How Is It Made?

(Aside: my policy on scientific explanations.)

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There are all kinds of criteria that have to be met in order to have a functioning device. I can't go into all of them, but here are a few:

The materials used on the device must not react with each other all the way up to 800 K.
The membrane must be robust enough to survive deposition of thin films and subsequent photolithography steps.
The leads going off the membrane must be made of a material and be of a size which compromises between low electrical resistance (so the thermometers can be measured) and low thermal conductance (so they don't carry away too much heat), and the thermal conductivity should have a weak temperature dependence.
Care should be taken when positioning features on the chip to avoid capacitance between elements of the circuit.
Addenda should be reduced whenever possible (thin membrane, thin leads, low heat-capacity materials).

If you are clever, you will end up with a microcalorimeter which has an internal time constant much shorter than the external one to be measured, as mentioned above. Much of this is described in greater detail in the our paper (Denlinger et. al., Rev. Sci. Instrum. 65, 946 (1994)); here I will simply write down what we found to work.

The Membrane

The only material capable of making strong, thin, large-area membranes (that we know of now) is low-stress amorphous silicon-nitride (Si-N). It is made in a chemical vapor deposition (CVD) furnace, and has extra Si compared with "stoichiometric" Si-N, which is Si₃N₄. Low-stress means the film feels neither stretched nor compressed by the substrate it is deposited on (a Si crystal in this case). Amorphous Si-N can have such low stress that it doesn't even notice if the substrate is removed from under it-- that's how we make the membrane (we etch the Si away from below the Si-N). No other material we have made yet can exist as a free-standing membrane of macroscopic size in the plane, but only a thousand atoms thick. Wonderful stuff!

The Leads

I said above that we use gold-palladium for the leads, and indeed that works. But recently we have found that Pt also works. This is something of a surprise since Pt is a pure material, and will thus have a peak in its thermal conductivity (for reasons why, see Ashcroft and Mermin, Solid State Physics). We don't want this peak-- we want the leads to be nice and boring, which is why we originally chose Au-Pd (alloys don't show the characteristic thermal conductivity peak). But the Pt we make at the Berkeley Microlab is sputtered, and the target is pretty old, which makes for a highly polycrystalline material. The electrical resistivity is nearly 3 times higher than single crystal Pt, and the thermal conductivity is quite smooth. By making wider leads than the ones shown in the figure above, we were able to meet the criteria of low electrical resistance compared to the thermometer, but still low enough thermal conductance to allow good measurements.

High-Temperature Thermometer/Heater

From 77-800K, we use a thin-film Pt thermometer. Pt has many favorable qualities-- it doesn't oxidize so it won't change over time, its resistance vs. temperature is very nearly linear over this whole regime, and it is strong enough chemically to withstand acid etching of other layers. Thus it is deposited first (well, after the Si-N of course). Below liquid nitrogen temperatures, the resistance of the Pt begins to level off (due to impurities), and the thermometer is no longer sensitive enough.

The heater is also Pt, and it functions over the entire temperature range because its R vs. T is not relevant, only its fast, predictable response to the dc pulse. Most metals would have worked; Pt makes sense since we have to deposit it anyway.

Low-Temperature Thermometer

The essence of a resistive thermometer is its temperature response, and below about 50 K, metals just aren't sensitive enough. An insulating material performs much better. We have used two different materials for this purpose, but again, these are not the only choices.

Boron-doped polycrystalline silicon (poly-Si): Poly-Si is an amazingly useful material that has not been fully exploited at low temperatures; in particular, it works very well as a thermometer. The poly-Si is deposited by chemical vapor deposition just like the Si-N for the membrane, and then it is implanted with boron and annealed. The boron nuclei take the place of some of the Si nuclei, but they each have one fewer electron in their outer shell than Si. This absence of an electron looks like a positive charge (called a "hole"), and the hole can conduct electricity. The process of introducing holes or extra electrons (say if we had used phosphorous instead of boron) into a semiconductor is called "doping."

Having a few holes per million atoms hardly compares to having one or more free electrons per atom, as in a metal. Doped semiconductors still have resistivities that are orders of magnitude higher than those of metals, and more importantly, the resisitive behavior is still insulating-- ie, they become more resistive as the temperature drops, reaching infinite resistance at zero temperature. (This is because the current carriers-- electrons or holes-- are not free; they are still effectively bound to a certain nucleus. See an undergraduate textbook on solid state physics for more details).

The great utility of these materials arises from the controllability of the resistance vs. temperature. By putting in more or less boron, we can adjust the resistance to have any value within a very wide range at a given temperature. The amount of boron also determines, to some extent, the shape of the R vs. T curve: it will always be exponential in this case, but the coefficients in front and in the exponent depend on the B concentration. We tune the doping so that the resistance has easily measurable values near the temperature we wish to use the thermometer. Since the exponential function varies so strongly with temperature, we cannot use a single thermometer between 1 K and 50 K (a resistance that works near 50 K will have increased beyond what we can measure on a voltmeter by 1 K). So the device has 2 low-temperature thermometers (see the figure above), one with peak sensitivity near 25 K, and one near or below 10 K.

Unfortunately, using poly-Si thermometers makes the construction of the device very complicated. The membrane cannot be fabricated before the doping of the poly-Si, because the doping process is rather rough and tends to break the fragile membrane. But the poly-Si cannot be exposed to the Si etch which is used to remove the Si from under the Si-N to make the membrane. This puts us in the uncomfortable position of wanting to deposit the thermometers neither before nor after making the membrane. What we ended up doing was protecting the thermometers during the etch by sandwiching them between two Si-N layers, a process that adds many steps to the fabrication. So the real solution was to find an alternative to poly-Si.

Amorphous niobium-silicon (NbSi): Niobium is a metal; silicon is a semiconductor. What happens when you jumble them together in an amorphous thin film? That depends on how much of each you use. If you have more than 12 atomic % Nb (ie, out of 100 atoms, 12 are Nb and 88 are Si), the film is metallic-- ie, it has finite conductance at zero temperature. Less than 12 at. % Nb yields an insulating film (zero conductance at zero temperature). This behavior is called the "metal-insulator transition as a function of composition." On the metallic side, the resistance is fairly flat at low temperatures, as is expected. Near 100% Si, the R vs. T curve grows exponentially at low temperatures, also as expected. And in between, the two behaviors merge smoothly-- compositions between 12 and about 3 at. % Nb can be fit by a variety of polynomials.

For our devices, we prefer R vs. T to vary as 1/T² at low temperatures. The reasons why are obscure, and are discussed in the paper (it has to do with being able to use the same sensitivity on the lockin amplifier for all low-temperature measurements). We have found that approximately 8 at. % Nb yields 1/T² behavior, and by making the two thermometers different sizes, we control at which temperature the sensitivity peaks. Adjusting the actual function of R vs. T was not a luxury we had with the poly-Si. And the fabrication has proved to be much simpler.

Sample Deposition

Once all the photolithography has been done on the front, we deposit the sample onto the backside. The easiest way is to put a mask with a square hole over the device, then evaporate the sample material in a vacuum chamber through the hole. However, we have to be a bit clever about this: the membrane is stretched across the front of the device, so on the back there is a square "pit"; the membrane is about 13 mils (.013 inches; 330um) below the back surface. Depositing thorugh a mask at the level of the back surface would give a very fuzzy square.

Instead, we take advantage of the fact that the Si etch used to cut through the device and make the membrane in the first place proceeds at an angle (we use KOH as the etchant; the angle is about 37 degrees). We fabricate by photolithography a mask made of Si that fits perfectly into the etch pit. The hole is designed to sit only a mil (25.4 um) away from the membrane-- this gives nice sharp edge to the sample square. (This mask is called a shadow mask; there's a picture of it fitting into a device shown above).

Incidentally, it is also possible to deposit the sample all over the back of the device and then pattern it photolithographically. Of course a shadow mask is preferable (no patterning step means one less chance for the membrane to break), but in some special cases may not be possible.

So there you have it. The world's most sensitive calorimeter. As far as I know, there is no other way to measure the heat capacity of a microgram of material at room temperature. And no other microcalorimeter is sensitive over such a wide temperature range.

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