Profilometry of thin films on rough substrates by Raman spectroscopy

Thin, light-absorbing films attenuate the Raman signal of underlying substrates. In this article, we exploit this phenomenon to develop a contactless thickness profiling method for thin films deposited on rough substrates. We demonstrate this technique by probing profiles of thin amorphous silicon stripes deposited on rough crystalline silicon surfaces, which is a structure exploited in high-efficiency silicon heterojunction solar cells. Our spatially-resolved Raman measurements enable the thickness mapping of amorphous silicon over the whole active area of test solar cells with very high precision; the thickness detection limit is well below 1 nm and the spatial resolution is down to 500 nm, limited only by the optical resolution. We also discuss the wider applicability of this technique for the characterization of thin layers prepared on Raman/photoluminescence-active substrates, as well as its use for single-layer counting in multilayer 2D materials such as graphene, MoS2 and WS2.


Contrast in local reflection
In this part we discuss the role of reflection on the a-Si:H film and the flat c-Si substrate. Since the total reflection of a-Si:H depends on the refraction index n (and therefore on the effective doping level of a-Si:H) and on the thickness of the a-Si:H layer, its evaluation is a complex problem. That is why we have measured reflection directly by detecting reflected laser light intensity (signal at zero Raman shift, see fig. S1).
Figure S1: Intensity of reflected laser light measured across the transition of the flat c-Si wafer and the a-Si:H stripe. The first tens nm of the a-Si:H stripe have lower reflection most probably due to higher roughness of thin silicon layer (may contain microcrystalline silicon fraction). This part was not taken into account. Lines are guides for the eyes only.
The c-Si reflection at 442 nm was calculated from known index of refraction (n = 4.7) to R c = 0.42. The laser reflected light detected on the a-Si:H stripe was 4 % lower in comparison with the c-Si part. It means that the corresponding reflection of the a-Si:H stripe is R a = 0.40. If we apply this correction, the a-Si:H stripe thickness will slightly decrease. For 40 nm thick layer (as measured on the widest a-Si:H stripe) the reflection correction will be less than 1 nm. Since the relative change is roughly 2 % only, we decided to keep the evaluation procedure straightforward and do not take in to account the minor reflection effect.
Moreover we have applied this method on MoO x stripes deposited through the same mask by using thermal evaporation of MoO 3 powder [1] on flat and textured c-Si wafers. In contrast to the a-Si:H stripes, the index of refraction for the MoO x layer and the c-Si substrate is very different (at 442 nm n = 2.3 [2]). Therefore the measured c-Si Raman intensity distinctly depends on the sample reflection. And as the absorption of this film is rather weak, its role will be minimal. This reasoning is well validated by results in figure S2.  Figure S2.b) we can conclude that the stripe reflection is lower, as the MoO x layer serves as an antireflection coating. Thanks to the lower reflectivity more photons enter the c-Si substrate and therefore more Raman photons are created -Raman signal increases. The laser reflection ("Raman" signal at 0 cm -1 ) was measured directly together with the c-Si Raman intensity. Assuming no absorption in MoO x layer, local reflection was calculated from the Raman intensity data as well (Raman intensity proportional to squared transmission -to the laser intensity entering the c-Si wafer and the probability that the Raman photon escape the sample). Reflection is in both cases (for Raman line and laser line) calibrated by the known value for a flat c-Si wafer. We find very good correlation between calculated and directly measured reflection values proving our concept. Less than 3% discrepancy may be ascribed to the scattering on the sample surface and not fully negligible absorption in the MoO x film.
The same measurement was performed on the MoO x stripes deposited on textured c-Si wafer. The main difference compared to the deposition on flat wafer is very small contrast in absolute Raman intensity on MoO x stripe and plain c-Si wafer. The pyramids on the wafer surface serve for effective antireflection, therefore the additional contribution of MoO x layer is roughly 6% relative only (see Fig. S3). Within this precision we can conclude that for the main applicationthe thickness measurement of layer deposited on rough substrate -there is no need to apply reflection corrections. For flat samples both the reflection and Raman signal should be detected in order to interpret the results correctly.