Why is it not practical to connect the two drains of the MOSFETs together? Is it not practical to connect the source of one MOSFET to the gate of another?
The main advantage of Darlington and Sziklai BJT pair arrangements is that you get the product of the current gains of the two transistors.
But MOSFETs already have essentially infinite DC current gain, so you don't typically use these configurations at low frequencies.
The above is valid for low frequencies, but when considering fast dynamics, there are of course situations where you use one small MOSFET to drive the gate of another larger one, to speed up operation. Just think of gate drivers.
I cant answer the question why you don't use them.
But there are cases where MOSFET are used in darlington like configurations. It's apparently used in low voltage applications to reduce power consumption.
It's mentioned for example in the research paper Design of Low Voltage, Low Power (IF) Amplifier Based-On MOSFET Darlington Configuration (in the abstract) (direct Link to pdf of the paper)
Why should anybody use a Darlington combination with FETs? For which purpose? In this context, it makes sense to ask for the benefits of a BJT-based Darlington configuration.
- The transconductance of the Darlington stage - most important for the voltage gain - is only 50% of the transconductance of a single BJT (with the same collector current). So - this offers no advantages.
- The input impedance of a BJT-based Darlington stage is twice the input impedance of a single BJT (same DC operating point). This is an improvement - however, only in case of bipolar transistors. Due to the large FET input impedance this aspect seems not to be very important.
To expand on tobalt's mention of gate drivers, an example:
On page 4, note the diagram specifically shows dual N-channel outputs. It, uh, erroneously shows their gates tied together, which would make one hell of a short circuit when 'on'... a perfect example of manufacturers not inspecting their own damn diagrams -- always take them with a grain of salt...
But, assuming they mean that in a less literal sense (signal flow, polarities resolved in a useful way)... they're using a source follower to drive the output high, and common-source to drive it low.
This is in agreement with the characteristics (page 3), VOH max 1.2V from VBS or VCC respectively -- and this at zero load current, so presumably it will be even lower than this in practice.
Having measured one myself, it does indeed lose about two volts from the supply. Drive is strong below there (i.e. for most of the 0 < VO < VOH range) so it's quite effective, as long as you don't need those extra couple of volts on top.
Why choose this design? NMOS perform better than PMOS: lower RDS(on) per unit (gate / drain) capacitance, so the rising edge can be stronger and faster. They might also have trouble making PMOS in the HVIC process (the high-side circuitry is indeed on the same silicon chip, isolated by a huge diode junction it's built on top of); though it seems likely it is indeed CMOS on both sides, and this is more for performance reasons.
Earlier/smaller drivers in this family, like IR2101, are fully CMOS, i.e. a PMOS pull-up driver -- but only rated for ~200mA output current, so, they are unsuitable for high power and fast switching circuitry. Presumably, they didn't want to spend more die area on these transistors; perhaps the same limitation applies to the IR2181.
There are other versions of drivers, such as onsemi (née Fairchild) which use bipolar transistors to boost the drive strength; in this case you get effectively a hybrid Darlington, with an NPN follower into a common-source MOSFET.
Note that those are all switching applications, so all the effort is strictly about shoving around gate charge through large voltage swings (~10V). The beauty of general transistor applications is almost all in the analog domain.
In analog terms, the bipolar Darlington is excellent for reducing input current, at modest expense to VCE(sat) (and usually speed as well). This applies over much of the useful range of the pair (i.e., over a huge current range, and from DC to medium frequencies).
For MOSFETs, we can think in terms of the first (driving) transistor having some transconductance, and by reciprocity, its source terminal having a source impedance around 1/gm, which makes an RC time constant with the driven gate's capacitance. All together, a high impedance node can drive a much larger transistor while keeping bandwidth high, at some expense to the bias current that must be drawn through the driver transistor. An external bias resistor (or CCS or whatever) is required, since transistors don't transconduct without bias current.
The same analysis applies to BJTs of course, but the driver transistor's quiescent current can be the driven's base current. Often, a B-E resistor is added anyway, to speed turn-off, and to bias the driver transistor (in the same way as the MOSFET case requires), keeping it fast even at low currents.