Ultrafast laser-induced strain waves in thin ruthenium layers

G. de Haan; G. de Haan; T. J. van den Hooven; T. J. van den Hooven; P. C. M. Planken; P. C. M. Planken

doi:10.1364/OE.438286

Optics Express
Vol. 29,
Issue 20,
pp. 32051-32067
(2021)
•https://doi.org/10.1364/OE.438286

Ultrafast laser-induced strain waves in thin ruthenium layers

G. de Haan, T. J. van den Hooven, and P. C. M. Planken

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G. de Haan, T. J. van den Hooven, and P. C. M. Planken, "Ultrafast laser-induced strain waves in thin ruthenium layers," Opt. Express 29, 32051-32067 (2021)

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- Ultrafast Optics and Attosecond/High-field Physics
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About this Article
History
- Original Manuscript: July 21, 2021
- Revised Manuscript: September 1, 2021
- Manuscript Accepted: September 10, 2021
- Published: September 21, 2021

Abstract

We report on the time-dependent optical diffraction from ultra-high frequency laser-induced acoustic waves in thin layers of ruthenium deposited on glass substrates. We show that the thermo-optic and strain-optic effects dominate the optical response of Ru layers to a traveling longitudinal strain wave. In addition, we show the generation and detection of acoustic waves with a central frequency ranging from 130 GHz to 750 GHz on ultra-thin layers with thicknesses in the range of 1.2 - 20 nm. For these ultra-thin layers we measure a strong dependency of the speed of sound on the layer thickness and, thus, the frequency. This frequency-dependent speed of sound results in a frequency-dependent acoustic impedance mismatch between the ruthenium and the glass substrate, leading to a faster decay of the measured signals for increasing frequency. Furthermore, for these extremely high-frequency oscillations, we find that the frequency and phase remain constant for times longer than about 2 ps after optical excitation. Back extrapolation of the acquired acoustic signals to t = 0 gives a starting phase of −π/2. As this seems unlikely, we interpret this as an indication of possible dynamic changes in the phase/frequency of the acoustic wave in the first 2 ps after excitation.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Fig. 1. Schematic drawing of the setup used in our experiments. The output of a 1 kHz repetition rate regenerative amplified Ti:Sapphire laser is split into a pump beam and a probe beam. The pump first travels through an optical delay line after which the optical frequency is doubled using a BBO crystal. Afterward, the pump is optically chopped to reduce the repetition rate by 50%. The pump is split into two beams. These two pump beams overlap in time and, noncollinearly, in space to form an intensity grating on the Ru surface. The probe is sent to an optical parametric amplifier (OPA) set to generate a signal beam with a wavelength of 1300 nm. This beam is subsequently frequency-doubled to create a beam with a central wavelength of 650 nm. Afterward, the probe beam is focused onto the sample in the same spot as the pump pair.

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Fig. 2. AFM images of three Ru layers on glass with thicknesses of 20 nm (a), 5.0 nm (b), and 2.3 nm (c). The RMS surface roughness for these thicknesses is 520 pm, 580 pm, and 460 pm, respectively.

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Fig. 3. Transient-grating pump-induced diffraction efficiency of the 650 nm central wavelength probe beam on a 107 nm Ru layer deposited on glass, as a function of time. The black dashed line is a calculation of the diffraction efficiency induced by a combination of the strain- and thermo-optic effect. This calculation does not include damping of the acoustic wave or partial transmission of the wave into the glass substrate.

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Fig. 4. Calculated diffraction efficiency of only the strain-optic, only the thermo-optic and only the displacement effects. All contributions have been normalized to their respective maximum.

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Fig. 5. Transient-grating pump-induced changes to the diffraction efficiency. (a) The measured diffraction efficiency for 20 nm and 5 nm thick Ru layers on a long timescale. (b) The measured diffraction for multiple layer thicknesses, here the curves have been normalized to their respective electronic peaks and have been given an offset for clarity.

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Fig. 6. (a) Measured diffraction efficiency of multiple layer thicknesses, also shown in Fig. 5(b) but with the thermal background removed. The dashed lines correspond to a fit of a single-frequency, damped sine to the data. (b) The speed of sound extracted from the fit as a function of layer thickness.

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Fig. 7. The red dots show the damping rate versus the frequency of the acoustic wave. The blue dot corresponds to the damping rate acquired for the 1.2 nm thick Ru layer, for which an accurate oscillation frequency could not be determined. The yellow crosses represent the calculated damping rate caused by interface roughness and the dashed line going through the crosses acts as a guide to the eye. The blue triangles represent the calculated damping rate caused by transmission of acoustic energy into the substrate, and again, the dashed line going through the triangles acts as a guide to the eye.

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Fig. 8. Measured pump-power dependence of the diffraction for a 5 nm (a) Ru layer and a 2.3 nm (b) Ru layer. The black dashed lines are single frequency dampened sinusoidal fits to the data, starting from the dashed vertical red line and extrapolated backwards to t = 0.

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Fig. 9. The starting phase and the frequency of the generated acoustic wave, extracted from the fits shown in Fig. 8(a) and (b). Note that for both thicknesses the frequency and phase remain almost constant as a function of pump pulse energy and that the phase equals -

$\pi /2$

for all pump powers.

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Fig. 10. The different steps undertaken to remove the slowly decaying thermal background from the measured signal on the 3.3 nm thick Ru layer. In green, we show the nearest neighbor average of the normalized acoustic-wave-induced diffracted probe signal as a function of pump-probe delay. The red curve shows the exponential fit to the data truncated at the time t = 0.7 ps, indicated by the vertical dashed line. After subtraction of the exponential fit, we end up with the acoustic signal shown in yellow.

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Fig. 11. Electron (a) and lattice (b) temperature as a function of time in the center of a 5 nm thick Ru layer in a bright fringe of the transient grating. The legend shows the total energy of the two incident pump beams which form the transient grating.

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Tables (2)

Table 1. Calculated acoustic impedance of Ru at the different measured acoustic frequencies.

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Table 2. ruthenium material parameters used in the TTM calculations, taken from Ref. [28].

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Equations (10)

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\begin{aligned} C_{e} (T_{e}) \frac{\partial T_{e}}{\partial t} & = \frac{\partial}{\partial z} (k_{e} (T_{e}, T_{l}) \frac{\partial T_{e}}{\partial z}) - g (T_{e} - T_{l}) + S (z, t), \\ C_{l} \frac{\partial T_{l}}{\partial t} & = g (T_{e} - T_{l}), \end{aligned}

σ_{z}^{t h} (z, t) = - 3 B β Δ T_{l} (z, t),

\begin{aligned} s_{z} (z, t) & = \frac{\partial u (z, t)}{\partial z}, \\ σ_{z} (z, t) & = σ_{s t r} + σ_{z}^{t h} = (λ + 2 μ) s_{z} (z, t) - 3 B β Δ T_{l} (z, t), \\ ρ \frac{\partial^{2} u (z, t)}{\partial t^{2}} & = \frac{\partial σ_{z} (z, t)}{\partial z}, \end{aligned}

η_{d i s p} = {| i r k_{z} h_{0} (t) |}^{2} \propto {| k_{z} \int_{0}^{L} s_{z} (z, t) d z |}^{2},

η_{s t r} = {| δ r_{s t r} |}^{2} \propto {| k_{s t r} \int_{0}^{L} \exp (2 i k_{z} n z - \frac{2 z}{d_{p}}) s (z, t) d z |}^{2},

η_{t h} = {| δ r_{t h} |}^{2} \propto {| k_{t h} \int_{0}^{L} \exp (2 i k_{z} n z - \frac{2 z}{d_{p}}) Δ T (z, t) d z |}^{2},

η_{t o t} \propto {| i r k_{z} h_{0} (t) + δ r_{s t r} + δ r_{t h} |}^{2},

R (f) = {(\frac{Z_{R u} (f) - Z_{s u b}}{Z_{R u} (f) + Z_{s u b}})}^{2},

σ_{e} = γ_{e} Δ E_{e},

f (t) = a e^{b (t - c)} + d,

Frequency (GHz)	131	421	564	659	693
$Z_{R u} (10^{6} N s / m^{3})$	64.4	52.5	46.4	37.7	31.1

Parameter	Value
$A_{e} ({Jm}^{- 3} K^{- 2})$	385
$k_{0} ({Wm}^{- 1} K^{- 1})$	117
$g (10^{16} {Wm}^{- 3} K^{- 1})$	185
$C_{l} (10^{6} {Jm}^{- 3} K^{- 1})$	2.95

Frequency (GHz)	131	421	564	659	693
$Z_{R u} (10^{6} N s / m^{3})$	64.4	52.5	46.4	37.7	31.1

Parameter	Value
$A_{e} ({Jm}^{- 3} K^{- 2})$	385
$k_{0} ({Wm}^{- 1} K^{- 1})$	117
$g (10^{16} {Wm}^{- 3} K^{- 1})$	185
$C_{l} (10^{6} {Jm}^{- 3} K^{- 1})$	2.95

Abstract

Data availability

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Figures (11)

Tables (2)

Equations (10)

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