Quantum calculations of the change of refractive index due to free carriers in silicon with nonparabolic band structure

A quantum‐mechanical approach used to calculate the change of refractive index, Δn, due to free carriers in various doped silicon is presented. This approach uses a numerical Kramers–Kronig relation to analyze a calculated carrier‐related absorption spectrum below or near the energy‐band gap. The absorption spectrum is obtained by considering the optical transitions between energy bands and impurity bands, and the free‐carrier absorption due to acoustic phonons, optical phonons, and ionized impurities in a spherical nonparabolic band model. Values of Δn at wavelength λ=1.3 and 1.6 μm for different doping levels are obtained. The results are applicable to both the integrated‐optics applications and optical‐probing applications in silicon.

[1]  B.R. Hemenway,et al.  Optical detection of charge modulation in silicon integrated circuits using a multimode laser-diode probe , 1987, IEEE Electron Device Letters.

[2]  R. Soref,et al.  Electrooptical effects in silicon , 1987 .

[3]  W. Kuzmicz.  Ionization of impurities in silicon , 1986 .

[4]  H. K. Heinrich,et al.  Measurement of real-time digital signals in a silicon bipolar junction transistor using a noninvasive optical probe , 1986 .

[5]  R. Soref,et al.  All-silicon active and passive guided-wave components for λ = 1.3 and 1.6 µm , 1986 .

[6]  H. K. Heinrich,et al.  Noninvasive sheet charge density probe for integrated silicon devices , 1986 .

[7]  B. Ridley.  Quantum Processes in Semiconductors , 1982 .

[8]  P. Schmid,et al.  Optical absorption in heavily doped silicon , 1981 .

[9]  Carlo Jacoboni,et al.  Bulk hot-electron properties of cubic semiconductors , 1979 .

[10]  C. Jacoboni,et al.  A review of some charge transport properties of silicon , 1977 .

[11]  P. K. Basu,et al.  Infrared Free‐Carrier Absorption in n‐Type Silicon , 1972 .

[12]  N. O. Folland.  Shapes of Two-Phonon Recombination Peaks in Silicon , 1970 .

[13]  A. Onton.  Evidence of Intervalley Scattering of Electrons in the Extrinsic Photoconductivity ofn-Type Silicon , 1969 .

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

[15]  M. O. Vassell,et al.  High-Field Transport inn- Type GaAs , 1968 .

[16]  C. M. Randall,et al.  Refractive indices of germanium, silicon, and fused quartz in the far infrared. , 1967, Applied optics.

[17]  H. Ehrenreich.  Band Structure and Electron Transport of GaAs , 1960 .

[18]  D. Long.  Scattering of Conduction Electrons by Lattice Vibrations in Silicon , 1960 .

[19]  W. Dumke.  Two-Phonon Indirect Transitions and Lattice Scattering in Si , 1960 .

[20]  W. G. Spitzer,et al.  Infrared Absorption in n-Type Silicon , 1957 .

[21]  Walter Kohn,et al.  Shallow Impurity States in Silicon and Germanium , 1957 .

[22]  W. Spitzer,et al.  Infrared Absorption in n-Type Germanium , 1956 .