SEM Optics and Application to Current Research

Transcription

1 SEM Optics and Application to Current Research Azure Avery May 28, Introduction 1.1 History The optical microscope was invented in the early 17th century. Although revolutionary, the earliest microscopes were not much more than strong magnifying glasses. Over the next several hundred years, many toiled to invent new versions of the microscope and improve the resolution of the existing ones. Antony van Leeuwenhoek, a Dutch tradesman, invented over 500 different microscopes, one of which consisted of tiny glass beads mounted on a plate. These were held close to the eye and showed detail down to 1 micron [4, 5]. Leeuwenhoek used his microscopes to make groundbreaking discoveries in biology including bacteria, blood cells, and the inner structure of animal tissue cells [2]. In the 19th century, the microscope saw its next major advance with the invention of the compound microscope which improved resolution. However, by 1900 the optical microscope had reached its resolution limit of approximately.2 micron [4]. The next major advance in microscopy was made by using a beam of electrons instead of light to form magnified images. The electrons were deflected to follow a curved trajectory and created lenses that could magnify images. The technology was improved and developed and by 1935 the first scanning electron microscope (SEM) was built [4]. 1

2 Figure 1: A two-stage electron microscope with a horizontal optical axis from the 1930 s [2] 1.2 Resolution: An Example of Improved Microscopy The scanning electron microscope offers improvement of most microscopy principles including resolution. Resolution is defined as the closest two points can be to each other and still be able to be seen as separate points [3]. Lord Rayleigh, through observation, determined that the greatest resolution of two interference patterns occurs when the maximum intensity of one aligns with the minimum intensity of the second. Called the Rayleigh criterion, this gives the resolution for two spatially separated sources with an angular separation of a = a o = λ D where D is the diameter of the opening in a diffraction grating, a o is the resolving power or angular resolution and gives the minimum separation of two point sources [1]. Optical microscopes use visible light wavelengths which range from nm. However, the wavelength of an electron is determined by de Broglie s formula λ = h mv. In the SEM, a potential difference is used to accelerate the electrons. If the accelerating voltage is large, the velocity of the electrons approaches c and relativistic effects must be taken into account. The relativistic change in mass gives an energy which can be used to calculate the wavelength of an accelerated electron ( ) 1.5 λ = V V 2 (1) after substituting in the values for c, h, m e, and e [3]. Using this relativistic correction, the wavelengths of the electron can be calculated to range from nm to nm depending on the value of the accelerating voltage. This shorter wavelength gives the SEM a better angular resolution than that achieved with the comparatively long wavelengths of visible light. 2

3 2 Scanning Electron Microscope 2.1 The Electron Gun One of the most common methods for generating a beam of electrons is to heat a tungsten filament. In a typical tungsten filament electron gun, an electron beam is created using a tungsten filament (cathode), an anode, and a Wehnelt cap. Tungsten is a metal with work function φ and fermi energy E f. When the tungsten is heated, the atoms in the metal vibrate and transfer their thermal energy to the electrons at the top of the conduction band. The mean thermal energy of the atoms is kt where k is the Boltzmann s constant and T the temperature in Kelvin. When the mean thermal energy transferred from the atoms is greater than φ, electrons are emitted from the metal surface. The majority of the electron emission occurs at the tip of the V-shaped filament, because the tip is where the temperature of the filament is the highest [2]. A current is run through the filament causing it to heat to a temperature of 2800 K. The voltage difference, generally hundreds of kv s, between the filament cathode and the anode below is large enough that the electrons are accelerated toward the anode. This creates an electron beam [3]. Once the electron beam is generated, a Wehnelt cylinder is used to control the emission current. The cylinder is a conductor that surrounds the filament. It has a small opening right underneath the filament tip that allows the electron beam to pass through to the anode. The Wehnelt cylinder controls the emission current by holding a potential more negative than the filament itself. This current control is important to maximize image quality of the SEM, as well as prevent changes in the emission current due to factors such as upward drift of temperature in the filament. The variation of the Wehnelt negative potential allows control of the size of the area on the filament producing electrons, and therefore affects the strength of the electron current generated. This variation is achieved by the use of a bias resistor placed between the filament and the voltage supply [2]. After the beam is generated, it passes through the lensing system of the SEM. 2.2 Lenses: Electrostatic The first lenses in the SEM are electrostatic and are created by the electron gun. In general, an electrostatic lens is formed by holding a circular conductor with an aperture at a constant potential. This aperture is centered along the optical axis of the microscope. When the potential is negative, the electrons are repelled by the equipotential surface and those not traveling back along the optical axis are deflected to travel along the axis through the aperture [2]. The effect of the cathode and Wehnelt cylinder together is to create curved electric field lines that form what is called a crossover in the electron beam. This crossover creates an effect like a convex optical lens. The anode creates a similar effect, curving the electrons into the electron equivalent of a concave optical lens [2]. The diverging of the electron beam caused by the concave lensing effect causes the electrons to appear to come from a 3

4 source in front of the Wehnelt cap and to diverge with a half-angle of α. The half-angle α can be used in the equation to determine the electron-optical brightness β = I e /(A s πα 2 ) with I e the emission current, and A s the emitting area [2]. 2.3 Lenses: Magnetic The remaining lenses in the SEM are magnetic. Magnetic lenses use an electric current through a coil of copper wires to create an inhomogeneous magnetic field B with axial symmetry only. The resultant force that accelerates the electrons is given by the Lorentz force equation F = q( v B). The direction of the force on the electrons is constantly changing as a result of the inhomogeneity of the magnetic field and the deflection of the electrons. Using cylindrical coordinates, and Newton s second law, the acceleration of a single electron is given by a = e m [ (v φ B z )ˆr + (v z B r v r B z ) ˆφ ] (v φ B r )ẑ As the electrons travel through the magnetic field created by the coils, they spiral around the optical axis. Once the electrons have passed through the center of the magnetic coils, their spiral motion causes the Lorentz force to pull them back toward the optical axis, causing the electrons to be focused at another crossover point [2]. Control of the magnetic field is accomplished by almost completely surrounding the copper coil with a ferromagnetic material such as iron. The iron acts as a shield, preventing the magnetic field from extending beyond the magnetic material, while the gaps allow magnetic field to extend inside the coil. Iron is also used to make pole pieces, which are machined parts that sit in the gaps to further intensify the magnetic field inside the solenoid [2, 6]. The magnetic field inside a solenoid is given by B = µ o ni. Because it is proportional to the current, the strength of the magnetic field inside the coil can be changed by varying the current. Variation in the strength of the magnetic field causes the convergence of the electron beam to change, thus changing the focal length of the lens [2,3]. 2.4 Electron Specimen Interaction Once through the lenses in the optical column, the electrons interact with the sample and are collected to form an image. To create an image, the design of the SEM relies on two types of electron scattering, elastic and inelastic. Elastic scattering of the primary electrons is called backscattering. Backscattered electrons (BSEs) are electrons which have interacted with the surface of the specimen and through an elastic collision been scattered at an angle θ > 90. BSEs have an final kinetic energy roughly equal to their initial kinetic energy. Due to the proportional relationship between the scattering cross section for BSEs (2) 4

5 and Z 2 where Z is the atomic number, BSEs are used to show contrast due to atomic or molecular surface variations [2]. Inelastic scattering of the primary electrons creates what are termed secondary electrons. When the primary electrons from the electron beam interact with the specimen surface, some of the electrons are absorbed by the atoms. This atomic excitation eventually results in a secondary electron (SE) being emitted as the atom de-excites. Because these secondary electrons cover a greater range in energy than the primary electrons, focus of the SEs is difficult. To alleviate this problem, the SEM is designed to scan or raster back and forth across the specimen and collect the SEs from each point. This rastering is accomplished by using scan coils that create and control E and B fields orthogonal to the electron trajectories v to deflect the electron beam back and forth across the specimen [2]. Most of the SEs are absorbed into the sample and eventually lose their kinetic energy through multiple collisions. However, those that escape the surface of the specimen are generated within a region called the escape depth. Although it depends on the chemical composition of the sample, escape depth is generally less than 2 nm. SE yield is a function of the cross sectional area created by the escape depth and the width of the electron beam, so tilted specimens or those with topographic variation, have a greater yield and therefore create a brighter image. Most SEMs use the cross sectional area and the orientation of the detector with respect to the specimen to distinguish features on the surface of the specimen. The effect of using both SEs and BSEs is an image of the specimen given by both the contrast resulting from surface topography and variations due to specimen chemical composition that appears to be 3-dimensional [2]. 3 Application to Current Research In current research, the SEM is applied in various ways including imaging of a sample, measurement of sample features, and e-beam lithography. One group of researchers is using the SEM in a novel way. They are using the electron beam as both a driving force to create oscillations in nanocantilevers made of SiC nanowires and a detector to determine the resonant frequencies of the nanowires. In this study single nanowires were attached to tungsten tips using carbon tape. Vincent et al found that focusing a SEM electron beam in spot, or non-rastering, mode provided the energy necessary to drive the wire to oscillate at its resonant frequency. This technique offers the ability of researchers to determine the natural frequencies of individual nanowires. New methods for driving nanocantilevers are improvements that could be applied to the field of single molecule detection [8]. In my own research we have used the SEM to image and to measure the dimensions of our micromachined thermal conductivity measurement devices. This summer we will be applying the SEM and its pattern generation software to fabricate new nanomachined devices using e-beam lithography [7]. 5

6 4 Conclusion Using electrons to form lenses was a discovery that revolutionized the field of microscopy. Though they are complex and expensive instruments, scanning electron microscopes are modeled using the basic governing principles of electricity and magnetism. The SEM and related electron microscopes are a powerful tools with many implications for the continued advancement of future research in the field of science. References [1] G. Bekefi and A.H. Barrett. Electromagnetic Vibrations, Waves, and Radiation. The MIT Press, Key: Bekefi Annotation: A book used for applied E and M class at MIT. Its derivations of key E and M concepts are useful. The book concentrates on application. I used it for more in depth look at resolution for optical microscopy. [2] R. F. Egerton. Physical Principles of Electron Microscopy. Springer, Key: Egerton Annotation: This was a great source for information. Slightly more quantitative treatment of electron microscopy principles than Goodhew s. It had clear figures that were more detailed than Goodhew s, but lacked a vigorous mathematical treatment of the underlying principles. [3] P.J. Goodhew. Electron Microscopy and Analysis. Wykeham Publications, Key: Goodhew Annotation: A good qualitative treatment of the basic principles of electron microscopy. It starts with a comparison between optical and electron microscopy. It also has separate chapters on electron specimen interaction, the Transmission Electron Microscope, and the Scanning Electron Microscope. The figures are simple, but helpful in understanding key concepts governing electron microscopy. [4] J.W.S. Hearle, J.T. Sparrow, and P.M. Cross. The Use of the Scanning Electron Microscope. Pergamon Press, Key: Hearle Annotation: I only used this for information on the history of microscopy. Egerton and Goodhew are better sources for information about scanning electron microscopy. 6

7 [5] Antony van leeuwenhoek. Key: ucmp Annotation: A webpage with a short biography on Antony van Leeuwenhoek. It included several pictures. It is part of the University of California Museum of Paleontology website. [6] Swiss Federal Institute of Technology Zurich. Key: Swiss Annotation: Web site with a basic explanation of an electromagnetic lens. Maintained by the Swiss Federal Institute of Technology in Zurich [7] B. Revaz, B.L. Zink, and F. Hellman. Si-n membrane-based microcalorimetry: Heat capacity and thermal conductivity of thin films. Thermochimica Acta, 432: , Key: Zink Annotation: This is research reported on the square membrane devices engineered and tested by Frances Hellman s group at Berkeley and UC San Diego. Our research has altered the design of the device offering a better measurement device for thermal conductivity due to the absence of radiation contribution to k. [8] P. Vincent, S. Perisanu, A. Ayari, M. Choueib, V. Gouttenoire, M. Bechelany, A. Brioude, D. Cornu, and S. T. Purcell. Driving self-sustained vibrations of nanowires with a constant electron beam. Physical Review B (Condensed Matter and Materials Physics), 76(8):085435, Key: Vincent Annotation: This article uses the SEM to create mechanical oscillations of SiC nanowires called nanocatilevers. The ability to manipulate these oscillations has implications for single molecule detection or quantum macroscopic oscillations. The SEM was used to determine the frequency dependent amplitude of the nanowires using the line scan mode, and then in spot mode to generate an oscillation in the wire. This article explains the interaction of the electron beam with the semiconducting SiC nanowires, therefore giving an illustrative application of the SEM to current research. 7