Strain distribution in Si capping layers on SiGe islands: influence of cap thickness and footprint in reciprocal space. N Hrauda 1. J J Zhang 1,2. M J Süess 3. E Wintersberger 1,4. V Holý 5. J Stangl 1.
C Deiter 4. O H Seeck 4 and G Bauer 1. 1. Introduction.
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The properties of strained silicon channels are of high interest both for fundamental material science and for their application in electronic devices. A significant fraction of the research concerning semiconductors is dedicated to the development of transistors that utilize the lattice mismatch of 4. 2% between Si and Ge to induce strain in the active area of the device [1 –7 ]. To circumvent the use of plastically relaxed and therefore dislocated planar SiGe layers, our research focuses on epitaxially grown, defect-free three-dimensional (3D) SiGe islands grown on Si substrates suitable for transistor technology [8. 9 ]. Such islands form as a way to geometrically relax strain [10 ] when a material B is grown on a different material A with compatible crystal structures but different lattice parameters, as is the case for Ge and Si.
The relaxation of compressive strain within the islands is further enhanced if they are grown on prepatterned substrates [11. 12 ]; furthermore, predefined growth sites are necessary for subsequent device processing.
Similar islands to those presented here have been successfully integrated into strain-enhanced metaloxide semiconductor field-effect transistors based on strained Si channels. Tensile strain, which enhances the mobility of electrons as needed for n-type transistors [13 ], can be induced by growing a Si layer on top of SiGe islands, thereby stretching the Si lattice.
The transistor is then centered around such an island in a way that the strained section of the Si cap on top of it forms the active channel between source and drain [14. 15 ].
Several parameters are vital in the optimization of the strain properties of this channel: to maximize the tensile strain, a high Ge content within the stressor structure would be desired. In combination with a high Ge percentage a high aspect ratio of the stressor structure would even further increase the relaxation within the stressor itself and thereby the tensile strain within the Si layer grown on top. In this paper, we focus on the influence of the Si-channel thickness itself, as this parameter can be refined concerning strain maximization and device processing.
A sample series containing highly uniform, two-dimensional periodic SiGe island arrays capped with silicon layers of different thicknesses ranging from 5 to 30 nm was investigated by means of x-ray diffraction (XRD) experiments and finite element method (FEM) simulations. The combination of XRD experiments and FEM calculations was employed to get a realistic idea about the strain distribution within the SiGe islands and the Si layers on top. Parameters obtained from XRD measurements such as the average Ge content serve as input for strain calculations. The diffraction signal originating from the SiGe dots subsequently acts as the main fit parameter when XRD simulations based on the FEM models are compared to the experimental data. As the precise determination of Ge contents and strains directly from experimental data is hampered in the case of capped samples due to the hydrostatic pressure that the Si cap applies to the buried dot [16 ], the FEM simulations provide crucial information on the degree of alloying within the SiGe islands and therefore their strain distribution—along with the thickness of the Si channel, these attributes significantly influence the strain properties of the entire structure and therefore the characteristics of any device built around such a capped island. 2.
Experimental details. 2. Sample growth and AFM studies. On 9 × 9 mm 2 pieces of silicon(001) substrate, square-shaped fields with a size of 400 × 400 μm 2 (width of unpatterned area between the fields 100 μm) were defined by electron-beam lithography and reactive ion etching, resulting in a regular 2D array of circular pits with a diameter of 180 nm and a depth of 80 nm. The periodicity of the pit-pattern was 800 nm. After a standard cleaning procedure [17 ], the substrates were introduced in a molecular beam epitaxy (MBE) chamber, where a 36 nm thick Si buffer was deposited at substrate temperatures which were increased from 450 to 550 °C.
Subsequently, five monolayers of Ge were deposited at 720 °C with a growth rate of 0. 03 Å s −1. Dome-shaped SiGe island arrays with perfect uniformity were observed (see figure 1 (a)) with one island per pit site. One sample remained uncapped; the rest were capped at 360 °C with 5, 10, 20, and 30 nm of Si, respectively. During the entire sample growth process the sample rotation in the MBE chamber was switched off in order to minimize the introduction of impurities. However, as we will see in later sections of this paper this has consequences even for small substrate pieces. 2.
X-ray measurements. Figure 3. Reciprocal space maps of the (004) and (224) Bragg peaks recorded at beamline P08, Petra III (HASYLAB at DESY, Hamburg). The RSMs include the Si bulk signal, the diffuse SiGe island signal and the crystal truncation rod (CTR). The oscillations of the CTR arise due to the overall thickness of the Si capping layer and correspond well to the nominal values, respectively. Please note the asymmetric SiGe(004) signal for the samples capped with 20 nm and 30 nm Si.
Strain values discussed in this paper are always given with respect to the corresponding bulk material in its relaxed state, i. by comparing the lattice constant of a SiGe alloy in the actual sample to the nominal value of the lattice constant of a relaxed SiGe alloy with the same composition:. where a strained is the lattice constant of a strained crystalline material as determined by an XRD experiment and a relaxed a relaxed bulk lattice constant of this material. Thus, strain values in the SiGe domains will always be displayed as negative (their lattice is compressed, meaning shorter lattice constant compared to the relaxed state), while the positive strain values represent the sections in the Si domains under tensile strain (elongated lattice constant with respect to the relaxed Si lattice).
In-plane and out-of-plane strain values calculated from five datapoints evenly distributed over the length of the SiGe scattering signal show that the islands start out with comparable strain values at their base (associated with sections of the diffuse Ge signal close to the CTR) with roughly −1. 4% compressive in-plane strain. Out-of-plane strains are approximately the same with reversed sign. Towards the island apex it becomes obvious that relaxation is suppressed more and more with increasing capping layer thickness. While up to a cap thickness of 5 nm nearly complete relaxation occurs at the island apex (meaning that both in-plane and out-of-plane strain values are approximately zero), islands capped with 30 nm Si still show compressive in-plane strain values of −0. 5% at their apex. Furthermore, in the symmetric (004) maps the island signals display a splitting in the vertical ( Q z ) direction.
This is caused by the rather sharp interfaces separating sections with different Ge contents in the core–shell-like distribution discussed above (see figure 1 (c) or Zhang et al [21 ]). For the two samples with cap thicknesses of 20 and 30 nm, respectively, a distinct asymmetry of the SiGe signal in the symmetric (004) map can be observed. This can only be caused by a coherent tilt of the lattice planes within the buried island with respect to the bulk lattice, due to either the island geometry or Ge distribution being asymmetric. The actual cause for this effect will be discussed in section 4. 3.
Finite element and x-ray simulations. While other experimental methods such as Raman spectroscopy have the problem of low penetration depth and therefore a strain sensitivity restricted to the upper 5 nm of the Si capping layer [25 ], XRD leaves us with rather the opposite of that problem.
Due to the large penetration depth of the chosen coplanar geometry, a large volume of bulk material contributes to the scattered x-ray intensities recorded in an experiment. For the samples shown in this paper, the strained section of the Si cap above the SiGe islands does not provide enough scattering volume to produce a signal that can be distinguished from the diffuse scattering around the Si bulk peak. The SiGe signal, although stemming from a rather small amount of contributing volume, is well separated from the Si bulk peak. In the case of samples of simpler nature, for example homogeneous layers or uncapped samples, it would be straightforward to directly determine the Ge content and thereby the strain state directly from the XRD measurement. However, in our case we have to consider that the islands display a rather complex Ge distribution. Additionally, in the case of capped samples the Ge contents obtained directly from XRD experiments are incorrect due to the hydrostatic pressure applied by the Si cap [16 ]. Therefore, we use FEM models in combination with XRD simulations to determine the strain state of both the SiGe island and the Si cap.
To calculate the strain distributions, the commercial COMSOL Multiphysics program package [26 ] was used. The geometry for the FEM models was derived from AFM measurements; initial parameters for the Ge distribution were obtained from the XRD measurement of the uncapped sample and the etching profiles. The displacement fields obtained by FEM calculations also served as input for XRD simulations based on kinematical scattering theory [23 ]. These XRD simulations were then compared to the experimental data to refine the FEM calculations; the Ge distribution within the model island is altered until the SiGe signals in XRD simulations and measurements match sufficiently. The shape and Ge distribution of the buried islands were determined based on the uncapped reference sample. The properties thus found were used for the buried islands in the models of the capped samples, meaning that for each model the same geometry and Ge distribution for the buried dot was used; only the thickness of the Si cap was varied (for an example of a model geometry, see figure 4 (b)). The assumption that the shape of the buried islands does not change while capping at such low temperatures as used here is justified by previous XRD-based work [18 ] as well as TEM investigations on the 30 nm capped sample of this batch (see figure 8 ).
In the model coordinate system the bottom of the downward facing pit pyramid below the island is situated at the origin, which makes it convenient to introduce analytical functions for the Ge distribution (see the inset of figure 4 (a)). Zoom In Zoom Out Reset image size. 4. Results and discussion. 4.
Strain calculations for different capping layer thicknesses. The x-ray measurements shown in figure 3 indicate a trend towards less relaxation with increasing capping layer thickness. The thicker the Si cap, which is tensile strained and therefore wants to contract, the larger is the stress on the buried SiGe island. Due to the lattice mismatch between Si and Ge of 4.
2%, the relaxation states of these two materials act counter-productively—a more relaxed SiGe island induces higher tensile strain in a Si capping layer, whereas the thicker the capping layer gets the more this layer itself is able to relax towards unstrained Si and thus compress the buried island by a higher amount. According to this, line plots of the in-plane strain based on the FEM models displayed in figure 4 (a) show that, for islands with the same size, shape, average Ge content and Ge distribution, an increase of the capping layer thicknesses results in lower tensile strains in the Si cap while the overall compressive strain in the buried island increases.
The SiGe signal in x-ray simulations based on these models (figure 4 (b)) display the same behavior as the measurements which can be seen in figure 5. The thin 5 nm Si layer on top of an island obviously displays the highest tensile strain with in-plane strain values around 1. 3%, which would be desirable for the creation of strain-based devices. A thicker Si layer on the other hand, while being more relaxed with peak values around 0. 8% for a 30 nm Si cap, is easier to maintain during device processing, as fabrication and etching steps can result in the loss of a few nanometers of the Si cap layer [15 ]. 4.
Origin of the asymmetric intensity distributions in (004) reciprocal space maps.
In this section we discuss the cause for the asymmetric intensity distributions of the SiGe signal in the reciprocal space maps around the (004) Bragg peak mentioned earlier. An asymmetric intensity distribution around a symmetric Bragg peak as seen in the two lowermost sections of figure 3 can only be caused by a mutual tilt of the lattice planes of the probed material. In the case of the samples containing islands capped with 20 and 30 nm, respectively, only the island signal itself is affected (see figure 3 ), and the Si(004) substrate peak and the corresponding CTR are perfectly in line. This means that specifically the lattice planes within the SiGe islands are tilted with respect to the substrate in a coherent way throughout the entire illuminated sample area, otherwise such an effect would be averaged out due to the large number of probed islands (for an illuminated area of 200 × 200 μm 2 and a pattern period of 800 nm, roughly between 6 × 10 4 and 7 × 10 4 islands are included in the measurement). Reference measurements of the (004) Bragg peak in two perpendicular sample azimuths (both along 〈1 1 0〉 directions) performed at a laboratory rotating anode x-ray source confirmed that the asymmetric SiGe signal appears only along one [1 1 0] direction, while for the azimuth perpendicular to it the signal is symmetric. There are several possible reasons for such a lattice plane tilt: one is an asymmetric Ge distribution, which has been observed for islands grown on flat surfaces [27. 28 ].
On patterned substrates this could be caused by a depletion effect [29 ], which occurs at the border between patterned and flat substrate areas: the predefined and favored nucleation sites in the pattern draw Ge from the surrounding flat substrate. Islands growing at the outskirts of a patterned field thus incorporate more Ge and develop in an irregular way compared to islands in the center of the pattern. In turn, a certain amount of the flat area surrounding the pattern is depleted of Ge; no islands nucleate there. However, in the case of the uncapped sample and the ones with 5 and 10 nm Si cap, no asymmetry of the SiGe signals is visible in the (004) RSMs (see figure 3 ); therefore, the tilted signal cannot be caused by the SiGe islands themselves. This rules out the depletion effect or an asymmetric Ge distribution due to some other cause.
This leads to the conclusion that the Si cap itself is the cause of the asymmetric intensity distribution we see in our XRD measurements. AFM scans of capped samples did not show shape irregularities of the Si cap in a preferential direction; its surface looks perfectly symmetric, as shown in figures 2 (c) and (d). However, as no sample rotation was used during the whole growth process, the complete cap could be shifted with respect to the buried island due to the geometric setup in the MBE chamber. The beams of both Si and Ge adatoms do not impinge on the sample vertically; in the case of the Si source, the inclination angle with respect to the sample surface normal is approximately 20°. This had no detectable effect on the Ge distribution of the islands due to the higher mobility of Ge adatoms to begin with and the higher growth temperature of 720 °C during Ge deposition.
The diffusion rate of Si adatoms is much smaller; additionally, a lower substrate temperature of 360 °C was used during the capping process. This lead to a slightly higher Si coverage on the island slopes facing the Si source, while the overall cap shape still looks symmetric. This inhomogeneous coverage, which appears to be more or less uniform for the entire island array, leads to a mutual tilt of the lattice planes within the SiGe islands, resulting in a signal that is tilted with respect to the (0 0 1) axis in reciprocal space.
Corresponding FEM models were set up for the samples with 20 and 30 nm Si caps with an island displaying a perfectly symmetric Ge distribution and a Si cap with a lateral shift with respect to the buried island (see figures 6 and 7. respectively). Shifts ranging from 5 to 15 nm were tried (in 5 nm steps), where a shift of 10 nm leads to a significant tilt of the SiGe signal in the x-ray simulations, comparable to the effect seen in the experimental data. The direction of the tilt in the RSM depends on the sample orientation with respect to the incident x-ray beam.
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