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Negative Capacitance in BaTiO3/BiFeO3 Bilayer Capacitors Ya-Fei Hou,† Wei-Li Li,†,‡ Tian-Dong Zhang,† Yang Yu,† Ren-Lu Han,† and Wei-Dong Fei*,† †

National Key LAB for Advanced Welding and Joining, and ‡National Key Laboratory of Science and Technology on Precision Heat Processing of Metals, Harbin Institute of Technology, Harbin 150001, P. R. China S Supporting Information *

ABSTRACT: Negative capacitances provide an approach to reduce heat generations in field-effect transistors during the switch processes, which contributes to further miniaturization of the conventional integrated circuits. Although there are many studies about negative capacitances using ferroelectric materials, the direct observation of stable ferroelectric negative capacitances has rarely been reported. Here, we put forward a dc bias assistant model in bilayer capacitors, where one ferroelectric layer with large dielectric constant and the other ferroelectric layer with small dielectric constant are needed. Negative capacitances can be obtained when external dc bias electric fields are larger than a critical value. Based on the model, BaTiO3/BiFeO3 bilayer capacitors are chosen as study objects, and negative capacitances are observed directly. Additionally, the upward self-polarization effect in the ferroelectric layer reduces the critical electric field, which may provide a method for realizing zero and/or small dc bias assistant negative capacitances. KEYWORDS: BaTiO3/BiFeO3 bilayer capacitor, negative capacitance, dc bias assistant model, critical electric field, ferroelectric, self-polarization effect

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ferroelectric capacitor.3,11 For example, O’Neill et al.10 have reported that the total capacitance of BaTiO3/SrTiO3 bilayer capacitor is enhanced in a series combination of BaTiO3 and SrTiO3 capacitors, and the capacitance enhancement in the BaTiO3/SrTiO3 bilayer capacitor indicates a stable state of negative capacitances in the BaTiO3 capacitor. Although negative capacitances have been confirmed through an indirect mode in the early days, the direct measurement of negative capacitances in ferroelectric materials had never been reported until 2015. Recently, Salahuddin et al.19 have observed an instantaneously negative capacitance for the first time in the ferroelectric capacitor when a voltage pulse is applied. Therefore, to realize stable negative capacitances in ferroelectric materials, much more work needs to be done. In this study, we put forward a dc bias assistant (DBA) model to realize negative capacitances in bilayer capacitors. Based on the model, a stable and controllable negative capacitance has been observed directly in the BaTiO3/BiFeO3 (BT/BFO) bilayer capacitors when dc bias electric fields are larger than a critical value.

INTRODUCTION The management of heat generation in field-effect transistors (FETs) during the switching process has become one of the most difficult problems in conventional integrated circuits, and it ultimately restricts the further miniaturization of integrated circuits.1,2 The problem derives from the inability to reduce the fundamental limit of the operational voltage of FETs, because a minimum gate voltage is necessary to maintain a good on/off current ratio in FETs.3−7 In order to deal with the problem above, Salahuddin et al.8,9 have proposed that the heat generation during the switching process in FETs can be reduced by replacing the standard insulator with a ferroelectric insulator to realize a negative capacitance, and the negative capacitance acts as a step-up voltage transformer to amplify the input gate voltage of transistors; therefore, the limit operational voltage and heat generation are reduced in FETs. Inspired by the potential applications in integrated circuits, negative capacitances have been widely investigated recently,10−18 especially in ferroelectric materials. However, the possibility of stable negative capacitances using ferroelectric materials has been controversial. According to the double-well energy landscape, based on the Landau theory, negative capacitances and negative differential capacitances in the individual ferroelectric material appear only in nonequilibrium conditions, and it is hard to be experimentally measured in the single- or multidomain ferroelectric materials.19−21 For example, Krowne et al.22 have measured 2185 ferroelectric capacitors and have shown no instance of negative capacitances in their database. Subsequently, it has been reported that the nonequilibrium negative capacitance can be stabilized by putting a dielectric capacitor in series with the © XXXX American Chemical Society

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RESULTS AND DISCUSSION Let us consider a bilayer capacitor shown in Figure 1a. In the case of ideal insulator layers, the electric displacement continuous condition at the interface without free charges can be expressed as follows Received: June 12, 2016 Accepted: August 9, 2016

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DOI: 10.1021/acsami.6b07060 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

polarization of layer 2 can be easily saturated under a certain external dc bias electric field, and the state of layer 2 may be in the CD section of the P ∼ E loop, as shown in Figure 1b. In this case, the polarization (P2) of layer 2 changes slowly with the variation of E2, and ε2 can be expressed as follows under small signal measurement of capacitance23 ε2 = 1 +

dP2 = ε20 − kE2 − k′E22 + ... ε0dE2

(3)

ε02

where represents the dielectric constant of layer 2 without polarization, which is smaller than ε1, and k and k′ are positive constants. Neglecting higher order terms of E2, eq 3 can be rewritten as ε2 ≈ ε20 − kE2

(4)

ε02/k.

The approximation of eq 4 is valid only when E2 < Moreover, on the basis of above analysis, the α value cannot be very small or very large. The capacitance of the bilayer capacitor can be described as C=

dQ 1 dQ 2 dQ = + dV l dE l dE

(5)

where Q1 (= ε0ε1SE1) and Q2 (= ε0ε2SE2) represent the surface charges of layer 1 and layer 2, respectively, and S is the electrode area of the bilayer capacitor. Substituting eqs 1 and 4 into eq 5 and after arranging terms, we get C=

2ε0S 0 dE (ε2 − 2kE2) 2 l dE

(6)

Because dE2/dE > 0, the necessary condition for negative capacitances in the bilayer capacitor can be described as

E2 > Figure 1. (a) Schematic diagram of a bilayer capacitor composed of layer 1 with large dielectric constant and layer 2 (ferroelectric film) with small dielectric constant. (b) Polarization states of layer 1 and layer 2 under a dc bias electric field. (c) Effect of thickness fraction of layer 1 (α) on the critical dc bias electric field for negative capacitances.

ε0ε1E1 = ε0ε2E2

E2 = (1 − α)ε1 + αε20 −

[(1 − α)ε1 + αε20]2 − 4kαε1E 2kα

(1)

V l

(7)

In addition, E2 can be obtained from eqs 1, 2, and 4 such that

(8)

where ε0 represents the vacuum permittivity, ε1 and ε2 represent the dielectric constants of layer 1 and layer 2, and E1 and E2 represent the electric fields across layer 1 and layer 2. In addition, αE1 + (1 − α)E2 = E =

ε20 2k

Substituting eq 8 into eq 7 and after simplification, the critical condition for negative capacitance in the bilayer capacitor can be described as 2(1 − α)ε1ε20 + αε20 E > EC = 4kε1

(2)

2

(9)

Therefore, the negative capacitance in the bilayer capacitor can be obtained when the following conditions are satisfied: first, the dielectric constant of one ferroelectric or dielectric layer must be large; second, the dielectric constant of the other ferroelectric layer must be small; finally, the external dc bias electric field should be larger than the critical value (EC). Because negative capacitances can only be obtained with a certain dc bias assistant, the model above is called as DBA model. Because BaTiO3 (BT) shows a large dielectric constant (εBT ∼ 1500 at 1 kHz),24,25 and BiFeO3 (BFO) exhibits a small dielectric constant (εBFO ∼ 50 at 1 kHz),26,27 BT/BFO bilayer capacitors are chosen as examples to explore the possibility for

where α (= l1/l) is the thickness fraction of layer 1, l1 and l represent the thickness of layer 1 and the total thickness of the bilayer, E is the external dc bias electric field, and V is the voltage across the bilayer capacitor. We suppose that ε2 is much smaller than ε1, and layer 2 is a ferroelectric one. The hypothesis can be satisfied through material selection of the layers in the bilayer capacitor. In this case, E2 is much larger than E1 since ε2 is much smaller than ε1 according to eq 1. In other words, the external dc bias electric field is mainly applied to layer 2. Therefore, the polarization state of layer 1 may be in the AB section of the polarization curve (dε1/dE1 ≈ 0), as shown in Figure 1b. In addition, the B


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Figure 2. θ−2θ scan XRD patterns of the 0.30BT/BFO(MS) film (a), the 0.45BT/BFO(MS) bilayer film (b), the 0.60BT/BFO(MS) bilayer film (c), and the 0.45BT/BFO(PLD) bilayer film (d) (inset curves in (a)−(c) are the corresponding rocking curves), the measured and fitted profiles of (110) peaks of the 0.30BT/BFO(MS) bilayer film (e), the 0.45BT/BFO(MS) bilayer film (f), the 0.60BT/BFO(MS) bilayer film (g), and the 0.45BT/BFO(PLD) bilayer film (h).

Figure 3. Surface and cross-sectional morphologies of the 0.30BT/BFO(MS) bilayer film (a), the 0.45BT/BFO(MS) bilayer film (b), the 0.60BT/ BFO(MS) bilayer film (c), and the 0.45BT/BFO (PLD) bilayer film (d).

The XRD patterns of resultant BT/BFO bilayer films are shown in Figure 2. As shown in Figure 2a−c, 0.30BT/ BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer films are well crystallized with high I001/I110 ratio, and there are no detectable impurities. The inset curves in Figure 2a−c are the rocking curves of 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO (MS) bilayer films for (001) reflection, which are of benefit in evaluating the misorientation degree of 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer films. The Gaussian width (fwhm) of rocking curves is about 7°, demonstrating the high (001) orientation nature of 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/ BFO(MS) bilayer films. Figure 2d shows the θ−2θ scan XRD patterns of the 0.45BT/BFO(PLD) bilayer film, and it can be observed that the 0.45BT/BFO(PLD) bilayer film is crystallized without obvious preferential orientation. To further investigate the phase structures of 0.30BT/ BFO(MS), 0.45BT/BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer films, fine scan XRD measurement were carried out. The measured and fitted profiles of (110)

negative capacitances according to the DBA model. In addition, the effect of thickness fraction of layer 1 on the critical dc bias electric field for negative capacitance is shown in Figure 1c according to the DBA model. It can be found that negative capacitances appear when the external dc bias electric field is larger than the critical electric field, and the critical electric field decreases with the thickness fraction of layer 1 increasing. In order to verify the rationality of the DBA model, the BT/ BFO bilayer capacitors with different thickness fraction values of BT (α) were prepared by radio frequency magnetron sputtering (RF-MS). The three resultant BT/BFO bilayer films prepared by RF-MS are termed αBT/BFO(MS), where α = 0.30−0.60. For comparison, the BT/BFO bilayer film prepared by pulse laser deposition (PLD) is termed 0.45BT/BFO(PLD). During electrical property measurements, positive bias is defined as the electric potential of the top electrode being higher than that of the bottom electrode, as shown in Figure 1. The detailed experimental and characterization procedures are given in the Supporting Information. C


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Figure 4. Capacitance−frequency curves at various dc bias for the 0.30BT/BFO(MS) bilayer capacitor (a), the 0.45BT/BFO(MS) bilayer capacitor (b), the 0.60BT/BFO(MS) bilayer capacitor (c), and the 0.45BT/BFO(PLD) bilayer capacitor (d).

reflections of 0.30BT/BFO(MS), 0.45BT/BFO(MS), 0.60BT/ BFO(MS), and 0.45BT/BFO(PLD) bilayer films are shown in Figure 2e−f. All the (110) reflections of 0.30BT/BFO(MS), 0.45BT/BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer films can be simulated using four peaks. According to the PCPDF data (#83-1880 and #74-2493), the left two peaks (green line in Figure 2e−g) correspond to BT, and the others (blue line in Figure 2e−g) correspond to BFO. The results above indicate that BT and BFO in the bilayer films are both well crystallized and clearly indentified. It can be observed from the surface micrographs (Figure 3a− d) that 0.30BT/BFO(MS), 0.45BT/BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer films are composed of uniform nanoparticles with small surface roughness, and the sizes of nanoparticles and surface roughness in the 0.30BT/ BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer films are much smaller than that of the 0.45BT/BFO(PLD) bilayer film. The cross-sectional images (Figure 3a−d) show that there are many nanoparticles in the 0.30BT/BFO(MS), 0.45BT/BFO (MS), and 0.60BT/BFO(MS) bilayer films, and a clear interface between BT and BFO can be observed owing to the different particle shapes. The thickness of the 0.30BT/BFO(MS) film is 360 nm (Figure 3a), where the thickness of BT and BFO is 110 and 250 nm, respectively. The thickness of the 0.45BT/BFO(MS) film is 510 nm (Figure 3b), where BT and BFO are 230 and 280 nm, respectively. The thickness of the 0.60BT/BFO(MS) film is 660 nm, where 400 nm BT and 260 nm BFO are included (Figure 3c). Meanwhile for the 700 nm 0.45BT/BFO(PLD) film, there are no obvious grain and interface in the crosssectional micrographs (Figure 3d). Considering the surface and cross-sectional morphologies, 0.30BT/BFO(MS), 0.45BT/

BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer films have a crack-free and densely packed microstructure at the microscopic scale. The capacitance−frequency curves of 0.30BT/BFO(MS), 0.45BT/BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer capacitors under various dc biases are shown in Figure 4. It can be found that negative capacitances gradually appear at low frequency and become more and more apparent in the bilayer capacitors with the positive dc bias increasing. The realization of negative capacitance in 0.30BT/BFO(MS), 0.45BT/BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer capacitors under sufficiently large dc biases can be understood as the results of the DBA model. According to the discussion above, the external dc bias is mainly applied to the BFO film since ε2 is much smaller than ε1, and ε2 will become smaller with the external dc bias increasing. In other words, the dc bias applied to the BFO film will increase, and the dc bias applied to the BT film may decrease with the external dc bias increasing. Therefore, the surface charges of BFO film will increase, while the surface charges of BT film will decrease, with the external dc bias increasing. In this case, if the decrease of surface charges of BT film is larger than the increase of surface charges of BFO film, a negative capacitance will be realized because the voltage of the bilayer capacitor increases as surface charges are reduced.4 However, negative capacitances cannot be obtained at high frequency, which may be caused by the following reasons. At low frequency, the ferroelectric layers are approximately at equilibrium during the measurements,28 and the necessity of continuity of electric displacement can be satisfied.29 But the relaxation of polarization response to electric fields cannot be neglected at high frequency. The ferroelectric layers are not at D


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Figure 5. PFM images and I−V curves of the 0.30BT/BFO(MS) bilayer film (a), the 0.45 BT/BFO(MS) bilayer film (b), the 0.60BT/BFO(MS) bilayer film (c), and the 0.45BT/BFO(PLD) bilayer film (d).

Figure 6. Relationships between the capacitance and electric field of dc bias for the 0.30BT/BFO(MS) bilayer capacitor (a), the 0.45BT/BFO(MS) bilayer capacitor (b), the 0.60BT/BFO(MS) bilayer capacitor (c), and the 0.45BT/BFO(PLD) bilayer capacitor (d) at 1 kHz.

equilibrium state at high frequency because of different relaxation time constants of the layers. In the case of high frequency, the necessity of continuity of electric displacement cannot be satisfied.29 Therefore, negative capacitances can be observed only in the low-frequency region. In addition, the capacitance responses of 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors under positive and negative dc biases are different as shown in Figure 4a−c, and negative capacitances only appear under positive dc biases in 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors. However, the capacitance responses of the 0.45BT/BFO(PLD) bilayer capacitor under positive and negative dc biases are almost symmetric as shown in Figure 4d, and negative capacitances appear under both positive and negative dc biases. According to

previous studies, the asymmetric feature in the capacitance responses of 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors under positive and negative dc biases may be caused by the self-polarization effect30−32 in ferroelectric films, which will be discussed in detail later. In order to study the domain structures of 0.30BT/ BFO(MS), 0.45BT/BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer films, piezoelectric force microscopy (PFM) was used to capture images of domain structures in the samples. The recorded domain structures and I−V curves of 0.30BT/BFO(MS), 0.45BT/BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer films without prepoling are shown in Figure 5, where the bright domains result from upward polarization and the dark domains correspond to E


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can be effectively reduced (or enhanced) in the upward selfpolarization bilayer capacitors by the built-in electric field under positive (or negative) dc biases, so zero and/or small dc bias assistant negative capacitances may be obtained in the upward self-polarization bilayer capacitors through regulating the upward self-polarization effect, thickness fraction, and other material parameters.

downward or in-plane polarization. In Figure 5a−c, it can be seen that most domains of 0.30BT/BFO(MS), 0.45BT/ BFO(MS), and 0.60BT/BFO(MS) bilayer films are bright, which indicates the existence of upward self-polarization in 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer films.31 Additionally, the diode-like behavior in 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors as shown in Figure 5a−c further confirms the existence of upward self-polarization in 0.30BT/ BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer films. In contrast, the areas of bright and dark domains in the 0.45BT/BFO(PLD) bilayer film are roughly the same as shown in Figure 5d, which corresponds to the random orientation of domains in the 0.45BT/BFO(PLD) bilayer film. Moreover, the symmetric I−V curve of the 0.45BT/BFO(PLD) bilayer capacitor can be observed in Figure 5d, which is corresponding to no self-polarization in the 0.45BT/BFO(PLD) bilayer film. Therefore, the asymmetric feature in capacitance responses of 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors is caused by the upward selfpolarization effect. Furthermore, the upward self-polarization severely affects the appearance of negative capacitances in 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors. To further investigate the effects of BT thickness fraction and upward self-polarization on negative capacitances in the bilayer capacitors, the relationships between the capacitance and electric field of dc bias for 0.30BT/ BFO(MS), 0.45BT/BFO(MS), 0.60BT/BFO(MS), and 0.45BT/BFO(PLD) bilayer capacitors at 1 kHz are shown in Figure 6. It can be observed from Figure 6a−c that the critical electric field decreases when the α value increases from 0.30 to 0.60, which is in accordance with the DBA model. However, the critical electric fields of 0.45BT/BFO(MS) and 0.45BT/ BFO(PLD) bilayer capacitors are different although the BT thickness fractions of the two capacitors are the same, as shown in Figure 6b and d. It is found that the critical electric field of the 0.45BT/BFO(MS) bilayer capacitor under a positive bias is reduced compared with that of the 0.45BT/BFO(PLD) bilayer capacitor, which results from the upward self-polarization effect. Moreover, to understand the asymmetric feature in capacitance responses of 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors, the DBA model should be revised to take the upward self-polarization effect into consideration. As the result of upward self-polarization effect, the built-in electric field (Ein) pointing from BT to BFO films should be considered in the model above, so the critical electric field for negative capacitances should be revised as EC − Ein. In this way, the effect of built-in electric field is responsible for the following results: first, the asymmetric feature in capacitance responses of 0.30BT/BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors under positive and negative dc biases; second, the reduction of critical electric fields of 0.30BT/ BFO(MS), 0.45BT/BFO(MS), and 0.60BT/BFO(MS) bilayer capacitors with α value increasing under positive dc biases; third, the reduction of critical electric field of the 0. 45BT/ BFO(MS) bilayer capacitor under positive bias compared with that of the 0.45BT/BFO(PLD) bilayer capacitor. Therefore, the experimental results can be well understood by the DBA model when self-polarization is taken into consideration. Furthermore, it can be obtained that the critical electric field

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CONCLUSION To conclude, a dc bias assistant model is put forward for the realization of negative capacitances in the bilayer capacitors under sufficiently large external dc bias electric field. In principle, one ferroelectric or dielectric layer with large dielectric constant and the other ferroelectric layer with small dielectric constant are needed. Based on this model, BT/BFO bilayer capacitors are chosen as research objects, and a stable and controllable negative capacitance is observed directly when external dc bias electric field is larger than the critical value. Considering the self-polarization effect in the ferroelectric layer, the built-in electric field contributes to reduce the critical electric field for negative capacitances in the bilayer capacitors. In addition, the dc bias assistant model and direct observation of negative capacitances in the BT/BFO bilayer capacitors provide an effective method for exploring the intrinsic negative capacitance in the bilayer systems.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b07060. Details of deposition of the ferroelectric capacitors, phase and structure characterizations, and dielectric properties (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research was financially supported by the National Natural Science Foundations of China (No. 11272102, and 51471057). REFERENCES

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BiFeO3 Bilayer ... - ACS Publications

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