Characterization of the high harmonics source for the VUV ellipsometer at ELI Beamlines

In this paper


I. INTRODUCTION
While more experimentally demanding, vacuum ultraviolet (VUV) ellipsometry is a powerful complementary technique to VUV reflectance as it provides better capabilities to study thin film and layered materials due to the degree of freedom introduced by the light phase.VUV ellipsometry allows the possibility of studying large bandgap semiconductors and allows the study of transitions from shallow core levels.The interpretation of core level to conduction band transitions has been shown to be easier than the interpretation of valence to conduction band excitations. 1 Commercial VUV ellipsometers achieving up to 8.86 eV (140 nm) 2,3 are currently available.For higher energies, the only ellipsometer available is the one at the Metrology Light Source of the Physikalisch-Technische Bundesanstalt (PTB) in Berlin, 4,5 which uses synchrotron light and has a documented VUV operational energy range extending up to 40 eV.
The possibility of building cost-effective high harmonic generation (HHG) sources drives the recent interest in transient VUV reflectance experiments using laser driven HHG secondary sources.Among recent publications is a study on time-resolved VUV absorption on germanium. 6,7Important work has also been done on probing ultrafast element-specific magnetization dynamics targeting, e.g., M-absorption edges of Fe (54 eV) and Ni (67 eV). 8omplementary to these developments in VUV material science, and aiming for a more robust data interpretation, at ELI Beamlines, an ultrafast spectroscopic ellipsometry setup in the optical range with femtosecond time resolution has been developed and is now available to the international user community. 9,10t the ELI Beamlines facility, 11 a new station named ELIps is undergoing implementation to become a user oriented endstation with capabilities for pump-probe VUV ellipsometry in time scales from picoseconds to femtoseconds.It uses a VUV beam generated by an HHG source.ELIps is considered to be the first time-resolved ellipsometer in the VUV region.In contrast to the PTB instrument, 4,5 it uses a femtosecond HHG source as the source of VUV light.Reflective optics are used to assure high throughput also in the VUV region.Here, we present the state of its implementation as well as the results from the first characterization experiments.This paper is focused on results obtained in the spectral region between 30 and 45 eV; however, the ELIps instrument works over an extended energy range, covering transition metal M-absorption edges.

II. EXPERIMENTAL SETUP A. Light source
ELIps uses the VUV-high harmonic (HH) light generated in an argon, neon, or krypton gas cell using either a 12 mJ, 15 fs, 1 kHz in-house-developed L1 ALLEGRA laser 12 with central wavelength 830 nm or a commercial 6 mJ, 30 fs, 1 KHz Astrella-Coherent laser with central wavelength 800 nm.L1 ALLEGRA is based on a broadband optical parametric chirped-pulse amplifier pumped by picosecond Yb:YAG thin disk lasers.After the amplification, the broadband pulses are compressed to ,20 fs using chirped mirrors.
HHG was done in neon or argon gas and was analyzed before being sent to the ELIps instrument by the VUV spectrometer of the HHG beamline consisting of a toroidal mirror, a motorized slit of variable width, a reflection grating, and a back-illuminated charge-coupled device (CCD). 13The 12 mJ of the in-house developed laser, L1 ALLEGRA, allows the generation of harmonics in a neon gas cell.With such harmonics, the cut of the aluminum filter at H47 is observed and then the CCD can be calibrated.For more time consuming measurements, i.e., for the experiments when the analyzer is rotated, we switched to the Astrella laser, which is more stable.However, the harmonics generated by the power of this laser in the neon gas cell are too weak to be detected.While using the Astrella laser, the harmonics are generated in an argon gas cell, whose maximum intensity is in the region between 30 and 70 eV.The details about the development of the HHG source were recently published by Hort et al. 13 Important for the development of the ELIps is the fact that all the harmonics of the HHG beam keep the polarization of the 830 nm or 800 nm HHG-pump-laser; for the experiments reported here, the polarization of the HHG beam was kept linear and vertical.
The spectrum of the HH generated by the L1 ALLEGRA laser pulse on a neon cell is shown in Fig. 1.The position of the detector with respect to the grating is changed in order to focus different harmonics.The high harmonic source generates harmonics between 10 and 121 eV. 13 Once a desired energy range is chosen for a sample, the position of the camera will be fixed for the experiment.The spectrum of the L1 ALLEGRA laser pulse is shown in the inset of Fig. 1.

B. VUV chamber
The ELIps instrument consists of two chambers as illustrated in Fig. 2. The main chamber contains the polarization optics, and the grating chamber contains the grating of the spectrometer.Each of two chambers is pumped by independent turbomolecular pumps while using the backing and roughing pumps from the central vacuum system of ELI Beamlines.
The ELIps is designed in a linear configuration, the incident VUV beam from the HHG is deviated from the VC3 chamber of the HHG source 13 by a SiC mirror with an angle of incidence of 70 , the IR laser is rejected in a 200 nm aluminum filter and enters the ELIps chamber where it is cut by a 2 mm pinhole.Additionally, for cooling samples, a cryostat can be connected to the main chamber.It has been tested for reflectivity measurements at temperatures ranging between 70 and 450 K.

C. Analyzer and sample stage
The ellipsometer was tested as a rotating analyzer ellipsometer (RAE) similar to the one described in Barth et al. 14 The analyzer is a triple-reflection polarizer formed by three plane mirrors with gold coatings.Other materials include ruthenium, platinum, and molybdenum.The angle of incidence on the first mirror of the gold polarizer is 82 .A discussion about the coating materials and the design of the triple-reflection polarizers is published in Ref. 15.The analyzer is mounted in a rotational stage as shown in Fig. 3.It is manually aligned using the HeNe alignment laser of the HHG source.The VUV beam enters the ellipsometer vertically polarized and so the analyzer 0 angle was set to the vertical too.
The sample stage is inserted before the analyzer stage, and it is similar to the analyzer.It consists of two gold mirrors "A" and "B" of Fig. 3 and a third mirror, mirror "C," is replaced by the sample.Three reflections are needed in order to keep the optical axis of the beam straight according to the design described in Ref. 11.The angle of incidence for the sample is 74 .At the moment, the sample stage does not a rotational stage.

D. Detection system
After passing the analyzer, the light goes to a concave gold coated diffraction grating with 1200 g/mm, 1500 mm radius of curvature, ruled 6 saw tooth blaze, clear aperture 50 Â 10 mm where the different harmonics are separated to form a VUV spectra such as the ones shown in Fig. 1.The VUV spectrum is measured by a 2048 Â 2048 pixels (27:6 Â 27:6 mm) back-illuminated CCD (BEN) Andor iKon-L SO camera cooled to À40 C. The CCD detector needs to be moved in the x and y directions in order to focus different harmonics as illustrated in Fig. 2. For the experiments, the analyzer was rotated from 0 to 360 and at each 10 step, a spectrum was taken.A laptop connected to the CCD and the rotational stage of the analyzer records the signal as a function of the angle of rotation of the analyzer, thanks to an in-house developed Labview application.The acquisition time was 10 s per accumulation and three accumulations were obtained at each step.

III. RESULTS AND DISCUSSIONS
The first measurements were done without the sample stage in order to characterize the harmonics after passing the optics of the ELIps and HHG chambers.For the experiments, the harmonics were generated in a cell containing argon gas and using the Astrella laser with a central wavelength of 800 nm.The wavelength of the laser then changes the energy of the observed harmonics compared with the ones shown in Fig. 1.The theory we followed for the characterization of the VUV analyzer is the one described by Barth et al. 14 for the characterization of the optics of the first VUV ellipsometer, which used synchrotron light.The intensity measured for different harmonics as a function of angle takes the form of a cosine curve, and it is shown in Fig. 4.
This intensity obtained as a function of angle can be written as The coefficients a 0 , a 1 , b 1 , a 2 , and b 2 obtained from the Fourier analysis are reported in Table I.The Fourier coefficients compare our analyzer with a perfect polarizer, with linearly polarized input light, the rotation of a polarizer should result in an intensity curve described by Eq. ( 2), which means a 2 should be much greater than all the other coefficients.If the zero angle is arbitrary, the sum 2 should be large and all other coefficients should be close to zero.The extinction ratio was calculated for the most focused harmonic of Fig. 4, which has a high signal noise ratio.So, at 38.8 eV, the extinction ratio of our triple reflection gold polarizer is in the order of 100:1.A misalignment could be observed in a nonzero a 1 and b 1 , in our case, this misalignment was small and could not be eradicated due to the, at present, lack of in vacuum motors.Vacuum motors will be installed soon for the ELIps.Following the characterization of the analyzer, the sample stage was inserted containing a silicon sample.The sample stage was kept at 0 , and the analyzer was then rotated 360 in 10 steps.The acquisition time was 2 s per accumulation, with three accumulations for each step.
The determination of the ellipsometry parameters for the silicon sample using the Mueller calculus will only be possible with a new upgrade that allows the change in the polarization of the HH beam or an upgrade in the motorization capabilities of the sample stage that allows changes in the polarization of the incident light on the sample.We would then be able to get the Muller matrices, M mA and M mB , of the two mirrors contained in the sample holder (see Fig. 5).
An issue to take into account is the polarization-dependence of the detection grating.It acts as another polarizer behind the analyzer.After calculations from different databases for optical constants, it can be concluded that the polarization sensitivity of the grating can be expected to become less important for higher energies, since r p and r s approach similar values.

IV. CONCLUSIONS AND PERSPECTIVES
We tested the VUV ELIps capabilities to study the optical properties of materials in the VUV spectral region between 30 and 70 eV using a triple reflection gold polarizer.Experiments with other materials and different angles are needed to have a choice for the best possible polarizer for a given range of energy.The potential of the HHG source was demonstrated and its next upgrade, which will allow the change of polarization of the VUV beam, would make possible the determination of the ellipsometric parameters of an unknown sample.On the side of the ELIps instrument, the expected upgrade includes the introduction of a secondary beam in order to excite the sample by a 800 nm (1.55 eV) optical laser and its second and third harmonic, 400 nm (3.10 eV) and 266 nm (4.66 eV).This upgrade should make possible the use of the femtosecond time resolution of the ELIps for pump-probe transient experiments.

FIG. 1 .
FIG.1.Spectra of the harmonics generated by L1 ALLEGRA laser in neon gas cell after passing the analyzer when no sample is installed.The position of the detector with respect to the grating is changed in order to focus different harmonics.The distance of grating-detector is (a) 52 cm, (b) 56 cm, and (c) 60 cm.The spectrum of the L1 ALLEGRA laser pulse is shown in the inset.

FIG. 3 .FIG. 4 .FIG. 2 .
FIG. 3. Scheme of the analyzer.The angle of incidence on mirror A and C is 82 and on mirror B is 74 .The analyzer is mounted in a rotational stage.(a) shows the axis of rotation of the analyzer and (b) shows the angle of incidence on the first mirror and the scheme of polarization after a θ angle of rotation of the analyzer.

FIG. 5 .
FIG. 5. Scheme of the propagation of the light in the system.Including the HHG: high harmonic generation source; sample stage: Mirror A + Mirror B + Sample; Analyzer and CCD detector.S HHG stands for Stokes vector generated by the HHG, M mA : Mueller matrix of the first mirror, M mB : Mueller matrix of the second mirror, M S : Mueller matrix of the sample, S in : Stokes vector entering the analyzer, M pol : Mueller matrix of the analyzer, S out : Stokes vector at the detector.

TABLE I .
Fourier coefficients and extinction ratio (Ext.ratio)calculated for the gold triple reflection analyzer.