Physica B 263—264 (1999) 730—732
Nonequilibrium acoustic phonons in diamond: generation, scattering, reflection T.I. Galkina*, A.I. Sharkov, A.Yu. Klokov, R.A. Khmelnitskii, V.A. Dravin, A.A. Gippius Solid State Department, P.N. Lebedev Physical Institute RAS, Leninskii pr. C53, 117924 Moscow, Russia
Abstract A heated thin gold film as a generator of nonequilibrium phonons in diamond was studied both theoretically and experimentally. The cooling times q of the film obtained theoretically are of the order of experimental bolometric ! response widths. Since q 'q (time of phonon ballistic propagation in the sample under study), the “gold” phonon ! generator proved to be inadequate. A novel method of phonon generation is proposed — photoexcitation of buried implanted layer that allowed us to resolve the arrival of LA and TA phonons. Comparison of the heat pulses observed with those calculated by the Monte Carlo method yields the constant of elastic phonon scattering A "2;10\ s\, 1!2 which coincides with that calculated by taking into account scattering only by the isotopes C. 1999 Elsevier Science B.V. All rights reserved. Keywords: Diamond; Implanted amorphized layer
1. Introduction Diamond still remains a rather exotic material. However, it is obvious that its unique high thermal conductivity inevitably will find applications. From the viewpoint of fundamental physics — diamond is an exclusively isotopically pure material (99% of the main isotope). Nonetheless, the information on the microscopical behavior of phonons in diamond is practically absent. It is the heat-pulse technique that can yield these parameters. The optical excita-
* Corresponding author. Fax: #7-95-135-2408; e-mail: [email protected]
tion of phonons in diamond is rather sophisticated. Hence, the aim of this work was to elaborate an adequate phonon generator and then, to determine a value of the phonon elastic scattering constant.
2. Experimental results and discussion Nonequilibrium acoustic phonons were generated in the sample as a result of pulsed excitation. The phonons propagated along the sample were absorbed in a detector. The detector response when resolved in time allows one to judge the features of phonon propagation. The nitrogen laser (j" 337 nm, E"6.2 lJ, t"7.5 ns) was used as an
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 2 7 7 - 0
T.I. Galkina et al. / Physica B 263–264 (1999) 730–732
Fig. 1. Normalized bolometric responses for diamond as a function of the incident energy density P: 1 — 0.15; 2 — 0.30; 3 — 0.40; 4 — 0.70 mJ/mm.
excitation source. A thin film superconducting bolometer based on granular aluminum was used as a detector at ¹"1.4 K (see insert in Fig. 1). First, the possibility of using thin gold films deposited onto the sample and heated by laser pulse as a generator of acoustic phonons was studied. The specific feature of our experiment was a small thickness of diamond samples (0.4—0.8 mm). One can see that in this case (Fig. 1) the heat pulses had large duration and, in addition, a significant dependence of the heat pulse width on the excitation energy was observed: e.g., 35 ns for P" 0.15 lJ/mm and 240 ns for P"0.7 lJ/mm. Two factors can explain physically this phenomenon: 1. The gold film has been cooling for a rather long time: a numerical solution of the nonlinear system of thermal conductivity equations with account of temperature dependence of thermal conductivity coefficient, specific heat and boundary resistance (for Au and diamond) showed that the film cooling time is &150 ns and weakly depends on the excitation level in the range 0.15—0.7 lJ/mm (Fig. 2). It was supposed that the gold film is in vacuum which corresponds to the well-known fact — formation of a bubble of the gaseous helium onto the excited surface. Hence, the calculations were almost consistent with the experimental conditions.
Fig. 2. Dependence of the mean temperature on time for a gold film (diamond sample as a substrate) under pulsed excitation. Excitation energy density, mJ/mm: 0.15 (1), 0.30 (2), 0.40 (3), 0.70 (4).
2. A diamond is rather defective. Experimentally observed broadening of the response with the increase of excitation level can be explained by increasing the film temperature  and, consequently, frequencies of phonons emitted by a gold film into the diamond — more high-frequency phonons are scattered more intensively. The comparison of experimental responses with those calculated by the Monte Carlo simulation  showed that the phonon scattering rate should be approximately 150 times larger than for phonons scattering by isotopes only. Thus, the results presented in Fig. 1 cannot be unambiguously explained, and a large duration of the responses observed allows us to conclude that the use of the phonon generator based on the Au film is inadequate for diamond in our experimental conditions. A novel phonon generator was proposed to exclude the problems of metal/diamond interface. Implantation of He> ions into a diamond sample was performed . An amorphized layer (thickness 150 nm) was produced at a depth of 700 nm. This layer absorbs the laser light and emits phonons. The experimental response in Fig. 3 corresponds to phonon propagation in the diamond of IIa-type (thickness 0.7 mm). It is seen that LA phonons arrive at the bolometer with the time-delay (37 ns) consistent with their velocity (18 lm/ns) for [1 1 0]
T.I. Galkina et al. / Physica B 263–264 (1999) 730–732
Fig. 3. Bolometric response for diamond, when the photoexcited buried implanted layer serves as a phonon source. Dashed lines are the Monte Carlo simulation responses with variation of A : 1;10\ for the left curve, 2;10\ for the middle, and 1!2 4;10\ s\ for the right one.
direction. The TA peak is well resolved. The response widths (25—30 ns) were comparable with excitation pulse duration and were independent of the response shape of the excitation energy (as opposed to Fig. 1). These facts are evidence for a perfect acoustic match of the implanted layer with the host lattice of diamond and nonthermal character of phonon generation. The results of Monte Carlo simulation of phonon propagation are presented in Fig. 3. The values of the phonon decay constant obtained in Ref.  were taken into account. We have used in the Monte Carlo simulation the assumption on the initial phonon frequency 20 THz (according to Orbach’s model, which is valid in the case of photoexcitation). However, it is not sufficiently justified due to the fact that the absorption
mechanism in the amorphized diamond as well as the processes of phonon emission and conversion in amorphized media are not yet clear. The fit of experimental and calculated (suggesting scattering only by isotopes) responses means that in this case phonon scattering by impurities is negligible, and A is equal to 2;10\ s\. 1!2 In the inset of Fig. 3 the response of a “thick” (1.7 mm) diamond sample is shown to demonstrate the better resolution. Preliminary experiments in the “reflection” geometry showed that there are no characteristic sharp peaks for “reflection” geometry, and the fit of calculated responses with experimental results allows us to conclude that the interface diamond—liquid helium is almost transparent for phonons.
Acknowledgements This work was supported by the Russian Foundation for Basic Research, project no. 98-02-16892.
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