Phonon modification in SOI structures and its impact on electron transport

Introduction Acoustic phonons in silicon-on-insulator (SOI) structures are different from those in bulk Si because of the large mechanical mismatch between Si and SiO2. Therefore, conventional modeling of electron transport in SOI, where bulk phonon wave function is assumed, must be re-examined. Equivalent investigations have been done for ILL-V semiconductors [1-3]. However, there are few investigations on Si/SiO2 systems such as SOI structures in spite of their technological significance. In this work, the impact of phonon wave modulation on electron transport in SOI is investigated theoretically. Phonon Normal Modes in SOI Structure Figure 1 shows an illustration of our SOI model used in the following analysis. The silicon plate is assumed to be embedded in bulk SiO with infinite extent. For mathematical convenience stress free boundaries are assumed at z + LJ2, and L is set much larger than the thickness of the Si plate, d. As the system is isotropic along the Si plate, the phonon normal modes in the x/l direction are simply plane waves. On the other hand, nonnal modes are more complicated in the z direction due to mechanical mismatch between Si and SiO2. Such phonon normal modes are often categorized using Fig. 2, where phonon frequency, a4 vs. wave vector along xll axis, qll, is plotted [4]. The two straight lines are defined by longitudinal sound velocities in Si (vsi,l = 9.0 x 10 m/s ) and SiO2 (v0,.l = 5.9 x 103 m/s). Type (I) w> viq,ll,: longitudinal phonon normal modes have sinusoidal wave forms as shown in Fig. 3 (I). Type (II) vsil qH > a)> vo,, qH,: normal modes are sinusoidal in SiO2, and decay exponentially in Si as in Fig. 3 (II). Type (III) vox,1q/l > w: normal modes decay exponentially both in Si and SiO2 as shown in Fig. 3 (III) (surface mode). It is important to note that no confined mode exists in the SOI structure, that is, there is no normal mode such that amplitude is limited in the Si region and energy is quantized. Reduction of Acoustic Phonon Scattering Potential The dominant electron-phonon interaction in Si is the acoustic deformation potential (ADP) scattering, and its scattering potential is written as HADP (z) = DADpV * u, where DADP is a coupling constant, and u is a phonon normal mode. Figure 4 shows the squared absolute value of V u as a function of z, which is equivalent to the strain caused by the phonon vibration u. Note that the strain in the Si region is less than that in bulk Si (dashed line), while the strain in the oxide region is increased. This has been observed in a similar SiISiO2 system, and referred to as 'strain absorption' [5]. Figure 5 shows an integral of HADP within Si region (-d/2 < z < d/2) plotted as a function of w. The value of qll was fixed, and the thickness of the Si region was set as (a) d = 50 nm (b) d = 10 nm. The spikes observed in solid curves are caused by interference between longitudinal and transverse phonon modes. The three types of phonon modes appear in different ranges of w, as indicated in the figure. Note that the reduction of the strain seen in Fig. 4 leads to reduction of HADp compared to that in bulk Si (dashed curve) independently of c and d. We found that this reduction also occurs at different values of qll. Thus, the ADP scattering potential in the SOI structure becomes less than that in bulk Si for phonon wave modulation. However, we cannot yet conclude decisively that this leads to reduction of electron-phonon scattering rate, because in SOI the phonon modes of type (H) and (IIH) exist, which do not exist in bulk Si. In order to verify this, the total scattering rate must be calculated, and this will be discussed in our presentation. Conclusion Rigorous treatment of the acoustic phonon modification in the SOI structure revealed that the acoustic phonon scattering potential is reduced compared to that in bulk Si, independently of phonon energy, wave number, and Si layer thickness. These results indicate a possibility of reduced electron-phonon interaction in SOI due to phonon wave modulation. Acknowledgements The authors are indebt to Prof. Cumberbatch of Claremont Graduate University for his support. The authors would also like to thank Prof. H. Williams and Prof. D. Yong of Harvey Mudd College for their helpful discussions. Dr. S. Uno was supported by a Fellowship from I. S. I. MOSIS Service, University of Southern California. Reference [1] S. M. Komirenko et. al., Phys. Rev. B 62., p. 7459 (2000). [2] B. A. Glavin et. al., Phys. Rev. B 65., p. 205315 (2002). [3] E. P. Pokatilov et. al., J. Appl. Phys. 95., p. 5626 (2004). [4] L. Wendler et. al., Surface Science 206, p. 203 (1988). [5] S. Uno et. al., SSDM 2004, H-1-5, 2004, Tokyo; J. Appl. Phys. to be published in May 2005.