimize E r for (1)-(3). Table III presents the parameters determined using E r and the value of E r . R g_in is 8. 8 and very close to 9 . This agreement indicates that the measurements of Z DS , Z GSO , and Z GSS can experimentally determine R g_in . The revised method was also applied to SCT2080KE (ROHM Company Ltd.), which is the same generation of SCT2450KE [19] and different rated drain current [20]. R g_in for SCT2080KE was 5.0 using the revised method, smaller than the values of 6.3 shown on the datasheets. E r of SCT2080KE was 0.18, close to 0.20 of SCT2450KE. This shows that the revised method is applicable to other SiC MOSFETs.

VI. CONCLUSION
The widely utilized conventional measurement of R g_in does not provide a genuine R g_in for SiC MOSFETs because it ignores the relatively large R sp in the transistors. We determined R sp using the TLM method and the results were verified using the impedance characteristics of the DS and GS. This validated that R g_in accurately reproduces the measured switching waveforms in the DPT of the SiC MOSFET. An unsatisfactory aspect of this method is that it requires knowledge of the structure of the target device. Accordingly, to resolve this problem, we developed another measurement scheme for R g_in that does not require prior knowledge of device structures. R g_in obtained using this revised measurement scheme is very close to that of the first scheme. This facilitates the design optimization of power supplies using SiC MOSFETs.