EUROSOI 2007 – Conference Proceedings 39 January 24-26, 2007, Leuven, Belgium Influence of Uniaxial [110] Stress on Silicon Band Structure and Electron Low-Field Mobility in Ultra- Thin Body SOIs Viktor Sverdlov, Enzo Ungersboeck, and Hans Kosina Institute for Microelectronic, TU Wien, Gusshausstrasse 27-29, Wien A-1040 sverdlov|ungers|kosina@iue.tuwien.ac.at 1. Abstract Uniaxial [110] stress induced valley shifts and effective masses modifications are analyzed. Analytical expressions for both transversal and longitudinal masses are obtained for the first time. Analytical results are verified with pseudo-potential band structure calculations and excellent agreement is found. The low-field mobility enhancement in the direction of tensile [110] stress is due to the conductivity mass modification and is shown to exist in SOIs with arbitrary small body thickness. 2. Method and Results Strain induced mobility enhancement is one of the ways to boost performance of modern CMOS devices. In biaxial stressed devices the mobility can be enhanced by 100%. Biaxial stress is naturally introduced by growing Si epitaxially on SiGe. This method requires a substantial modification of CMOS fabrication process and is not yet used in mass production. Instead industry is exploiting advantages of compatible with CMOS process uniaxial stress, which is created by local stressors and/or additional cap layers. Although already successfully used in mass production, the technology relevant stress along [110] has received little attention within the research community. Only recently a systematic experimental study of the mobility modification due to stress in [110] was performed [1]. It was shown that, contrary to [100] uniaxial stress, the electron mobility data under [110] stress condition is consistent with conductivity mass being a function of the stress value. The [110] stress produces off-diagonal elements xy e of the strain tensor, which lift the degeneracy between the two lowest conduction bands at the X points along [001] axis in the Brillouin zone [2]: xy X De E 2 = ∆ , (1) where D is interpreted as the deformation potential due to shear strain component. Since the conduction band minimum along [001] axis is located near the X point, it is affected by the strain xy e . First, the conduction band minimum k min moves closer to the X point: 2 0 min 1 / ε − = k k , (2) where k 0 is the position of the minimum with respect to the X point in unstrained Si, ∆ = / 2 xy De ε , and ∆ is the conduction bands splitting at k 0 . It is interesting to note that for 1 ≥ ε the conduction band minimum stays exactly at the X point. Second, the minimum of each of the two [001] valleys moves down in energy with respect to the four remaining degenerate valleys. However, for 1 | | ≤ ε it is proportional to the stress square: 4 / 2 min ∆ − = ∆ ε E , 1 | | ≤ ε ; (3a) while a linear dependence is recovered for 1 | | ≥ ε 4 / ) 1 | | 2 ( min ∆ − − = ∆ ε E , 1 | | ≥ ε . (3b) Finally, the shear stress modifies the effective masses in [001] valleys. The transversal mass m t acquires two different values along (+) and across (-) tensile [110] stress: [ ] 1 / 1 / ) ( − ± = M m m m t t t ε ε , 1 | | ≤ ε ; (4a) [ ] 1 / 1 / ) ( − ± = M m m m t t t ε , 1 | | ≥ ε . (4b) A closed expression for M is found within the kp perturbation theory. The longitudinal mass m l is expressed [ ] 1 2 1 / ) ( − − = ε ε l l m m , 1 | | ≤ ε ; (5a) [ ] 1 1 | | 1 / ) ( − − − = ε ε l l m m , 1 | | ≥ ε . (5b) In order to verify these expressions the band structure calculations with empirical pseudo-potentials method (EPM) [3] were performed. Results of comparison are reported in Figs 1-3 and display an excellent agreement. Comparisons with experimental data from [1] and [2] are shown in Fig.4 and Fig.5, correspondingly. Finally, an example of mobility calculations for UTB SOI is shown in Fig. 6. While the stress along [100] direction doesn't have an affect on the mobility, the mobility in a [110] stretched UTB SOI is enhanced along the stress. 3. Conclusion Analytical expressions for the [110] stress induced valley splitting and effective masses variation are obtained and verified against band structure calculations. Results are used to demonstrate the mobility enhancement even in UTB stressed SOIs. References [1] K. Uchida et al., IEDM 2005, p.135. [2] J.C. Hensel et al., Phys.Rev., 138, p.A225, 1965. [3] M. Rieger and P. Vogl, Phys.Rev.B, 48, p.14275, 1993.