ARTOF Next generation Electron spectroscopy
Since the start of Photo Electron Spectroscopy (PES) around 1950, resolution has improved in a dramatic way over the years, from a few eV to the sub-meV range. During the same time the transmission has been increased, although not to the same extent. In valence photoelectron spectroscopy the energy band structure can be determined by performing angular resolved measurements. In the first experiments of this kind a typically very small and light-weight spectrometer was mounted on a goniometer. Using such an arrangement one could obtain angular resolved spectra and this meant that the dispersion of binding energy with momentum could be measured. However, the experiments were difficult and time-consuming most often only single channel detectors were used and for precise measurements the precision and stability of the goniometer presented severe obstacles. In Fig. 1 we show how the angular resolved measurements were performed. The two important angles to measure is φ and θ and the precision in the determination comes partly from the mechanical properties of the goniometer and partly from the acceptance angle of the spectrometer.
The situation was dramatically changed by the introduction of the angular resolved mode of the electron lens. This meant that the full angular resolved dispersion curve could be rapidly measured along one direction in the Brillouin zone of the crystal. The precision of the measurement increased from a few degrees using a goniometer to almost one tenth of a degree. This more or less revolutionized the field of Angular Resolved Photo Electron Spectroscopy (ARPES). However, for obtaining the dispersion in other directions one still had to rotate the sample. And there could sometimes be difficulties in finding the Γ-point. For these measurements the low transmission of the hemispherical analyzer may also present a problem. The hemispherical analyzer using a multichannel detection system has a very high information rate, but the transmission is limited due to the slits in the system.
The ArTOF 10k analyzer allows to answer all three challenges: resolution down to 100µeV, transmission more then 250 times higher then R4000 and simultaneous measurement of both φ and θ angles with angular resolution better then 0.1˚. In the seventies pulsed synchrotron radiation sources were developed, allowing the use of electron spectrometers based on the time-of-flight principle. These instruments are particularly suited for time resolved and coincidence experiments. The latter was a consequence of the very high transmission one can obtain in such a scheme. In principle it is possible to get close to 100%. A typical instrument is shown in Fig. 2. The high transmission can be achieved in various ways. For example, an inhomogeneous magnetic field can drive the electrons into the analyzer or a strong acceleration field can be used for the same purpose. The electrons then typically enter into a so called drift tube of length L, where they are allowed to pass with a constant velocity v. If we know the start time t0 for the electron to enter the instrument and we measure the time t when it arrives to the detector, and if the drift tube has the length L we get the energy of the electron from a simple division and using the expression for the classical kinetic energy of a moving particle v=L/∆t, where ∆t=t-t0. However the classical TOF analyzers have limited resolution due to uncontrolled trajectories inside the drift tube.
In the ArTOF we instead use a combination of a drift tube with an electron lens system and position and time-resolved detector. In short, the lens system first produces a focal plan in the lens and the pattern in this plane is subsequently projected by the rest of the lens system onto the detector plane. The magnification can be controlled and we will be able to utilize the whole detector surface. Since all electrostatic potentials in the lens are pre-set we can calculate all the trajectories of the electrons through the lens and we can also calculate the velocities in each point along the tracks. It is therefore possible to construct a transformation matrix relating the arrival time, measured positions x, and y on the detector to the take off angles θ and φ and kinetic energy of electrons.
The transformation matrix T depends in a complex way of the geometric design of the lens elements and of the electrostatic potentials, but we can illustrate a part of the properties of T in a diagram. The lens is cylindrically symmetric so the energies can be obtained from the measured times and the radius r. In Fig. 3 we illustrate an example. For a full characterization we need several of such matrixes, one for each setting of the spectrometer. The electron tracks are typically quite complicated, as can be seen in Fig.4. The performance of the ArTOF instrument depends on the accuracy we can measure the take-off angles and the time difference ∆t. Via the transformation matrix this problem goes back to how precisely the sample spot is defined, the precision of the measurement of the x and y coordinates on the detector, of the pulse length from the exciting radiation and on the response times of the electronics and of time constants in the electric cabling etc.
