Tikalon Blog by Dev Gualtieri

Walter Schottky

December 3, 2018

Central heating is a necessity in our home in Northern New Jersey. While some homes have forced air heating, our house is heated by an hydronic system in which the room air is heated by water flowing through baseboard pipes covered with thin aluminum fin heat exchangers. The water is heated by natural gas in a boiler (the water does not actually boil) and circulated by a pump in two heating zones controlled by motorized valves connected to thermostats.

Aluminum fin heat-exchanger in a home hydronic heating system

Aluminum fin heat exchanger in the baseboard radiator of a home hydronic heating system manufactured by Slant/Fin.

Aluminum is an ideal material for a heat exchanger, since it has the high thermal conductivity of 235 watts/meter/kelvin.

(Photo by the author)

The heating boiler is connected to the house water supply, which supplies the initial and any subsequent water fills. The water that circulates in the baseboard radiators is not potable water, so the boiler water needs to be isolated from the house potable water supply. This is done with a backflow preventer that allows water flow in one direction only, into the heating system.

One other mechanical device designed to be unidirectional is the ratchet, which is used in such things as socket wrenches. The ratchet was also the basis of a famous thought experiment in thermodynamics proposed by Gabriel Lippmann in 1900. This thought experiment is now known as the Brownian ratchet, or the Feynman-Smoluchowski ratchet after the two physicists who showed that the device (see figure) is not a perpetual motion machine. The Brownian appellation comes from the Brownian motion of the gas molecules that act as the energy source for this device.

Diagram of the Brownian ratchet.

Since this device is part of a thought experiment, its actual size and construction are adjusted so that the paddles will be moved by impact with the gas molecules.

Work is done in lifting the mass m against gravity.

(Created by the author using Inkscape. Also available at Wikimedia Commons. Click for larger image.)

The device acts as a Maxwell's demon that produces useful work from the random thermal motion of molecules. Molecules that impinge the paddle wheels would rotate the shaft in one direction only; and, since the device will operate when T₁=T₂ and there is no temperature difference between thermal reservoirs, the device violates the second law of thermodynamics if it produces work.

Polish physicist Marian Smoluchowski did a detailed analysis in 1912 that proved that no work will be done if T1 = T2, thus vindicating the second law. Richard Feynman did a more thorough analysis in the 1960s, and he showed that work will be done if T₁ > T₂, reducing the device to a typical heat engine that obeys all laws of thermodynamics.

The electrical analog to Brownian motion is Johnson-Nyquist noise, the electrical noise voltage across a resistor caused by the thermal motion of electrons. The root mean square (RMS) of this noise voltage v_n for a resistor R at absolute temperature T is as follows,

where Δf is the bandwidth in hertz over which the noise is measured, and k_B is the Boltzmann constant. Fortunately for circuit designers, this noise voltage is very small. A 1 k-ohm resistor at room temperature, measured over a 10 kHz bandwidth, has an RMS noise voltage of just 400 nanovolt.

This brings us to the electrical analog of the Brownian ratchet that uses another unidirectional device, the diode. In 1950, Léon Brillouin, known to materials scientists for his eponymous Brillouin zone, proposed the circuit shown in the figure as a way to extract a direct current from the Johnson-Nyquist noise in a resistor. In this case, the diode acts as the ratchet, but analysis shows that energy will be extracted only when this ratchet is also at a temperature lower than the noise source.

Brillouin's electrical version of a Brownian ratchet

Brillouin's electrical analog of the Brownian ratchet.

In this thought experiment, the terminals produce a net DC voltage just as a battery would.

(Created using Inkscape)

While the thought experiment would envision diode D as an ideal diode having perfect conductance in one direction and no conductance in the other, real diodes have very low conductance below a voltage called the forward voltage. For a typical silicon p-n junction diode such as the 1N4148, this voltage is about 0.7 volts at room temperature. This voltage is lower, 0.3 volts, for a germanium p-n junction diode such as the 1N34A. These diodes will conduct at lower voltages if the current demand is low. For example, the 1N4148 will have a forward voltage of just 0.4 volts at 10 nanoamps.

This forward voltage leads to inefficiencies in circuitry since the diode will have an equivalent resistance specified by the forward voltage drop at the operating current. Interestingly, long before the development of the modern p-n junction diodes. there was a diode with a very low forward voltage. This was the Schottky diode, named after the German physicist, Walter Schottky (1886-1976). This diode has the favorable characteristics of both low forward voltage, of the order of 0.2 volts, and high frequency operation. These properties are important for diodes in switching power supplies. Schottky diodes are formed by a contact between a metal and a semiconductor, the earliest example being the "cat's-whisker" detectors used in early radio receivers.

It was nearly inevitable that Walter Schottky would become a physicist, since his father, Friedrich, was a mathematics professor. Walter was granted a B.S. degree in physics from the University of Berlin in 1908, and he completed his Ph.D. in 1912 under Max Planck and Heinrich Rubens. This was just twelve years after Planck explained blackbody radiation by proposing that energy was quantized. Although Schottky had several academic positions, much of his important work was conducted at the Siemens Research laboratories.

Walter H. Schottky (23 July 1886 - 4 March 1976) in a c. 1920 photograph.

(Wikimedia Commons image, exhibited at the Deutsches Museum, Munich, modified for artistic effect.)

Schottky's research at Siemens was on the development of theories to explain ion and electron emission, one practical outcome of which was his invention of the screen-grid vacuum tube (tetrode) in 1915. With Erwin Gerlach (not to be confused with Walther Gerlach (1889-1979), who discovered spin quantization with Otto Stern (1888-1969)), he invented the ribbon microphone and its complement, the ribbon loudspeaker.

The superheterodyne principle, in which a signal is mixed with a local oscillator to produced a low frequency signal that's more easily amplified, was an important radio invention that's attributed to Edwin Armstrong (1890-1954), who patented the concept in 1918. Armstrong is also credited with the invention of FM radio.[2] Schottky apparently invented superheterodyne radio independently at about the same time,[3] although Lucien Lévy was able to assert a legal claim that superseded both Armstrong and Schottky.

One of Schottky's most important scientific accomplishments was his use of what's now known as the image charge method to calculate the interaction energy between a point charge and an infinite conducting plane (see figure). This fundamental calculation was applied to thermal emission of electrons, field-emission of electrons, and electrons in a semiconductor near a metal surface in a Schottky diode.

Illustration of the image charge method. An image charge, -q, replaces the infinite conducting sheet to produce the electric field distributionelectric field distribution from charge +q. (Created by the author using Inkscape. Also available at Wikimedia Commons. Click for larger image.)

Schottky's name is also associated with the Schottky defect, a point defect in a crystal lattice caused by absent atoms, but his earliest work was on shot noise in 1918. Shot noise (surprisingly, not called "schott noise") is electrical noise associated with the fact that current flows as discrete packets of electrons, so it has a stochastic character. This noise is most prevalent at small currents and short time scales (wide bandwidth), and the signal-to-noise ratio can be approximated by the square root of the number of electrons in the current. An ampere is 6.242 x 10¹⁸ electrons per second.

Since 2018 is the centenary of publication of Schottky's paper on this topic, the SPIE has published a translation of Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern" that appeared in Annalen der Physik.[4-5] As Schottky wrote,

"The intention of the following text is to prove certain impassable limits for the amplification using hot cathode and gas discharge tubes. The first insurmountable obstacle is oddly given by the size of the elementary quantum of electricity."[4]

In honor of this centenary, the SPIE Journal of Micro/Nanolithography, MEMS, and MOEMS has published an open access English translation of this paper by Martin Burkhardt, a member of the editorial board of that journal, with additional editing by SPIE fellow Anthony Yen.[5] John Wiley & Sons, who own the copyright to the original German language Annalen der Physik, have given permission to make this translation an open access paper.[5]

Walter Schottky

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