Simultaneous determination of the thermal diffusivity and a drum factor for CdBeMnTe crystals with the photoacoustic method
Introduction
Diluted magnetic semiconductors (DMS) are materials with magnetic ions implemented into the crystal structure. These materials are interesting because of a potential application in optoelectronics and spintronics [1]. DMS based on mixed crystals of II–VI compounds with the manganese are very promising materials for spintronics due to unique magneto-optical properties [2]. In the case of a quaternary diluted magnetic semiconductor the magnetic properties do not change with the variation of lattice parameters when the second non magnetic component of the alloy is incorporated. Very interesting are tellurium based II–VI compounds with a partial cationic substitution by Be atoms. Beryllium as a component, improves material properties inducing noticeable lattice strengthening because of a dominant covalent bonding and a high cohesive energy of BeSe or BeTe. Photothermal methods have been widely applied to estimate thermal or transport properties of solid samples using contact photopyroelectric method [3], [4], [5], [6] and noncontact methods such photothermal infrared radiometry [7], [8], [9] and photoacoustic spectroscopy [10], [11], [12]. Thermal diffusivity is one of the basic thermal parameters used in photoacoustics. Correctness of its determination influences calculations of other parameters which can be extracted from photoacoustic experiments [13], [14]. Thermal diffusivity can be determined from the frequency dependence of the amplitude or phase of the photoacoustic signal as it depends on the thermal diffusion length μ of the thermal wave which is a function of the thermal diffusivity and the frequency of modulation of the intensity of light illuminating the sample, see Formula (5). The presence of the temperature gradient is the reason of the bending of the sample what is called a Drum effect which has been described elsewhere [15], [16], [17]. This effect causes additional contribution to the photoacoustic signal which cannot be neglected and must be taken into account in calculations. The Sf/Sr and Phase-Lag methods are very practical for determination of the thermal diffusivity as they do not depend on the experimental apparatus frequency characteristics. In other methods the experimental apparatus characteristics must be measured in the independent experiments. Sf means the amplitude of the photoacoustic signal in the front experimental configuration called in some papers the reflection configuration. Sr means the amplitude of the photoacoustic signal in the rear experimental configuration called in some papers the transmission configuration. They were applied for determination of the changes of the thermal diffusivity with the composition of the mixed crystals SixGe1−x [18]. For thermally thin samples the drum effect can be neglected. For thermally thick samples this effect must be however considered. The sample is thermally thin or thick when the diffusion length μ of the thermal wave is bigger or smaller than the thickness d of the sample respectively. This paper shows that for thermally thick samples it is possible to determine values of the thermal diffusivity and a drum factor from the simultaneous fitting of the theoretical Sf/Sr and Phase-Lag frequency characteristics to the experimental ones.
Section snippets
Materials
Mixed Cd1−x−yBexMnTe crystals have been obtained by the high pressure Bridgman method under an argon overpressure of 11 MPa. The intentional beryllium content ranged from 0.00 up to 0.15, whereas the manganese content was 0.10 for all investigated samples. Produced crystal rods were cut perpendicular to the growth axis into about 1 mm thick plates and ground with a standard grounding powder (10 μm). Next samples were polished using Al2O3 polishing powder (1 μm) until obtained surface was of a good
Experimental results and discussion
The experimental and theoretical Sf/Sr and Phase-Lag photoacoustic frequency characteristics of the CdTe sample are presented in Fig. 8, Fig. 9.
Thermal diffusivity and a drum factor values have been obtained from the best fit of the theoretical characteristics to experimental data and were: α = 0.0515 cm2/s, B = 0.565 cm−1. The literature values of thermal diffusivity for CdTe crystals met in the literature differ considerably. They change from 0.03 cm2/s through 0.05 cm2/s [21], to the value 0.0515 cm2
Conclusions
The experiments and numerical analysis performed and presented in this paper indicate that it is possible to simultaneously determine both the thermal diffusivity and the drum factor B from the Sf/Sr and Phase-Lag characteristics. It is possible even for thermally thick samples. For CdBeMnTe samples the increase of the of Be content from x = 0.00 to x = 0.15 resulted in four times decrease of the value of the thermal diffusivity. Thermal diffusivity of CdTe crystal agrees with the values met in the
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