The basic definitions of the three capacitors related to MOSFET are shown in figures 1a and1b. Measuring these capacitors as a function of VDS is not a simple task, and some of them need to be short-circuited or suspended. Finally, three values defined as follows are measured and given in the product data:
CISS = CGS+CGDCOSS = CDS+CDGCRSS = CGD
Among these three values, the nonlinearity of input capacitance CGS is the smallest. It is the capacitance between the gate structure and the source and will not change much as a function of VDS. On the other hand, CGD is extremely nonlinear. For superjunction devices, the variation range of front 100V is almost three orders of magnitude. This is also the reason for the tiny step size of CISS when VDS= 0.
Recently, many people are interested in understanding the characteristics of COSS and its influence on high-frequency switches. There are several reasons for this, for example, the charge and loss stored by COSS have become the biggest challenge to realize high-frequency AC-DC converter. Generally speaking, any loss associated with capacitance is proportional to the square of the applied voltage. As the reference [3] points out, the energy storage and loss of the same capacitor at 550V are 2 100 times higher than that at12 V. As people pay more and more attention to reducing RDSON, the conduction loss decreases obviously, but COSS does not decrease proportionally. For example, earlier, the lowest RDSON of 600V MOSFET in TO-220 was 340 mW. Now, this value has been reduced to 65 mW in 600V superjunction devices. For capacitors, it is more meaningful to compare devices with similar RDSON values between different technologies. Figure 2 compares the capacitances of two devices: one is SiHP 17N60D, which is a planar device; The other is SiHP 15N60E, which is a super junction MOSFET, and the RDSON is close to but slightly lower. Note that these values are plotted on a logarithmic scale. For superjunction devices, COSS decreases from 136 pF to 67 pF at 100V, but it also becomes more nonlinear. In planar devices, when VDS= 0V and 100V, the COSS ratio was 25: 1, but now it has tripled to 75: 1. When VDS= 0, it is not uncommon that the COSS value is greater than the input capacitance CISS.
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Figure 2. Capacitance comparison between planar MOSFET and superjunction MOSFET
References [4]-[9] try to explain the nonlinear characteristics of COSS from many aspects, and put forward new opinions on its influence on high-frequency switching. After complex processing such as integration and simulation of COSS curve, most of these documents reconfirm the nonlinear nature of capacitance. The terms of "small signal" capacitance and "large signal" capacitance are introduced, and the simulation and analysis are carried out. Apart from being technically incorrect, there is no difference between these new terms from the perspective of industry practice. It can be seen that the so-called large signal capacitance is nothing more than the time-related value COTR, which has been standardized by MOSFET industry for many years after the publication of reference [4]. The significant difference between the fine simulation results and the product data values is still within the tolerance range involved in MOSFET product description and mass production.
Another analysis method puts forward a hidden resistor in series with COSS, namely ROSS, to describe all unexplained losses related to nonlinear capacitance (see reference [10]). However, this is contrary to the basic circuit theory, which clearly points out that the charging and discharging loss of capacitors is completely determined by the energy stored in them, and has nothing to do with the value of any series resistance. As for ROSS, no one has put forward any explanation or experimental verification at the semiconductor level, but the waveform provided in this paper clearly shows the MOSFET body diode that is turned on, which provides a simpler (if not too strange) explanation for these losses. In fact, the conduction of body diode is the basic consideration in analyzing any bridge circuit with inductive load. In other recent peer review conference publications (references [1 1] and [12]), it has been pointed out that the charge and energy stored in COSS are lagging behind, and there may be differences under different voltage paths. The significance of this lag is that the principle of charge conservation is not applicable to power MOSFET.
Instead of challenging the basic laws of physics, it is more enlightening to re-examine and verify whether it is used correctly in appropriate occasions. This survey raises a mystery, so it may be a bit fascinating—
If two capacitors are connected in parallel, charged to the same voltage and keep the same stored charge, does it necessarily follow that they also store the same energy?
According to the well-known formulas Q=CV and E=? CV2, the answer should be yes. It seems that even if the capacitance is nonlinear, this conclusion should be true at any voltage. Unfortunately, those familiar formulas for storing charge and energy are not universally effective, and they are only applicable to the special case of constant capacitance. The more basic relationship is that the capacitance is defined as the rate of change of the charge transfer (w.r.t) voltage, and the voltage itself is defined as a measure of the change of unit charge energy. In other words, the basic relationship is
C = dQ/dV，V = dE/dQ。
There is an implicit assumption that simple charge and energy equations have static capacitance when they are derived. For nonlinear capacitors, charge and energy must be obtained by integrating the capacitor and charge in voltage respectively. To further illustrate this point, consider two capacitors shown in Figure 3. The reference value is provided by the capacitor CREF. The CV of the other capacitor changes linearly from 1.5 times CREF to 0.5 times CREF. At 100 volts, they have the same charge.
This can be clearly seen by observing the C x V area of these two capacitors, and can also be verified by voltage integration of capacitor values. However, the stored energy is completely different. If the stored charge is integrated on the voltage, it can be found that CREF has only 83.3% stored energy at100V. It can also be seen that at 75V, CV has more stored charge than CREF 10%, but their energy is the same.
Figure 3. Comparison between constant capacitance and variable capacitance
MOSFET manufacturers have been doing these integrations for many years, but instead of designating them as charge and energy, they convert them into two different equivalent capacitors.
Cotr-–A fixed capacitor with the same storage charge as COSS when charged to 80% VDSS.
Coer-–Fixed capacitor with the same energy storage as COSS when charged to 80% VDSS.
Reference [4] gives the empirical value of "effective" COSS at 80% rated voltage, which is the same as the time-varying equivalent capacitance. However, this application note does not distinguish between COTR and COER, which have become very different and need to be handled separately. Note that COTR and COER are both functions of voltage; Any integral of a nonlinear function will always produce another nonlinear function. Therefore, the product data defines them at a specific voltage, such as 80% of the rated VDS or 400V V V. The same COSS has two different "equivalent" values, one for storing charge and the other for storing energy, which can solve the above problems more or less.
COTR and division are not only different from each other, but also the degree of difference between them can be used as an index to measure nonlinearity. In our example, the capacitance range of 1.5:0.5 will produce a difference of 16.7% between COTR and COER. For SiHP 15N60E, the same COTR/COER ratio is almost 3.6. For other superjunction devices, the capacitance range may be wider than 100: 1, and the COTR/COER ratio may be higher than 10. Fig. 4a highlights the difference between charge and energy stored in SiHP 15N60E. As a function of voltage, the change rates of these two related parameters are significantly different. In all bridge configurations, especially those operating in ZVS mode, it is necessary to consider the oversized COTR and its implied oversized total stored charge. The discharge of MOSFET output capacitor is different from de-excitation, and the design and calculation should be based on COTR, not COER. Of course, COER and energy are still needed to calculate the switching loss (Reference [3]).
It should be clear by now that the absolute value of COSS at any voltage is no longer meaningful. Users no longer need it. It is not the capacitance that interacts with the circuit itself, but the stored charge and energy that determine the behavior. If you look at any design calculation involving COSS, you will find that somewhere, it is converted into stored charge or energy by multiplying the relevant voltage factor. In order to further help system designers, some MOSFET manufacturers, including Vishay, provide complete EOSS curves in their high-voltage product data in addition to COTR and Cole, as shown in Figure 4b. For 100V MOSFET, QOSS is usually set to 50% to help the dead time analysis in the 48V ZVS bridge line.
Similar considerations apply to the gate-drain capacitance CRSS, but its value is much lower than COSS. By definition, its value has been included in the measurement of COSS mentioned at the beginning of this article. In fact, the nonlinear characteristics of CRRSS have long been considered as a problem and have been expounded in various literatures. The QGD component in the gate charge curve is the total charge stored in CRSS, which needs to be injected into or removed from the gate during the on or off of the switch. Please note that the piecewise linear division of the gate charge curve is not due to any nonlinear characteristics of the capacitors involved. The process of turning on MOSFET includes charging two different capacitors, which have different voltages in the off state (see reference [2]).
When dealing with a MOSFET, it is useful to remember that its capacitance is not composed of two electrodes separated by a dielectric. Its capacitance is transient in nature, mainly during the switching interval, when the device is affected by high dV/dt. The capacitance shown in the equivalent circuit reveals the interaction between the effective electric field and its current in semiconductor materials. Only when this relationship is linear can this revelation be meaningful. For the extremely nonlinear situation we see in today's MOSFET devices, it is no exaggeration to say that there is no such thing as COSS or CRSS. Integral capacitance curves can't reveal any information about how they interact with the rest of the circuit. Designers need to focus on the basic knowledge and directly deal with the stored charge and energy, instead of trying to linearize and straighten the curve in some way.
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