In the quest of accessing subsurface physical properties with scanning probe mi- croscopy, we used a unique sample preparation tool. By cutting the sample at a shallow angle with Ar ion beams in BEXP configuration as represented on Fig. 5.1a ), we create an easily accessible surface well suited for scanning probe methods as reported elsewhere[158, 160].
In the case of SThM, the BEXP procedure is particularly powerful as it enables the measurement of a sample thermal resistance as the material thickens from the substrate to the surface. Furthermore, several reports have shown the necessity in SThM experiments to measure samples with several thicknesses to deduce quan- titative properties[72–74, 161]. This often requires a change of manufacturing process, preparation of special samples and does not allow measurement of the real devices. The combination of SThM and BEXP drastically reduces these hur- dles. Using a single and one measurement step, the thermal resistance of various materials and thicknesses are obtained.
We demonstrate the usefulness and precision of the method on a molecular beam epitaxy (MBE) grown multilayer sample of Si/SixGe1−x/Ge/Ge0.9Sn0.1 that
has potential use in Si based optoelectronics due to the potential of achieving direct bandgap in such a structure. First, a 100 nm Ge layer is grown on a silicon substrate. During the process, Si atoms diffuse inside the Ge layer due to the high process temperatures[162] and therefore create SiGe alloy of varying concentrations. Si concentration is difficult to estimate in the first few nanometers
of the Ge layer. However Si concentration decreases with increasing thickness as diffusion does not reach 100 nm[163]. Then, another 100 nm Ge layer is grown creating a virtual Ge substrate. Finally, 200 nm of Ge0.9Sn0.1 are grown on the
Ge virtual substrate. These MBE grown samples were prepared by the Institute of Semiconductor Engineering at the University of Stuttgart and interpretation of the results was realised in collaboration with Linda Haenel and Jorg Schulz.
Figure 5.1: (a) Schematic beam-exit cross-section polishing (BEXP) principles.
Ar ions are impinging the sample surface at shallow angle (∼5◦) creating a SPM
friendly surface. (b) Thermal resistance as a function of height starting from the first SiGe layer. Inset: 3D topography overlaid with SThM response. Arrow indicates the direction of the average thermal resistance profile.
Thermal properties of Si1−xGex alloys have been studied extensively. Its ther- mal conductivity changes drastically with Ge concentration[164] and always re- duces compared to the bulk values of both Si and Ge. When the SThM probe scans across the different layers, the thermal resistance at the tip apex will be affected by the thermal transport happening at a particular nanoscale volume in the 3D space of the sample. This transport depends on the local thermal conduc- tance which is determined by both the local thermal conductance in the material, and for the nano-section, corresponding thickness of the subsurface layer along the z-coordinate.
Fig. 5.1b shows the thermal resistance at the tip apex as a function of height inside the sample and a 3D topography representation overlaid with SThM con- trast. Three regions corresponding to the silicon substrate, the virtual substrate
and the Ge0.9Sn0.1 layer are observed. We can distinguish the relatively low re-
sistance silicon substrate then a sharp increase at the transition to the Si1−xGex layer with high density of misfit dislocations, followed by a decrease and roughly constant signal in the relaxed dislocation free Ge layer. Finally, as the tip enters the Ge0.9Sn0.1 layer, the heat resistance increases again.
As we will explain in the following section, the thermal spreading resistance of a layer on a substrate is expected to increase (decrease) if the thermal conductivity of the layer is smaller (larger) than that of the substrate ( klayer
ksubstrate < 1 or >
1). Therefore, the resistance lowering observed in the Si1−xGex region is counter intuitive as, for any Ge content, the thermal conductivity of Si1−xGex is always lower than that of silicon[164]. However, the Ge content is varying from around 80% to 100%. In this region, the thermal conductivity of Si1−xGex is increasing.
It can be shown that in such case of an increasing layer thermal conductivity, the spreading resistance will first increase and then reduce as the thickness in- creases and the probe contacts more thermally conductive material. Using Finite Element modelling with a fine mesh, we can model the spreading resistance of a 40 nm diameter heat source on the surface. The spreading resistance is defined as
Rspr =
Tav−T0
Q (5.1)
where Tav is the average temperature over the heat source surface and T0 is the
boundary temperature and Q is the total power set on the heat source. We can
then model the spreading resistance as a function of sample thickness probed. Due to the thermal conductivity profile, the material under the heat source has a gradually increasing thermal conductivity. It can be seen in Fig. 5.2 that the spreading resistance is first increasing and then reducing with increasing thickness (blue triangles), whereas with a constant conductivity, the resistance monotonously increases (red circles).
Figure 5.2: Thermal spreading resistance computed for a constant (red cirlces)
and an increasing (blue triangles) layer thermal conductivity and the modelled increasing layer thermal conductivity distribution of SiGe.
This explains the trend observed in the SiGe layer and demonstrates the po- tential applications of the BEXP-SThM combination. It is remarkable therefore that nano-section and SThM allow the detection of variation of the local thermal conductance due to the composition and crystalline defects in the layers with a vertical resolution of around 5 nm in thickness.
In order to perform quantitative analysis of inhomogeneous and anisotropic gradient SixGe1−x and Ge0.9Sn0.1 samples, we present an analytical model for the
nanothermal characterization of ultrathin layers and confirm the accuracy of the method using well defined isotropic layered samples.