Permittivity of Strontium Titanate R. C. Neville, B. Hoeneisen, and C. A. Mead Citation: Journal of Applied Physics 43, 2124 (1972); doi: 10.1063/1.1661463 View online: http://dx.doi.org/10.1063/1.1661463 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/43/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Thickness-induced resonance-based complex permittivity measurement technique for barium strontium titanate ceramics at microwave frequency Rev. Sci. Instrum. 80, 114703 (2009); 10.1063/1.3237244 Surface structure of strontium titanate J. Appl. Phys. 105, 083526 (2009); 10.1063/1.3106615 Anomalous resonance of strontium titanate J. Appl. Phys. 43, 3903 (1972); 10.1063/1.1660845 Photoconductivity in Photochromic Strontium Titanate J. Appl. Phys. 42, 1131 (1971); 10.1063/1.1660156 Raman Spectrum of Strontium Titanate J. Chem. Phys. 48, 2240 (1968); 10.1063/1.1669418 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 131.215.225.197 On: Mon, 15 Dec 2014 18:05:37 Permittivity of Strontium Titanate R. C. Neville Department of Electrical Engineering, University of California, Santa Barbara, California 93106 and B. Hoeneisen and C. A. Mead Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91109 (Received 25 October 1971) The permittivity of single-crystal single-domain strontium titanate has been measured in detail in the [001), [011), and [111) directions, as a function of temperature (from 4.2 to 300 o K), electric field (from - 23000 to +23000 V/cm, and frequency (from 1 kHz to 50 MHz). The free energy of the crystal is determined as a function of polarization with tem­ perature as a parameter. The Curie-Weiss law is satisfied in the temperature range 60- 300oK, giving a Curie temperature of 30± 2 oK for the three crystal orientations. The Lyddane-Sachs-Teller (LST) relation is satisfied for temperatures between 30 and 300 0 K and for electric fields between 0 and 12000 V/cm. A generalized LST relation is used to calculate the permittivity of strontium titanate from zero to optic frequencies. Two active optic modes are important. The lower-frequency mode is attributed mainly to motion of the strontium ions with respect to the rest of the lattice, while the higher-frequency active mode is attributed to motion of the titanium ions with respect to the oxygen lattice. The re­ storing forces that act on the Ti ions begin to "harden" when these ions are displaced ap­ proximately 0.002 A from their equilibrium positions. I. INTRODUCTION helium temperatures is consistent with the presence of strontium titanate has been studied only relatively re­ multiple domains at temperatures below 65 OK, and that cently and is becoming increasingly important as a suppression of the domains results in a dielectric con­ dielectric material in high-value capacitors. I As a stant which is frequency independent between 1 kHz and member of the peroskvite family of compounds, 2 stron­ 50 MHz. tium titanate is cubic in structure at room temperature. We report in this paper on the relative permittivity of The cube structure consists of a small titanium atom at Single -domain strontium titanate crystals. Crystal the center, and oxygen atoms in each of the six cube samples oriented in the [100], [110], and [111] direc­ walls forming a cage around the titanium atom, and tions were used. A temperature range from 4.2 to small strontium atoms at the cube corners. 3 As the 300 OK was covered for applied dc field strengths from temperature is reduced the crystal structure becomes - 23000 to + 23 000 V /cm and measurement frequencies tetragonal at 110 OK, and at 65 OK the structure becomes from 1 kHz to 50 MHz. A careful search for thermal orthorhombic. 2 The pure crystal is an insulator at room and electrical hystereSis and other evidences of ferro­ temperature with a band gap of 3.15 eV.4 Upon reduction electricity14_16 was made although none was found. by heating in a hydrogen atmosphere, the clear color­ less insulating crystal becomes an n-type semiconduc­ As reported for multiple-domain strontium titanate,6,IO tor, and the color shifts to a varying shade of blue as a the observed inverse dielectric constant, for tempera­ tures above 65 OK, follows a Curie-Weiss-law tempera­ result of the free-carrier absorption. 5 ture variation9 ,lO,17,lB with a Curie temperature of Although used extensively in capacitors, no systematic 30 OK. 6 The relative permittivity was determined to be a study of the relative permittivity of single-domain smooth function of temperature and electric field in the strontium titanate has been conducted. Reported studies vicinity of the Curie temperature. A phenomenological have primarily concerned themselves with multidomain expression was developed for the free energy of the structure strontium titanate crystals, and the published crystal as a function of orientation. The relative per­ data have been a function of temperature, electrical bi­ mittivity is extrapolated to optical frequencies using a as, and frequency of measurement. At room tempera­ generalized Lyddane-Sachs-Teller relation. 19 Evidence ture the value for the relative permittivity of [001]­ indicates that both the titanium and the strontium atoms oriented strontium titanate has been determined to be contribute to the polarization effects. 330± 10,6 independent of frequency of measurement and applied field strength. For [Ol1]-oriented material the II. SAMPLE PREPARATION relative permittivity was found to be 458 and for [111] Two clear colorless boules of strontium titanate with orientations 448. At 77 OK the relative permittivity of reSistivity in excess of 1011 n cm were used. The strontium titanate was found to be 1880 for [OO1]-orient­ boules, obtained from the National Lead Company, were ed material, 2640 for [Oll]-oriented material, and grown with the same processing.l Using a diamond saw, 2580 for [111] orientation. 6 Ruppreche reports that the the boules were sliced into 10 thin wafers 1. 5 mm thick relative permittivity is independent of the measurement in a direction parallel to the (100), (110), or (111) face. frequency from 1 kHz to 26 GHz between 93 and 300 OK. Itschner and GrlUlicherB report field strength indepen­ One thin wafer from each boule was cut into bars 1 x 1. 5 dence of the relative dielectric constant for fields up to xl. 5 mm using a diamond saw. These bars were 106 V fcm above 110 OK. At liquid-helium temperature cleaned by etching in phosphoric acid for 10 min fol­ (4.2 OK) there is a wide range in reported values of the lowed by immersion in hydrochloric acid for 10 min to B 13 relative permittivity of strontium titanate - under a remove the phosphates. After 15-min rinse in flowing wide range of applied bias field and measurement fre­ deionized water, the sample bars were dried in a jet of quencies. Neville et al.6 have shown that the behavior of dry filtered air. One bar from each boule was tested for the relative permittivity of strontium titanate at liquid- resistivity by soldering leads on each of the two small J. Appl. Phys., Vol. 43, No. S, May 1972 2124 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 131.215.225.197 On: Mon, 15 Dec 2014 18:05:37 PERMITTIVITY OF STRONTIUM TITANATE 2125 ends and two more leads along one side of the rectang­ subdomains can form with different a orthorhombic-axis ular bar. Using a 4-point method, the resistivity was orientations. confirmed to be in excess of 1011 n cm for both bouleS. We have observed a large anomalous resonance of the To determine the purity of the material and confirm the permittivity of multidomain crystals. The "resonance" information furnished with the boules by the manufac­ is observed below 65 OK, between 1 and 10 MHz, and turer, a sample bar from each boule was submitted to will be reported elsewhere. If an electric field of at the Geology Department of the California Institute of least 20300 V /cm is applied to the [100]-, [110]- or Technology for an impurity analySis. There, a semi­ [l11]-oriented samples while they are cooled through quantitative analysis was performed using an electron the 110 ° and 65 OK phase transition temperatures, the microprobe. Principal impurities were found to be anomalous resonance is not observed. (We note that the 0.0002% barium, 0.01% calcium oxide, and less than crystal orientations have a one-sigma error of 1°. ) It 0.1% tungsten. These data are in agreement with those is important to apply the electric field while cooling furnished by the manufacturer. through both the 110 and 65 OK transition temperatures. If applied solely through the 65 OK transition tempera­ The eight sample wafers to be used in the dielectric ture, the full anomalous resonance is observed. If ap­ investigation were hand lapped and polished on a suc­ plied only through the 110 OK phase transition tempera­ cession of silk cloths, starting with an 800-mesh grit, ture, about 10% of the anomalous resonance is ob­ progressing through 1200 and 3200 grits, 1- and O. 3-JJ. served, probably indicating the presenee of subdomains. polishing compounds, and finishing with a 500-A alumi­ These observations lead us to believe that the crystals num polishing compound. Final wafer thickness lay be­ cooled with a large applied electric fiel.d became single tween 0.125 and 1 mm with wafer orientation yielding domained.