Thermal Wave Techniques

  • Gunnar SuchaneckEmail author
  • Agnes Eydam
  • Gerald Gerlach
Reference work entry


Thermal wave techniques can be used to excite thermal gradients within the volume to be evaluated and, hence, to achieve information on the interior of the sample under test.

The opportunities of thermal waves will be considered for the particular case of embedded piezoelectrics and the evaluation of their polarization state in construction elements, e.g., adaptronic structures. The described methods for this application are based on the pyroelectric effect whereas thermal excitation is induced by laser irradiation. Fundamentals of the pyroelectric effect are given and the resulting thermal problems are analyzed. Thermal methods recording the pyroelectric response both in the frequency (laser intensity modulation method including two- and three-dimensional polarization mapping) and in the time domains (thermal pulse method including thermal pulse tomography, thermal step method, thermal square wave method) are examined. Emphasis is given to the nonuniform resolution of thermal methods providing higher resolution in the near-surface region. Experimental pitfalls are highlighted. Nondestructive evaluation of piezoelectric transducers is illustrated by examples of lead zirconate titanate (PZT) plates embedded into low-temperature co-fired ceramics (LTCC), epoxy resins, thermoplastics, and die-casted aluminum.


  1. Adby PR (1980) Applied circuit theory: matrix and computer methods. Ellis Horwood series in electrical and electronic engineering. Ellis Horwood Ltd, LondonGoogle Scholar
  2. Agnel S, Toureille A, Le Gressus C (1996) Study of the aging of impregnated paper of high power capacitors using the thermal step method and the thermally stimulated currents. Proceedings of conference on electrical insulation and dielectric phenomena – CEIDP ’96.
  3. Ahmed NH, Srinivas NN (1997) Review of space charge measurements in dielectrics. IEEE Trans Dielectr Electr Insul 4:644–656CrossRefGoogle Scholar
  4. Amjadi H (1996) Thermal-pulse investigation of thermally grown silicon dioxide electrets. In: 9th international symposium on electrets (ISE 9).
  5. Angström AJ (1863) XVII. New method of determining the thermal conductibility of bodies. Philos Mag Ser 4 25(166):130–142CrossRefGoogle Scholar
  6. Aryal S, Mellinger A (2013) Resolution-enhanced polarization imaging with focused thermal pulses. J Appl Phys 114:154109CrossRefGoogle Scholar
  7. Bauer S (1993) Method for the analysis of thermal-pulse data. Phys Rev B 47:11049–11055CrossRefGoogle Scholar
  8. Bauer S, Bauer-Gogonea S (2003) Current practice in space charge and polarization profile measurements using thermal techniques. IEEE Trans Dielectr Electr Insul 10:883–902CrossRefGoogle Scholar
  9. Bauer S, Ploss B (1988) Analysis of the spatial distribution of polarization in PVDF-foils from the frequency spectra of the pyroelectric current. In: Proceedings of 6th international symposium on electrets (ISE 6).
  10. Bauer S, Ploss B (1990) A method for the measurement of the thermal, dielectric, and pyroelectric properties of thin films and their applications for integrated heat sensors. J Appl Phys 68:6361–6367CrossRefGoogle Scholar
  11. Baumann T, Dacol F, Melcher RL (1983) Transmission thermal-wave microscopy with pyroelectric detection. Appl Phys Lett 43:71–73CrossRefGoogle Scholar
  12. Bezdetny NM, Zeinally AK, Khutorsky VE (1984) Investigation of the polarization distribution in ferroelectics by a dynamic pyro-effect method [in Russian]. Izv AN SSSR Ser Fiz 48:200–203Google Scholar
  13. Biot MA (1970) Variational principles in heat transfer. Clarendon Press, OxfordzbMATHGoogle Scholar
  14. Blevin WR, Geist J (1974) Influence of black coatings on pyroelectric detectors. Appl Opt 13:1171–1178CrossRefGoogle Scholar
  15. Bloß P, DeReggi AS, Schäfer H (2000) Electric-field profile and thermal properties in substrate-supported dielectric films. Phys Rev B 62:8517–8530CrossRefGoogle Scholar
  16. Bosworth RCL (1946) Thermal inductance. Nature 158:309CrossRefGoogle Scholar
  17. Braccini M, Dupeux M (2012) Mechanics of solid interfaces. Wiley, Hoboken, chapter 8.3.1CrossRefGoogle Scholar
  18. Burfoot JC, Latham RV (1963) A new method for studying movements of electric domain walls. Br J Appl Phys 14:933–934CrossRefGoogle Scholar
  19. Cady WG (1964) Piezoelectricity, vol 2. Dover, New York, pp 699–711Google Scholar
  20. Camia FM (1967) Traité de thermocinétique impulsionelle. Dunod, ParisGoogle Scholar
  21. Carslaw HJ, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Oxford University Press, New YorkzbMATHGoogle Scholar
  22. Chen J, Zhang W, Feng Z, Cai W (2014) Determination of thermal contact conductance between thin metal sheets of battery tabs. Int J Heat Mass Transf 69:473–480CrossRefGoogle Scholar
  23. Chynoweth AG (1956) Dynamic method for measuring the pyroelectric effect with special reference to barium titanate. J Appl Phys 27:78–84CrossRefGoogle Scholar
  24. Clay W, Evans BJ, Latham RV (1974) A nondestructive pyroelectric display of an antiparallel polarization distribution in single-crystal barium titanate. J Phys D Appl Phys 7:1291–1295CrossRefGoogle Scholar
  25. Cole KS, Cole RH (1941) Dispersion and absorption in dielectrics I. Alternating current characteristics. J Chem Phys 9:341–351CrossRefGoogle Scholar
  26. Collins RE (1977) Measurement of charge distribution in electrets. Rev Sci Instrum 48:83–91CrossRefGoogle Scholar
  27. Cook WR, Berlincourt DA, Scholz FJ (1963) Thermal expansion and pyroelectricity in lead titanate zirconate and barium titanate. J Appl Phys 34:1392–1398CrossRefGoogle Scholar
  28. Coufal H, Grygier RK (1989) Charge profiles of thin electret films mapped with subnanosecond thermal pulses. J Opt Soc Am B6:2013–2017CrossRefGoogle Scholar
  29. Coufal HJ, Grygier RK, Horne DE, Fromm JE (1987) Pyroelectric calorimeter for photothermal studies of thin films and adsorbates. J Vac Sci Technol A 5:2875–2889CrossRefGoogle Scholar
  30. D’Azzo JJ, Houpis CH (1999) Nyquist, Bode and Nickols plots. In: Levine WS (ed) Control system fundamentals. CRC Press, Boca Raton, chapter 10.3Google Scholar
  31. Dagher G, Holé S, Lewiner J (2006) A preliminary study of space charge distribution measurements at nanometer spatial resolution. IEEE Trans Dielectr Electr Insul 13:1036–1041CrossRefGoogle Scholar
  32. Davidson DW, Cole RH (1951) Dielectric relaxation in glycerol, propylene glycol, and n-propanol. J Chem Phys 19:1484–1490CrossRefGoogle Scholar
  33. Devonshire AF (1954) Theory of ferroelectrics. Adv Phys 3:85–130zbMATHCrossRefGoogle Scholar
  34. Eydam E, Suchaneck G, Esslinger S, Schönecker A, Neumeister P, Gerlach G (2014) Polarization characterization of PZT disks and of embedded PZT plates by thermal wave methods. AIP Conf Proc 1627:31–36CrossRefGoogle Scholar
  35. Eydam A, Suchaneck G, Schwankl M, Gerlach G, Singer RF, Körner C (2015) Evaluation of polarisation state of light metal embedded piezoelectrics. Adv Appl Ceram 114:226–230CrossRefGoogle Scholar
  36. Eydam A, Suchaneck G, Gerlach G (2016a) Characterisation of the polarisation state of embedded piezoelectric transducers by thermal waves and thermal pulses. J Sensor Sensor Syst 5:165–170CrossRefGoogle Scholar
  37. Eydam A, Suchaneck G, Gerlach G (2016b) Non-destructive evaluation of integrated piezoelectric transducers by thermal waves and thermal pulses. Procedia Technol 26:59–65CrossRefGoogle Scholar
  38. Eydam A, Suchaneck G, Gerlach G (2016c) Thermal-pulse method for life monitoring of integrated piezoelectric transducers. Procedia Eng 168:848–851CrossRefGoogle Scholar
  39. Flössel M, Gebhardt S, Schönecker A, Michaelis A (2010) Development of a novel sensor-actuator-module with ceramic multilayer technology. J Ceram Sci Technol 1:55–58Google Scholar
  40. Gaudenzi P (2009) Smart structures: physical behaviour, mathematical modelling and applications. Wiley, ChichesterCrossRefGoogle Scholar
  41. Gerlach G, Shvedov D, Norkus V (2004) Packaging influence on acceleration sensitivity of pyroelectric infrared detectors. In: Proceedings of sixth IEEE CPMT conference on high density microsystem design and packaging and component failure analysis, HDP’04.
  42. Gerlach G, Suchaneck G, Movchikova A, Malyshkina OA (2007) Nondestructive testing of ferroelectrics by thermal wave methods. Proc SPIE 6530:65300B. Scholar
  43. Glass AM (1968) Dielectric, thermal, and pyroelectric properties of ferroelectric LiTaO3. Phys Rev 172:564–571CrossRefGoogle Scholar
  44. Göber H, Erk S, Grigull U (1955) Die Grundgesetze der Wärmeübertragung. Springer, Berlin, p 82CrossRefGoogle Scholar
  45. Groetsch CW (2007) Integral equations of the first kind, inverse problems and regularization: a crash course. J Phys Conf Ser 73:012001CrossRefGoogle Scholar
  46. Hadni A, Thomas R (1972) Laser study of reversible nucleation sites in triglycine sulphate and applications to pyroelectric detectors. Ferroelectrics 4:39–49CrossRefGoogle Scholar
  47. Hadni A, Henninger Y, Thomas R, Vergnat P, Bruno Wyncke B (1965) Sur les propriétés pyroélectriques de quelques matériaux et leur application à la détection de l’infrarouge. J Phys France 26:345–360CrossRefGoogle Scholar
  48. Hadni A, Thomas R, Perrin J (1969) Response of a triglycine sulphate pyroelectric detector to high frequencies (300 kHz). J Appl Phys 40:2740–2745CrossRefGoogle Scholar
  49. Havriliak S, Negami S (1967) A complex plane representation of dielectric and mechanical relaxation processes in some polymers. Polymer 8:161–210CrossRefGoogle Scholar
  50. Holé S (2008) Resolution of direct space charge distribution measurement methods. IEEE Trans Dielectr Electr Insul 15:861–871CrossRefGoogle Scholar
  51. Hufenbach W, Gude M, Modler N, Heber T, Winkler A, Weber T (2013) Process chain modelling and analysis for the high-volume production of thermoplastic composites with embedded piezoceramic modules. Smart Mater Res 2013:201631Google Scholar
  52. Imburgia I, Romano P, Caruso M, Viola F, Miceli R, Riva Sanseverino E, Madonia A, Schettino G (2016) Contributed review: review of thermal methods for space charge measurement. Rev Sci Instrum 87:111501CrossRefGoogle Scholar
  53. Kepler RG, Anderson RA (1978) Piezoelectricity and pyroelectricity in polyvinylidene fluoride. J Appl Phys 49:4490–4494CrossRefGoogle Scholar
  54. Kremer F, Schoenhals A (eds) (2003) Broadband dielectric spectroscopy. Springer, Berlin, pp 62–72Google Scholar
  55. Landau LD, Lifshitz EM (1969) Mechanics (Volume 1 of a course of theoretical physics). Pergamon Press, Oxford, p 59Google Scholar
  56. Lang SB (1990) New theoretical analysis for the laser intensity modulation method (LIMM). Ferroelectrics 106:269–274CrossRefGoogle Scholar
  57. Lang SB (1991) Laser intensity modulation method (LIMM): experimental techniques, theory and solution of the integral equation. Ferroelectrics 118:343–361CrossRefGoogle Scholar
  58. Lang SB (1998) An analysis of the integral equation of the surface laser intensity modulation method using the constrained regularization method. IEEE Trans Dielectr Electr Insul 5:70–76CrossRefGoogle Scholar
  59. Lang SB (2004) Laser intensity modulation method (LIMM): review of the fundamentals and a new method for data analysis. IEEE Trans Dielectr Electr Insul 11:3–12CrossRefGoogle Scholar
  60. Lang SB (2006) Fredholm integral equation of the laser intensity modulation method (LIMM): solution with the polynomial regularization and L-curve methods. J Mater Sci 41:147–153CrossRefGoogle Scholar
  61. Lang SB, Das-Gupta DK (1986) Laser-intensity-modulation method: a technique for determination of spatial distributions of polarization and space charge in polymer electrets. J Appl Phys 59:2151–2160CrossRefGoogle Scholar
  62. Lang SB, Fleming R (2009) A comparison of three techniques for solving the Fredholm integral equation of the laser intensity modulation method (LIMM). IEEE Trans Dielectr Electr Insul 16:809–814CrossRefGoogle Scholar
  63. Lang SB, Rosenman G, Rushin S, Kugel V, Nir D (1992) Electron emission and spontaneous polarization distribution of proton-exchanged LiNbO3. Ferroelectrics 133:253–258CrossRefGoogle Scholar
  64. Leal Ferreira GF (1989) On the deconvolution of heat-pulse like signals. J Appl Phys 66:4924–4927CrossRefGoogle Scholar
  65. Lines ME, Glass AM (1977) Principles and application of ferroelectrics and related materials. Clarendon Press, Oxford, chapter 5.2Google Scholar
  66. Liu ST, Zook JD (1974) Evaluation of Curie constants of ferroelectric crystals from pyroelectric response. Ferroelectrics 7:171–173CrossRefGoogle Scholar
  67. Liu S, Grinberg I, Rappe AM (2013) Exploration of the intrinsic inertial response of ferroelectric domain walls via molecular dynamics simulations. Appl Phys Lett 103:232907CrossRefGoogle Scholar
  68. Mah JW, Shanmugan S, Mutharasu D (2017) Impact of temperature, pressure, and current on thermal resistance of thermal interface material in optoelectronics device. J Optoelectron Biomed Mater 9:79–84Google Scholar
  69. Malyshkina OV, Movchikova AA, Suchaneck G (2007) New method for the determination of the pyroelectric current spatial distribution in ferroelectric materials [in Russian]. Phys Solid State 49:2144–2147 [Fiz Tverd Tela 49:2045–2048]CrossRefGoogle Scholar
  70. Malyshkina OV, Movchikova AA, Grechishkin RM, Kalugina ON (2010) Use of the thermal square-wave method to analyze polarization state in ferroelectric materials. Ferroelectrics 400:63–75CrossRefGoogle Scholar
  71. Mandelis A, Zver MM (1985) Theory of photopyroelectric spectroscopy of solids. J Appl Phys 57:4421–4430CrossRefGoogle Scholar
  72. Mandelis A, Nicolaides L, Yan C (2001) Structure and the reflectionless/refractionless nature of parabolic diffusion-wave fields. Phys Rev Lett 87:020801CrossRefGoogle Scholar
  73. Mellinger A (2004) Unbiased iterative reconstruction of polarization and space charge profiles from thermal-wave experiments. Meas Sci Technol 15:1347–1353CrossRefGoogle Scholar
  74. Mellinger A, Singh R, Gerhard-Multhaupt R (2005a) Fast thermal-pulse measurements of space-charge distributions in electret polymers. Rev Sci Instrum 76:013903CrossRefGoogle Scholar
  75. Mellinger A, Singh R, Wegener M, Wirges W, Gerhard-Multhaupt R, Lang SB (2005b) Three-dimensional mapping of polarization profiles with thermal pulses. Appl Phys Lett 86:082903CrossRefGoogle Scholar
  76. Mellinger A, Flores-Suárez R, Wegener M, Wirges W, Gerhard-Multhaupt R, Singh R (2006) Thermal-pulse tomography of polarization distributions in a cylindrical geometry. IEEE Trans Dielectr Electr Insul 13:1030–1035CrossRefGoogle Scholar
  77. Mopsik FI, DeReggi AS (1982) Numerical evaluation on the dielectric polarization distribution from thermal pulse data. J Appl Phys 53:4333–4339CrossRefGoogle Scholar
  78. Movchikova A, Malyshkina OV, Pedko BB, Suchaneck G, Gerlach G (2008a) Polarization profiling of ferroelectrics by thermal square wave methods. Ferroelectrics 367:38–44CrossRefGoogle Scholar
  79. Movchikova A, Malyshkina O, Suchaneck G, Gerlach G, Steinhausen R, Langhammer HT, Pientschke C, Beige H (2008b) Study of the pyroelectric behavior of BaTi1-xSnxO3 piezo-ceramics. J Electroceram 20:43–46CrossRefGoogle Scholar
  80. Movchikova A, Malyshkina OV, Pedko BB, Suchaneck G, Gerlach G (2009) The influence of doping on the pyroelectric response of SBN single crystals. Ferroelectrics 378:186–194CrossRefGoogle Scholar
  81. Movchikova A, Suchaneck G, Malyshkina OV, Pedko BB, Gerlach G (2010) Thermal wave study of piezoelectric coefficient distribution in PMN-PT single crystals. Adv Appl Ceram 109:131–134CrossRefGoogle Scholar
  82. Neugschwandtner GS, Schwödiauer R, Bauer-Gogonea S, Bauer S (2001) Piezo- and pyroelectricity of a polymer-foam space-charge electret. J Appl Phys 89:4503–4511CrossRefGoogle Scholar
  83. Notingher P, Agnel S, Fruchier O, Toureille A, Rousset B, Sanchez JL (2004) On the use of the thermal step method as a tool for characterizing thin layers and structures for micro and nano-electronics. J Optoelectron Adv Mater 6:1089–1906Google Scholar
  84. Notingher P, Holé S, Baudon S, Fuchier O, Boyer L, Agnel S (2012) Toward non-destructive high resolution thermal methods for electric charge measurements in solid dielectrics and components. In: ESA2012- electrostatics joint conference, Cambridge, June 2012. Online publication. Accessed 24 Nov 2017
  85. Nye JF (1995) Physical properties of crystals: their representation by tensors and matrices. Clarendon Press, Oxford, chapter 10.4.4zbMATHGoogle Scholar
  86. Parker WJ, Jenkins RJ, Butler CP, Abbott GL (1961) Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J Appl Phys 32:1679–1684CrossRefGoogle Scholar
  87. Perrin B, Bonello B, Jeannet J-C, Romatet E (1996) Interferometric detection of hypersound waves in modulated structures. Prog Nat Sci 6:444–448Google Scholar
  88. Perry CH, Khan BN, Rupprecht G (1964) Infrared studies of perovskite titanates. Phys Rev 135:A408–A412CrossRefGoogle Scholar
  89. Peterson RL, Day GW, Gruzensky PM, Phelan RJ (1974) Analysis of response of pyroelectric optical detector. J Appl Phys 45:3296–3303CrossRefGoogle Scholar
  90. Petre A, Marty-Dessus D, Berquez L, Franceschi JL (2006) Space charge cartography by FLIMM on SEM-irradiated PTFE thin films. J Electrost 64:492–497CrossRefGoogle Scholar
  91. Petzelt J, Nuzhnyy D, Bovtun V, Kempa M, Savinov M, Kamba S, Hlinka J (2015) Lattice dynamics and dielectric spectroscopy of BZT and NBT lead-free perovskite relaxors – comparison with lead-based relaxors. Phase Transit 88:320–332CrossRefGoogle Scholar
  92. PI Ceramic GmbH (2017) Piezoelectric ceramic products: fundamentals, characteristics and applications. Accessed 24 Nov 2017
  93. Ploss B, Bianzano O (1994) Polarization profiling of the surface region of PVDF and P(VDF-TrFE).In: IEEE 8th international symposium on electrets.
  94. Ploss B, Emmerich R, Bauer S (1992) Thermal wave probing of pyroelectric distributions in the surface region of ferroelectric materials: a new method of analysis. J Appl Phys 72:5363–5370CrossRefGoogle Scholar
  95. Prudnikov AP, Brychkov YA, Marichev OI (1992) Integrals and series, vol. 1: Elementary functions. Taylor & Francis, London, p 730Google Scholar
  96. Putley EH (1970) The pyroelectric detector. In: Willardson RK, Beer AC (eds) Semiconductors and semimetals, vol 5. Academic, New York, pp 259–285Google Scholar
  97. Qiu X, Hollander L, Flores Suarez R, Wirges W, Gerhard R (2010) Polarization from dielectric-barrier discharges in ferroelectrets: mapping of the electric-field profiles by means of thermal-pulse tomography. Appl Phys Lett 97:072905CrossRefGoogle Scholar
  98. Raffmetal (2017) EN 46000 data sheet. Accessed 24 Nov 2017
  99. Reboul JM (2011) Thermal waves interferences for space charge measurements in dielectrics. In: 14th international symposium on electrets (ISE).
  100. Reboul JM, Mady F (2004) Space charge measurements by the alternating thermal wave method: thermal analysis and simulations for data processing improvement. In: Proceedings of the 2004 I.E. international conference on solid dielectrics ICSD.
  101. Reboul JM, Cherifi A, Carin R (2001) A new method for space charge measurements in dielectric films for power capacitors. IEEE Trans Dielectr Electr Insul 8:753–759CrossRefGoogle Scholar
  102. Rose A (1973) Vision – human and electronic. Plenum Press, New YorkGoogle Scholar
  103. Rübner M, Körner C, Singer RF (2008) Integration of piezoceramic modules into die castings – procedure and functionalities. Adv Sci Technol 56:170–175CrossRefGoogle Scholar
  104. Sakai S, Date M, Furukawa T (2002) Development of polarization distribution in fatigued films of ferroelectric vinylidene fluoride/trifluoroethylene copolymer. Jpn J Appl Phys 41:3822–3828CrossRefGoogle Scholar
  105. Salazar A (2006) Energy propagation of thermal waves. Eur J Phys 27:1349–1355MathSciNetzbMATHCrossRefGoogle Scholar
  106. Samoilov VB, Yoon YS (1998) Frequency response of multilayer pyroelectric sensors. IEEE Trans Ultrason Ferroelectr Freq Control 45:1246–1254CrossRefGoogle Scholar
  107. Sandner T (2003) Verfahren zur tiefenaufgelösten Polarisationsbestimmung von pyroelektrischen PZT-Dünnschichten für IR-Sensoren. w.e.b.-Universitätsverlag, DresdenGoogle Scholar
  108. Sandner T, Suchaneck G, Koehler R, Suchaneck A, Gerlach G (2002) High frequency LIMM – a powerful tool for ferroelectric thin film characterization. Integr Ferroelectr 46:243–257CrossRefGoogle Scholar
  109. Schein LB, Cressman PJ, Cross LE (1978) Electrostatic measurements of tertiary pyroelectricity in partially clamped LiNbO3. Ferroelectrics 22:945–948CrossRefGoogle Scholar
  110. Sea Ceramics Technology (2017a) Thermal properties of ceramics and metal/metal composites. Accessed 24 Nov 2017
  111. Sea Ceramics Technology (2017b) Table of LTCC materials properties. Accessed 24 Nov 2017
  112. Sessler GM (1997) Charge distribution and transport in polymers. IEEE Trans Dielectr Electr Insul 4:614–628CrossRefGoogle Scholar
  113. Stewart M, Cain M (2008) Spatial characterization of piezoelectric materials using the scanning laser intensity modulation method (LIMM). J Am Ceram Soc 91:2176–2181CrossRefGoogle Scholar
  114. Suchaneck G, Lin W-M, Koehler R, Sandner T, Gerlach G, Krawietz R, Pompe W, Deineka A, Jastrabik L (2002) Characterization of RF-sputtered self-polarized PZT thin films for IR sensor arrays. Vacuum 66:473–478CrossRefGoogle Scholar
  115. Suchaneck G, Hu W, Gerlach G, Flössel M, Gebhardt S, Schönecker A (2011) Nondestructive evaluation of polarization in LTCC/PZT piezoelectric modules by thermal wave methods. Ferroelectrics 420:25–29CrossRefGoogle Scholar
  116. Suchaneck G, Eydam A, Hu W, Kranz B, Drossel W-G, Gerlach G (2012) Evaluation of polarization of embedded piezoelectrics by the thermal wave method. IEEE Trans Ultrason Ferroel Freq Control 59:1950–1954CrossRefGoogle Scholar
  117. Suchaneck G, Eydam A, Rübner R, Schwankl M, Gerlach G (2013a) A simple thermal wave method for the evaluation of the polarization state of embedded piezoceramics. Ceram Int 39-S1:S587–S590CrossRefGoogle Scholar
  118. Suchaneck G, Eydam A, Gerlach G (2013b) A laser intensity modulation method for the evaluation of the polarization state of embedded piezoceramics. Ferroelectrics 453:127–132CrossRefGoogle Scholar
  119. Toureille A, Reboul JP (1988) The thermal-step-technique applied to the study of charge decay in polyethylene thermoelectrets. In: IEEE 6th international symposium on electrets (ISE 6).
  120. Tuncer E, Lang SB (2006) Kramers-Kronig relations in laser intensity modulation method. Phys Rev B 74:113109CrossRefGoogle Scholar
  121. van der Ziel A (1973) Pyroelectric response and D* of thin pyroelectric films on a substrate. J Appl Phys 44:546–549CrossRefGoogle Scholar
  122. Voigt W (1910) Lehrbuch der Kristallphysik. Teubner, LeipzigzbMATHGoogle Scholar
  123. von Laue M (1925) Piezoelektrisch erzwungene Schwingungen von Quarzstäben. Z Phys 34:347–361zbMATHCrossRefGoogle Scholar
  124. von Seggern H (1978) Thermal-pulse technique for determining charge distributions: effect of measurement accuracy. Appl Phys Lett 33:134–137CrossRefGoogle Scholar
  125. von Seggern H, West JE, Kubli RA (1984) Determination of charge centroids in two-side metallized electrets. Rev Sci Instrum 55:964967Google Scholar
  126. Wilkie WK, Bryant GR, High JW. Fox RL, Hellbaum RF, Jalink A, Little BD, Mirick PH (2000) Low-cost piezocomposite actuator for structural control applications. In: Proceedings of SPIE 3991, smart structures and materials 2000: industrial and commercial applications of smart structures technologies.
  127. Wu Q, Zhang X-C (1995) Free-space electro-optic sampling of terahertz beams. Appl Phys Lett 67:3523–3525CrossRefGoogle Scholar
  128. Xu-Sheng W (1993) Tertiary pyroelectric effect on thick ferroelectric crystal plates with partially uniform heating. Ferroelectr Lett Sect 15:159–165CrossRefGoogle Scholar
  129. Yilmaz S, Bauer S, Wirges W, Gerhard-Multhaupt R (1993) Scanning electro-optical and pyroelectrical microscopy for the investigation of polarization patterns in poled polymers. Appl Phys Lett 63:1724–1726CrossRefGoogle Scholar
  130. Zajosz J (1979) Pyroelectric response to step radiation signals in thin ferroelectric films on a substrate. Thin Solid Films 62:229–236CrossRefGoogle Scholar
  131. Zheng F, Zhang Y, An Z, Liu C, Dong J, Lin C (2013) Thermal pulse method with an applied field. In: IEEE international conference on solid dielectrics (ICSD).
  132. Zook JD, Liu ST (1978) Pyroelectric effect in thin film. J Appl Phys 49:4604–4606CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Solid State ElectronicsTechnische Universität DresdenDresdenGermany

Section editors and affiliations

  • Ida Nathan
    • 1
  • Norbert Meyendorf
    • 2
  1. 1.Department of Electrical and Computer EngineeringUniversity of AkronAkronUSA
  2. 2.Center for Nondestructive EvaluationIowa State UniversityAmesUSA

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