-100
Strain Relaxation of SiGe (%)
Wafer Bow Height (um)
0
FWHM in Si peak (sec-1)
Slightly
Strain Relaxation of SiGe (%)
Wafer Bow Height (um)
0
FWHM in Si peak (sec-1)
Slightly
Relaxation of strain SiGe (%)
Figure 2.4.19. Correlation between relaxation of strain SiGe and injection of defects, determined from wafer bow height and full width at half maximum (FWHM) of Si XRD peak.
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in Fig. 3(b), the very high thermal stress caused by the huge thermal gradient induced very large wafer bending, which can be expressed as, [22]
E T where is the thermal expansion coefficient; ES, T is Young’s modulus at the MSA temperature, and T is the effective temperature difference between the surface of the wafer and the position of zero temperature gradient, where T/x=0. Since the MSA chamber was thermally insulated, the decrease in the temperature across the Si substrate is given by, [23]
where Tf is the temperature at zero temperature gradient across the wafer. The experimental MSA temperature profile across the surface of the wafer was fitted using parameters Tf, A1, and xc set to 490C, 814C and 106μm. Therefore, the effective temperature difference due to the thermal gradient is represented by
] where xT=396μm, and a=0.4 to fit the experimental data in Fig. 3(b). Accordingly, the magnitude of the MSA thermal stress across Si wafer surface was,
] The MSA thermal tensile stress in this experiment at approximately 1200°C for 500μs was
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thus around 0.6GPa. The thermal stress caused by MSA pulse heat in the Si surface region, df, is given by Stoney’s equation,
d k where r denotes radius of the wafer, and k is the curvature of the wafer. Substituting Eq. (5) into Eq. (6) yields the k value, and the bow height of Si wafer following the MSA process is given by Given the experimental parameters, the change in the bow height of the pure Si wafer without SiGe layer during the MSA process was small, at around few 10m.
The bow height, however, changed significantly around 150m when the relaxation of the strained-SiGe was introduced into the MSA process. When both of the film stress and the thermal stress have been determined, the wafers bow height of the strained-SiGe and MSA was as presented in Fig. 10(b). It was modeled using the Gaussian function to obtain an empirical formula to illustrate the bow height change of the SiGe wafer by the compressive stress of the strained-SiGe layer and tensile stress of the MSA, as follows.
}
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where y0, A, and b are constants; R is the relaxation of strained-SiGe and fin is the interaction factor,
MSA SG
in m n
f , where m and n are also fitting constants. According to Eq. (8), the bow height reached its maximum when b(1-R)SG was close to MSA. Therefore, the bow height depended on both the magnitude of the strained-SiGe film stress and the MSA thermal stress. Shallow implant Rp in the surface region would cause only an 11% relaxation of the whole strained-SiGe layer, and the compressive film stress was sufficiently high to resist wafer bending associated with MSA thermal tensile stress. Hence, the bow height was negative as compressive as that of the initial strained-SiGe film. When implantation is performed using medium projection range Rp to induce 51% relaxation of the strained-SiGe, the film stress, SG, was reduced by a factor (1-R) showing lower shear yielding stress for deformation during MSA thermal stress as shown in Fig. 2.4.20 [24-29], and was then too small to resist the MSA tensile stress and the relaxed strained-SiGe wafer buckled in the maximum tensile state. This phenomenon is described by a second moment of inertia as shown in Fig. 2.4.21 [30-31], which demonstrates that a suddenly large deformation or over-bending occurred when the applied force exceeded a critical stress or over shear stress for yielding. At the experimental condition, while strained-SiGe relaxation is over around 20%, large SiGe wafer bending occurred under applying MSA tensile stress corresponding to the concept of the second moment of inertia.
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When deep implantation of Rp destroyed most of the strained-SiGe layer at close to 75%
relaxation, the yield-point of relaxed strained-SiGe was further reduced to cause much bending under MSA process. However, the 75% relaxation of strained SiGe was formed with lots of interfacial misfit dislocations and low-density of coherent bonding with Si substrate.
The highly relaxed strained-SiGe film is then expanded and contracted along with the externally thermal stress and would not cause any residual strain to the underlying Si substrate during the MSA thermal cycle.
Figure 2.4.20 the shear stress of yielding point of silicon is linearly dependent on the annealing temperature. (S.P. Nikanorov, et. al., Materials Science and Engineering, 2006)
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We would like to investigate for a MSA acting on the relaxation of the strained SiGe when defect formed in the underlying Si substrate and how the wafer underwent such a significant bending during MSA process. The relaxation of the strained SiGe induced defect formation in the underlying Si substrate is taken place during MSA ramp-up or cool-down that is a puzzle for us. A model of MSA temperature ramp-up and cool down acting on a medium-level of relaxed strained-SiGe to caused defect formation in the underlying Si and wafer bending was therefore proposed. In Fig. 2.4.22, by using micro-second camera and comparing wafer shape with the ellipsometer wafer bow height to investigate real-time wafer
second moment of inertia second moment of inertia
Figure 2.4.21 the second moment of inertia shows large over-bending while external loading over critical point. (L. Zhang et. al. NSTI-Nanotech, 2006)
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bending during MSA heating and cooling on the medium relaxed SiGe wafer. The wafer showed a little compressive bending after SiGe deposition at initial stage. At the next stage the coefficient of thermal expansion is greater for SiGe than for Si such that the SiGe layer expanded more than the silicon substrate during MSA surface heating. The surface expansion induced a compressive stress exceeding the lower yielding stress of the relaxed strained-SiGe caused a significant compressive bending approaching wafer bow height near -185um from -30um. Thus, brittle silicon substrate suffered a great tensile stress to generate lots of defects into plastic deformation as shown in Fig. 2.4.23 (a) and (b).
Medium-Rp IMP+
RTA+MSA heat-up As-grown SiGe
Start (blanket)
wafer
SiGe
Medium-Rp IMP+RTA +MSA cool down Medium-Rp IMP+
RTA+MSA heat-up As-grown SiGe
Start (blanket)
wafer
SiGe
Medium-Rp IMP+RTA +MSA cool down
Figure 2.4.22 (b) the metrology concept of how to in-situ measure wafer warpage Figure 2.4.22 (a) Real-time micro-second camera image of wafer warpage change associated with as-grown SiGe and the MSA temperature ramp-up and cool down.
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Figure 2.4.23 (a)(b) microscope of lattice deformation during post-implant, RTA and MSA temperature heat-up
Figure 2.4.23 (c)(d) microscope of lattice deformation and wafer bending during MSA heat-up and MSA temperature cool-down
(a) SiGe+ medium Rp IMP+RTA
SiGe
Si sub.
h
sstrained relaxed
(a) SiGe+ medium Rp IMP+RTA