ARPES exploits the photoelectric effect. UV or x-ray photons are directed onto a sample where they interact with the electrons within the sample, ejecting them into the vacuum. By analyzing these emitted electrons, we can learn about the properties of electrons within the sample. The success of ARPES experiments hinges on how well we can control the energy and flux of photons incident on the sample and the accuracy to which we can analyze the emitted electrons. The brightness and tunability of synchrotrons make them ideal light sources for ARPES.
Synchrotron light is generated via a single physical principle: accelerating electrons emit radiation. While the concept seems simple enough, generating intense beams of light from electrons is not trivial. One electron moving along a sinusoidal path will emit radiation as it accelerates around each curve in the path, but the amount of radiation is too weak for our purpose. For that, we need many, many electrons moving together within a small volume, which is tricky due to the strong Coulomb repulsion between electrons. However, special relativity tells us that we can overcome this problem by accelerating electrons to high velocities. At the SSRL, the energy of the electrons is 3GeV, corresponding to a velocity of approximately 0.9999999885c (where c is the speed of light). This means that a ~1 meter long strand of electrons gets "bunched" into a length ~0.1mm in our laboratory reference frame. These electron bunches orbit in a vacuum storage ring 234 meters in circumference. Currently, the storage ring houses ~280 electron bunches, each with a FWHM of ~15 picoseconds and separated by ~2 nanoseconds. Each bunch carries 0.36 mA for a total of 100 mA within the ring.
To create light from the orbiting electrons, various insertion devices are installed to alter the trajectories of the bunches within the ring. At beamline 5-4 we utilize a 10 period linearly polarized undulator which employs a series of permanent magnets with alternating poles to move electron bunches in a sinusoidal pattern. As the electron bunch traverses a period of the sine wave, the light emitted adds coherently to the light from previous periods. At the end of the undulator, a bright beam of coherent light is produced and directed toward the beamline. Each electron bunch creates a bright pulse of light and the number of bunches with the small time separation yields a quasi-continuous light source. The beamline also include an elliptically polarized undulator to allow control of the light polarization.
As with any spectroscopic technique, resolution is vital. In ARPES, the energy and momentum resolution is intrinsically linked to the energy of the incoming photons. At SSRL, the photon beam has a wide energy spectrum from which we pick a specific photon energy by adjusting the angle of a normal incidence monochromator (NIM) grating relative to the incident beam. We can select monochromatic beams from ~10 eV – 30 eV and perform experiments with energy resolutions down to less than 5 meV. Future beamline plans include a new branchline with a grazing monochromator apable of higher photon energies and higher photon flux.
After the photoenergy is selected, vertical and horizontal focusing mirrors focus the light down to a 150 x 300 micron spot size on the sample, which sits inside an ultra high vacuum chamber maintained at ~3 x 10-11 Torr. The sample is mounted on an automated 5-axis manipulator (with a manual 6th axis), allowing an angle-resolved experiment, and the sample stage is liquid Helium cooled, allowing variable temperature measurements from ~7 Kelvin up to room temperature.
The centerpiece of beamline 5-4 is a Scienta R-4000 hemispherical analyzer. The analyzer consists of two concentric hemispheres capable of resolving the electron’s energy momentum simultaneously. Electrons from the sample enter into an electrostatic lens system that focuses the them onto an entrance slit. The inner and outer hemispheres are held at different potentials altering the electron’s trajectory, depending on their incoming energy: slower electrons will follow a smaller radius. In the neighboring figure, the red and green electron paths have the same momentum, but different energies. Electrons with different momenta will enter the slit at different locations, allowing the electron’s momentum to be measured along the direction of the slit. The yellow and blue paths have the same energy, but different momenta. Opposite to the entrance slit is a 2D detector consisting of a multi-channel plate, a phosphor screen and a CCD camera, which yields a 2D energy and momentum map. To measure electron momentum perpendicular to the slit, the sample is rotated, and the maps are added together to yield a 3D measurement of the sample’s electronic structure as shown below. While the 3D map consists of the electron’s in-plane momentum and energy, the electron’s out-of-plane momentum can be probed by varying the energy of the incoming photons. Thus beamline 5-4 is capable of mapping the full electronic band structure of a crystalline sample.