This blog post details how electron microscopes leverage the properties of matter waves and magnetic field lenses to surpass the resolution limits of optical microscopes, and what new possibilities they open for microstructure analysis.
In advanced materials research, electron microscopes are essential for observing microstructures smaller than a micrometer. While electron and optical microscopes share a fundamental operating principle, they differ significantly: optical microscopes use visible light as the observation medium and glass lenses to focus light, whereas electron microscopes employ an electron beam and utilize magnetic fields generated by current-carrying coils to focus the beam.
An optical microscope illuminates a sample with visible light and forms an image by focusing the light scattered from each point on the sample through a lens. However, it has limitations in observing fine structures for the following reasons. Light from a very small point light source diffracts as it passes through the lens, forming a circular interference pattern larger than the original light source, called an Airy disk. When light originating from two points on the sample at a certain distance apart passes through the lens, two separate Airy disks form on the screen. If the distance between these two points is too close, and the distance between the centers of the two Airy disks becomes excessively small compared to the size of the disks, the observer can no longer distinguish the two points and perceives them as a single point. The distance between these two points on the sample at this limit is called the resolution. Generally, the minimum resolution achievable by a microscope is proportional to the wavelength of the wave used and the focal length of the lens, and inversely proportional to the diameter of the lens. Therefore, the shorter the wavelength used, the smaller the minimum resolution, allowing for a sharper image. Even when using visible light, which has the shortest wavelength, the resolution of an optical microscope cannot be smaller than approximately half the wavelength, or 200 nm.
In contrast, the electrons in the electron beam used in electron microscopes behave like waves due to the wave-particle duality described in quantum mechanics; this wave is called the de Broglie matter wave. The wavelength of the matter wave is inversely proportional to the electron’s momentum, which is the product of its mass and velocity. In electron microscopes, higher accelerating voltages increase the electron’s velocity. Thus, electrons accelerated by tens of kV have a matter wave wavelength of approximately 0.01 nm. However, the lens performance of electron microscopes is inferior to that of optical lenses, so the actual resolution typically remains at the level of several nanometers.
The lenses in an electron microscope use the magnetic field generated by coils carrying current to bend the path of the electrons and focus them. When a charged particle passes through a magnetic field region, it experiences a force proportional to the particle’s velocity and the magnetic field strength, with the direction of this force perpendicular to the magnetic field. Electron lenses are designed by appropriately arranging coils to generate a specific magnetic field shape, ensuring electrons passing through the lens experience a force directed toward the lens center. Increasing the current through the coils enhances the magnetic field strength, thereby increasing the force on the electrons. This causes the electron beam to bend more sharply, achieving the effect of a shorter focal length. A shorter focal length of the objective lens increases the microscope’s magnification. Therefore, while optical microscopes require changing the objective lens to alter magnification, electron microscopes can freely adjust magnification within a certain range by controlling the current flowing through the coils. However, precisely controlling the force acting on electrons passing through the center and edges of the lens to converge them at a single point is difficult. Consequently, electron microscopes tend to have less precise focus position clarity compared to optical microscopes.
Electron microscopes use electron beams accelerated by high voltage, requiring the interior to be maintained under high vacuum conditions, typically below 10⁻¹⁰ atmospheres. This is because when electrons collide with air, energy is lost or their trajectory is deflected, making it difficult to control the electron beam as desired. Furthermore, when observing insulating samples, electrons from the beam can accumulate on the sample surface, creating a repulsive effect that pushes the beam away and distorts the image. To prevent this, the surface of insulating samples is coated with a thin layer of a conductor, such as gold or platinum. While optical microscopes allow direct visual observation of the actual image, electron microscopes detect the material waves of electrons scattered from the sample. They focus these waves onto a detector and measure the electron distribution at the point where the image is formed, thereby reproducing the surface morphology of the sample as a digital image. Leveraging this characteristic of electron microscopes allows for the installation of various detectors and peripheral devices, significantly expanding the range of applications for electron microscopy.
