It’s a hot summer day. You desperately want something cold to drink, but unfortunately, your bottle of root beer has been sitting in a hot car all day. You put it into a bucket full of ice to cool it down. But it’s taking forever! How, you wonder, could you speed the process up?
The same question, it turns out, is important for understanding how electronic devices work, and how we can make them work better by controlling the temperature of the electrons that power them. In some cases, like your cell phone, we want the electrons to cool as rapidly as possible to increase the speed of the device. In other cases, like some solar cells, keeping the electrons hot improves the efficiency of the cell’s electrical production. Read on to find out what a bottle of root beer in a cooler full of ice and a nanowire in a vat of liquid helium have in common!
Temperature is a measure of energy. More specifically, it measures kinetic energy, or how fast the atoms or molecules in a substance are moving. Heat is transferred between atoms in much the same way the energy of motion is transferred between billiard balls. Just as a moving cue ball colliding with a stationary 8-ball transfers some of its energy to the 8-ball (Fig. 1), molecules in a hotter substance that collide with molecules in a cooler substance transfer some of their energy to that substance. As its molecules move faster, the temperature of the substance increases (Fig. 2). In the case of our root beer, the molecules in the glass bottle have more energy than the water molecules in the surrounding ice. The glass and root beer transfer their energy to the ice, melting it. Eventually all three substances (root beer, glass, and the ice water in the cooler) reach the same temperature of 32°F—the temperature at which ice melts. The molecules in all three substances have the same average energy, and while the particles continue to jostle each other, there will be no net transfer of energy between substances. At this point, the system—root beer, glass, and ice—has reached thermal equilibrium.
The amount of time needed to reach thermal equilibrium depends on the materials involved. For example, aluminum has a thermal conductivity nearly 150 times larger than glass, so an aluminum can of root beer will cool MUCH more quickly than a glass bottle. (But once you open it, you better drink it fast, because the aluminum can will get warm more quickly, too!)
There is one additional twist to the concept of thermal equilibrium when the substances involved are solids. All solids can be imagined as a background lattice of positively charged ions with electrons swarming around them (Fig. 3). Generally, the lattice and surrounding electrons are the same temperature, but for very, very short times—shorter than a billionth of a second—the electrons in a solid can be at a very different temperature than the underlying lattice.
This phenomenon is important for understanding the behavior of electrons in semiconductors. To study how temperature changes affect semiconductors, we start with two different semiconducting nanowires on a copper block that is cooled to -452°F by liquid helium. (For a sense of just how cold this is, see Fig. 4!) Both nanowires are made of the same material (GaAsSb), but one is bare and the other is coated with a different semiconducting material (InP). See Fig. 5 for a closer view of the nanowires.
Once this system reaches thermal equilibrium, all parts of the system—the liquid helium, the copper block, and the nanowire, including both the lattice and the electrons—are at the same temperature of -452°F. We then use an ultrafast laser to deliver a very short pulse of heat. This heats up the electrons, but not the lattice of positively charged ions, to a temperature close to that of boiling water in just one picosecond—that’s a millionth of a millionth of a second! But the real fun begins as we observe how quickly the wires cool back down following the laser pulse. The coated nanowire takes hundreds of times longer than the bare nanowire to cool back down. In this case, the electrons are HOT but the lattice stays COLD. Somehow just having the outer coating of InP completely changes how fast the electrons transfer their energy to the lattice, even though the nanowire material (GaAsSb) is identical in both cases. To understand how surprising this is, imagine discovering that an external change like dying your hair a different color completely changed the function of your brain by, say, giving you a photographic memory!
This result is also quite exciting, because controlling how fast materials warm up and cool down is vital for designing new devices with optimal performance characteristics. For example, a silicon solar cell used in a power station converts light from the Sun into electrical energy, but nearly half of the energy is lost to heating up the silicon lattice as the electrons cool down. If you could extract this energy from the electrons before they cool down, you could double the efficiency of solar cells—even if it doesn’t help you cool down your root beer any faster.
Fig. 1 (Click to enlarge) Kinetic energy is transferred between colliding atoms and molecules in much the same way it is transferred between colliding billiard balls.
Fig. 2 (Click to enlarge) This animation shows the transfer of energy from faster-moving molecules (red) to slower-moving ones (blue). The rate at which this happens depends on the specific materials involved. When all the molecules have roughly the same kinetic energy (purple), the temperature difference vanishes and the system reaches thermal equilibrium.
Fig. 3 (Click to enlarge) All solids consist of a lattice of positively charged nuclei with negatively charged electrons swarming around them. This arrangement is responsible for many of the unique properties of solids, including what happens when semiconductors change temperature.
Fig. 4 (Click to enlarge) These temperature scales give you a sense of just how cold our liquid helium is, and how hot the electrons in the nanowires get in only a millionth of a millionth of a second when we expose them to an ultrafast laser pulse!
Fig. 5 (Click to enlarge) The nanowires grown for this study are so small we can only see them with an electron microscope! On the left, we see the uncoated GaAsSb nanowires (top) and a cross-section of an uncoated wire (bottom). On the right, we see the GaAsSb nanowires coated with an InP shell (top) and a cross-section of a coated wire (bottom). The cross-section images are color-coded to show where atoms of different elements are located. To see how the nanowires are grown, check out the video below!