Reflection high-energy electron diffraction

Reflection high-energy electron diffraction (RHEED) is a technique used to characterize the surface of crystalline materials. RHEED systems gather information only from the surface layer of the sample, which distinguishes RHEED from other materials characterization methods that also rely on diffraction of high-energy electrons. Transmission electron microscopy, another common electron diffraction method samples mainly the bulk of the sample due to the geometry of the system, although in special cases it can provide surface information. Low-energy electron diffraction (LEED) is also surface sensitive, but LEED achieves surface sensitivity through the use of low energy electrons.

Introduction

A RHEED system requires an electron source (gun), photoluminescent detector screen and a sample with a clean surface, although modern RHEED systems have additional parts to optimize the technique. The electron gun generates a beam of electrons which strike the sample at a very small angle relative to the sample surface. Incident electrons diffract from atoms at the surface of the sample, and a small fraction of the diffracted electrons interfere constructively at specific angles and form regular patterns on the detector. The electrons interfere according to the position of atoms on the sample surface, so the diffraction pattern at the detector is a function of the sample surface. Figure 1 shows the most basic setup of a RHEED system.

thumbnail|400px|Figure 1. Systematic setup of the electron gun, sample and detector/CCD components of a RHEED system. Electrons follow the path indicated by the arrow and approach the sample at angle θ. The sample surface diffracts electrons, and some of these diffracted electrons reach the detector and form the RHEED pattern. The reflected (specular) beam follows the path from the sample to the detector.

Surface diffraction

In the RHEED setup, only atoms at the sample surface contribute to the RHEED pattern. The glancing angle of incident electrons allows them to escape the bulk of the sample and to reach the detector. Atoms at the sample surface diffract (scatter) the incident electrons due to the wavelike properties of electrons.

The diffracted electrons interfere constructively at specific angles according to the crystal structure and spacing of the atoms at the sample surface and the wavelength of the incident electrons. Some of the electron waves created by constructive interference collide with the detector, creating specific diffraction patterns according to the surface features of the sample. Users characterize the crystallography of the sample surface through analysis of the diffraction patterns. Figure 2 shows a RHEED pattern. Video 1 depicts a metrology instrument recording the RHEED intensity oscillations and deposition rate for process control and analysis.

thumbnail|400px|Figure 2. A RHEED pattern obtained from electron diffraction from a clean TiO2 (110) surface. The bright spots indicate where many electrons reach the detector. The lines that can be observed are [[Kikuchi lines (physics)|Kikuchi Lines.]]

Two types of diffraction contribute to RHEED patterns. Some incident electrons undergo a single, elastic scattering event at the crystal surface, a process termed kinematic scattering. These rods originate at the conventional 2D reciprocal lattice points of the sample's surface.

The Ewald's sphere is centered on the sample surface with a radius equal to the magnitude of the wavevector of the incident electrons,

where λ is the electrons' de Broglie wavelength.

alt=|thumb|400x400px|Figure 3. The construction of the Ewald's sphere for elastic diffraction in RHEED. The radius of the Ewald's sphere is equal to the magnitude of the incoming electron's wave vector ki, which ends at the origin of the two-dimensional reciprocal lattice. The wave vector of the outgoing electron khl corresponds to an allowed diffraction condition, and the difference between the components parallel to the surface of the two wave vectors is the reciprocal lattice vector Ghl.

Diffraction conditions are satisfied where the rods of reciprocal lattice intersect the Ewald's sphere. Therefore, the magnitude of a vector from the origin of the Ewald's sphere to the intersection of any reciprocal lattice rods is equal in magnitude to that of the incident beam. This is expressed as

<math>|k_{hl}|=|k_{i}|</math> (2)

Here, khl is the wave vector of the elastically diffracted electrons of the order (hl) at any intersection of reciprocal lattice rods with Ewald's sphere

The projections of the two vectors onto the plane of the sample's surface differ by a reciprocal lattice vector Ghl,

<math>G_{hl}=k^{||}_{hl}-k^{||}_{i}</math> (3)

Figure 3 shows the construction of the Ewald's sphere and provides examples of the G, khl and ki vectors.

Many of the reciprocal lattice rods meet the diffraction condition, however the RHEED system is designed such that only the low orders of diffraction are incident on the detector. The RHEED pattern at the detector is a projection only of the k vectors that are within the angular range that contains the detector. The size and position of the detector determine which of the diffracted electrons are within the angular range that reaches the detector, so the geometry of the RHEED pattern can be related back to the geometry of the reciprocal lattice of the sample surface through use of trigonometric relations and the distance from the sample to detector.

The k vectors are labeled such that the vector k00 that forms the smallest angle with the sample surface is called the 0th order beam. RHEED specialists characterize film morphologies by measuring the changes in beam intensity and comparing these changes to theoretical calculations, which can effectively model the dependence of the intensity of diffracted beams on the azimuth angle. The newly exposed, cleaved surface is analyzed. Large samples, or those that are not able to be cleaved prior to RHEED analysis can be coated with a passive oxide layer prior to analysis. Superimposed patterns of the substrate and heterogeneous materials, complex interference patterns and degradation of the resolution are characteristic of complex surfaces or those partially covered with heterogeneous materials.

Specialized RHEED techniques

Film growth

RHEED is an extremely popular technique for monitoring the growth of thin films. In particular, RHEED is well suited for use with molecular beam epitaxy (MBE), a process used to form high quality, ultrapure thin films under ultrahigh vacuum growth conditions. The intensities of individual spots on the RHEED pattern fluctuate in a periodic manner as a result of the relative surface coverage of the growing thin film. Figure 8 shows an example of the intensity fluctuating at a single RHEED point during MBE growth.

thumbnail|400px|Figure 8. The curve is a rough model of the fluctuation of the intensity of a single RHEED point during MBE deposition. Each peak represents the forming of a new monolayer. Since the degree of order is at a maximum once a new monolayer has been formed, the spots in the diffraction pattern have maximum intensity since the maximum number of diffraction centers of the new layer contribute to the diffracted beam. The overall intensity of the oscillations is dropping the more layers are grown. This is because the electron beam was focused on the original surface and gets out of focus the more layers are grown. Note that the figure is only a model similar in shape to those used by film growth experts.

Each full period corresponds to formation of a single atomic layer thin film. The oscillation period is highly dependent on the material system, electron energy and incident angle, so researchers obtain empirical data to correlate the intensity oscillations and film coverage before using RHEED for monitoring film growth. RHEED-TRAXS analyzes X-ray spectral lines emitted from a crystal as a result of electrons from a RHEED gun colliding with the surface.

RHEED-TRAXS is preferential to X-ray microanalysis (XMA)(such as EDS and WDS) because the incidence angle of the electrons on the surface is very small, typically less than 5°. As a result, the electrons do not penetrate deeply into the crystal, meaning the X-ray emission is restricted to the top of the crystal, allowing for real-time, in-situ monitoring of surface stoichiometry.

The experimental setup is fairly simple. Electrons are fired onto a sample causing X-ray emission. These X-rays are then detected using a silicon-lithium Si-Li crystal placed behind beryllium windows, used to maintain vacuum.

MCP-RHEED

MCP-RHEED is a system in which an electron beam is amplified by a micro-channel plate (MCP). This system consists of an electron gun and an MCP equipped with a fluorescent screen opposite to the electron gun. Because of the amplification, the intensity of the electron beam can be decreased by several orders of magnitude and the damage to the samples is diminished. This method is used to observe the growth of insulator crystals such as organic films and alkali halide films, which are easily damaged by electron beams.