Rare Earth doped YAG crystals with controlled variable doping, are laser gain materials recently attracting much attention due to the unique properties it offer in terms of laser engineering. It is very important to perform an accurate and reliable doping spatial distribution measurement in order to be capable to fully map the doping values in the obtained material. We therefore cross-evaluated most common methods. We also mapped doping distribution in a Bagdasarov grown Yb:YAG crystal.
© 2014 Optical Society of America
The elaboration and processing of Yttrium Aluminum Garnet Y3Al5O12 (YAG) laser crystals with controlled spatial distribution of activator ions (Nd3+, Yb3+, Er3+,…) has been demonstrated with the very peculiar experimental arrangement offered by the Bagdasarov growth method [1,2]. Of course inhomogeneous distribution of rare earth dopants in YAG crystals takes place in other melt growth techniques as well, especially with large ions (like Nd3+) when the segregation coefficient significantly differs from 1. In these cases, a continuous inhomogeneous distribution takes place naturally. However for Yb, the segregation coefficient is very close to 1 in Bagdasarov method and very homogeneous and large samples can be obtained . For Czochralski and Temperature Gradient technique growth of Yb:YAG crystals inhomogeneities in the Yb ions distribution was also observed and was regarded more as a drawback . In our case, we control the Yb doping distribution in order to obtain crystals with more favorable laser characteristics. Accurately characterizing the resulting boule doping ion spatial distribution is obviously the first and most essential measurement to be performed. It indeed provides information very valuable not only to adjust the crucible starting material spatial distribution, but also to understand the growth process dynamics. The doping ions concentration in a laser gain medium host matrix is a key parameter for predicting lasing characteristics and estimating thermal or Amplified Spontaneous Emission (ASE) effects.
In this paper, several methods are first cross-evaluated (section 2), then, the gathered data (Yb3+ doping distribution mapping) give access to the evolution of the growth front orientation during growth process (section 3). The current investigation is a part of the “LUCIA” laser project  at the Laboratoire pour l’Utilisation des Laser Intenses (LULI) of the Ecole Polytechnique, Palaiseau, France. While designing amplifier for LUCIA laser, it is crucial to have a clear knowledge of the absorption cross section of the selected gain medium. Accurate energetic and efficiency predictions rely on this information. A simple absorption measurement performed at the relevant wavelength (for instance 941 or 970 nm for Yb:YAG) is usually sufficient but it first requires to have access to an accurate knowledge of the Ytterbium concentration obtained from composition measurement techniques. Knowing the material doping concentration, transmission can then be measured and absorption cross-section value for the relevant wavelength can be derived.
2. Experimental techniques for composition evaluation
Various research groups refer to different methods for doping concentration evaluation in YAG crystals [6–8]. In order to define the most suitable and reliable technique for our application, we performed a series of measurements with different methods on two homogeneously doped samples obtained with ytterbium oxide starting powder stoichiometric concentration carefully adjusted to produce 2 and 20 at% Yb doped YAG crystal.
The cross evaluated methods are Inductively-Coupled Plasma Mass Spectroscopy (ICPMS), Electron Probe Micro Analysis (EPMA), Rutherford Back Scattering (RBS) and Energy-Dispersive X-Ray Spectroscopy (EDX). These methods are used not only for optical materials but also for a wide range of different materials in order to accurately define its composition. EPMA, EDX and RBS are surface techniques while ICP-MS is a bulk technique. We did not found any reference in the literature dedicated to the comparison of these techniques for doping measurements in YAG crystals. For Bagdasarov grown gradient-doped crystals, it is very important to accurately measure the distribution of the doping ions at any point of the grown boule in order to obtain necessary feedback to adjust the starting material composition and distribution in the crucible and the growth conditions (crucible speed for instance).
2.1 Inductively-coupled plasma mass spectroscopy (ICPMS)
ICPMS  is a bulk measurement destructive technique. The samples are dissolved into a liquid solution. The inductively coupled plasma is used as an excitation source to generate ions. These ions are introduced to a mass analyzer, separated and collected and the total ratio of elements of interest is measured.
The measurement with ICPMS technique was performed using Chem-Lab MISA-01 standards as a reference and with the Argon ICPMS Spectrometer at the Laboratoire des Sciences du Climat et de l'Environnement (LSCE) in Gif-sur-Yvette, France.
2.2 Electron probe micro analysis (EPMA)
EPMA  provides quantitative and qualitative determination of chemical composition at the micrometer scale in solid materials without any destruction.
It is a surface technique which allows deriving dopant ions distribution maps for any crystal. The sample is bombarded with a beam (5 to 10 nm diameter) of low energy electrons. Emitted X-rays at characteristic wavelengths for the elements are recorded and analyzed (Wavelength Dispersive Spectrometry-WDS). The analyzed volume at one measurement point is in a range of 0.3-3 μm3. The measurements were performed with a CAMECA SX 100 microanalyzer equipped with four WDS spectrometers at the Laboratoire Magmas et Volcans (LMV) in Clermont-Ferrand, France.
2.3 Energy-dispersive X-ray spectroscopy
EDS or EDX  is another analytical technique used for the elemental analysis or chemical characterization of a sample. It is one of the variants of X-ray fluorescence spectroscopy which relies on the investigation of a sample through interactions between electromagnetic radiation and matter, analyzing X-rays emitted by the matter in response to being hit with charged particles. Characteristic X-rays emission stimulation is somehow similar to EPMA technique. A high-energy beam (e-, p+, X-rays) is focused into the sample to be studied and excites characteristic radiations. The number and energy of the X-rays emitted from the specimen are analyzed by an energy-dispersive spectrometer.
EDS measurements were performed at the Laboratory of High Temperature Superconductivity, Institute of Physical Research of National Academy of Sciences, Armenia. For these measurements, we used Silicon detector (Nato) model EDS7378. The sample compartment limits the sample size to be tested to 15 mm. This implies cutting long reference samples into smaller pieces.
2.4 Rutherford backscattering spectrometry (RBS)
RBS  is a nuclear method dedicated to the near surface analysis of solids, it is quantitative, nondestructive and very sensible for heavy elements. Ions with energy in the 0.5-4 MeV range bombard the target and the energy of backscattered particles is recorded with an energy sensitive solid state detector. The penetration depth is 2 µm for incident He-ions and 20 µm for incident protons.
For our samples, RBS measurements were performed with the Van der Graaff ion accelerator of the Institut des Nanosciences de Paris (INP), Paris, France.
The atomic ratio of Yb and Y ions can be directly deduced from the recorded data. RBS spectra for two samples with 2 at% and 20 at% doping references were registered at two different points for each one (Fig. 1).
The sample holder is attached to a step machine allowing acquiring measurements on several points and even on several samples by one loading. The measurements performed at different locations for each sample illustrate the good homogeneity of the doping distribution. The doping distribution can be directly derived from the spectrum by simply comparing Yb/Y steps. The most convenient way is to model the RBS spectrum with the help of the SIMNRA software, which is calculating the distribution of reflected particles by reflection angle for a given composition. We observe a very satisfying accordance of the SIMNRA simulated RBS spectrum for 2 at% Yb doped YAG crystal (black curve) with experimentally gathered data (Fig. 1). With this technique, for both samples, we obtain respectively 19.3 and 2 at% with associated precisions of 0.2 and 0.1 at%.
2.5 Cross-evaluation of the different techniques
Each of these doping measurement techniques carries its advantages and disadvantages. Point-by-point spatially resolved measuring techniques are connected with somehow larger values of errors and uncertainties. On the other hand, it provides maneuverability, which cannot be offered by volume measurement techniques. Two constant doped samples (here “constant” refers to the fact that no gradient doping scheme was applied during growth) with Yb concentration of 2 at% and 20 at% (these are growth reference values, which corresponds to the amount of Yb concentration in starting material) are tested with almost all techniques. The measurements of constant samples revealed quite similar values for most of the cases. The largest divergence was observed when comparing ICP-MS to other techniques. In Table 1, the results collected for the different doping measurement techniques for 2 at% and 20 at% are presented.
These results give, according to our best knowledge, the most complete cross evaluation of different measurements technique for trivalent Yb ion concentration in YAG matrices. EPMA, EDS and RBS give very close results showing good agreement with the growth reference.
ICPMS leads, for both samples, to underestimated doping values. Also, it is a destructive technique and implies a certain level of technical difficulties to get YAG in soluble forms. These drawbacks make this technique the less favorable for our application.
EDS technique is associated with quite large error bars which can be crucial for precise measurements. Moreover, the rather strong size limitation for the samples to be tested with the available EDS device let us considered this technique also as quite unfavorable for doping gradient measurements.
RBS and EPMA seem to be the most convenient techniques. Unfortunately RBS requires running a large installation with access and time constraints. In contrary, EPMA is a much simpler and faster technique to use and not less accurate. It was ultimately chosen as the most favorable technique for doping measurements.
These results offer the possibility to estimate the absorption cross-section σabs(λ) at 1030 nm. Before absorption measurements our samples were annealed in oxygen atmosphere in order to eliminate Yb2+ ions. Relying on absorption data obtained from 2 at% doped sample, we obtain 9.55 10−22 cm2. Different values for absorption cross-sections can be found in the literature ranging from 9.5 10−22 cm2  to 1.1 10−21 cm2 . In the reference  the authors use 2 at% doped sample and for room temperature they obtain 9.5 10−22 cm2 which is very close to the value obtained for our sample. This value will be used for the absorption cross-section at 1030 nm in order to have access to the doping level through optical absorption technique in future studies. Doping measurements performed with this technique for gradient crystals are explained in [1,2].
Four doping concentration techniques were cross evaluated. These techniques were chosen due to their relevance for this specific application and the availability of the measuring stations. This study could be even more exhaustive by adding techniques like Electron Paramagnetic Resonance or Electron Spin Resonance  for instance, providing that access to such specific apparatus would be granted.
3. Doping ion mapping with EPMA
The idealized case implies that the crystallization front stays always in a plane perpendicular to the growth direction. This is of course idealized case, and in practice, during a growth process, the crystallization front rarely exhibits such orientation. In this section, we will concentrate on experimental post-growth analysis of the front behavior. We indeed acquired a quite complete tridimensional doping level mapping for one of the grown crystal. It provided reliable information about crystallization front orientation. Figure 2 illustrates most common possibilities for crystallization front orientation.
All these cases can be observed by measuring the doping distribution in the relevant direction. The direction X is parallel to the growth direction, i.e. along the desired doping distribution gradient. The existence/absence of any gradient in Y direction is related to a front orientation like displayed on the cases (a) and (b) of Fig. 2. The vertical inclination of the crystallization front can be detected by observing the doping distribution along the Z direction. Several combinations of these cases are theoretically possible and only (c) and (d) cases are mutually exclusive. Tridimensional mapping of the grown boule allows reconstructing the front geometry at any position, i.e. at any moment of the growth process.
The curvature (Fig. 2(a)) of the crystallization front almost always exists with a radius of curvature evolving during the growth. It is nevertheless significant only at the beginning of the boule (triangular part), the end of the boule and more pronounced near the lateral edges (interface between the boule and crucible). The effect of this curvature does not play any major role for gradient doping crystal growth because:
- the starting material is distributed in such a way, that we do not obtain any doping variations in the triangular part,
- the crystal layers near the lateral edges and the tail are discarded.
So, practically speaking, one should not observe any doping variation in Y direction in our extracted samples.
Trivalent Yb ion concentration in all three directions has been measured by the EPMA technique for a 10x10x12 mm3 sample extracted from a gradient-doped boule (Fig. 3). Information on the growth of this boule can be found in [1,2]. Doping distribution in the starting material was 0% and 20% for this boule .
Figure 4(a) gives Yb ion doping distributions along X and Y directions. The measurement along the Y direction clearly indicates that the crystallization front stays parallel to this axis throughout this sample. Figure 4(b) illustrate that the transverse (Y axis) growth front curvature can be observed by eyes. At the central location of the boule where crystals are extracted it indeed appear flat over almost the full crucible width. A 1.2 at%/cm pretty linear gradient is observed along the X axis. The intersection of both set of experimental points reveals that the Y measurements were recorded on a line at an x = 5 mm distance from the edge.
Figure 5(a) illustrates the doping distribution along the Z1 and Z2 axes shown on Fig. 3(b). A non negligible (~0.5 at%/cm) variation is revealed which shall be related to an inclination of the crystallization front.
Considering a linear fit, the generalized doping spatial distribution can be derived as:Eq. (1), the doping value at any point of the sample can be obtained. Figure 5(b) gives a doping distribution map in the Oxz plane. We observe iso-doping curves with a 35° inclination for this 1 cubic centimeter sample. These lines are footprints of the crystallization front.
4. Conclusion and outlook
To our knowledge, a first cross-evaluation of different composition verification methods was performed for Yb:YAG crystals. EPMA is considered to be the most convenient method in the case under study here, i.e. doping mapping of variably doped Yb:YAG crystals. This method was used to find 3D doping values in Bagdasarov grown variably doped Yb:YAG crystal and to define iso-doping planes. This allows obtaining information about growth kinetics and can serve as an excellent post-growth diagnostics together with crystallo-physical methods, such as growth velocity junctions, which permits to “freeze” a trace of growth front position at the moment of junction. In the 3rd direction, no significant difference in doping values confirms that, in the part of the crucible where crystals are extracted, the growth front stays flat.
The authors gratefully acknowledge the support the Délégation Générale à l’Armement of the Ministry of Defense of France and of the Ministry of Education, Youth and Sports of the Czech Republic in supporting this work through the HiPER  program. Authors also express their gratitude to I. Vickridge (Institut des NanoSciences de Paris, France), J.-C. Devidal (Laboratoire Magmas et Volcans, Clermont-Ferrand, France), E. Douville (Laboratoire des Sciences du Climat et de l'Environnement, Gif-sur-Yvette, France) and V. Kuzanyan (Laboratory of High Temperature Superconductivity, Institute for Physical Research, Ashtarak, Armenia) for providing access to respectively RBS, EPMA, ICP-MS and EDX apparatus.
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