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Edit: It seems my initial question (Why are there no insulating heatsinks?) was based on a false premise, and there are in fact insulating heatsinks--I just wasn't able to find them with a cursory search. So instead, I'm changing this to ask about their rarity instead.

Heatsinks seem to be almost universally made of aluminum, copper, or some combination thereof. This makes sense; aluminum and copper are easy to work and have high thermal conductivity. But diamond has one of the highest thermal conductivities of any known substance--it's obvious, of course, that diamond of the type suitable for use as a heatsink would be inordinately expensive to say the least, as it would probably have to be a single gem-quality crystal, but would it not be possible to use, for example, cubic boron nitride, which has a similar thermal conductivity?

And yes, the manufacturing difficulties with making a large single crystal of c-BN would probably be about the same as making a large single crystal of diamond, but I expect the end price wouldn't be as much because there's no De Beers group to come after you for boron nitride. And there are surely other nonmetallic compounds that have good heat conductivity, and some of them would presumably be better suited to manufacture. I doubt they'd be able to even approach the price point of extruded aluminum, but sometimes you do need higher performance.

So, in summary, my question is: Is it only cost that makes nonmetallic heatsinks so rare, or are there some other drawbacks that make them less desirable outside of the most esoteric of applications?

One thing that other answers don't seem to have covered is that you only need a very thin layer of electrical insulator (at modest voltages) while the heat spreader part of a heat sink works best if it's thick. So it's more efficient to use a thin electrically-insulating barrier followed by a thick, cheap, and easily-made metal heatsink than it would be to use a single piece of a material that's thermally conductive and electrically insulating. The few materials that do exist (such as diamond) can't be extruded or otherwise easily formed into a heatsink shape. Some can be sintered but sintering can't generally reach the thermal conductivity of bulk material. The engineering effect of all this materials science is that we end up doing what we've always done.

This is hardly a new problem; those of us of a certain age remember the heatsinks with mica insulators for the TO-220 and TO-3 packages.

The issue (at the time) was both material cost and availability and materials science. We have come a long way in our understanding of thermal conductivity of various compounds over the years, but it is still relatively new technology (there are things such as thermally conductive pads that have been around for decades but are not really heat sinks in their own right).

The TO-220 has the heat spreader on the collector / drain of the device, which is usually at an elevated voltage, so the typical arrangement used this technique:

Source.

It was not unusual to use some thermal paste as well to maximise the heat transfer.

Now that does not really explain the relative rarity of integrated insulated heatsinks; that really comes down to 'is it necessary' or can I simply use the well known method of a heat sink and an electrically insulating barrier material which is less expensive (at least, it is today).

The old tried and true method has served well for many decades, but for some applications (particularly those in small devices) such a solution may well not fit.

There are quite a few offerings available, but they tend to be a bit more expensive (on a per watt basis). There is also a lot of research into other materials.

Of course, for the bling factor, you could use these.

So it comes down to a number of things and cost is a major driver. I will also note that a large market for heat sinks is for CPUs and GPUs where the case of the IC is electrically insulated anyway.

Polymer heatsinks deserve a mention. Polymer heatsinks aren't that uncommon. I come across polymer heat sinks industrial, automotive, prosumer goods once in a while. They are often hard to recognize as heatsinks, because they can have a second mechanical purposes (an enclosure, a bracket, a reflector of a lamp). These heat sinks are always custom injection-molded parts.

Polymers have a small heat conductivity, compared to any metal. This prompts a question: how can a polymer make an acceptable heatsink? In some cases, the thermal resistance of the heatsink becomes dominated by transfer from heatsink to air, rather than by conduction within the heatsink itself. This can happen when dumping heat into air with natural convection. In these cases, a heatsink made of a special polymer with a relatively high thermal conduction ( $ mathrm20 frac W mcdot K $ ) can be comparable to an aluminium ( $ mathrm200 frac W mcdot K $ ) heatsink with the same geometry.

E2 is the plastic (source)

Some additional discussion in this old answer.

The thing about a heat sink is that there are only really two ways to ultimately dispose of the heat, conduction and radiation.

So ultimately, assuming your emmisivity is reasonably close to 1 (Only really matters if you can run HOT, power loss to radiation is 4th power of absolute temperature), and you can make the thing have good thermal contact with the surrounding cooling media (Air, water, whatever), what you make it from only matters a little (That interface is the killer for performance, not the bulk thermal conductivity of the heatsink).

Now clearly you need to design the heatsink so that heat travels thru it reasonably efficiently and in the area where there is a lot of power flux density that might argue for something other then ally, for the bulk of the thing where you have plenty of metal to keep delta T low, cheapest is best.

For a heat spreader or insulating washer it is different of course, heat spreaders by definition are used where the power flux density is very high and minimal thermal resistance is a very good thing, hence the usual use of copper in this role.

For the insulator you do see exotic materials used, because a good thermal conductor that is also an electrical insulator is not that common, so Boron Nitride, Alumina, Beryllium Oxide(!) and the like all see service here, and I would not be shocked by someone using diamond (Probably in some weird RF device).

From a technical standpoint its certainly possible to manufacture heatsinks with built in isolator pads. The reason they don't do it is economics.

Between the different mechanical, electrical, and thermal choices there are a lot of different combinations. If the isolator and heatsink were one part then the vendors would have to stock a lot more unique part numbers.

By factoring out the isolator and heat sink into unique products the user has a lot more choices.

Here are some of the things to consider.

1) In many cases the user will use gap pads between heat-sinks and hot components to pick up slack in mechanical tolerances. This means that each user will want the pad to be a different thickness.

2) Thermal isolator pad materials vary in how well they are able to conform to rough surfaces. There is often a trade between how squishy the material is and how well it conducts heat.

3) Different users will have different isolation requirements in terms of voltage. There is a trade off between isolation voltage, the material thickness and the thermal resistance.

3) Adding an insulator between a heat-sink and a part has a penalty in terms of thermal resistance. If its possible to not use an insulating layer then you will get the best thermal performance in that case.