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Tailoring of the coercive voltage in a ferroelectric polymer capacitor
Microelectronic Engineering 166 (2016) 19–25
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Accelerated publication
Tailoring of the coercive voltage in a ferroelectric polymer capacitor Woo Young Kim a,⁎, Hee Chul Lee b a b
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 5 August 2016 Accepted 17 September 2016 Available online 21 September 2016 Keywords: P(VDF-TrFE) Ferroelectric capacitor Coercive voltage Nonlinearity
a b s t r a c t For an identical ferroelectric material, operation at a different voltage means that all ferroelectric films should be designed for different thicknesses, though this increases the degree of process complexity. Here, a technique which can be used to adjust the coercive voltage (VC) of a metal-ferroelectric film-metal capacitor is demonstrated. The VC-adjustable capacitor was fabricated with ferroelectric polymer film and the capacitor consists of two sub-capacitors with different thicknesses. For a common top and bottom electrode, the sub-capacitors are equivalent to two parallel-connected capacitors. With regard to the variance of the ratio of the area of the sub-capacitors, a VC-adjustable capacitor can take coercive voltage between two VC values, each of which correspond to the VC value of each respective sub-capacitor. In this demonstration, the width of the tuning range of the VC values was 3.6 V. In addition, the strategy for a linear VC adjustment of a VC-adjustable capacitor is discussed in terms of the concept of nonlinearity. This demonstration with a ferroelectric polymer is predicted to be applicable to emerging organic electronic applications. © 2016 Published by Elsevier B.V.
1. Introduction Ferroelectric materials are very attractive materials for a range of applications, such as memory devices [1,2] as well as nonvolatile circuits [3], neuron-mimicking circuits [4,5], tunable antennas [6], sensors and actuators [7,8]. If these components can be combined in a single system, such an integrated system will be very versatile. If only one type of ferroelectric material is used, the ferroelectric films for different devices should be fabricated with different thicknesses because different devices operate in different voltage ranges. In other words, all ferroelectric devices should be fabricated with different process steps. Given this point of view, a method by which all ferroelectric devices can be fabricated in a single step but where all devices can operate in different voltage ranges should be encouraged, leading to a reduction in the overall number of process steps and an improvement of the process yield. In this work, a method to tailor the coercive voltage using a ferroelectric polymer is demonstrated. The coercive voltage is one of the main parameters in ferroelectric films; it is defined as external voltage which creates net polarization of a ferroelectric film zero. The polarity of the surface charge in a ferroelectric film changes upon coercive voltage, which is why coercive voltage is used as a reference (or its corresponding voltage is) to compare ON and OFF states in switching devices or 0 and 1 states in memory devices. The ferroelectric polymer used here was selected for its superior properties, such as easy processability and environment inertness. Therefore, it is expected that ⁎ Corresponding author. E-mail address: [email protected] (W.Y. Kim).
http://dx.doi.org/10.1016/j.mee.2016.09.009 0167-9317/© 2016 Published by Elsevier B.V.
tailoring the coercive voltage in a ferroelectric polymer capacitor will be a useful method for emerging applications. In the next section, the principle used to tailor the coercive voltage will be described in detail. 2. Principle For a ferroelectric capacitor with large surface roughness, it has been reported that the switching time of polarization is retarded compared to a ferroelectric capacitor with a flat surface, as an external electric field is applied non-uniformly to the ferroelectric film [9]. The method to tailor the coercive voltage of a ferroelectric capacitor was inspired by the nonuniform distribution of the electric field. Fig. 1 describes the principle behind the tailoring of the coercive voltage of a ferroelectric capacitor. Fig. 1a represents a normal ferroelectric capacitor with a flat surface, where the two terminals are connected to an external voltage (VA) source and the ground, respectively. In reality, however, surface roughness exists to a certain extent on account of the crystallinity of the ferroelectric film. For a conceptual understanding, assume that the film morphology consists of only two terrains, a plateau and a valley. The height of the plateau from an electrode connected to the ground is ΔB above a reference thickness of t0. Conversely, the valley is positioned below ΔA from t0. If all plateaus and valleys correspond to parallel-connected capacitors, the ferroelectric capacitor in Fig. 1b is electrically equivalent to the ferroelectric capacitor shown in Fig. 1c. Therefore, the entire ferroelectric capacitor with an area of A0 consists of two different sub-capacitors, CA and CB. When external voltage VA sweeps from 0 to VMAX, as represented in Fig. 1d, the coercive voltage of CA (VCA) is applied prior to the coercive voltages of CB (VCB). Assume that
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W.Y. Kim, H.C. Lee / Microelectronic Engineering 166 (2016) 19–25
Fig. 1. Principle behind the tailoring of the coercive voltage. Schematics of (a) a flat ferroelectric capacitor with area A0 and thickness t0. (b) A rough ferroelectric capacitor with two terrains, a plateau and a valley. The film thicknesses of the plateau and the valley are t0 + ΔB and t0 - ΔA, respectively. (c) Structure electrically equivalent to the structure depicted in (b). The area ratio of CA and CB is α: 1- α. (d) Profile of the applied voltage with the maximum voltage VMAX. VCA and VCB indicate the coercive voltages of CA and CB, respectively. (e) Schematic of the polarization-voltage relationship between CA and CB when α exceeds 0.5.
the area ratio of CA to CB is α: (1- α). For an α value larger than 0.5, each hysteresis loop for CA and CB will be measured, as shown in Fig. 1e. It is possible to imagine that a certain voltage VX between VCA and VCB exists to make the polarization of CA at VX (PA(VX)) equal to the polarization of CB at VX (PB(VX)). Therefore, it is certain that the coercive voltage of the entire ferroelectric capacitor with area A0 is positioned between VCA and VCB. Ferroelectric polarization (P) can be quantitatively described with a hyperbolic tangent function, as expressed below [10,11]. P ¼ P S tanhðkðV A −V C ÞÞ
ð1Þ
Here, PS is the spontaneous polarization of the ferroelectric capacitor when the external voltage VA is VMAX; VC is the coercive voltage. The fitting constant k determines how fast P approaches Ps. Thus, PA and
PB are modelled as αPS tanh (k(VA − VCA)) and (1 − α)PS tanh (k(VA − VCB)), respectively. To apply VA = VX to make the net polarization zero throughout a ferroelectric capacitor, the following equation applies. P ¼ P A þ P B ¼ αP S tanhðkðV X −V CA ÞÞ þ ð1−α ÞP S tanhðkðV X −V CB ÞÞ ¼0 ð2Þ When the parameter k and the capacitor structure are known, the only variable in Eq. (2) is the area ratio, α. In other words, the solution of Eq. (2) depends solely on α to determine the areas of the two capacitors. The fact that the term α can be manipulated intentionally suggests that it is possible to fabricate a ferroelectric capacitor with random values of the coercive voltage VC = VX between VCA and VCB. If such an important factor VC can be manipulated simply by tuning the area
W.Y. Kim, H.C. Lee / Microelectronic Engineering 166 (2016) 19–25
ratio of two capacitors with different thicknesses, a circuit design will be straightforward in a system which includes ferroelectric film. In this work, a ferroelectric capacitor with two different thicknesses was fabricated with a ferroelectric polymer. To realize the thickness difference, the ferroelectric capacitor was fabricated via the patterning and transferring of a ferroelectric thin film. More details will be discussed in the subsequent sections.
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evaporation was conducted at 1 × 10−6 Torr at an evaporation rate of 0.3 Å/s. To confirm that the area ratio α between the area of CA and the area of CB affects the coercive voltage in the ferroelectric capacitor with two thicknesses, an array of circles with diameters of 180 μm on a shadow mask was aligned at an angle corresponding to the patterned lines of the FPF. The polarization-voltage relationships were measured with a ferroelectric measurement system (RT-66A, Radiant Technologies). All fabrication processes are depicted in Fig. 2.
3. Experiment 4. Results and discussion 3.1. Preparation of the ferroelectric film The ferroelectric polymer used here, poly(vinylidene fluoride-cotrifluoroethylene) ((P(VDF-TrFE)), 75/25 mol%), was manufactured from Elf Atochem. First, 0.03 g of P(VDF-TrFE) was dissolved in 1 mL of methyl-ethyl-ketone (MEK) (3 wt%). The thickness of the ferroelectric polymer film (FPF) could be controlled linearly by adjusting the solution concentration. By adding additional MEK to the solution of 3 wt%, the solution concentration was varied. The spin speed and the spin time were fixed at 1500 rpm and 10 s, respectively. Under these conditions, the correlation between the film thickness and the solution concentration was 90 nm/1 wt%. After spin-coating, the FPF was annealed at 130 °C for 10 min. to increase the crystalline β-phase. The thickness of the FPF was measured using an α-step (Dektak 6 M, Veeco Instruments, Inc.). 3.2. Patterning of the ferroelectric film The FPF was patterned by conventional photo-lithography technology. First, 60 nm of FPF was spin-coated onto an Au-deposited SiO2/Si wafer. A positive photoresist (AZ 1512, AZ Electronic Materials) was then spin-coated, after which soft-baking was performed at 95 °C for 90 s. Next, the sample was exposed at the g-line (436 nm) for 20 s. A photoresist developer (AZ 300MIF, AZ Electronic Materials) was used for the development process. Photoresist-uncovered FPF was etched in oxygen plasma ambient with the following process conditions. The oxygen flow rate was 50 mL/min, the process pressure was 36 Pa, the RF power was 200 W, and the process time was 30 s. For the removal of the photoresist, a photoresist stripper (AZ 400T, AZ Electronic Materials) was used, but the solubility of the pristine AZ 400T needed to be weakened because the main solvent of the original AZ 400T is n-methyl-2-pyrrolidone, which can definitely dissolve the FPF. Thus, the AZ400T solution was diluted with deionized water. Details of the dilution ratio and its results are explained in our previous publication [12]. The width and the length of the final line patterns were 500 μm and 1 cm, respectively. 3.3. Transferring of the ferroelectric film On a thermally oxidized silicon wafer, 60 nm of FPF was prepared as described in Section 3.1. By dipping the FPF deposited onto a SiO2/Si wafer into aqueous hydrofluoric (HF) acid, the oxide layer SiO2 was etched in the HF solution. The FPF was then separated from the wafer. It floated on the surface of the HF solution on account of surface tension. Subsequently, the floating FPF was lifted out and moved onto the surface of deionized water. And, 60 nm of the floating FPF was transferred onto the patterned FPF 60 nm on an Au-deposited wafer prepared as described in Section 3.2. After the transfer, the sample was thermally treated at 80 °C for 30 min. to remove the water residue and then again at 130 °C for 10 min to ensure strong adhesion between the two FPFs. 3.4. Ferroelectric capacitor with two thicknesses For the top electrode, Au was thermally evaporated through a shadow mask on a sample that consisted of FPF with two thicknesses: one at 60 nm (CA) and the other at 120 nm (= 60 nm + 60 nm, CB). Au
Fig. 3a shows schematic of the displacement (D) - voltage (VA) hysteresis loop of a normal ferroelectric capacitor. Here, PS, PR, and VC denotes the spontaneous polarization, remnant polarization, and the coercive voltage, respectively. Fig. 3b shows the measured D-VA hysteresis loops of three capacitors with different α values. When α is unity, only CA contributes to the total hysteresis loop. The PS and PR values are determined to be 10.81 μm/cm2 and 8.52 μm/cm2, respectively. The VCA value is calculated to 4.13 V; thus, the coercive field (ECA) is 68.8 MV/m. When α is null, the capacitor CB has PS values of 9.94 μm/ cm2 and PR of 8.34 μm/cm2. The coercive voltage VCB of CB is 7.75 V, and the coercive field thus becomes 64.6 MV/m. All of the hysteresis loops were measured with the RT-66A ferroelectric measurement system. This equipment operates as follows. Before a triangular VA is used to sweep the ferroelectric capacitor, a single voltage pulse of -VMAX is applied to initialize the polarization of the ferroelectric capacitor to -PR. After a duration of 1 s from initialization, the triangular voltage shown in Fig. 1d is applied [13]. Therefore, the greater the polarization becomes, the more the screening charge accumulates around the surfaces of the ferroelectric film [14]. Therefore, the polarization differences between CA and CB are not a crucial issue but are instead a natural phenomenon in ferroelectric films. It is important to note that, when α is halved, the hysteresis loop is plotted between two hysteresis loops of CA and CB. The PS and PR values are determined to be 10.49 μm/cm2 and 8.493 μm/cm2, respectively. Though the coercive field cannot be simply defined in a capacitor when α = 0.5, the coercive voltage is positioned between VCA and VCB, as expected. Fig. 3c was devised from the differentiation of the measured data in Fig. 3b. The square of the hyperbolic secant function (the derivative of the hyperbolic tangent function as expressed in Eq. (1)) has two maxi− mum values at VA = V+ C and VC . Therefore, the VA-axis positions of the peak values shown in Fig. 3c indicate the coercive voltages of each ferroelectric capacitor. When α = 0.5, two peak values on the positive and negative axes are observed, each of which nearly consistent with VCA and VCB. Thus, the coercive voltage of the capacitor when α = 0.5 does not match VCA and VCB. The solid green line in Fig. 3c is the result of the average of 0.5 × (∂DA/∂VA) + 0.5 × (∂DB/∂VA), in good agreement with the solid red line (α = 0.5). This indicates that each dipole in the two capacitors CA and CB switches independently of the other, with the coercive voltage of the total capacitor with two thicknesses then needing to be determined by the linear combination of the two sub-capacitors. Fig. 3d shows the relationships between the maximum applied voltage VA = VMAX and the PR values. The solid black line Fit\\CA is a fitted line for α = 1, and the solid blue line Fit-CB corresponds to α = 0. The average line from the calculation of 0.5 × Fit-CA + 0.5 × Fit-CB matches the measured results (red dot) well. Thus, these results are equivalent to those described in Fig. 3c. Therefore, it is possible to estimate that if two hysteresis loops of CA and CB are known, any hysteresis loop for a random value of α can be generated regardless of the magnitude of VMAX. Using two hysteresis loops from CA and CB, any hysteresis loop (H) with a value of α between 0 and 1 can be determined by a weighted averaging calculation. Fig. 4a shows ten hysteresis loops with different α values. For example, the hysteresis loop H(α = 0.3) was derived through the equation 0.3 × H(α = 1) + 0.7 × H(α = 0). Fig. 4b presents
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Fig. 2. Fabrication process steps: (a) P(VDF-TrFE) spin-coating onto an Au-deposited SiO2/Si wafer, (b) P(VDF-TrFE) patterning, (c) P(VDF-TrFE) spin-coating onto a SiO2/Si wafer, (d) detaching of the P(VDF-TrFE), (e) transfer of P(VDF-TrFE) onto the patterned P(VDF-TrFE) (f) Au electrode deposition, (g) profile of the final structure, and (h) optical microscopy image of the final devices. The tA region and the tB region are denoted by CA and CB, respectively.
the relationship between α value and the VC values extracted from Fig. 4a. Graph H(α = 0) has a VC value of 7.75 V and graph H(α = 1) has a VC value of 4.13 V. Thus, the ferroelectric capacitor with two sub-capacitors CA and CB can have any VC value between 4.13 V and 7.75 V. Accordingly, the width of the tuning range is 3.62 V. If a dependent parameter, VC can be linearly modulated by the variable α, the final VC values are easily predictable. Fig. 4b shows an example of S-shaped dependency in which nonlinear dependence originates from the nonlinearity of hyperbolic tangent function described in Eq. (1). At this point, this nonlinearity and a method to reduce the nonlinearity will be discussed. Eq. (2) can be simplified into the following equation. α¼
−1 tanhðkðV C −V CA ÞÞ 1− tanhðkðV C −V CB ÞÞ
ð3Þ
Assume that the relationship between V C and α can be expressed as VC = f(α). Though the relationship VC = f(α) is transposed into another form, i.e., α = f− 1(VC), its nonlinearity remains unchanged. Thus, Eq. (3) corresponds to α = f− 1(VC), which is useful for discussing the nonlinearity. The solution to Eq. (3) is schematically represented as the S-shaped dotted line in Fig. 5a. The ideally desirable relationship is the solid line shown in Fig. 5a, which is a straight line between the two points (VC, α) = (VCA, 1) and (VCB, 0). The symbols αI and αR denote the ideal and the actual case of α, respectively. Here, the nonlinearity (NL) can be defined as
the area surrounded by two curves, α I and α R . Then NL can be expressed using the following equation. V ZCB
jα I −α R j dV C
NL ¼
ð4Þ
V CA
From Eq. (4), it is certain that the only variable is the fitting parameter k. For simplification, let the k value in CA be equal to k in CB. For a variable k between 0 and 1, the NL values were calculated, as shown in Fig. 5c and Fig. 5d. Fig. 5d is the logarithmic form of Fig. 5c. As shown in Figs. 5c and d, smaller k values result in smaller NL values. Less nonlinearity is equivalent to more linearity. However, the fitting constant k reflects the ratio of PR and PS. According to the literature, a smaller value of k indicates that the ferroelectric film has a small PR value compared to the PS value, which can normally be observed in a fatigued ferroelectric films [15,16] or a relaxor ferroelectrics [17,18]. Therefore, a strategy to reduce k is not desirable to improve the linearity. By shifting VCB as shown in Fig. 5b, a new pathway to overcome the nonlinearity can be suggested. As V CB moves to the right, NL increases. Inversely, movement of V CB to the left reduces NL. For different V CB values between 7.5 V and 4.5 V, Fig. 5c and Fig. 5d show that NL decreases as V CB approaches V CA . As noted above, a high k value is recommended in electronic switches or memory applications; accordingly, the NL values at k = 1 are plotted in Fig. 5e. This relationship
W.Y. Kim, H.C. Lee / Microelectronic Engineering 166 (2016) 19–25
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Fig. 3. Displacement-voltage (D-V) measurement (a) schematic of the D-V hysteresis loop. PS and PR indicate the spontaneous polarization and remanant polarization, respectively. V+ C and V− C are correspondingly the coercive voltage in the positive and negative voltage regions. (b) D-V hysteresis loops for α = 1, 0.5 and 0. (c) Differentiation of the D-V hysteresis loop depicted in (b). The average line shown in green is the result calculated by averaging the two differentiation results for α = 1 and 0. (d) Relationship between PR and VMAX. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
infers that the tuning ranges of V C and NL exist in a counterpart relationship. To overcome this trade-off, the assumption that the total capacitor consists of two thicknesses must be modified.
If an intermediate thickness t i between t A and t B is included or if the transition between t A and t B is gray-scale changed, as shown in Fig. 5f, NL and the tuning range can be reasonably
Fig. 4. Tailoring of the coercive voltage (VC): (a) D-V hysteresis loops calculated by the weighted averaging of two D-V hysteresis loops for α = 1 and 0, and (b) relationship between VC and α.
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Fig. 5. Nonlinearity in the tailoring of the coercive voltage: (a) schematic of the ideal (αI) and actual (αR) α -VC relationships. The nonlinearity (NL) is defined by the gray region surrounded by αI(VC) and αR(VC). (b) α-VC relationships when VCB moves to the left (VCBL) or to the right (VCBR). (c) NL-k relationship calculated for various VCB values. (d) Logarithmic expression of (c). (e) NL-tuning range relationship. (f) Alternative device structures to reduce the NL values, in which an intermediate film with a thickness of ti or a gray-scaled transition region is inserted.
compromised. Those kinds of films with intermediate step and/or gray-scaled slope can be easily fabricated by adapting nanoimprint process as described the previous literatures [19,20]. 5. Summary and conclusion In this work, a ferroelectric capacitor with two different thicknesses was suggested to tailor an important parameter, i.e., the coercive voltage. A capacitor with two different thicknesses was prepared by a patterning process followed by the transfer of the ferroelectric polymer film. The only variable during the tailoring of the coercive voltage in a ferroelectric capacitor is the area ratio of the two sub-capacitors, which are relatively thin and thick capacitors. This approach to tailor the coercive voltage offers simplicity in the design of an electronic system which includes ferroelectric film. Though the width of the tuning
range was approximately 3.6 V, nonlinearity clearly arose due to the nonlinear response of the dipoles in the ferroelectric film. In this study, it was demonstrated that one of the strategies which can be used to realize both a wide tuning range and considerable linearity is to ensure an intermediate thickness between the two different thicknesses.
Footnote & acknowledgments In this work, the experiment results and the measured data were based on the main author's Ph.D dissertation entitled of “A study on the fabrication and characterization for multi-bit memory device using multilayer structured ferroelectric polymer thin film” in Korea Advanced Institute of Science and Technology (KAIST). Also, this work
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was partially supported by the Preparatory Project (N10110074) in KAIST. References [1] J.A. Caraveo-Frescas, M.A. Khan, H.N. Alshareef, Polymer ferroelectric field-effect memory device with SnO channel layer exhibits record hole mobility, Sci. Report. 4 (2014) 5243, http://dx.doi.org/10.1038/srep05243. [2] J.H. Park, P.K. Nayak, H.N. Alshareef, Novel ferroelectric polymer memory coupling two identical thin-film transistors, Adv. Electron. Mater 2 (2016) 1500206. [3] S. Yamamoto, S. Inoue, H. Ishiwara, Analysis of non-volatile latch circuits with ferroelectric-gate field effect transistors for low power and low voltage operation, International Conference on Microelectronics 2 (2002) 589–592. [4] A. Chanthbouala, V. Garcia, R.O. Cherifi, K. Bouzehouane, S. Fusil, X. Moya, S. Xavier, H. Yamada, C. Deranlot, N.D. Mathur, M. Bibes, A. Barthélémy, J. Grollier, A ferroelectric memristor, Nat. Mater. 11 (2012) 860–864. [5] Z. Wang, W. Zhao, W. Kang, Y. Zhang, J.-O. Klein, D. Ravelosona, C. Chappert, Compact modelling of ferroelectric tunnel memristor and its use for neuromorphic simulation, Appl. Phys. Lett. 104 (2014) 053505. [6] S. Gevorgian, Ferroelectrics in Microwave Devices, Circuits and Systems: Physics, Modelling, Fabrication and Measurements, Springer (2009) e-ISBN 978-1-84882507-9. [7] P. Muralt, Ferroelectric thin films for micro-sensors and actuators: a review, J. Micromech. Microeng. 10 (2000) 136–146. [8] J.M. Herbert, Ferroelectric Transducers and Sensors, CRC Press, 1982 (ISBN 0-67705910-8). [9] T. Nakajima, R. Abe, Y. Takahashi, T. Furukawa, Intrinsic switching characteristics of ferroelectric ultrathin vinylidene fluoride/trifluoroethylene copolymer films revealed using Au electrode, J. Jpn. Appl. Phys 44 (2005) L1385–L1388.
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[10] S.L. Miller, R.D. Nasby, J.R. Schwank, M.S. Rodgers, P.V. Dressendorfer, Device modeling of ferroelectric capacitors, J. Appl. Phys. 68 (1990) 6463–6471. [11] N. Inoue, Y. Hayashi, Effect of imprint on operation and reliability of ferroelectric random access memory (FeRAM), IEEE Trans. Electron Devices 48 (2001) 2266–2272. [12] W.Y. Kim, H.C. Lee, Development of manipulation technology of ferroelectric polymer film: photo-lithographic patterning and multilayer formation, Microelectron, Engineering 88 (2011) 1576–1581. [13] RT 66A Standardized Ferroelectric Test System V2.1 Operating Manual, Radiant Technologies, 1992. [14] M. Lallart, Ferroelectrics - physical effects, INTECH (2011), ISBN 978-953-307-453-5. [15] Y.A. Genenkoa, J. Glaumb, M.J. Hoffmannc, K. Albea, Mechanisms of aging and fatigue in ferroelectrics, Mater. Sci. Eng. B 192 (2015) 52–82. [16] D. Zhao, I. Katsouras, M. Li, K. Asadi, J. Tsurumi, G. Glasser, J. Takeya, P.W.M. Blom, D.M. de Leeuw, Polarization fatigue of organic ferroelectric capacitors, Sci. Report. 4 (2014) 5075, http://dx.doi.org/10.1038/srep05075. [17] Q.M. Zhang, V. Bharti, X. Zhao, Giant electrostriction and relaxor ferroelectric behavior in electron-irradiated poly(vinylidene fluoride-trifluoroethylene) copolymer, Science 280 (1998) 2101–2104. [18] A.A. Bokov, Z.-G. Ye, Recent progress in relaxor ferroelectrics with Perovskite structure, J. Mater. Sci. 41 (2007) 31–52. [19] J.D. Ryckman, Y. Jiao, S.M. Weiss, Three-dimensional patterning and morphological control of porous nanomaterials by gray-scale direct imprinting, Sci. Report. 3 (2013) 1502, http://dx.doi.org/10.1038/srep01502. [20] H. Schift, Nanoimprint lithography: 2D or not 2D? A review, Appl. Phys. A Mater. Sci. Process. 121 (2015) 415–435.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Accelerated publication
Tailoring of the coercive voltage in a ferroelectric polymer capacitor Woo Young Kim a,⁎, Hee Chul Lee b a b
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 5 August 2016 Accepted 17 September 2016 Available online 21 September 2016 Keywords: P(VDF-TrFE) Ferroelectric capacitor Coercive voltage Nonlinearity
a b s t r a c t For an identical ferroelectric material, operation at a different voltage means that all ferroelectric films should be designed for different thicknesses, though this increases the degree of process complexity. Here, a technique which can be used to adjust the coercive voltage (VC) of a metal-ferroelectric film-metal capacitor is demonstrated. The VC-adjustable capacitor was fabricated with ferroelectric polymer film and the capacitor consists of two sub-capacitors with different thicknesses. For a common top and bottom electrode, the sub-capacitors are equivalent to two parallel-connected capacitors. With regard to the variance of the ratio of the area of the sub-capacitors, a VC-adjustable capacitor can take coercive voltage between two VC values, each of which correspond to the VC value of each respective sub-capacitor. In this demonstration, the width of the tuning range of the VC values was 3.6 V. In addition, the strategy for a linear VC adjustment of a VC-adjustable capacitor is discussed in terms of the concept of nonlinearity. This demonstration with a ferroelectric polymer is predicted to be applicable to emerging organic electronic applications. © 2016 Published by Elsevier B.V.
1. Introduction Ferroelectric materials are very attractive materials for a range of applications, such as memory devices [1,2] as well as nonvolatile circuits [3], neuron-mimicking circuits [4,5], tunable antennas [6], sensors and actuators [7,8]. If these components can be combined in a single system, such an integrated system will be very versatile. If only one type of ferroelectric material is used, the ferroelectric films for different devices should be fabricated with different thicknesses because different devices operate in different voltage ranges. In other words, all ferroelectric devices should be fabricated with different process steps. Given this point of view, a method by which all ferroelectric devices can be fabricated in a single step but where all devices can operate in different voltage ranges should be encouraged, leading to a reduction in the overall number of process steps and an improvement of the process yield. In this work, a method to tailor the coercive voltage using a ferroelectric polymer is demonstrated. The coercive voltage is one of the main parameters in ferroelectric films; it is defined as external voltage which creates net polarization of a ferroelectric film zero. The polarity of the surface charge in a ferroelectric film changes upon coercive voltage, which is why coercive voltage is used as a reference (or its corresponding voltage is) to compare ON and OFF states in switching devices or 0 and 1 states in memory devices. The ferroelectric polymer used here was selected for its superior properties, such as easy processability and environment inertness. Therefore, it is expected that ⁎ Corresponding author. E-mail address: [email protected] (W.Y. Kim).
http://dx.doi.org/10.1016/j.mee.2016.09.009 0167-9317/© 2016 Published by Elsevier B.V.
tailoring the coercive voltage in a ferroelectric polymer capacitor will be a useful method for emerging applications. In the next section, the principle used to tailor the coercive voltage will be described in detail. 2. Principle For a ferroelectric capacitor with large surface roughness, it has been reported that the switching time of polarization is retarded compared to a ferroelectric capacitor with a flat surface, as an external electric field is applied non-uniformly to the ferroelectric film [9]. The method to tailor the coercive voltage of a ferroelectric capacitor was inspired by the nonuniform distribution of the electric field. Fig. 1 describes the principle behind the tailoring of the coercive voltage of a ferroelectric capacitor. Fig. 1a represents a normal ferroelectric capacitor with a flat surface, where the two terminals are connected to an external voltage (VA) source and the ground, respectively. In reality, however, surface roughness exists to a certain extent on account of the crystallinity of the ferroelectric film. For a conceptual understanding, assume that the film morphology consists of only two terrains, a plateau and a valley. The height of the plateau from an electrode connected to the ground is ΔB above a reference thickness of t0. Conversely, the valley is positioned below ΔA from t0. If all plateaus and valleys correspond to parallel-connected capacitors, the ferroelectric capacitor in Fig. 1b is electrically equivalent to the ferroelectric capacitor shown in Fig. 1c. Therefore, the entire ferroelectric capacitor with an area of A0 consists of two different sub-capacitors, CA and CB. When external voltage VA sweeps from 0 to VMAX, as represented in Fig. 1d, the coercive voltage of CA (VCA) is applied prior to the coercive voltages of CB (VCB). Assume that
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Fig. 1. Principle behind the tailoring of the coercive voltage. Schematics of (a) a flat ferroelectric capacitor with area A0 and thickness t0. (b) A rough ferroelectric capacitor with two terrains, a plateau and a valley. The film thicknesses of the plateau and the valley are t0 + ΔB and t0 - ΔA, respectively. (c) Structure electrically equivalent to the structure depicted in (b). The area ratio of CA and CB is α: 1- α. (d) Profile of the applied voltage with the maximum voltage VMAX. VCA and VCB indicate the coercive voltages of CA and CB, respectively. (e) Schematic of the polarization-voltage relationship between CA and CB when α exceeds 0.5.
the area ratio of CA to CB is α: (1- α). For an α value larger than 0.5, each hysteresis loop for CA and CB will be measured, as shown in Fig. 1e. It is possible to imagine that a certain voltage VX between VCA and VCB exists to make the polarization of CA at VX (PA(VX)) equal to the polarization of CB at VX (PB(VX)). Therefore, it is certain that the coercive voltage of the entire ferroelectric capacitor with area A0 is positioned between VCA and VCB. Ferroelectric polarization (P) can be quantitatively described with a hyperbolic tangent function, as expressed below [10,11]. P ¼ P S tanhðkðV A −V C ÞÞ
ð1Þ
Here, PS is the spontaneous polarization of the ferroelectric capacitor when the external voltage VA is VMAX; VC is the coercive voltage. The fitting constant k determines how fast P approaches Ps. Thus, PA and
PB are modelled as αPS tanh (k(VA − VCA)) and (1 − α)PS tanh (k(VA − VCB)), respectively. To apply VA = VX to make the net polarization zero throughout a ferroelectric capacitor, the following equation applies. P ¼ P A þ P B ¼ αP S tanhðkðV X −V CA ÞÞ þ ð1−α ÞP S tanhðkðV X −V CB ÞÞ ¼0 ð2Þ When the parameter k and the capacitor structure are known, the only variable in Eq. (2) is the area ratio, α. In other words, the solution of Eq. (2) depends solely on α to determine the areas of the two capacitors. The fact that the term α can be manipulated intentionally suggests that it is possible to fabricate a ferroelectric capacitor with random values of the coercive voltage VC = VX between VCA and VCB. If such an important factor VC can be manipulated simply by tuning the area
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ratio of two capacitors with different thicknesses, a circuit design will be straightforward in a system which includes ferroelectric film. In this work, a ferroelectric capacitor with two different thicknesses was fabricated with a ferroelectric polymer. To realize the thickness difference, the ferroelectric capacitor was fabricated via the patterning and transferring of a ferroelectric thin film. More details will be discussed in the subsequent sections.
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evaporation was conducted at 1 × 10−6 Torr at an evaporation rate of 0.3 Å/s. To confirm that the area ratio α between the area of CA and the area of CB affects the coercive voltage in the ferroelectric capacitor with two thicknesses, an array of circles with diameters of 180 μm on a shadow mask was aligned at an angle corresponding to the patterned lines of the FPF. The polarization-voltage relationships were measured with a ferroelectric measurement system (RT-66A, Radiant Technologies). All fabrication processes are depicted in Fig. 2.
3. Experiment 4. Results and discussion 3.1. Preparation of the ferroelectric film The ferroelectric polymer used here, poly(vinylidene fluoride-cotrifluoroethylene) ((P(VDF-TrFE)), 75/25 mol%), was manufactured from Elf Atochem. First, 0.03 g of P(VDF-TrFE) was dissolved in 1 mL of methyl-ethyl-ketone (MEK) (3 wt%). The thickness of the ferroelectric polymer film (FPF) could be controlled linearly by adjusting the solution concentration. By adding additional MEK to the solution of 3 wt%, the solution concentration was varied. The spin speed and the spin time were fixed at 1500 rpm and 10 s, respectively. Under these conditions, the correlation between the film thickness and the solution concentration was 90 nm/1 wt%. After spin-coating, the FPF was annealed at 130 °C for 10 min. to increase the crystalline β-phase. The thickness of the FPF was measured using an α-step (Dektak 6 M, Veeco Instruments, Inc.). 3.2. Patterning of the ferroelectric film The FPF was patterned by conventional photo-lithography technology. First, 60 nm of FPF was spin-coated onto an Au-deposited SiO2/Si wafer. A positive photoresist (AZ 1512, AZ Electronic Materials) was then spin-coated, after which soft-baking was performed at 95 °C for 90 s. Next, the sample was exposed at the g-line (436 nm) for 20 s. A photoresist developer (AZ 300MIF, AZ Electronic Materials) was used for the development process. Photoresist-uncovered FPF was etched in oxygen plasma ambient with the following process conditions. The oxygen flow rate was 50 mL/min, the process pressure was 36 Pa, the RF power was 200 W, and the process time was 30 s. For the removal of the photoresist, a photoresist stripper (AZ 400T, AZ Electronic Materials) was used, but the solubility of the pristine AZ 400T needed to be weakened because the main solvent of the original AZ 400T is n-methyl-2-pyrrolidone, which can definitely dissolve the FPF. Thus, the AZ400T solution was diluted with deionized water. Details of the dilution ratio and its results are explained in our previous publication [12]. The width and the length of the final line patterns were 500 μm and 1 cm, respectively. 3.3. Transferring of the ferroelectric film On a thermally oxidized silicon wafer, 60 nm of FPF was prepared as described in Section 3.1. By dipping the FPF deposited onto a SiO2/Si wafer into aqueous hydrofluoric (HF) acid, the oxide layer SiO2 was etched in the HF solution. The FPF was then separated from the wafer. It floated on the surface of the HF solution on account of surface tension. Subsequently, the floating FPF was lifted out and moved onto the surface of deionized water. And, 60 nm of the floating FPF was transferred onto the patterned FPF 60 nm on an Au-deposited wafer prepared as described in Section 3.2. After the transfer, the sample was thermally treated at 80 °C for 30 min. to remove the water residue and then again at 130 °C for 10 min to ensure strong adhesion between the two FPFs. 3.4. Ferroelectric capacitor with two thicknesses For the top electrode, Au was thermally evaporated through a shadow mask on a sample that consisted of FPF with two thicknesses: one at 60 nm (CA) and the other at 120 nm (= 60 nm + 60 nm, CB). Au
Fig. 3a shows schematic of the displacement (D) - voltage (VA) hysteresis loop of a normal ferroelectric capacitor. Here, PS, PR, and VC denotes the spontaneous polarization, remnant polarization, and the coercive voltage, respectively. Fig. 3b shows the measured D-VA hysteresis loops of three capacitors with different α values. When α is unity, only CA contributes to the total hysteresis loop. The PS and PR values are determined to be 10.81 μm/cm2 and 8.52 μm/cm2, respectively. The VCA value is calculated to 4.13 V; thus, the coercive field (ECA) is 68.8 MV/m. When α is null, the capacitor CB has PS values of 9.94 μm/ cm2 and PR of 8.34 μm/cm2. The coercive voltage VCB of CB is 7.75 V, and the coercive field thus becomes 64.6 MV/m. All of the hysteresis loops were measured with the RT-66A ferroelectric measurement system. This equipment operates as follows. Before a triangular VA is used to sweep the ferroelectric capacitor, a single voltage pulse of -VMAX is applied to initialize the polarization of the ferroelectric capacitor to -PR. After a duration of 1 s from initialization, the triangular voltage shown in Fig. 1d is applied [13]. Therefore, the greater the polarization becomes, the more the screening charge accumulates around the surfaces of the ferroelectric film [14]. Therefore, the polarization differences between CA and CB are not a crucial issue but are instead a natural phenomenon in ferroelectric films. It is important to note that, when α is halved, the hysteresis loop is plotted between two hysteresis loops of CA and CB. The PS and PR values are determined to be 10.49 μm/cm2 and 8.493 μm/cm2, respectively. Though the coercive field cannot be simply defined in a capacitor when α = 0.5, the coercive voltage is positioned between VCA and VCB, as expected. Fig. 3c was devised from the differentiation of the measured data in Fig. 3b. The square of the hyperbolic secant function (the derivative of the hyperbolic tangent function as expressed in Eq. (1)) has two maxi− mum values at VA = V+ C and VC . Therefore, the VA-axis positions of the peak values shown in Fig. 3c indicate the coercive voltages of each ferroelectric capacitor. When α = 0.5, two peak values on the positive and negative axes are observed, each of which nearly consistent with VCA and VCB. Thus, the coercive voltage of the capacitor when α = 0.5 does not match VCA and VCB. The solid green line in Fig. 3c is the result of the average of 0.5 × (∂DA/∂VA) + 0.5 × (∂DB/∂VA), in good agreement with the solid red line (α = 0.5). This indicates that each dipole in the two capacitors CA and CB switches independently of the other, with the coercive voltage of the total capacitor with two thicknesses then needing to be determined by the linear combination of the two sub-capacitors. Fig. 3d shows the relationships between the maximum applied voltage VA = VMAX and the PR values. The solid black line Fit\\CA is a fitted line for α = 1, and the solid blue line Fit-CB corresponds to α = 0. The average line from the calculation of 0.5 × Fit-CA + 0.5 × Fit-CB matches the measured results (red dot) well. Thus, these results are equivalent to those described in Fig. 3c. Therefore, it is possible to estimate that if two hysteresis loops of CA and CB are known, any hysteresis loop for a random value of α can be generated regardless of the magnitude of VMAX. Using two hysteresis loops from CA and CB, any hysteresis loop (H) with a value of α between 0 and 1 can be determined by a weighted averaging calculation. Fig. 4a shows ten hysteresis loops with different α values. For example, the hysteresis loop H(α = 0.3) was derived through the equation 0.3 × H(α = 1) + 0.7 × H(α = 0). Fig. 4b presents
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Fig. 2. Fabrication process steps: (a) P(VDF-TrFE) spin-coating onto an Au-deposited SiO2/Si wafer, (b) P(VDF-TrFE) patterning, (c) P(VDF-TrFE) spin-coating onto a SiO2/Si wafer, (d) detaching of the P(VDF-TrFE), (e) transfer of P(VDF-TrFE) onto the patterned P(VDF-TrFE) (f) Au electrode deposition, (g) profile of the final structure, and (h) optical microscopy image of the final devices. The tA region and the tB region are denoted by CA and CB, respectively.
the relationship between α value and the VC values extracted from Fig. 4a. Graph H(α = 0) has a VC value of 7.75 V and graph H(α = 1) has a VC value of 4.13 V. Thus, the ferroelectric capacitor with two sub-capacitors CA and CB can have any VC value between 4.13 V and 7.75 V. Accordingly, the width of the tuning range is 3.62 V. If a dependent parameter, VC can be linearly modulated by the variable α, the final VC values are easily predictable. Fig. 4b shows an example of S-shaped dependency in which nonlinear dependence originates from the nonlinearity of hyperbolic tangent function described in Eq. (1). At this point, this nonlinearity and a method to reduce the nonlinearity will be discussed. Eq. (2) can be simplified into the following equation. α¼
−1 tanhðkðV C −V CA ÞÞ 1− tanhðkðV C −V CB ÞÞ
ð3Þ
Assume that the relationship between V C and α can be expressed as VC = f(α). Though the relationship VC = f(α) is transposed into another form, i.e., α = f− 1(VC), its nonlinearity remains unchanged. Thus, Eq. (3) corresponds to α = f− 1(VC), which is useful for discussing the nonlinearity. The solution to Eq. (3) is schematically represented as the S-shaped dotted line in Fig. 5a. The ideally desirable relationship is the solid line shown in Fig. 5a, which is a straight line between the two points (VC, α) = (VCA, 1) and (VCB, 0). The symbols αI and αR denote the ideal and the actual case of α, respectively. Here, the nonlinearity (NL) can be defined as
the area surrounded by two curves, α I and α R . Then NL can be expressed using the following equation. V ZCB
jα I −α R j dV C
NL ¼
ð4Þ
V CA
From Eq. (4), it is certain that the only variable is the fitting parameter k. For simplification, let the k value in CA be equal to k in CB. For a variable k between 0 and 1, the NL values were calculated, as shown in Fig. 5c and Fig. 5d. Fig. 5d is the logarithmic form of Fig. 5c. As shown in Figs. 5c and d, smaller k values result in smaller NL values. Less nonlinearity is equivalent to more linearity. However, the fitting constant k reflects the ratio of PR and PS. According to the literature, a smaller value of k indicates that the ferroelectric film has a small PR value compared to the PS value, which can normally be observed in a fatigued ferroelectric films [15,16] or a relaxor ferroelectrics [17,18]. Therefore, a strategy to reduce k is not desirable to improve the linearity. By shifting VCB as shown in Fig. 5b, a new pathway to overcome the nonlinearity can be suggested. As V CB moves to the right, NL increases. Inversely, movement of V CB to the left reduces NL. For different V CB values between 7.5 V and 4.5 V, Fig. 5c and Fig. 5d show that NL decreases as V CB approaches V CA . As noted above, a high k value is recommended in electronic switches or memory applications; accordingly, the NL values at k = 1 are plotted in Fig. 5e. This relationship
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Fig. 3. Displacement-voltage (D-V) measurement (a) schematic of the D-V hysteresis loop. PS and PR indicate the spontaneous polarization and remanant polarization, respectively. V+ C and V− C are correspondingly the coercive voltage in the positive and negative voltage regions. (b) D-V hysteresis loops for α = 1, 0.5 and 0. (c) Differentiation of the D-V hysteresis loop depicted in (b). The average line shown in green is the result calculated by averaging the two differentiation results for α = 1 and 0. (d) Relationship between PR and VMAX. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
infers that the tuning ranges of V C and NL exist in a counterpart relationship. To overcome this trade-off, the assumption that the total capacitor consists of two thicknesses must be modified.
If an intermediate thickness t i between t A and t B is included or if the transition between t A and t B is gray-scale changed, as shown in Fig. 5f, NL and the tuning range can be reasonably
Fig. 4. Tailoring of the coercive voltage (VC): (a) D-V hysteresis loops calculated by the weighted averaging of two D-V hysteresis loops for α = 1 and 0, and (b) relationship between VC and α.
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Fig. 5. Nonlinearity in the tailoring of the coercive voltage: (a) schematic of the ideal (αI) and actual (αR) α -VC relationships. The nonlinearity (NL) is defined by the gray region surrounded by αI(VC) and αR(VC). (b) α-VC relationships when VCB moves to the left (VCBL) or to the right (VCBR). (c) NL-k relationship calculated for various VCB values. (d) Logarithmic expression of (c). (e) NL-tuning range relationship. (f) Alternative device structures to reduce the NL values, in which an intermediate film with a thickness of ti or a gray-scaled transition region is inserted.
compromised. Those kinds of films with intermediate step and/or gray-scaled slope can be easily fabricated by adapting nanoimprint process as described the previous literatures [19,20]. 5. Summary and conclusion In this work, a ferroelectric capacitor with two different thicknesses was suggested to tailor an important parameter, i.e., the coercive voltage. A capacitor with two different thicknesses was prepared by a patterning process followed by the transfer of the ferroelectric polymer film. The only variable during the tailoring of the coercive voltage in a ferroelectric capacitor is the area ratio of the two sub-capacitors, which are relatively thin and thick capacitors. This approach to tailor the coercive voltage offers simplicity in the design of an electronic system which includes ferroelectric film. Though the width of the tuning
range was approximately 3.6 V, nonlinearity clearly arose due to the nonlinear response of the dipoles in the ferroelectric film. In this study, it was demonstrated that one of the strategies which can be used to realize both a wide tuning range and considerable linearity is to ensure an intermediate thickness between the two different thicknesses.
Footnote & acknowledgments In this work, the experiment results and the measured data were based on the main author's Ph.D dissertation entitled of “A study on the fabrication and characterization for multi-bit memory device using multilayer structured ferroelectric polymer thin film” in Korea Advanced Institute of Science and Technology (KAIST). Also, this work
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