Picosecond Ultrasonics for Studying Elastic Modulus of Polycrystalline Chromium Nanofilms: Thickness Dependence and Stiffness Enhancement

Abstract

Accurate measurement of elastic constants in thin films is still an important issue to understand the scale behavior of nanosized materials. In the present study, we introduced an advanced non-destructive method, picosecond ultrasonics (PU), for measuring the out-of-plane elastic modulus of thin chromium (Cr) films. The femtosecond light pulse is focused on the Cr film to excite the longitudinal acoustic phonons (LAP), which propagate along the thickness direction and repeat reflections inside the Cr film. Then, the propagation/distribution of LAP is detected by the time-delayed probe light pulse through the photoelastic effect. Therefore, we can determine the out-of-plane modulus by measuring the periodic pulse echoes or the breathing mode vibrations within the Cr film. For most Cr films, the determined modulus is smaller than the corresponding bulk value and decreases with the decreasing thickness, while for some Cr films, it closes and may exceed the bulk value. This work describes the thickness-dependent elasticity of thin Cr films and provides evidence of the stiffness enhancement in Cr films on the Si substrate. In addition, since LAP with central frequency up to 310 GHz is excited in Cr films on the SiO₂ substrate, we also demonstrate the potential of Cr films as high-frequency photoacoustic transducers.

1. Introduction

Chromium (Cr) films are widely used in various engineering applications as an adhesive layer [1], thermal diffusion barrier [2], solar absorber [3], and plasmonic sensor [4]. It is generally known that the properties of thin films are different from those of bulk materials. Many scientists have studied the structural variation, morphological variation, optical constants, and electrical properties of Cr films using a series of testing techniques such as X-ray diffraction (XRD) [1,2,5], scanning electron microscope (SEM) [1,4], and atomic force microscopy (AFM) [3]. As we know, few studies about the elasticity of Cr films have been reported to date. Notably, Nilsson et al. [6] calculated Young’s modulus of thin chromium cantilevers based on its bending behavior obtained with AFM. However, the above measurement always involves ambiguous effects caused by the gripping condition or nanocrystalline structure of the cantilevers. An alternative route to measure the elastic modulus of thin films is picosecond ultrasonics (PU), an advanced non-destructive testing technique based on the ultrafast laser pump–probe method [7,8]. Different from XRD, SEM or AFM, PU is based on the time-resolved photoacoustic signals and provides a deeper acoustic penetration than the optical absorption depth.

Various metal films, including Al [9,10,11], Au [12,13], Pt [14,15,16], Ni [17,18], and Cr [18,19], have been proven suitable for PU to generate and detect longitudinal acoustic phonons (LAP), which travels and repeat reflections along the film’s thickness direction. Based on the film thickness and the measured round trip time of LAP, we can determine the sound velocity related to the out-of-plane elastic modulus [20]. Among the above metals, the Pt, Ni, and Cr [18] have strong electron–phonon coupling constants and their thermal diffusion is typically confined to the optical absorption depth, resulting in ultrashort pulses of LAP; therefore, such metals are considered candidates for high-frequency photoacoustic transducers. Previous studies have shown that Pt [15] and Ni [17] can generate LAP with central frequency up to hundreds of gigahertz (GHz). For thin metal films, the out-of-plane elastic modulus can also be determined by the breathing mode central frequency of non-propagating LAP trapped in the film [16,20].

In this work, we present a systematic study on the measurement of elastic constant in Cr nanofilms using a two-color femtosecond laser pump–probe method. Four groups of polycrystalline Cr films (<200 nm) are deposited onto Si and SiO₂ substrates as experimental samples. By utilizing the femtosecond light pulses, we excite and detect the typical acoustics signals in thin Cr films, including the periodic pulse echoes [18] and the breathing mode vibrations. With the detected round-trip time or breathing mode frequency, we determine the out-of-plane elastic modulus of thin Cr films. We investigated the thickness dependence, the softening effect and stiffening behavior of elasticity in thin Cr films. We also demonstrated the potential of thin Cr films as high-frequency photoacoustic transducers.

2. Materials and Methods

2.1. Sample Preparation

To ensure the universality of our research results, we prepare polycrystalline Cr films synthesized using two different physical deposition techniques on two different substrates. The first two groups of Cr films with thicknesses of 20 to 200 nm were sputtered onto Si and SiO₂ substrates using magnetron sputtering (MS). The base pressure was 7.5 × 10⁻⁷ Torr, the deposition chamber pressure was maintained at 1.5 × 10⁻² Torr of Ar, and the sputter power was set at 60 W. The sputter rate was about 2.0 Å/and we changed the film thickness by controlling the sputter time.

For Cr films sputtered at 100 s, the cross-section image using SEM (ZEISS Gemini SEM 500, Oberkochen, Germany) in Figure 1a shows the thickness is around 18.55 nm, and the film thickness fitted using an ellipsometer in Figure 1b (Eoptics Technology Co., Wuhan, China) is approx. 19.87 nm. Therefore, we estimated the thickness of Cr film sputtered at about 100 s is approximately 20 nm. In Figure 1c, we also show an AFM (Olympus LEXT 4100 OLS, SPM mode, Tokyo, Japan) image of the Cr film sputtered at 100 s on the Si substrate. From the AFM images, we find that the root means square (RMS) surface roughness values are 1.163, 1.209 and 1.960 for the 20, 30, and 50 nm Cr films sputtered on the Si substrate, respectively. We also took AFM images of the glass substrate and obtained the RMS roughness values of 1.118, 1.148, and 1.517 nm for the 20, 30, and 50 nm Cr films, respectively.

The second two groups of Cr films with a thickness of 8 to 200 nm were vaporized onto the Si and SiO₂ substrates using an electron beam (EB) created by H-Chip Tech Group (Tianjin, China). Their chamber pressure was maintained at 5 × 10⁻⁶ Torr and the vaporization rate was about 0.5 Å/s.

2.2. Picosecond Ultrasonics Method

2.2.1. Experimental Setup

A typical time-resolved femtosecond laser pump−probe experiment setup was employed for the PU measurements of Cr films [19]. A mode-locked Ti:sapphire pulsed laser (Vitara-T, Coherent Inc., Santa Clara, CA, USA) was used to generate light pulses with a wavelength of 800 nm and duration of 20 fs at a repetition rate of 80 MHz. A two-color scheme was employed to enhance the signal-to-noise ratio of the experiment setup to ∼10⁻⁷. The laser beam was divided into the pump beam and the probe beam by a polarizing beam splitter and a half wave plate with an intensity ratio of 10:1. The pump beam was first focused onto a nonlinear BiB₃O₆ crystal to change the wavelength to 400 nm by the second harmonic generation, and then modulated at a reference frequency of 1 MHz using an electro optic modulator (Model 25A + 370-01, Conoptics Inc., Danbury, CT, USA) and a function generator (33509B, Keysight Technologies, Colorado Springs, CO, USA). The probe beam with a wavelength of 800 nm entered a variable optical delay path, a combination of two retroreflective mirrors mounted on a motorized linear stage (LTS300/M, Thorlabs Inc., Newton, NJ, USA). Both the probe beam and the pump beam were coaxially focused at vertical incidence to the sample using a cold mirror and a 10× objective lens. The diameter of the pump and probe beam is 90 and 30 µm (1/e² diameter for intensity), respectively. The intensity of the reflected probe beam was converted to voltage signals and recorded by a Si amplified fixed-gain photodiode detector (PDA36A2, Thorlabs Inc., Newton, NJ, USA). Lock-in detection using a lock-in amplifier (SRS844, Stanford Research Systems, Sunnyvale, CA, USA) at the reference frequency of 1 MHz allows relative reflectivity change $\mathit{\Delta }R/R$ ∼ 10⁻⁷ to be extracted. The parameters of the lock-in detection were fixed in the measurement procedure. Therefore, the sampling speed was dependent on the movement of the motorized linear stage and configured to have a time step of 0.25 ps/pt in this study.

2.2.2. Measurement Theory

In the PU measurements discussed below, the metal film in the sample is used as a photoacoustic transducer to generate and detect high frequency LAP in the femtosecond pump–probe experiment. Once the pump beam enters the metal film, the electrons in the optical absorption depth are excited to higher states by the photons. Then, the hot electrons will diffuse into the metal film interior and heat the lattices through the electron–phonon coupling. The final spatial profile of the LAP is determined by the depth of heated region (that is, thermal diffusion). For metals with weak electron–phonon coupling such as Au [12,13] or Al [9,10,11,21], the depth of thermal diffusion can be up to ~100 nm and the corresponding frequency of LAP is ~10 GHz. In the case of metals with strong electron–phonon coupling, the depth of thermal diffusion is relatively small, usually in the order of the optical absorption depth. For example, for a vertical incident pump beam at 415 nm, the depth of thermal diffusion in sputtered Cr films is about 15 nm [18]. In addition, when the metal film is thin enough, the depth of thermal diffusion is also limited by the film thickness of thin film. Therefore, the relatively short diffusion depths allow the excitation of much higher-frequency LAP > 100 GHz.

For the PU measurement, the reflected probe beam monitors the relative reflectivity change $\mathit{\Delta }R/R$ of the metal film transducer, including the LAP disturbance as acoustic signals and temperature change as thermal signals. For the analysis of the measured acoustic signals from the Cr films, it is important to separate the slow decaying thermal signal caused by the thermal diffusion. In this study, we removed the thermal signals by subtracting an exponentially decaying function from the data [22]. By solving Maxwell’s equations inside the metal film [7], the acoustic signals in the reflectivity change can be expressed as

$$\mathit{\Delta }R\left(t\right)={{\displaystyle \int }}_0^{\infty }f\left(z\right){\eta }_{zz}\left(z,t\right)dz,$$

(1)

where

$$f\left(z\right)=f_0\left[\frac{\partial n}{\partial {\eta }_{zz}}\mathit{sin}(\frac{4\pi nz}{\lambda }-\phi )+\frac{\partial \kappa }{\partial {\eta }_{zz}}\mathit{cos}(\frac{4\pi nz}{\lambda }-\phi )\right]\mathit{exp}(-\frac{z}{\xi }),$$

(2)

$$f_0=16\frac{\pi {\left[n^2{(n^2+{\kappa }^2-1)}^2+k^2{(n^2+{\kappa }^2+1)}^2\right]}^{1/2}}{\lambda {\left[{(n+1)}^2+{\kappa }^2\right]}^2},$$

(3)

$$\mathit{tan}\phi =\frac{\kappa \left(n^2+{\kappa }^2+1\right)}{n\left(n^2+{\kappa }^2-1\right)}.$$

(4)

In Equations (1)−(4), the $f\left(z\right)$ was defined as “sensitivity function”, which determines how the LAP at different depths below the film surface contributes to the reflectivity change $\mathit{\Delta }R\left(t\right)$, $\lambda$ is the wavelength of probe beam, $n$ and $\kappa$ are the real and imaginary components of the complex refractive index of film, ${\eta }_{zz}$ is the only nonzero component of the elastic strain tensor, $\xi$ is the optical absorption depth, and $\phi$ is the arbitrary phase in the range of 0 to π/2 [7].

2.2.3. Typical Acoustic Signals

Figure 2 shows the two kinds of typical acoustic signals and corresponding Fourier spectra of the first two groups of Cr films sputtered on the Si and SiO₂ substrates with MS. When the thickness of Cr films exceeds 60 nm, LAP are excited at a limited depth determined by thermal and nonequilibrium electron diffusion [18], propagate along the thickness direction, and repeat reflections between the film and the substrate surfaces. Considering that both the pump and probe beam diameters are much larger than the film thickness, a quasi-one-dimensional assumption was adopted for the propagation and reflection of LAP [7]. Therefore, several equally spaced echoes were observed in the acoustic signals of 100 nm Cr film (Figure 2a). Using the round-trip time between the successive echoes, the sound velocity can be expressed as

$$v=2d/t,$$

(5)

where d is the film thickness.

For thin Cr films (d ≤ 60 nm), we observe a rapidly decaying oscillation that appears just after the excitation, followed by another oscillation with different frequencies on different substrates (Figure 2b). The latter oscillation, typically identified as the Brillouin oscillation, is caused by the interference between the probe beam reflected at the substrate surface and diffracted by the propagating LAP in the substrate [23,24]. For materials that are transparent at the probe beam wavelength, the PU is originally referred to as picosecond acoustic interferometry and currently called the time–domain Brillouin scattering [23,24]. The corresponding Brillouin frequency is given by

$$f=2n{v}_s/\lambda ,$$

(6)

At vertical incidence, where n, v_s and $\lambda$ are the refractive index of the substrate, the sound velocity of the substrate, and the wavelength of the probe light. Taking standard handbook values, the calculated Brillouin oscillation frequencies are 79 GHz and 22 GHz for Si and SiO₂ substrates, respectively. The values agree with the arrow indicated in Figure 2c,d. In addition, the first peak around 10 GHz in Figure 2c is a false peak generated by the Fourier transform of signals in limited sampling time. Once we extend the time length of signals to 100 ps or more, the false peak will disappear.

The former oscillation, considered breathing mode vibrations [19], is caused by the non-propagating LAP trapped in the film. The LAP was induced by the uniform optical excitation of the thin film. Since the acoustic impedance $z=\rho v$ of the film is larger than that of the substrate, the sound velocity is given by

$$v=2df,$$

(7)

where d and f are the film thickness and breathing mode frequency [16,22]. It has been shown that thin Cr films on the Si substrate in Figure 2c have broader peaks than the SiO₂ substrate in Figure 2d, which is in accordance with the fact that the acoustic impedance mismatch of Cr-Si is larger than that of Cr-SiO₂.

As stated above, we showed the two typical acoustic signals: periodic pulse echoes in Figure 2a and breathing mode vibrations in Figure 2b, and we obtained the sound velocity by the round trip time or breathing mode frequency. Using the mass density ρ and the determined sound velocity v, we can calculate the out-of-plane elastic modulus as follows:

$$C_{33}=\rho v^2.$$

(8)

For the present calculation, we set the bulk value of ~7.2 g/cm³ [25] for the density ρ of Cr films.

3. Results

Figure 3 shows different breathing mode vibrations, corresponding Fourier spectra, and out-of-plane elastic modulus C₃₃ of Cr films vaporized on the SiO₂ substrate by EB. As shown in Figure 3a,b, the frequency of breathing mode is increased with the decrease of the film thickness. For the 8 nm Cr film, we generated LAP with the central frequency up to 310 GHz, whereas no breathing mode vibrations signals found in thinner Cr films on the SiO₂ substrate. Additionally, there are no photoacoustic signals in PU measurements of the vaporized Cr films on the Si substrate. Therefore, the result of vaporized Cr films on the Si substrate are not shown in Figure 3 and reported in this study.

Figure 3c show that the out-of-plane elastic modulus C₃₃ decrease with the decrease of the film thickness due to the thin-film softening effect, which has been reported in thin films of Au [12], Ni [17], and Ru [22]. For comparison, we calculated the elastic modulus along the <110> directions using the known C_ij of monocrystal Cr by $C_{\langle 110\rangle }=\left(C_{11}+C_{12}+2C_{44}\right)/2$ [26]. It has been reported that polycrystalline films made from fcc materials, like Cr [5], Pt [15] and Fe [16], have the preferred <110> crystallographic direction in the film thickness direction. Therefore, the $C_{\langle 110\rangle }$ is the ideal C₃₃ of bulk Cr, and the maximum value for C₃₃.

Figure 4 shows the out-of-plane elastic modulus C₃₃ of the first two groups of Cr films deposited sputtered on the Si substrate and SiO₂ substrates by MS. The trend like the thin-film softening effect in Figure 3c is observed in both Figure 4a,b that C₃₃ of Cr films first maintain a stable value in the range of 80 to 200 nm, and then decrease with the decrease of the film thickness in the range of 50 to 80 nm, regardless of the substrate materials. However, when the film thickness is smaller than 50 nm, C₃₃ of Cr films on the Si substrate in Figure 4a start to increase with the decrease of the film thickness, finally close and may exceeds the maximum $C_{\langle 110\rangle }$. In contrast, C₃₃ of Cr films on the SiO₂ substrate still smaller than the ideal value of bulk Cr in Figure 4b.

4. Discussion

As a transition metal with strong electron–phonon coupling, it has been investigated in 190 nm Cr film [18] that the relatively short diffusion depth governed by both thermal and nonequilibrium electron diffusion allows the excitation of high-frequency LAP; therefore, such Cr has potential as an ultrasonics transducer at frequencies >100 GHz. As shown in Figure 2a,b, the thinner thickness of Cr films results in the shorter diffusion depth and allows the excitation of higher-frequency LAP. It can be seen in Figure 1 and Figure 2b,c that the corresponding central frequency ranges from 50 to 310 GHz. The 20 nm and 10 nm Al films have been used as the photoacoustic transducer to generate 50 GHz and 100 GHz LAP [11], respectively. Here, our results in Figure 3b demonstrate that Cr films vaporized using EB can generate higher-frequency LAP at a thickness similar to that of Al films. This provides an alternative choice of the photoacoustic transducer for studying the attenuation of LAP in the GHz regime.

Based on periodic pulse echoes in Figure 2a and breathing mode vibrations in Figure 2b, we obtained the thickness dependence of C₃₃ of three groups of Cr films in Figure 3c and Figure 4a,b. It can be seen that most Cr films have a stable elasticity with values slightly smaller than the corresponding bulk value, which is consistent with the fact that thin films are softer than bulk materials. The softening trend of C₃₃ is observed for vaporized Cr films ranging from 8 to 50 nm in Figure 3c and sputtered Cr films ranging from 50 to 80 nm in Figure 4a,b. Since there are many mechanisms for the softening effect, including defects such as incohesive bonds, oriented nano-cracks, precipitates at grain boundaries, and interfacial strain, etc., it is difficult to identify the specific cause of the softening Cr films. The comparison between Figure 4a,b helps us to exclude the influence of substrate material on the softening trend of sputtered Cr film ranging from 50 to 200 nm.

Nilsson et al. reported Young’s modulus of 50, 68, and 83 nm thick Cr cantilevers measured using an AFM in contact mode [6]. Compared with our results, the reported Young’s modulus of Cr cantilevers is much smaller, which may be attributed to the decrease in Young’s modulus to the gripping condition [20], materials properties of the cantilevers, or the invalid equation for such nanosized beams, according to the authors of [6]. Nevertheless, similar softening trends were both observed in the sputtered Cr films in Figure 4a,b and Cr cantilevers [6] ranging from 50 to 83 nm. These trends may be helpful for us to further investigate the softening law of nano-sized chromium. Therefore, we can conclude that PU, as a non-destructive testing technique of elastic parameters, is competitive with the mechanical method using Cr cantilevers with an AFM in contact mode.

In addition, compared with sputtered Cr films on the SiO₂ substrate in Figure 4b, we observe the stiffness enhancement in Figure 4a, as the Cr film on the Si substrate gradually stiffens with decreasing thickness ranging from 20 to 50 nm, and the increasing C₃₃ finally may exceed its maximum value at 20 nm thickness. The stiffness enhancement in thin films on the Si substrate is rarely reported, which is attributed to strain-induced changes in third-order elasticity in thin Pt films [15]. The previous study of Ogi, H et al. [16] also reported the influence of substrate materials on the elasticity of thin Pt films. Comparing the Si and glass substrates, Ogi, H. et al. reported that the huge intrinsic stress inside the thin film and the low strength of the SiO₂ substrate may cause the local failure and softer elasticity of thin films on the SiO₂ substrate. This comparison is in accordance with our results in Figure 4a,b.

As discussed above, the out-of-plane elastic modulus of Cr films is affected by the film thickness, the deposition technique, and the substrate material. For the sputtered Cr films with a sputtering time of less than 100 s, there is no typical photoacoustic signal in PU measurements. To date, we attribute it to the existence of an island microstructure instead of a continuous structure in thinner sputtered Cr films. Further investigation of the effect of a microstructure on the generation of LAP should be considered.

5. Conclusions

In conclusion, we demonstrated the potential of Cr nanofilms as high-frequency photoacoustic transducers and systematically studied the thickness dependence of their out-of-plane elastic modulus C₃₃ by PU measurements. The LAP with central frequency that ranges from 50 to 310 GHz are excited and detected in vaporized and sputtered Cr films with different thicknesses. The elastic modulus is smaller than the monocrystal Cr for most samples; however, it is may exceed the maxima of bulk value at the 20 nm sputtered Cr film on the Si substrate. This work offers guidance for Cr nanofilms as GHz photoacoustic transducers in the laser ultrasonics application and the design of film–substrate structures in nanomechanical devices.