Doped n-Type Silicon (n-Si)

Publisher Summary The importance of knowing optical constants in the case of silicon points out to the technologically important applications of this knowledge, these applications include: (1) the determination of epilayer thickness, (2) the losses in all-silicon integrated optical devices, (3) silicon-wafer thermometry, infrared emissivity, and absorbance enhancement in silicon gratings. This chapter includes an overview of dielectric function partition and the relation of optical constants to the measured optical properties, semiclassical, and quantum absorption theory. It introduces the generalized Drude approximation. Further, the chapter illustrates experimental data and the Drude formula with empirically adjusted parameters. It presents a first-principle theory of free carrier contribution to the optical constants in doped n-type silicon (n-Si), based on the generalized Drude approximation. The chapter also outlines the calculations and emphasizes on the difficulties that the theory faces when being used to describe available experimental data. Electromagnetics of homogeneous material is completely defined by the dielectric function. However, the basic quantity of optics is the complex refractive index.

[1]  A. Aziza,et al.  Infrared Absorption in Heavily Doped n-Type Si , 1969 .

[2]  E. Barta Determination of effective mass values by a Kramers-Kronig analysis for variously doped silicon crystals , 1977 .

[3]  H. Meyer Infrared Absorption by Conduction Electrons in Germanium , 1958 .

[4]  David E. Aspnes,et al.  Dielectric properties of heavily doped crystalline and amorphous silicon from 1.5 to 6.0 eV , 1984 .

[5]  H. Driel Optical effective mass of high density carriers in silicon , 1984 .

[6]  Sernelius Temperature-dependent resistivity of heavily doped silicon and germanium. , 1990, Physical review. B, Condensed matter.

[7]  W. Götze,et al.  Homogeneous Dynamical Conductivity of Simple Metals , 1972 .

[8]  J. Humlíček,et al.  Infrared optical constants of n-type silicon , 1988 .

[9]  W. Harrison Scattering of Electrons by Lattice Vibrations in Nonpolar Crystals , 1956 .

[10]  A. Slaoui,et al.  Determination of the Electron Effective Mass and Relaxation Time in Heavily Doped Silicon , 1985, June 16.

[11]  A. Messiah Quantum Mechanics , 1961 .

[12]  M. Auslender,et al.  Theoretical dependence of infrared absorption in bulk-doped silicon on carrier concentration. , 1993, Applied Optics.

[13]  P. A. Schumann,et al.  Phase Shift Corrections for Infrared Interference Measurement of Epitaxial Layer Thickness , 1966 .

[14]  J. C. Irvin,et al.  Resistivity, mobility and impurity levels in GaAs, Ge, and Si at 300°K , 1968 .

[15]  H. Ehrenreich,et al.  Optical Properties of Semiconductors , 1963 .

[16]  L. M. Lambert Free Carrier Reflectivity in Optically Homogeneous Silicon , 1972, June 16.

[17]  Manuel Cardona,et al.  Effect of heavy doping on the optical properties and the band structure of silicon , 1984 .

[18]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[19]  M. Auslender,et al.  Free carrier contribution to dynamic dielectric function of heavily doped semiconductors. Application to n-type silicon , 1992 .

[20]  Olav Solgaard,et al.  All‐silicon integrated optical modulator for 1.3 μm fiber‐optic interconnects , 1989 .

[21]  H. Queisser,et al.  Electron scattering by ionized impurities in semiconductors , 1981 .

[22]  Zemel,et al.  Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: The normal direction. , 1988, Physical review. B, Condensed matter.

[23]  K. Taniguchi,et al.  Ionized impurity scattering rate for full band Monte Carlo simulation in heavily doped n‐type silicon , 1996 .

[24]  J. Irvin,et al.  Resistivity of bulk silicon and of diffused layers in silicon , 1962 .

[25]  M. Auslender,et al.  Zero infrared reflectance anomaly in doped silicon lamellar gratings. I. From antireflection to total absorption , 1995 .

[26]  W. Dumke Quantum Theory of Free Carrier Absorption , 1961 .

[27]  B. Donovan RESEARCH NOTES Note on the Treatment of Impurity Scattering in Optical Absorption in Semiconductors , 1960 .

[28]  M. Lax,et al.  Free-Carrier Absorption in n-Type Ge , 1958 .

[29]  W. Spitzer,et al.  Effect of Heat Treatment on the Optical Properties of Heavily Doped Silicon and Germanium , 1964 .

[30]  H. Mori A Continued-Fraction Representation of the Time-Correlation Functions , 1965 .

[31]  J. F. Gilbert,et al.  Determination of Free Electron Effective Mass of n‐Type Silicon , 1963 .

[32]  H. Meyer Theory of infrared absorption by conduction electrons in germanium , 1959 .

[33]  N. Natsuaki,et al.  Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing , 1981 .

[34]  R. Kubo Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems , 1957 .

[35]  W. Spitzer,et al.  Determination of Optical Constants and Carrier Effective Mass of Semiconductors , 1957 .

[36]  V. I. Fistul Heavily Doped Semiconductors , 1995 .

[37]  J. Sturm,et al.  Silicon temperature measurement by infrared absorption. Fundamental processes and doping effects , 1992 .

[38]  P. Timans Emissivity of silicon at elevated temperatures , 1993 .