Nanocomposites and nanomaterials

Strain-induced spliting in valence band of Si-Ge whiskers 
A.Druzhinin, I.Ostrovskii, Yu.Khoverko, N.Liakh-Kaguy,V.Mazur
Department of Semiconductor Electronics, Institute of Telecommunications, Radioelectronics and Electronic Engineering, Lviv Polytechnic National University, Kotliarevskyi Str., 1, Lviv-79013, Ukraine.
E-mail: druzh@polynet.lviv.ua

Nanostructures based on Ge are of great interest due to surprising physical effect such as SdH oscillations [1]. The good perturbation tool is strain. Due to application of strain to Ge sample  the six-fold degenerated valence band the splits on three sub-bands corresponding to light and heavy holes as well as sub-band of SO splitting, which is enough large and consists of 0.29 eV. Light and heavy hole sub-bands in turns splits due to spin-orbit coupling (SOC) under strain in k≠0 direction. Nevertheless, Ge whiskers have been investigated under strain action showing magnetophonon oscillations and giving the values of effective mass of heavy and light holes [2]. However, SOC in the whiskers have not been studied. Therefore, the purpose of the paper is to study the splitting of valence band of doped silicon-germanium whiskers with concentration in the vicinity to MIT under compressive strain to determine the conduction mechanism at low temperatures.
The longitudinal magnetoresistance of the p-type silicon-germanium whiskers with boron concentration of 1×1018cm-3 was measured in the range 0–14 T at temperatures 4.2–70 K under the compressive strain up to -3×10-3 rel.un.  The strain influence on the degenerate energy spectrum of heavy and light holes by the method of perturbation theory is described, summing up the well-known consideration to arbitrary strains and highlighting the geometric aspects of the theory. According with two-zone approximation of the kp-method, the strain removal twice degenerate level Г8+ that leads to the splitting of light and heavy hole branches. From the whisker magnetoresistance the effective mass of heavy holes mc = 0.2mo was calculated that is correspondent to decreased value due to the compressive strain.  The spin splitting energy for heavy holes HH = 1.6 meV was also obtained and discussed.

1.	H Morrison C., Foronda J., Wiśniewski P., Rhead S.D., Leadley D.R., Myronov M. Evidence of strong spin–orbit interaction in strained epitaxial germanium // Thin Solid Films.- 2016.- 602.- P. 84.
2.	Druzhinin A.A., Ostrovskii I.P., Khoverko Yu.N., Liakh-Kaguy N.S., Vuytsyk A.M. Low temperature characteristics of germanium whiskers // Functional Materials.- 2014.- 21(2).- P. 130.