4. Low temperature (LT) epitaxy of ultra-thin pure Ge buffer layers on Si(001) using
4.1. Background on pure Ge buffer layers
4.2.6. Temperature dependent strain variation in the buffer layers
buffer layers.
Due to the limitations of the triple axis detector, epitaxial layers with a thickness less than 78nm could not be detected in a 004 symmetrical scan, regardless of the amount of strain.
The in-plane strain in the Ge epilayer due to thermal expansion coefficient mismatch (ε∥−Ge
TH) is calculated by treating the substrate/epilayer as a bending
moment problem, where the shear force of the substrate on the epilayer and vice versa multiplied by the respective thicknesses (tGe and tSi) equals the bending moments [147]. An assumption is taken that all compressive strain due to the 4.2% lattice mismatch has been relieved. The higher thermal expansion coefficient of Ge means that when the wafer is cooled down to room temperature (TL≈ 26.85°C) from being
subjected to a higher temperature (TH), the Ge epilayer shrinks even more than the
Si(001) substrate. Given that the Ge is covalently bonded to the Si(001), this results in the entire wafer ‘bowing’ upwards. The radius of curvature of the bowed wafer, r, is given by equation 4.2, where the (001) Young’s modulus of Si and Ge are given as YSi and YGe respectively. The ε∥−Ge
TH is then calculated from equation 4.3 for the
wafer at various values of TH as seen in figure 4.17. The figure shows that the standard
deviation in strain values is 0.000071% from the thinnest (78nm) to the thickest epilayer (351nm).
(
1 r) =
6YGeYSitGetSi(tGe+tSi) ∫THTL[αSi(T)−αGe(T)]dT 3YGeYSitGetSi(tGe+tSi)2+(Y GetGe+YSitSi)(YGetGe3 +YSitSi3 ) (Equation 4.2)ε
∥−GeTH= (
1 r)
YGetGe3 +YSitSi3 6YGetGe(tGe+tSi) (Equation 4.3)162
Figure 4.17: Starting temperature TH vs thermal expansion coefficient mismatch strain between Ge epilayer
and 525µm Si(001) substrate (ε∥−Ge
TH)when cooled down to 26.85°C for various thickness of Ge film (tGe) listed in different colours. Inset, magnified section of the plot lines.
The complicated nature of strain relaxation makes it very difficult to determine the exact thermal energy needed to produce Ge layers with zero strain. According to figure 4.17, Ge layers grown below 400°C should be under tensile strain of less than 0.12%. However, HR-XRD RSMs of the thickest LT-Ge layers were carried out and showed that layers grown at 300°C, 350°C and 400°C are under relaxed with respect to the substrate i.e.: have some residual compressive strain as indicated in figures 4.18 (b), 4.19 (b) and 4.20 (b) respectively with the Ge peak lying on the right hand side of the relaxation line in the 224 scans. This means that below 351nm film thickness and below 400°C growth temperature, strain relaxation due to lattice mismatch through the formation of misfit dislocations has not been completed. From figure 4.18 it seems that for a 78.9 nm thick/ 300°C growth temperature Ge layer, the compressive strain is at its highest at -0.45% which is evident from the 224 scan however the difficulty in finding the peak in the 004 scan of this sample means that there is greater degree of error on this measurement as shown in figure 4.22.
For a Ge layer grown at 350°C to 174nm thickness the compressive strain reduces to 0.18% +/-0.03% and for a 400°C layer grown to 351nm thickness, the compressive strain reduces still to 0.11% +/- 0.01%. Figure 4.22 shows that a possible strain asymptote is reached with the thickest 400°C grown Ge sample. A possible
351nm 267nm 155nm 174nm 78nm 937°C
163
explanation to this is that at this amount of thermal budget, 60° misfit dislocations are kinetically limited to glide which leads to incomplete strain relaxation. Insufficient radial stresses mean that Lomer dislocations are also blocked from gliding along the (001) plane.
Figure 4.18: HR-XRD 004 (a) and 224 (b) RSM of sample 15-47: Ge buffer layer grown to 78.9nm thickness at 300°C.
Figure 4.19: HR-XRD 004 (a) and 224 (b) RSM of sample 15-43: Ge buffer layer grown to 174nm thickness at 350°C.
(a) (b)
164
Figure 4.20: HR-XRD 004 (a) and 224 (b) RSM of sample 15-38: Ge buffer layer grown to 351nm thickness at 400°C.
Figure 4.21: HR-XRD 004 (a) and 224 (b) RSM of sample 15-61 grown at 400°C and annealed at 650°C for 5mins.
When the 78nm thick/ 400°C growth temperature layer is subjected to annealing under hydrogen for 1 min at 650°C the strain in the layer has reduced to ≈ -0.037%, as shown in figure 4.22. When the same layer is annealed for additional 4 mins (5mins in total) at 650°C, the strain in the layer has now transitioned to become marginally tensile ≈ 0.036% as seen in figure 4.21, where the Ge peak is lying on the left hand side of the substrate relaxation line. This means that growing Ge at 400°C and subsequently annealing at 650°C for 5 mins has supplied sufficient thermal budget to shrink the Ge epilayer upon cooling to room temperature to overcome the residual compressive strain due to lattice mismatch. From figure 4.22, it is hypothesised that annealing a
(a) (b)
165
400°C grown layer at 78nm thickness for 3 mins should provide sufficient thermal budget to cause the Ge layer to become completely strain neutralised.
Figure 4.22: Strain in the LT Ge buffer layer measured using HR-XRD, grown at various temperatures and plotted against thickness. The error in the TEM thickness measurements is +/-0.5%.