Questions about the nonlinear capacitance of MOSFET tubes

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Questions about the nonlinear capacitance of MOSFET tubes [Copy link]

I want to know the analysis and introduction of the parameters of the various capacitors ciss, coss, crss, coer, and cotr of mosfet, in this article:

Since its first introduction more than 30 years ago, the MOSFET has become a mainstay of high-frequency switching power conversion. The technology has been steadily improving, and we now have low-voltage MOSFETs with RDSON values in the milliohm range. It is rapidly approaching single digits for higher voltage devices. The two major MOSFET technology advances that have enabled these improvements are the trench gate and the charge-balanced structure [1]. Charge-balance technology was originally developed for high-voltage devices that resulted in superjunction MOSFETs, and has now been extended to lower voltages as well. While this technology significantly reduces RDSON and all junction capacitances, it also makes the latter more nonlinear. The effective stored charge and energy in the MOSFET has indeed been reduced, and reduced significantly, but calculating these parameters or comparing different MOSFETs for optimal performance has become a rather complex matter.

Figure 1a: Structure of a trench MOSFET and its capacitance.

Figure 1b: Equivalent capacitance.

The basic definitions of the three capacitances associated with a MOSFET are shown in Figures 1a and 1b. Measuring these capacitances as a function of VDS is not a straightforward task and requires some of them to be shorted or left floating. The three values that are finally measured and given in the product datasheet are defined as follows:

CISS = CGS + CGD
COSS = CDS + CDG
CRSS = CGD

Of the three, the input capacitance, CGS, is the least nonlinear. It is the capacitance between the gate structure and the source, and does not vary much as a function of VDS. On the other hand, CGD is extremely nonlinear, varying by almost three orders of magnitude over the first 100V for superjunction devices. It also contributes to the tiny steps seen for CISS at VDS=0.

Recently, there has been a lot of interest in understanding the properties of COSS and its impact on high-frequency switching. There are several reasons for this, for example, the charge stored and losses in COSS have become the biggest challenge in implementing high-frequency AC-DC converters. Generally speaking, any capacitance-related losses are proportional to the square of the applied voltage. As pointed out in [3], the energy stored and losses in the same capacitor at 550V are 2100 times higher than at 12V. With the increasing focus on reducing RDSON, conduction losses have dropped significantly, but COSS has not dropped proportionally. For example, earlier, the lowest RDSON for a 600V MOSFET in TO-220 used to be 340mΩ. Today, this value has dropped to 65mΩ in a 600V superjunction device. For capacitors, it is more meaningful to compare devices with similar RDSON values between different technologies.

Figure 2 compares the capacitance of two devices: the SiHP17N60D, a planar device, and the SiHP15N60E, a superjunction MOSFET with a similar but slightly lower RDSON. Note that these values are plotted on a logarithmic scale. For the superjunction device, COSS has decreased from 136pF to 67pF at 100V, but it has also become more nonlinear. In the planar device, COSS was 25:1 at VDS=0V to 100V, but has now tripled to 75:1. It is not uncommon for COSS values to be greater than the input capacitance CISS at VDS=0 .

Figure 2: Capacitance comparison of planar MOSFET and superjunction MOSFET.

References [4] to [9] attempt to explain the nonlinear nature of COSS from various perspectives and provide new insights into its impact on high-frequency switching. Most of these references reaffirm the nonlinear nature of the capacitor after integrating, simulating, and otherwise complex processing the COSS curve. Terms such as “small-signal” capacitance and “large-signal” capacitance have been introduced, simulated, and analyzed. In addition to being technically incorrect, these new terms also make little difference from an industry practice perspective. It can be seen that the so-called large-signal capacitance is nothing more than the time-dependent value COTR , which has been standardized by the MOSFET industry for many years after the publication of reference [4]. The prominent differences between the detailed simulation results and the data sheet values are still well within the tolerances involved in MOSFET product descriptions and mass production.

Another analytical approach proposes a hidden resistance in series with COSS , ROSS , to describe all the unexplained losses associated with nonlinear capacitance (see reference [10]). This contradicts basic circuit theory, which states that capacitor charging and discharging losses are determined entirely by the energy stored in it and are independent of the value of any series resistance. No semiconductor-level explanation or experimental verification has been proposed for ROSS , and the waveforms presented in the paper clearly show the conducting MOSFET body diode, which provides a simpler (if less exotic) explanation for these losses. In fact, body diode conduction is a fundamental consideration in the analysis of any bridge circuit with an inductive load. In other recent peer-reviewed conference publications (references [11] and [12]), it has been proposed that both the stored charge and energy in COSS exhibit hysteresis and may differ for different voltage paths. The significance of this hysteresis is that the charge conservation principle does not apply to power MOSFETs.

It is more instructive not to challenge the fundamental laws of physics but to re-examine them and see whether they are correct and applicable in the right places. The investigation raises a puzzle and therefore may be somewhat fascinating -

If two capacitors are connected in parallel, charged to the same voltage and hold exactly the same stored charge, does it necessarily follow that they also store the same amount of energy?

According to the well-known equations Q=CV and E=CV2 , the answer should be a resounding “yes”. It would seem that this should hold true at any voltage, even if the capacitance is nonlinear. Unfortunately, the familiar equations for stored charge and energy are not universally valid, and only apply to the special case of constant capacitance. The more fundamental relationship defines capacitance as the rate of change of charge wrt voltage, while voltage itself is defined as a measure of the change in energy per unit charge. In other words, the basic relationship is:

C = dQ/dV and V = dE/dQ

Simple equations for charge and energy make an implicit assumption about static capacitance in their derivation. For nonlinear capacitance, charge and energy must be derived by integrating capacitance and charge over voltage, respectively. To further illustrate this, consider the two capacitors depicted in Figure 3. The reference value is provided by capacitor CREF . The other capacitor CV varies linearly from 1.5xCREF to 0.5xCREF. At 100V, they carry the same charge. This can be clearly seen by observing the CxV area of the two capacitors and can also be verified by integrating the capacitance value over voltage.

However, the energy stored is completely different. If we integrate the stored charge over voltage, we see that CREF has only 83.3% of the energy stored at 100 V. We can also see that at 75 V, CV stores 10% more charge than CREF , but the energy is the same.

Figure 3: Comparison of constant capacitance and variable capacitance.

MOSFET manufacturers have been doing these integrals for years, but instead of specifying it as charge and energy, they convert it into two different equivalent capacitances.

COTR - a fixed capacitor that has the same stored charge as COSS when charged to 80% VDSS
COER - a fixed capacitor that has the same stored energy as COSS when charged to 80% VDSS

Reference [4] gives an empirical value for the “effective” COSS at 80% of rated voltage, which is the same as the time-dependent equivalent capacitance. However, the application note does not distinguish between COTR and COER , which are already very different and need to be treated separately. Note that both COTR and COER are themselves functions of voltage; any integration of a nonlinear function will always produce another nonlinear function. Therefore, product data sheets define them at some specific voltage, such as 80% of rated VDS or 400V. The fact that there are two different “equivalent” values for the same COSS , one for stored charge and the other for energy, more or less solves the above puzzle.

Not only are COTR and COER different from each other, but the degree of their difference can be used as a measure of nonlinearity. In our example, a capacitance range of 1.5:0.5 produces a 16.7% difference between COTR and COER . For the SiHP15N60E, the same COTR/COER ratio is almost 3.6. For other superjunction devices, the capacitance range can be wider than 100:1, and the COTR/COER ratio can be higher than 10. Figure 4a highlights the difference between stored charge and energy in the SiHP15N60E. The rates of change of these two related parameters as a function of voltage are significantly different. The large COTR , and the resulting large total stored charge, need to be considered in all bridge configurations, especially those operating in ZVS mode. Discharging the output capacitance of a MOSFET is not the same as de-energizing it, and design calculations should be based on COTR , not COER . Of course, COER and energy are still needed to calculate switching losses (reference [3]).

It should be clear by now that the absolute value of COSS at any voltage is no longer meaningful. Nor is it needed by the user. It is not the capacitance itself that interacts with the circuit, but rather the stored charge and energy that defines that behavior. If you look at any design calculation involving COSS , you will find that somewhere it is converted to stored charge or energy by multiplying by a relevant voltage factor. To further assist system designers, some MOSFET manufacturers, including Vishay, now provide complete EOSS curves in their high voltage product datasheets in addition to COTR and COER , as shown in Figure 4b. For 100V MOSFETs, QOSS is often specified at 50% to aid dead time analysis in 48V ZVS bridge circuits.

Figure 4a: Comparison of COSS stored charge and energy vs. voltage.

Figure 4b: Capacitance and stored energy versus voltage.

Similar considerations apply to the gate-to-drain capacitance CRSS , but its value is much lower than COSS . By definition, its value is already included in the measurement of COSS mentioned at the beginning of this article . The nonlinear behavior of CRSS has actually been recognized as a problem for a long time and has been described in various literature. The QGD component in the gate charge curve is nothing more than the total stored charge in CRSS that needs to be injected into or removed from the gate during the switch on or off period. Note that the piecewise linear segmentation of the gate charge curve is not due to any nonlinear behavior of the capacitors involved. The process of turning on a MOSFET involves charging two different capacitors, which have different voltages in the off state (see reference [2]).

When dealing with MOSFETs, it is useful to remember that its capacitance is not made up of two electrodes separated by a dielectric. Their capacitance is transient in nature and occurs primarily during the switching intervals when the device is subject to high dV/dt. The capacitance shown in the equivalent circuit reveals the interaction between the active electric field in the semiconductor material and its current. This revelation is meaningful only if the relationship is linear. With the extreme nonlinearities we see in today’s MOSFET devices, it is no exaggeration to say that there is no such thing as COSS or CRSS . Integrating the capacitance curve does not reveal anything about how they interact with the rest of the circuit. Rather than trying to linearize and somehow straighten the curve, designers need to focus on the basics and deal directly with stored charge and energy.

references:

[1] Sanjay Havanur and Philip Zuk. “Power MOSFET Fundamentals: Understanding Superjunction Technology,” Vishay Application Note AN-849, April 2015, http://www.vishay.com/docs/66864/an849.pdf
[2] Sanjay Havanur, “Power MOSFET Fundamentals: Understanding the Switching Process,” Vishay Application Note AN-850, June 2015, http://www.vishay.com/docs/68214/turnonprocess.pdf
[3] Sanjay Havanur, “Careful Approach to Zero Voltage Switching,” April 2016 Newsletter, http://www.how2power.com/pdf_view.php?url=/newsletters/1604/articles/H2PToday1604_design_VishaySiliconix.pdf [4
] International Rectifier, “A More Realistic Characterization of Power MOSFET Output Capacitance COSS,” AN-1001, 1999. http://www.infineon.com/dgdl/an-1001.pdf?fileId=5546d462533600a401535590a5c70f36
[5] Shen, Z. John, Yali Xiong, Xu Cheng, Yue Fu, and Pavan Kumar. “Power MOSFET switching loss analysis: A new insight.” 2006 IEEE Industrial Applications Conference 41st IAS Annual Meeting, Volume 3, Pages 1438-1442.
[6] M. Orabi, A. Abou-Alfotouh, and A. Lotfi. “Contribution of Coss capacitance to synchronous buck converter losses.” Power Electronics Specialists Conference (PESC), 2008, Pages 666-672
[7] Drofenik, U., A. Muesing, and J. W. Kolar. “Voltage-dependent capacitors in multi-domain simulation of power electronics.” In Proceedings of the 2010 International Conference on Power Electronics (ECCE Asia), pp. 643-650. 2010.
[8] Costinett, Daniel, Regan Zane, and Dragan Maksimovic. “Circuit-Oriented Modeling of Nonlinear Device Capacitance in Switch-Mode Power Converters.” Control and Modeling of Power Electronics (COMPEL), 2012 IEEE 13th Symposium, pp. 1-8. IEEE, 2012.
[9] Elferich, Reinhold. “A General ZVS Half-Bridge Model with Nonlinear Capacitors and Application to LLC Design.” In Proceedings of the 2012 IEEE Energy Conversion Conference and Exhibition (ECCE), pp. 4404-4410.
[10] “Coss-Related Energy Losses in Power MOSFETs for Zero Voltage Switching Applications”, JB Fedison et al., IEEE Applied Power Electronics Conference and Exhibition (APEC), 2014, pp. 150-156
[11] Roig, Jaume, Filip Bauwens. “Origins of Anomalous Hysteresis in Resonant Converters Using Superjunction FETs”. IEEE Reports on Electron Devices, Vol. 62, No. 9 (2015), pp. 3092-3094.
[12] Fedison, JB and MJ Harrison. “Coss Hysteresis in Advanced Superjunction MOSFETs”. 2016 IEEE Applied Power Electronics Conference and Exhibition (APEC), pp. 247-252.