We report the temperature dependent capacitance-voltage characteristics of Pt/SrTiO3 Schottky diodes fabricated using compressively strained SrTiO3 thin films grown on (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT) substrates. The measurements reveal a divergence of the out of plane dielectric constant of SrTiO3 peaked at ∼140 K, implying a ferroelectric transition. A Curie-Weiss law fit to the zero-bias dielectric constant suggests a Curie temperature of ∼56 K. This observation provides experimental confirmation of the theoretical prediction of out of plane ferroelectricity in compressively strained SrTiO3 thin films grown on LSAT substrate. We also discuss the roles of the field-dependent dielectric constant and the interfacial layer in SrTiO3 on the extraction of the Curie temperature.

Ferroelectric crystals exhibit a spontaneous non-zero electric dipole moment below a certain transition temperature (Curie temperature TC) due to inversion symmetry breaking.1 Above this transition temperature, the crystal is in a paraelectric state with zero spontaneous electric dipole moment. This temperature-driven structural phase transition is accompanied by a divergence in the dielectric constant. As the temperature is decreased, the dielectric constant of a ferroelectric crystal increases in accordance with the Curie-Weiss law and peaks at the transition temperature.1,2 The dielectric constant decreases from this peak value on further reducing the temperature.

SrTiO3 (STO) is a transition metal oxide that crystallizes in a cubic perovskite crystal structure. Many commercially used ferroelectric materials such as BaTiO3, PbTiO3, and Pb(ZrxTi1−x)O3 (PZT) also crystallize in this crystal structure.3 Similar to these well-known ferroelectrics, the dielectric constant of bulk SrTiO3 increases as the temperature is lowered, following the Curie-Weiss law.4 However, in contrast to traditional ferroelectrics where the dielectric constant peaks and then decreases with temperature, in SrTiO3, the dielectric constant saturates below ∼4 K.4,5 Because of this unique behavior, SrTiO3 is often termed as an incipient ferroelectric. This very low temperature dielectric behavior arises because of the quantum fluctuations in SrTiO3 and a preceding antiferrodistortive structural phase transition.5,6 Theoretical calculations based on the Landau-Ginzburg-Devonshire theory have suggested that the ferroelectric state can be stabilized in SrTiO3 by applying a biaxial tensile or compressive strain.7 According to these predictions, a tensile strained (001) SrTiO3 crystal should exhibit ferroelectricity in the in-plane direction and a compressively strained (001) SrTiO3 crystal in the out-of-plane direction.7,8 Such biaxial strains can readily be achieved by heteroepitaxial growth of SrTiO3 on lattice-mismatched substrates.8,9 In agreement with the theoretical predictions, near room temperature ferroelectricity in the in-plane direction was discovered in tensile strained SrTiO3 thin films grown on DyScO3 substrates.8 In this earlier study, the capacitance of planar interdigitated capacitors was measured as a function of temperature to extract the temperature dependence of the in-plane dielectric constant.8 This earlier theoretical work also predicted a divergence in the out of plane dielectric constant in compressively strained SrTiO3 thin films grown on (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT) substrates with a TC of ∼50–200 K.8 Till date, there is no experimental evidence of such divergence for compressively strained SrTiO3.

In this work, we discover a strong signature of out-of-plane ferroelectricity in recently reported Pt/SrTiO3 Schottky diodes fabricated on compressively strained SrTiO3 thin films on LSAT substrates.10 The depletion capacitance of a Schottky diode is a function of the out-of-plane dielectric constant of the material.11 To capture the T-dependence of the out-of-plane dielectric constant of SrTiO3, we have performed temperature dependent capacitance-voltage measurements on Pt/SrTiO3 Schottky diodes. We find that the zero-bias Schottky depletion capacitance peaks at ∼140 K. The corresponding divergence in the out of plane dielectric constant implies a ferroelectric transition in the compressively strained SrTiO3 film. The presence of this ferroelectric transition and the extracted Curie temperature are in agreement with earlier theoretical predictions.7,8

For testing the out-of-plane ferroelectricity in compressively strained SrTiO3, we grew 160 nm thick SrTiO3 thin films on a (001) LSAT substrate using hybrid molecular beam epitaxy (MBE).10 In this growth technique, the organometallic precursor titanium tetra isopropoxide (TTIP) is used to provide Ti and O, while Sr is provided using an effusion cell.12,13 For the growth, Sr and TTIP beam equivalent pressures of 6.5 × 10−8 Torr and 2.3 × 10−6 Torr were used, respectively. The background pressure during the growth was ∼2 × 10−8 Torr. The growth was performed at a substrate temperature of 900 °C for 1 h at a growth rate ∼160 nm/h. In the MBE system, additional O can be provided during the growth using an oxygen plasma source to make the films insulating. However, to realize Schottky diode devices, the SrTiO3 films used in this study were grown without oxygen plasma. The resultant slightly oxygen deficient conditions dope the SrTiO3 thin films n-type with an electron concentration of ND ∼ 1019 cm−3. Since the conditions remained the same throughout the growth, uniform carrier concentration is expected in the film. Using Hall-effect measurements performed in a van der Pauw geometry, a sheet electron concentration of ∼1.28 × 1014 cm−2 was obtained.10 This sheet concentration value is lower than the expected value of ∼1.6 × 1014 cm−2 because of the surface depletion in the SrTiO3 thin film.14,15

Both STO and LSAT substrates have a cubic perovskite crystal structure with lattice constants of aSTO = 3.905 Å and aLSAT = 3.868 Å, respectively.16 A recent growth study using the same hybrid MBE technique has found the critical thickness of SrTiO3 thin films grown on LSAT substrate to be ∼180 nm.16 Below this critical thickness, SrTiO3 thin films are expected to grow coherently strained to the LSAT substrate with a compressive strain of (aLSAT − aSTO)/aSTO = −0.95%. The oxygen vacancy concentration corresponding to ∼1019 cm−3 electron concentration in our sample is quite low to cause any significant strain effects and all of the strain in the thin film is expected to arise from the lattice mismatch between the SrTiO3 thin film and the LSAT substrate.17 To confirm growth of stoichiometric SrTiO3 coherently strained to the LSAT substrate, we performed both (002) on-axis 2θ-ω scan and (013) off-axis reciprocal space mapping (RSM) in a high-resolution Philips Panalytical X'Pert Pro thin-film diffractometer using Cu Kα radiation. The results of the measurements are shown in Figs. 1(a) and 1(b), respectively. The SrTiO3 out of plane lattice parameter, as measured from the 2θ-ω scan (Fig. 1(a)) is a = 3.932 ± 0.001 Å, as expected from a completely coherent stoichiometric film.16 The RSM of the sample (Fig. 1(b)) shows that both the SrTiO3 thin film and the LSAT substrate have the same in-plane lattice parameter, further confirming the pseudomorphic film growth and the desired compressive strain in the SrTiO3 layer.

FIG. 1.

(a) (002) on-axis x-ray diffraction 2θ-ω scan of the grown SrTiO3/LSAT sample. (b) (013) off-axis reciprocal space map of the grown sample showing coherently strained pseudomorphic growth of the SrTiO3 thin film on the LSAT substrate.

FIG. 1.

(a) (002) on-axis x-ray diffraction 2θ-ω scan of the grown SrTiO3/LSAT sample. (b) (013) off-axis reciprocal space map of the grown sample showing coherently strained pseudomorphic growth of the SrTiO3 thin film on the LSAT substrate.

Close modal

To measure the out-of-plane dielectric constant of the compressively strained SrTiO3 thin film, we fabricated circular Schottky diodes. Optical photolithography was used to pattern the film. Al/Ni/Au (40/40/100 nm) ohmic contacts and Pt/Au (40/100 nm) Schottky contacts were deposited using e-beam evaporation. To reduce gate leakage and improve rectification, an oxygen plasma treatment of the SrTiO3 surface was performed in a reactive ion etching system prior to the Pt/Au Schottky metal deposition. More details on the device fabrication process have been reported elsewhere.10 

For measuring the Schottky diode current-voltage (I-V) and capacitance-voltage (C-V) characteristics, a Keithley 4200 semiconductor characterization system was used along with a Cascade probe station for room temperature measurements and a Lakeshore probe station for temperature dependent measurements. Rectifying I-V characteristics of a Pt/SrTiO3 circular Schottky diode of 10 μm radius measured at room temperature are shown in Fig. 2. From the forward bias characteristics, the barrier height for Pt was found to be ∼0.86 eV with an ideality factor of n ∼ 1.63. The temperature dependent C-V characteristics (frequency 100 kHz, signal amplitude 30 mV) of the Schottky diode are shown in Fig. 3(a) (80 K–140 K) and Fig. 3(b) (140 K–400 K). Near zero bias, where the loss is low and the capacitance extraction using a parallel R-C equivalent circuit is valid, the capacitance increases from 80 K to 140 K (Fig. 3(a)). On further increasing the temperature beyond 140 K, however, the measured capacitance decreases (Fig. 3(b)). All measured devices exhibited similar capacitance behavior as a function of temperature. To depict this capacitance variation more clearly, the zero bias capacitance is plotted as a function of the sample temperature in Fig. 3(c). The capacitance peaks at ∼140 K, increasing more than 60% compared to the value at 400 K.

FIG. 2.

Measured room temperature I-V characteristics of a 10 μm radius Pt/SrTiO3/LSAT circular Schottky diode.

FIG. 2.

Measured room temperature I-V characteristics of a 10 μm radius Pt/SrTiO3/LSAT circular Schottky diode.

Close modal
FIG. 3.

Measured temperature dependent C-V (100 kHz, 30 mV) characteristics of the 10 μm radius Pt/SrTiO3/LSAT circular Schottky diode showing increase in measured depletion capacitance (right axis/filled circles) in the temperature range (a) 80 K–140 K, followed by a decrease in the capacitance in the temperature range (b) 140 K–400 K. (c) Variation of zero bias measured capacitance with temperature, capacitance peaks at ∼140 K. Temperature dependence of loss is also plotted (left-axis/open squares). Loss is quite low around zero bias over the whole 80 K–400 K temperature range.

FIG. 3.

Measured temperature dependent C-V (100 kHz, 30 mV) characteristics of the 10 μm radius Pt/SrTiO3/LSAT circular Schottky diode showing increase in measured depletion capacitance (right axis/filled circles) in the temperature range (a) 80 K–140 K, followed by a decrease in the capacitance in the temperature range (b) 140 K–400 K. (c) Variation of zero bias measured capacitance with temperature, capacitance peaks at ∼140 K. Temperature dependence of loss is also plotted (left-axis/open squares). Loss is quite low around zero bias over the whole 80 K–400 K temperature range.

Close modal

The depletion capacitance of a Schottky diode is given as Cd(V)=qε0εrND/2V, where q is the electron charge, ε0 is the vacuum permittivity, εr is the out-of plane dielectric constant of SrTiO3, ND = 1019 cm−3 is the doping density, and V is the total voltage drop across the Schottky depletion region.11 In traditional semiconductors, carriers can freeze out at low temperatures, but because of the large dielectric constant of SrTiO3, impurity doped (La or Nb) or oxygen vacancy doped carriers in SrTiO3 do not freeze out even at liquid helium temperatures.18–20 Therefore, any temperature dependence of measured Schottky capacitance in our devices should arise from temperature dependence of SrTiO3 dielectric constant. Using the one to one mapping between the measured depletion capacitance and the out-of plane dielectric constant, we can extract the temperature dependence of the dielectric constant. As εrCd2, the capacitance peak at 140 K would imply a peak in SrTiO3 out-of plane dielectric constant at the same temperature. For the zero bias case V = 0.86 V due to the built-in bias due to Pt. The out-of-plane dielectric constant extracted from the zero bias measured capacitance value is shown in Fig. 4(a). Compared to bulk unstrained SrTiO3 where the dielectric constant saturates at low temperatures,4,5 the divergence in out-of plane dielectric constant observed in the compressively strained SrTiO3 thin films suggests a ferroelectric transition. A Curie-Weiss law fit to 1000/εr is shown in Fig. 4(b). From this fit, the extracted Curie temperature, TC, for the SrTiO3 ferroelectric transition is ∼56 K. This TC value lies towards the lower limit of the range of theoretically predicted ferroelectric transition temperatures in the SrTiO3/LSAT system (∼50–200 K).8 Our temperature dependent C-V results therefore confirm the theoretical predictions of out-of plane ferroelectricity in compressively strained SrTiO3 thin films grown on LSAT substrate.

FIG. 4.

(a) SrTiO3 dielectric constant calculated from the measured zero bias depletion capacitance (solid circles) and after removing the effect of interfacial capacitance Ci(open circles) (inset: effective capacitance model of the Pt/SrTiO3 Schottky diode). (b) Curie-Weiss law fit to the inverse of dielectric constant.

FIG. 4.

(a) SrTiO3 dielectric constant calculated from the measured zero bias depletion capacitance (solid circles) and after removing the effect of interfacial capacitance Ci(open circles) (inset: effective capacitance model of the Pt/SrTiO3 Schottky diode). (b) Curie-Weiss law fit to the inverse of dielectric constant.

Close modal

Compared to the peak dielectric constants observed for in-plane ferroelectricity in SrTiO3,8 the dielectric constants observed in this study are one order lower. A possible reason for lower dielectric constants measured is the presence of non-zero electric fields in the Schottky depletion region at zero bias; these fields were absent in the earlier studies that did not use Schottky diodes. Even modest dc electric fields of the order of ∼10 kV/cm can drastically reduce the dielectric constant of a ferroelectric material8 by Coulomb-clamping the motion of the ionic crystal responsible for high dielectric constants in ferroelectrics. The peak electric fields in our Schottky diode devices are certainly larger than 10 kV/cm. In addition to reducing the measured dielectric constant, non-zero electric fields can also cause a shift in dielectric constant vs temperature curves, moving the peak divergence to higher temperatures and the apparent TC to lower temperatures.21 We can estimate the order of magnitude of the shift in TC due to the non-zero electric field using the Landau-Ginzburg-Devonshire theory of ferroelectrics. For this estimate, assuming a uniform electric field E in SrTiO3, the expansion of free energy F in terms of the polarization order parameter P can be written as21 

F=EP+g0+γ(TTc,0)2P2+g44P4,
(1)

where g0, γ, and g4 are constants specific to the ferroelectric and Tc,0 is the actual ferroelectric transition temperature in the absence of an electric field. The value of the equilibrium polarization can be found by minimizing F with respect to P, F/P=0, leading to a relation between E and P, E=γ(TTc,0)P+g4P3. Because of the large dielectric constant values in a ferroelectric, the dielectric constant can be approximated by the dielectric susceptibility χ as

εr=1+χχ=1ε0PE=1/γε0T(Tc,03g4P2/γ).
(2)

The apparent reduction in TC due to the non-zero electric field is 3g4P2/γ. Comparing Eq. (2) to the fit εr=36200/(T56) shown in Fig. 4(b), we estimate the value of γ to be γ ∼ 3.12 × 106 m2N/C2. The linear fit to experimental data (Fig. 4(b)) is good for T ∼ 250 K–400 K. In this temperature range, P can be approximated as PE/γ(TTc,0). To get an estimate of 3g4P2/γ, we can take g4 ∼ 6.8 × 109 m6N/C4, equal to the bulk unstrained SrTiO3 value,22 and (TTc,0) ∼ 100 K. For an average electric field of ∼100 kV/cm in SrTiO3, the apparent reduction in TC would then be 3g4P2/γ ∼ 7 K.

In our experiment, the extracted TC value of ∼56 K directly depends on the measured capacitance. The presence of an interfacial low dielectric constant layer (also called dielectric dead layer) at the Schottky metal/SrTiO3 interface has been frequently reported in the literature.23–28 The capacitance Ci of such an interfacial layer acts in series with the Schottky depletion capacitance Cd (Fig. 4(a), inset), thus reducing the measured capacitance Cm=CdCi/(Cd+Ci) and hence the extracted dielectric constant.23–28 Since εr1/(TTC), this reduction in extracted dielectric constant would show up as an apparent reduction in TC, similar to the case of non–zero electric field in SrTiO3. To find this TC shift, we need an estimate of Ci.

Ci and Cd are related to the ideality factor n of the Schottky diode as Ci/Cd=1/(n1).28 Since Cm=CdCi/(Cd+Ci), we can also write this capacitance ratio in terms of the measured capacitance Cm and interfacial capacitance Ci as Ci/Cd=Ci/Cm1. Combining these two expressions, we can directly obtain Ci from the ideality factor n(∼1.63) and the measured capacitance Cm as Ci=nCm/(n1). At zero applied bias, the measured Schottky diode capacitance at room temperature is Cm ∼ 3.56 μF/cm2; therefore, Ci=nCm/(n1) 9.21 μF/cm2. Assuming that the interfacial capacitance is independent of temperature, the effect of interfacial capacitance can be de-embedded from the measured capacitance to calculate the actual Schottky depletion capacitance [Cd=CiCm/(CiCm)] at different temperatures. The out-of-plane dielectric constant extracted from this de-embedded Schottky capacitance is shown in Fig. 4(a) along with the Curie-Weiss law fit [Fig. 4(b)]. After removing the effect of the interfacial capacitance, the extracted Curie temperature, TC, for the SrTiO3 ferroelectric transition is ∼141 K. Combining this apparent reduction in TC due to the interfacial capacitance with the reduction in TC due to the non-zero electric fields in Schottky diodes, the actual Curie temperature for compressively strained SrTiO3 is expected to be ∼148 K, in the upper half of the theoretically predicted range of ∼50–200 K.

To summarize, in this work, using temperature dependent C-V measurements performed on Pt/SrTiO3/LSAT Schottky diodes fabricated using compressively strained SrTiO3 thin films, we have observed a divergence in the out-of plane dielectric constant in SrTiO3. This finding provides an experimental confirmation of theoretical predictions of out-of-plane ferroelectricity in SrTiO3 thin films coherently strained to LSAT substrate. We hope this work will help in designing and understanding of SrTiO3 based devices on this widely used substrate. In addition to the divergence of the dielectric constant, ferroelectricity is also accompanied with the emergence of field switchable non-zero spontaneous polarization below the Curie temperature. This property is difficult to probe in a Schottky diode geometry, but potentially can be demonstrated in future studies by other techniques.

The authors thank Evgeny Mikheev for useful discussions. This work was supported by the Extreme Electron Concentration Devices (EXEDE) MURI program of the Office of Naval Research (ONR) through Grant No. N00014-12-1-0976.

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