Temperature dependence of silicon carrier effective masses with application to femtosecond reflectivity measurements
JOSA B, Vol. 19, Issue 5, pp. 1092-1100 (2002)
http://dx.doi.org/10.1364/JOSAB.19.001092
Acrobat PDF (194 KB)
Abstract
The conductivity effective masses of electrons and holes in Si are calculated for carrier temperatures from 1 to 3000 K. The temperature dependence of the electron mass is calculated by use of a phenomenological model of conduction-band nonparabolicity that has been fitted to experimental measurements of the dependence of the electron conductivity effective mass on carrier concentration. The hole mass is investigated by tight-binding calculations of the valence bands, which have been adjusted to match experimental values of the valence-band curvature parameters at the top of the valence band. The calculations are in excellent agreement with femtosecond-laser reflectivity measurements of the change in optical effective mass as hot carriers cool from 1550 to 300 K.
© 2002 Optical Society of America
OCIS Codes
(160.4760) Materials : Optical properties
(160.6000) Materials : Semiconductor materials
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors
Citation
D. M. Riffe, "Temperature dependence of silicon carrier effective masses with application to femtosecond reflectivity measurements," J. Opt. Soc. Am. B 19, 1092-1100 (2002)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-5-1092
Sort: Year | Journal | Reset
References
- C. Jacoboni and L. Reggiani, “The Monte Carlo method for the solution of charge transport in semiconductors with application to covalent materials,” Rev. Mod. Phys. 55, 645–705 (1983).
- L.-A. Lompre, J.-M. Liu, H. Kurz, and N. Bloembergen, “Optical heating of electron–hole plasma in silicon by picosecond pulses,” Appl. Phys. Lett. 44, 3–5 (1984).
- J.-M. Liu, H. Kurz, and N. Bloembergen, “Picosecond time-resolved plasma and temperature-induced changes of reflectivity and transmission in silicon” Appl. Phys. Lett. 41, 643–646 (1982).
- D. von der Linde and N. Fabricius, “Observation of an electronic plasma in picosecond laser annealing of silicon,” Appl. Phys. Lett. 41, 991–993 (1982).
- C. V. Shank, R. Yen, and C. Hirlmann, “Time-resolved reflectivity measurements of femtosecond-optical-pulse-induced phase transitions in silicon,” Phys. Rev. Lett. 50, 454–457 (1983).
- H. M. van Driel, “Optical effective mass of high density carriers in silicon,” Appl. Phys. Lett. 44, 617–619 (1984).
- G.-Z. Yang and N. Bloembergen, “Effective mass in picosecond laser-produced high-density plasma in silicon,” IEEE J. Quantum Electron. QE-22, 195–196 (1986).
- T. Sjodin, H. Petek, and H.-L. Dai, “Ultrafast carrier dynamics in silicon: a two-color transient-reflection grating study on a (111) surface,” Phys. Rev. Lett. 81, 5664–5667 (1998).
- E. M. Conwell and M. O. Vassell, “High-field transport in n-type GaAs,” Phys. Rev. 166, 797–821 (1968).
- W. G. Spitzer and H. Y. Fan, “Determination of optical constants and carrier effective mass of semiconductors,” Phys. Rev. 106, 882–890 (1957).
- L. E. Howarth and J. F. Gilbert, “Determination of free electron effective mass of n-type silicon,” J. Appl. Phys. 34, 236–237 (1963).
- M. Miyao, T. Motooka, N. Natsuaki, and T. Tokuyama, “Change in the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing,” Solid State Commun. 37, 605–608 (1981).
- A. Borghesi, A. Stella, P. Bottazzi, G. Guizzetti, and L. Reggiani, “Optical determination of Si conduction-band nonparabolicity,” J. Appl. Phys. 67, 3102–3106 (1990).
- D. A. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids (Plenum, New York, 1986).
- D. J. Chadi, “Spin–orbit splitting in crystalline and compositionally disordered semiconductors,” Phys. Rev. B 16, 790–796 (1977).
- W. A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond (Dover, New York, 1989).
- Y. M. Niquet, C. Delerue, G. Allan, and M. Lannoo, “Method for tight-binding parameterization: application to silicon nanostructures,” Phys. Rev. 62, 5109–5116 (2000).
- J. J. Stickler, H. J. Zeigler, and G. S. Heller, “Quantum effects in Ge and Si. I,” Phys. Rev. 127, 1077–1084 (1962).
- J. C. Hensel and G. Feher, “Cyclotron resonance experiments in uniaxially stressed silicon: valence band inverse mass parameters and deformation potentials,” Phys. Rev. 129, 1041–1062 (1963).
- I. Balslev and P. Lawaetz, “On the interpretation of the observed hole mass shift with uniaxial stress in silicon,” Phys. Lett. 19, 6–7 (1965).
- K. Seeger, Semiconductor Physics: An Introduction (Springer, New York, 1982).
- C. Jacoboni, R. Minder, and G. Majni, “Effects of band nonparabolocity on electron drift velocity in silicon above room temperature,” J. Chem. Phys. Solids 36, 1129–1133 (1975).
- G. N. Koskowich, M. Soma, and R. B. Darling, “Near-infrared free-carrier optical absorption in silicon: effect of first-order phonon-assisted scattering in a nonparabolic conduction band,” Phys. Rev. B 41, 2944–2947 (1990).
- F. Wooten, Optical Properties of Solids (Academic, New York, 1972).
- N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).
- O. Madelung, Semiconductors—Basic Data (Springer, New York, 1996).
- J. C. Slater and G. F. Koster, “Simplified LCAO method for the periodic potential problem,” Phys. Rev. 94, 1498–1524 (1954).
- D. J. Chadi and M. L. Cohen, “Tight-binding calculations of the valence bands of diamond and zincblende crystals,” Phys. Status Solidi B 68, 405–419 (1975).
- K. C. Pandey and J. C. Phillips, “Atomic densities of states near Si(111) surfaces,” Phys. Rev. B 13, 750–760 (1976).
- D. A. Papaconstantopoulos and E. N. Economou, “Slater–Koster parameterization for Si and the ideal-vacancy calculation,” Phys. Rev. B 22, 2903–2907 (1980).
- D. N. Talwar and C. S. Ting, “Tight-binding calculations for the electronic structure of isolated vacancies and impurities in III–V compound semiconductors,” Phys. Rev. B 25, 2660–2680 (1982).
- Y. Li and P. J. Lin-Chung, “New semiempirical construction of the Slater–Koster parameters for group-IV semiconductors,” Phys. Rev. B 27, 3465–3470 (1983).
- C. Tserbak, H. M. Polatoglou, and G. Theodorou, “Unified approach to the electronic structure of strained Si/Ge superlattices,” Phys. Rev. B 47, 7104–7124 (1993).
- G. Grosso and C. Piermarocchi, “Tight-binding model and interaction scaling laws for silicon and germanium,” Phys. Rev. B 51, 16772–16777 (1995).
- G. Dresselhaus, A. F. Kip, and C. Kittel, “Cyclotron resonance of electrons and holes in silicon and germanium crystals,” Phys. Rev. 98, 368–384 (1955).
- R. N. Dexter, H. J. Zeigler, and B. Lax, “Cyclotron resonance experiments in silicon and germanium,” Phys. Rev. 104, 637–664 (1956).
- The universal model of Harrison16 has E_{sx}(111)=1.131. Increasing it by 15% to 1.301 produces much better curvature parameters and BZ edge band energies.
- The reported Niquet SK parameters E_{sx}(311), E_{sx}(113), E_{xy}(311), and E_{xy}(113) have signs opposite those of the convention of Papaconstantopoulos. The Papaconstantopoulos convention is used in Table 2.
- M. Dür, K. Unterrainer, and E. Gornik, “Effect of valence-band anisotropy and nonparabolicity on total scattering rates for holes in nonpolar semiconductors,” Phys. Rev. B 49, 13991–13994 (1994).
- B. Lax and J. G. Mavroides, “Statistics and galvanomagnetic effects in germanium and silicon with warped energy surfaces,” Phys. Rev. 100, 1650–1657 (1955).
- J. R. Goldman and J. A. Prybyla, “Ultrafast dynamics of laser-excited electron distributions in silicon,” Phys. Rev. Lett. 72, 1364–1367 (1994).
- S. Jeong and J. Bokor, “Ultrafast carrier dynamics near the Si(100)2×1 surface,” Phys. Rev. B 59, 4943–4951 (1999).
- F. E. Doany and D. E. Grischkowsky, “Measurement of ultrafast hot-carrier relaxation in silicon by thin film enhanced, time-resolved reflectivity,” Appl. Phys. Lett. 52, 36–38 (1988).
- W. Kütt, A. Esser, K. Seibert, U. Lemmer, and H. Kurz, “Femtosecond studies of plasma formation in crystalline and amorphous silicon,” in Applications of Ultrashort Laser Pulses in Science and Technology, A. Antonetti, ed., Proc. SPIE 1268, 154–165 (1990).
- T. Pfeifer, W. Kütt, H. Kurz, and R. Scholz, “Generation and detection of coherent optical phonons in germanium,” Phys. Rev. Lett. 69, 3248–3251 (1992).
- A. J. Sabbah and D. M. Riffe, “Measurement of silicon surface recombination velocity using ultrafast pump–probe reflectivity in the near infrared,” J. Appl. Phys. 88, 6954–6956 (2000).
- O. B. Wright and V. E. Gusev, “Acoustic generation in crystalline silicon with femtosecond optical pulses,” Appl. Phys. Lett. 66, 1190–1192 (1995).
- T. Tanaka, A. Harata, and T. Sawada, “Subpicosecond surface-restricted carrier and thermal dynamics by transient reflectivity measurements,” J. Appl. Phys. 82, 4033–4038 (1997).
- S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
« Previous Article | Next Article »
OSA is a member of CrossRef.