Abstract

Geometric scaling of Si devices has provided a continual performance improvement of integrated circuits. However, with each new technology generation geometric scaling has become an increasingly complex and expensive task. An additional way to improve device performance is to enhance the carrier transport by changing the material properties. A promising candidate is strained Si which shows significantly improved carrier transport properties.

This work deals with electron transport in strained $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ layers grown on $\textrm {Si}_{1-y}\textrm {Ge}_{y}$ substrates. The Ge compositions of both layers and substrates can vary in the whole range. Due to the strain the degeneracy of the conduction band states with different quasi-momentum is reduced. This degeneracy reduction depends on the relative orientation of the quasi-momentum of a band minimum and the forces applied to the layer. The strength of the minima splitting also depends on the Ge composition of both the layer and the substrate. Deformation-potential theory is applied to calculate the splitting of the conduction band extrema and the mean energy shift of both X and L valleys. Within this theory the strain tensor is used which depends on the substrate orientation. It can be diagonal and non-diagonal which strongly changes the influence of the conduction band minima of different types and leads to new kinetic properties of the material.

To investigate the kinetics in strained SiGe layers the formalism based on the semiclassical Boltzmann transport equation is used. This allows incorporation of scattering processes and band structure effects including the strain effects in a rather complete and comprehensive manner. In this work an analytical conduction band structure which considers the anisotropy and non-parabolicity is employed. In this case the scattering rates of different scattering mechanisms can be analytically obtained and modified so as to include strain effects.

The scattering mechanisms are intravalley acoustic phonon scattering treated as an elastic process, intervalley phonon scattering, which can be both of acoustic and optic type and which are considered inelastic, elastic alloy scattering originating from the alloy lattice disorder, inelastic electron-plasmon scattering coming into play at higher electron densities, elastic scattering on ionized impurities which includes effects such as two-ion scattering, momentum dependent screening and the second Born correction. The presence of strain modifies the scattering rates. Strain affects the phonon scattering rates through the final energy of scattered electrons and the number of available valleys. The ionized impurity scattering rate is modified through the screening parameters.

The Boltzmann kinetic equation is solved using the Monte Carlo method. By this approach semiclassical transport is exactly modeled without any additional physical approximations. To find the low field electron mobility tensor a zero field Monte Carlo algorithm is applied. Since at high electron concentrations the quantum mechanical Pauli exclusion principle becomes important, a new zero field Monte Carlo algorithm accounting for degeneracy effects is developed and applied to find the low field mobility tensor in strained doped SiGe. To perform a small signal analysis of highly degenerate SiGe layers for both low and high electric fields a new small signal Monte Carlo method is developed which takes the Pauli exclusion principle into consideration.

Finally, results obtained for strained SiGe layers are given. Both doped and undoped layers are considered for different Ge compositions $x$ and $y$ of the layer and the substrate, respectively. The substrate orientation dependence is also investigated. To explain the behavior of the low field electron mobility the valley population is analyzed as a function of the Ge compositions $x$ and $y$ and impurity concentration. The in-plane component of the electron mobility is found to be dependent on the in-plane angle for a general substrate orientation. The in-plane mobility, a key parameter for MOSFET performance, is highest for strained Si on $[001]$ SiGe substrates. For Ge compositions above 0.2, the enhancement of the pure lattice mobility saturates at 55% as compared to unstrained Si. In the case of HBT the perpendicular component of the electron mobility in the strained SiGe base increases due to the band minima splitting, but strong alloy scattering suppresses this gain. The interplay between strain effects and effects caused by the Pauli exclusion principle at high electron density is shown. The small signal response of strained Si layers is modeled and compared with the relaxed case. To understand the behavior of the response functions the energy distribution functions are analyzed for two carrier ensembles. It is shown that for the case of high degeneracy these distribution functions are nearly the same at the very beginning and strongly shifted to the high energy domain due to the Pauli exclusion principle.

S. Smirnov: