Dragana K. Markushev, Dragan D. Markushev, Slobodanka Galović, Sanja Aleksić, Dragan Pantić, Dragan М. Todorović

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The temperature distributions in the n-type silicon circular plate, excited by a frequency-modulated light source from one side, are investigated theoretically in the frequency domain. The influence of the photogenerated excess carrier density on the temperature distributions is considered with respect to the sample thickness, surface quality and carrier lifetime. The presence of the thermalization and non-radiative recombination processes are taken into account. The existence of the fast and slow heat sources in the sample is recognized. It is shown that the temperature distribution on sample surfaces is a sensitive function of an excess carrier density under a bulk and surface recombination. The most favorable values of surface velocities ratio and bulk lifetime are established, assigned for a simpler and more effective analysis of the carrier influence in semiconductors. The photothermal and photoacoustic transmission detection configuration is proposed as a most suitable experimental scheme for the investigation of the excess carrier influence on the silicon surface temperatures.


semiconductor, surface recombination, bulk lifetime, photogeneration, excess carriers, periodic thermal excitation, temperature distribution, frequency domain, photothermal, photoacoustic

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L. A. Skvortsov, “Laser photothermal spectroscopy of light-induced absorption”, Quantum Electronics, vol. 43, pp. 1–13, 2013.

P. Almond, P. Patel, 1996 Photothermal Science and Technique (London: Chapman and Hall)

S. Bialkowski, 1996 Photothermal Spectroscopy Methods for Chemical Analysis (New York: John Wiley)

B. G. Streetman and S. Banerjee, 2000 Solid State Electronic Devices, 5th edition (Prentice Hall)

S. M, Sze, Semiconductor Devices Physics and Technology, 2nd edition, (1985, 2002) by John Wiley & Sons

Shyn Wang, Fundamentals of Semiconductor Theory and Device Physics, Prentice Hall International, Inc, Englewood Cliiffs, Nj 07632, USA, ISBN 0-13-344425-2)

Y. Chen, Y. Dai, H. Chou, I. Chang, " Photoinduced Absorption Studied by Photothermal Deflection Spectroscopy: Its Application to the Determination of the Energy of Dangling-Bond States in a-Si:H", Chinese Journal of Physics, vol. 31, pp. 767-772, 1993.

J. Kitao, Y. Kasuya, T. Kunii, N. Yoshida, S. Nonomura, "Photoinduced effects on infrared and near infrared absorption of amorphous and microcrystalline Si measured by photothermal bending spectroscopy", Analytical Sciences, vol. 17, pp. 302-304, 2001.

M.A. Nigro, M. Gagliardi, F.G.D. Corte, "Measurement of the IR absorption induced by visible radiation in amorphous silicon and silicon carbide thin films by an in-guide technique", Optical Materials, vol. 30, p. 1240, 2008.

L. Goris, K. Haenen, M. Nesládek, P. Wagner, D. Vanderzande, L. Schepper, J. D’haen, L. Lutsen, J. Manca, "Absorption phenomena in organic thin films for solar cell applications investigated by photothermal deflection spectroscopy", Journal of Materials Sciences, vol. 40, pp. 1413-1418, 2005.

K. Tanaka, T. Gotoh, N. Yoshida, S. Nonomura, "Photothermal deflection spectroscopy of chalcogenide glasses", Journal of Applied Physics, vol. 91, p. 125, 2002.

L. Xiao, L. Changyoung, L. Zhang, Y. Zhao, S. Jia, G. Zhou, "Pulsed-laser Pumped Photothermal Deflection Spectroscopy for Liquid Thermal Diffusivity Measurement", Chinese Journal Lasers B, vol. B9, pp. 538-544, 2000.

Li Y., Gupta R., "An investigation of the photothermal deflection spectroscopy technique for temperature measurements in a flame" Applied Physics B: Lasers and Optics, 75, 103-112 (2002)

Photoacoustic and Thermal Wave Phenomena in Semiconductors by A. Mandelis (Editor), 1987 (North-Holland)

J. Batista, A. Mandelis and D. Shaughnessy, “Temperature dependence of carrier mobility in Si wafers measured by infrared photocarrier radiometry”, Appl. Phys. Lett., vol. 82, pp. 4077-4079 (Jun. 9, 2003).

K.M. Gupta, Nishu Gupta, "Carrier Transport in Semiconductors" in Advanced Semiconducting Materials and Devices, Part of the series Engineering Materials (2016) (Springer International Publishing Switzerland), pp 87-144.

Igor Lashkevych, Oleg Titov and Yuri G Gurevich, Recombination and temperature distribution in semiconductors, Semiconductor Science and Technology, vol. 27, 055014 (7pp), 2012.

Arnau Vives A. 2008 Piezoelectric Transducers and Applications (Springer-Verlag Berlin Haidelberg New York),

Min-hang Bao 2000 Micro Mechanical Transducers: Pressure Sensors, Accelerometers, and Gyroscopes Handbook of Sensors and Actuators, Volume 8, (Elsevier Publishing Company)

D.D. Markushev, M.D. Rabasovic, D.M. Todorovic, S. Galovic, S.E. Bialkowski, Review of Scientific Instruments, vol. 86, p. 035110, 2015.

Schroder, Dieter K. Semiconductor Material and Device Characterization 2006, 3rd Ed. John Wiley and Sons, Inc. Hoboken, New Jersey.

D. M. Todorović, P. M. Nikolić, M. D. Dramićanin, D. G. Vasiljević, Z. D. Ristovski, “Photoacoustic frequency heat-transmission technique: Thermal and carrier transport parameters measurements in silicon”, Journal of Applied Physics, vol. 78, p. 5790, 1995.

D. M. Todorović, P. M. Nikolić, A. I. Bojičić, and K. T. Radulović, " Thermoelastic and electronic strain contributions to the frequency transmission photoacoustic effect in semiconductors" Physical Review B, vol. 55, pp. 15631–15642, 1997.

A. Mandelis, R. Bleiss, F. Shimura, "Highly resolved separation of carrier‐ and thermal‐wave contributions to photothermal signals from Cr‐doped silicon using rate‐window infrared radiometry", Journal of Applied Physics, vol. 74, p. 3431, 1993 .

Y. G Gurevich, I. Lashkevych, "Sources of Fluxes of Energy, Heat, and Diffusion Heat in a Bipolar Semiconductor: Influence of Nonequilibrium Charge Carriers", International Journal of Thermophysics, vol. 34, p. 341, 2013.

O. Palais, J. Gervais, S. Martinuzzi, “High resolution lifetime scan maps of silicon wafers”, Materials Science and Engineering: B, vol. 71, pp. 47-50, 2000.

Andres Cuevas, Daniel Macdonald, "Measuring and interpreting the lifetime of silicon wafers", Solar Energy, vol. 76, no. 1-3, pp. 255-262, 2003.

K.T. Radulović, P.M. Nikolić, D. Vasiljević-Radović, D. M. Todorović, S.S. Vujović, A.I. Bojicić, V. Blagojević, D. Urosević, “A Contribition of Carrier Transport Processes to the Photoacoustic Effects in Doped Narrow Gap Semiconductors”, Review of Scientific Instruments, vol. 74, p. 595, 2003.

Gary Hodes, Prashant V. Kamat, "Understanding the Implication of Carrier Diffusion Length in Photovoltaic Cells", The Journal of Physical Chemistry Letters, vol. 6, pp. 4090−4092, 2015.

A. B. Sproul, “Dimensionless solution of the equation describing the effect of surface recombination on carrier decay in semiconductors”, Journal of Applied Physics, vol. 76, pp. 2851-2854, 1994.

M. D. Dramićanin, P. M. Nikolić, Z. D. Ristovski, D. G. Vasiljević, and D. M. Todorović, "Photoacoustic investigation of transport in semiconductors: Theoretical and experimental study of a Ge single crystal", Physical Review B, vol. 51, pp. 14226, 1995.

Yuri G. Gurevich, Georgiy N.Logvinov, Gerardo G. de la Cruz, and Gabino Espejo Lopez, "Physics of thermal waves in homogeneous and inhomogeneous (two-layer) samples", International Jornal of Thermal Sciences, vol. 42, pp. 63-69, 2003.

G. Gonzalez da la Cruz and Yu. G. Gurevich, Thermal diffusivity of a two-layered systems, Physical Review B, vol. 51, pp. 2188-2192, 1995.

Ordonez-Miranda, J.J. Alvarado-Gil, "Determination of thermal properties for hyperbolic heat transport using a frequency-modulated excitation source", International Journal of Engineering Science, vol. 50, pp. 101–112, 2012.

S. Galovic and D. Kostoski, "Photothermal wave propagation in media with thermal memory", Journal of Applied Physics, vol. 93, pp. 3063-3070, 2003.

A. Vedavarz, S. Kumar, & M. K. Moallemi, "Significance of non-Fourier heat waves in conduction", Journal of Heat Transfer–Transactions of the ASME, vol. 116, pp. 221–224, 1994.


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