Probing buried interfaces in SiO x N y thin films via ultrafast acoustics: the role transducing layer thickness

. Probing buried interfaces in thin films is a crucial task in many fields, including optical coating. Ultrafast acoustics provide a means to characterize the interfaces by using an acoustic wave localized on the nanometer scale. We provide a brief overview of our thorough study of the interface between SiO x N y thin films and Si substrate by using both single-color and broadband picosecond acoustics. The experiment allows us to track the effect of stoichiometry on the acoustics wave propagation and transition over the layer-substrate interface. To optimize the experiment, we also created simulations to study the effect of optoacoustic layer thickness. We show that the used Ti layer features an optimum thickness between 5-10 nm to reveal details of the interface properties.


Introduction
Interfaces are crucial components in many applications, including high-quality thin films for optics or laser applications.Controlling the thin film interface and its morphology is essential with respect to its mechanical and optical properties.However, it is a difficult task since the few nanometer-thin interfaces are typically buried hundreds of nanometers below a surface.
One of the well-known methods to probe buried interfaces is ultrafast acoustics.[1] It is a pump-probe experiment, where an excitation pulse is absorbed in a thin layer, which serves as an optoacoustic transducer.The excitation pulse, therefore, generates an acoustic wave propagating through the stack of thin films.A delayed probe pulse is able to sense the strain-induced changes in the layer refractive indices and thicknesses.As a result, it is possible to track the local properties of materials by using an acoustic wave localized on the nanometer scale.
We present a thorough study of silicon oxynitride thin films with a controlled stoichiometry of samples covering the entire range from Si3N4 up to SiO2.[2] We used ultrafast acoustics to study the properties of layers and their interface with the Si substrate.The optoacoustic response was attained by using a thin Ti layer on the top of the layer as an optoelectronic transducer.
In addition, we studied the effect of varying the transducing layer thickness, which led to a significant variation in the features connected to the layer-substrate interface and photon echo.We used a set of surface Ti layer thicknesses to simulate the optical response, and we demonstrated that the Ti layer thickness of 5-10 nm is the ideal choice to probe the properties of the layer-Si interface.
The simulations were carried out for the cases with and without an interlayer providing a distinct signal.They were also supported by extensive experimental work on the samples with targeted deposition of interlayers.Here we present a very brief selection of the results.

Experimental details
The samples were prepared by using dual ion-beam sputtering (DIBS), as it is described in detail elsewhere.[2] We deposited a set of homogeneous layers of silicon oxynitride SiOxNy with distinct stoichiometry varying from Si3N4 up to SiO2 by introducing a different flow of oxygen.A Ti layer (2 ns and 10 nm) was deposited on the top of the layer.Si wafer served as a substrate.
A fs laser system (230 fs, 100 kHz rep.rate) was used to study ultrafast acoustic response in a pump-probe experiment.A fundamental wavelength (1028 nm) was utilized as a pump.As a probe pulse, we employed both a single color probe at 514 nm, see Fig. 1(a), as well as a white-light supercontinuum probe covering the wavelengths of 480-700 nm, see Fig. 1(b).For all the presented data, the oscillatory signal was promoted by subtracting the multi-exponential decay caused by thermal effects and charge carrier excitation.

Features connected to interfaces
The recorded oscillatory signal consists of Brillouin oscillations from layer (see Fig. 1, delay 10-60 ps), and substrate (see Fig. 1, delays > 70 ps).In addition, we observed a prominent feature connected with the transition of the acoustic wave from the layer into the substrate -see Fig. 1 at delays approx.62 ps marked by an orange arrow.We will denote this as an interface signal.
Such an interface-related feature in the spectra can be induced both by an interlayer or a strain wave propagation across the interface.We carried out a set of experiments where we controlled the interlayer formation to distinguish these two cases.At the same time, we used a simulation described below to track the difference.
The reflected acoustic wave created an echo (see the signal at 125 ps marked by a green arrow), which we will denote as an echo signal.Finally, the back-reflected acoustic wave in the Si substrate can be spotted at 185 ps to reach the layer-substrate interface again.From the experimental data, we were able to extract the variation of the sound velocity with the layer stoichiometry, which is in good agreement with the previously published results on similar layers.[3] We could also observe the effect of layer composition on the features connected with the transition and reflection of acoustic waves between Ti-layer and layer-Si substrates, which is systematically changing with the layer stoichiometry.
Our aim was to optimize the experimental system to track reflections of the strain waves within the material and study the involved interfaces in close detail.

Role of Ti layer thickness
We employed a finite-element method to simulate acoustic wave propagation in the samples.The resulting strain waves were consequently applied in a model based on the thin-film matrix calculation of reflectivity.The model included the effect of strain-induced change in refractive index and strain-induced shift of the interfaces within the sample.[1] The model was able to reproduce well all the oscillatory, interface, and echo signals with notable differences in the interface and echo signal with respect to the Ti layer thickness.
The thin layers of Ti provided sharp interface and echo features, while their prominence was subtle for Ti thickness below 5 nm.On the contrary, Ti layer thickness exceeding 15 nm lead to smeared interface and echo features, where the information about the interface structure is already partly lost.

Conclusions
In conclusion, we created a faithful model of ultrafast acoustics measurements, which reproduces the attained data for silicon oxynitride thin films.
The model allowed us to closely discuss the effect of each parameter, such as interface character or interlayer presence, on the photoacoustic response.By combining the knowledge of the experimental properties and simulations, we could also discuss the limitations of ultrafast acoustics with respect to sensing features in a thin-film stack.

Fig. 1 .
Fig. 1.The pump-probe R/R signal from the sample of Si3N4 layer (624 nm) on Si substrate covered with 10 nm Ti layer to provide a photoacoustic response.(a) Acoustic waves were probed by a single-color probe at 514 nm.(b) Acoustic waves were probed by white-light supercontinuum.Excitation pulses for both were at 1028 nm.Exponential decay components were subtracted from the data in both panels.

Fig. 2 .
Fig. 2. Simulated ultrafast acoustics signal for a simulated strain wave in our samples.The simulations include Si3N4 layer (624 nm) on Si substrate covered with a Ti layer with a thickness varying between 3, 10, and 22 nm.