ABSTRACT
CONTENTS 4.1 Introduction .......................................................................................................................... 71 4.2 Semiclassical Electron Transport ....................................................................................... 72
4.2.1 Transport in Bulk Semiconductors......................................................................... 72 4.2.2 Low-Field Mobility ................................................................................................... 73 4.2.3 Transport in Confined, Low-Dimensionality Systems ........................................ 75 4.2.4 Collision Kernels ....................................................................................................... 76
4.3 Ionized Impurities ............................................................................................................... 78 4.3.1 Impurity Potential in Bulk Semiconductors.......................................................... 78 4.3.2 Dielectric Screening .................................................................................................. 80 4.3.3 Full-Band Expression for the Screened Impurity Scattering Rate ..................... 85 4.3.4 Additional Corrections to the Impurity Potential................................................ 88 4.3.5 2D Model.................................................................................................................... 90 4.3.6 Multi-Subband Linear Screening Approximations .............................................. 92 4.3.7 Ballistic Limit and the DOS Bottleneck: The Role of Impurity Scattering ....... 94
4.4 Interface Roughness ............................................................................................................ 98 4.4.1 Effective Potential in Thin-Body Si ........................................................................ 99 4.4.2 Roughness as a Perturbation................................................................................. 100 4.4.3 Direct Scattering at Atomic Steps......................................................................... 103 4.4.4 Scattering via Roughness-Induced Coulomb Terms ......................................... 105 4.4.5 Screening .................................................................................................................. 107 4.4.6 Mobility Calculation............................................................................................... 109 4.4.7 Simulation Results and Discussion ...................................................................... 109
4.5 Conclusions......................................................................................................................... 115 Acknowledgments ..................................................................................................................... 115 References.................................................................................................................................... 115
Crystal defects have long ceased to be a major concern in devices of the present very largescale integration (VLSI) technology, thanks to the dramatic improvements we have
and other radiation-rich processing steps (such as reactive-ion etching [RIE]). Ignoring neutral defects such as those associated with dislocations and stacking faults-possibly returning to the fore as strained channel materials are becoming more and more commonly employed-more realistically, defects to be considered at present are intentionally induced defects. If we define, from an electron transport perspective, a defect as any entity which breaks the three-dimensional (3D) symmetry of the semiconductor lattice, the ionized impurities introduced by doping and interfaces are the major defects to be considered. Here, first we consider ionized impurities, discussing the models employed to describe their associated potential, various approximations used to account for dielectric screening, and two major competing approximations, the Conwell and Weisskopf (CW) [1] and the Brooks-Herring (BH) [2] models, employed to obtain the associated scattering and momentum relaxation rates. Then, we consider genuine defects, namely those interfacial defects commonly labeled as interface roughness. As charge carriers are squeezed harder against the interfaces by the increasingly large perpendicular electric fields present in thin insulator devices, scattering with the roughness is a growing concern. We limit our analysis to extensions to thin bodies and quantum wells of the continuum empirical model originally proposed by Prange and Nee [3], Saitoh [4], Sakaki [5], and Ando et al. [6].
Before moving to the core of this chapter, we recall some basic tools employed in dealing with electronic transport in semiconductors.
