Systems to observe single-electron interference have been built by other groups, and a committed experimenter‡ who would like to build such a device should study the excellent papers written by these research groups. This will help you to gain an understanding of how they overcame some of the difficult technical challenges involved. Even with today’s technology, a system to conduct a single-electron interference experiment is a difficult project that should be undertaken only by very advanced experimenters.
In spite of this, one can work with the basic electron “optics” components to understand the operation and significance of Tonomura’s experiment. Moreover, one can perform the basic experiments that demonstrate complementarity for the electron by accepting that in these experiments individual electrons behave in the same way as a beam consisting of millions of particles at a time. Let’s consider this for a moment—can you see that what is happening in the humble Teltron 555 electron-diffraction tube is in principle the same as what Tonomura did one electron at a time? That is, the closely spaced atoms of a graphite crystal serve as the slit system, and the electrons exhibit the same interference effects as the photons in an optical double slit.
With this in mind, let’s take a look at the construction of a basic electron optics system that can be used to experiment with different aspects of the electron’s complementary properties.
Figure 98 shows our simple electron microscope. It is identical to the cold-cathode CRT that we built in (Figure 41), except that we added a sample within the anode’s exit orifice and a large coil that acts as an electron lens. We evacuate the tube with the refrigeration-service vacuum pump (Figure 35), and power the tube with the same high-voltage power supply we built to energize our CRTs (Figure 39).
Figure 98 Simple TEM. (a) Electrons are produced by glow discharge at a pressure of about 30 mTorr, directed through a 150-mesh calibration screen, magnified by a magnetic “lens,” and projected onto a fluorescent screen. (b) The screen of an oscilloscope CRT is coupled to a 25-mm Ace Glass threaded connector. Ace-Thred glassware and vacuum “Quick-Connec” couplings are used to build the rest of the electron tube.
The “lens” is an 8.0 mH inductor that we purchased from Parts Express (catalog number 266–854). Its turns are made of 18 AWG magnet wire that are wound very tightly and bonded together. This is important because it minimizes magnetic distortions that translate into image distortions. The DC resistance of this inductor is 1.6 Ω, with a power handling of 300 W.
You should already have some practical experience with magnetic focusing if you measured e/m using Hoag’s method with a CRT (Figure 51). As you may remember, the image of a line (formed by scanning electrons back and forth by electrostatic deflection) is brought to a very sharp focus as the magnetic field along the CRT’s axis is increased.
In that experiment, we assumed that all of the electrons would have the same velocity (determined by the accelerating potential applied between the cathode and the anode). We then slowly increased the magnetic field in strength until the time required for the electrons to make one complete revolution due to magnetic deflection is equal to the time for them to travel from the deflecting plates to the screen. At that point, all electrons were focused on a small spot at the screen. If we further increased the magnetic field, the electrons made more than one complete revolution while traveling down the tube. If they made two complete revolutions during this time, they were again brought into sharp focus on the screen.
This behavior is similar to the behavior of light passing through a converging lens. In the case of magnetic focusing, the focal length of the “lens” is proportional to the velocity of the electrons and inversely proportional to the strength of the magnetic field. As such, the solenoid we used in the e/m measurement experiment of Figure 51 is in fact acting as an electron lens.
In that experiment, we wanted a homogeneous magnetic field along the complete electron path. However, this is not necessary to make a coil act as a powerful converging lens. In fact, the magnetic field may be confined to a very short distance along the path of the electrons and still serve to focus the electrons sharply on the screen. This is exactly the purpose of the single “lens” that we use in our demonstration electron microscope. Figure 99 shows our results using a mesh intended for calibration of professional electron microscopes (structure probe catalog number 3011C). Try this out with your homemade CRT! It is a very educational and neat experiment!
Figure 99 The sample for the simple TEM is an structure probe #3011C mesh used to calibrate professional electron microscopes. (a) Geometry of copper mesh. (b) Detail of grid holes. In the photographs of fluorescent screen shown in (c) and (d), the dashed circle indicates the perimeter of the CRT screen: (c) 3.33 × magnification is achieved with a 1-A coil current, (d) 9 × magnification with a 9-A coil current.
If you want to use a biological sample (e.g., a cockroach leg), you will first have to coat it with a thin conductive layer. Attach the sample to a holder with silver-loaded glue (used to repair printed circuit boards), and then spray-paint it with an alcohol solution of very fine graphite.27
Just as in an optical microscope, higher levels of magnification can be obtained by using a series of lenses instead of a single large magnifying lens. As shown in Figure 100, a lens that acts as an optical “condenser” lens projects high-velocity electrons through the object to be imaged. Some of the electrons are stopped by the object, while others get through—just as with a transilluminated object on an optical microscope’s slide. Electrons that pass through the object are focused by the “objective” lens to form an inverted, magnified virtual image. This image is then magnified and reversed again by the “ocular” lens to produce a greatly magnified shadow of the object. In the case of an electron microscope, a fluorescent screen is used to render the electron image visible. Magnifications of 105 are common for TEMs using a two-stage system such as this.
Figure 100 A TEM is very similar to an optical microscope, but it uses electrons and magnetic lenses instead of light and glass lenses. Large amounts of magnification with small image distortion are obtained by amplifying the image in stages, rather than with a single large lens.
More importantly, however, small parts of the object can be distinguished from one another with an electron microscope. The great resolving power of the electron microscope is due to the de Broglie wavelength of the electrons, which is smaller than the wavelength of the light in an optical microscope. A two-stage TEM can resolve image features as small as 5 nm, which is more than a hundred times smaller than what can be distinguished with an optical microscope.
Back in 1973, the “Amateur Scientist” column of Scientific American reported on the electron microscopes built by a high school physics club.28 Their simple, one-lens units achieved a magnification of 100 x, while their homebuilt, multistage model reached a maximum magnification of 10,000 x. Very impressive when you consider that the best optical microscopes top off at around 2,500 x!
Leave a Reply