FERROELECTRIC NANOPARTICLE CAPACITOR FOR NON-BINARY LOGICS

Abstract

A ferroelectric nanoparticle capacitor-device comprises a pair of conductive elements electrically insulated from each other, and ferroelectric nanoparticles arranged between the conductive elements of the pair. The ferroelectric nanoparticles are adapted to provide at least three polarization states with different total ferroelectric polarizations.

Claims

1. A ferroelectric nanoparticle capacitor-device, comprising: a pair of conductive elements electrically insulated from each other; and a plurality of ferroelectric nanoparticles arranged between the pair of conductive elements; wherein the plurality of ferroelectric nanoparticles is configured to provide at least three polarization states with different total ferroelectric polarizations.

2. The ferroelectric nanoparticle capacitor-device of claim 1, wherein the plurality of ferroelectric nanoparticles includes: at most 10 ferroelectric nanoparticles; at most 5 ferroelectric nanoparticles; at most 3 ferroelectric nanoparticles; exactly 3 ferroelectric nanoparticles; or exactly 2 ferroelectric nanoparticles.

3. The ferroelectric nanoparticle capacitor-device of claim 1, wherein each conductive element of the pair of conductive elements comprises respective surfaces facing each other, and wherein a respective surface area of each of the respective surfaces exceeds an overall surface-projected area of the plurality of ferroelectric nanoparticles.

4. The ferroelectric nanoparticle capacitor-device of claim 1, wherein individual ferroelectric particles of the plurality of ferroelectric particles are spaced apart from each other.

5. The ferroelectric nanoparticle capacitor-device of claim 4, further comprising a dielectric separator material arranged between the individual ferroelectric nanoparticles.

6. The ferroelectric nanoparticle capacitor-device of claim 1, wherein a first ferroelectric nanoparticle of the plurality of ferroelectric nanoparticles has a first size and a second ferroelectric nanoparticle of the plurality of ferroelectric nanoparticles has a second size, and wherein the first size is larger than the second size.

7. The ferroelectric nanoparticle capacitor-device of claim 6, wherein the first size is larger than the second size by one of: at least 10%; at least 30%; at least 50%; and at least a factor of two.

8. The ferroelectric nanoparticle capacitor-device of claim 1, wherein respective sizes of the ferroelectric nanoparticles along any direction do not exceed 100 nm.

9. The ferroelectric nanoparticle capacitor-device of claim 1, wherein the plurality of ferroelectric nanoparticles comprises respective monodomain ferroelectric states.

10. The ferroelectric nanoparticle capacitor-device of claim 1, wherein a first conductive element of the pair of conductive elements is configured to carry a constant electrical charge and/or is electrically insulated and/or is electrically floating.

11. The ferroelectric nanoparticle capacitor-device of claim 10, further comprising a charge control device configured to control and/or change a charge on a second conductive element of the pair of conductive elements.

12. The ferroelectric nanoparticle capacitor-device of claim 11, wherein the charge control device comprises an additional conductive element that is electrically insulated from the pair of conductive elements, and wherein the charge control device (114) is adapted to apply a voltage between the additional conductive element and the second conductive element.

13. The ferroelectric nanoparticle capacitor-device of claim 1, further comprising at least one of: a temperature-control element configured to control and/or change a temperature of the plurality of ferroelectric nanoparticles; and a force control element configured to control and/or change a mechanical force applied to the plurality of ferroelectric nanoparticles.

14. A method for operating a ferroelectric nanoparticle capacitor-device, wherein the ferroelectric nanoparticle capacitor-device comprises: a pair of conductive elements that are electrically insulated from each other, and a plurality of ferroelectric nanoparticles arranged between the pair of conductive elements; wherein the plurality of ferroelectric nanoparticles is configured to provide at least three polarization states having different total ferroelectric polarizations, including a minimum-ferroelectric-polarization state, a maximum-ferroelectric-polarization state, and at least one intermediate-ferroelectric-polarization state; the method comprising: selecting a selected intermediate-ferroelectric-polarization state; selecting a first voltage or charge according to the selected intermediate-ferroelectric-polarization state; and applying the first voltage or charge to one of the pair of conductive elements to set the plurality of ferroelectric nanoparticles to the selected intermediate-ferroelectric-polarization state.

15. The method (400) of claim 14, further comprising, prior to applying the first voltage or charge to set the ferroelectric nanoparticles to the selected intermediate-ferroelectric-polarization state: providing the plurality of ferroelectric nanoparticles in a first polarization state of the at least three polarization states, wherein the first polarization state is different from the selected intermediate-ferroelectric-polarization state; selecting a second voltage or charge according to the selected intermediate-ferroelectric-polarization state and/or according to the first polarization state; and applying the second voltage or charge to the one of the pair of conductive elements to set the ferroelectric nanoparticles from the first polarization state to a second polarization state of the at least three polarization states; wherein the second polarization state is different from both the first polarization state and the selected intermediate-ferroelectric-polarization state.

16. The method of claim 14, wherein the selected intermediate-ferroelectric-polarization state is a remanent state.

17. The method of claim 14, wherein the method further comprises reducing the voltage or charge applied to the one conductive element thereby preserving the set intermediate-ferroelectric-polarization state.

18. The method of claim 17, wherein reducing the voltage or charge includes reducing the voltage by one of: at least 30%; at least a factor of 2; at least a factor of 3; at least a factor of 5; at least a factor of 10; and at least a factor of 100.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

[0084] The techniques of the present disclosure and the advantages associated therewith will be best apparent from a description of exemplary embodiments in accordance with the accompanying drawings, in which:

[0085] FIG. 1 illustrates the ferroelectric nanoparticle capacitor-device according to first embodiments;

[0086] FIG. 2a illustrates electrostatic energies of individual polarization states of a ferroelectric nanoparticle between conductive elements, and a switching between them;

[0087] FIG. 2b illustrates a charge-voltage hysteresis loop demonstrating the switching between the individual polarization states of the ferroelectric nanoparticle of FIG. 2a;

[0088] FIG. 3 illustrates an equivalent electric circuit of the ferroelectric nanoparticle capacitor-device of FIG. 1 connected to a charge control device;

[0089] FIG. 4a illustrates electrostatic energies of the polarization states of the ferroelectric nanoparticle capacitor-device according to an embodiment corresponding to FIG. 1, and routes for addressing and/or switching the polarization states;

[0090] FIG. 4b illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to the embodiment of FIG. 4a, and routes for addressing and/or switching the polarization states;

[0091] FIG. 5a illustrates electrostatic energies of the polarization states of the ferroelectric nanoparticle capacitor-device according to another embodiment corresponding to FIG. 1, and routes for addressing and/or switching the polarization states;

[0092] FIG. 5b illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to the embodiment of FIG. 5a, and routes for addressing and/or switching the polarization states;

[0093] FIG. 6a illustrates electrostatic energies of the polarization states of the ferroelectric nanoparticle capacitor-device according to another embodiment corresponding to FIG. 1, and routes for addressing and/or switching the polarization states;

[0094] FIG. 6b illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to the embodiment of FIG. 6a, and routes for addressing and/or switching the polarization states;

[0095] FIG. 7a illustrates the ferroelectric nanoparticle capacitor-device according to an embodiment with a temperature-control element and a force-control element;

[0096] FIG. 7b illustrates an equivalent electric circuit of the ferroelectric nanoparticle capacitor-device of FIG. 7a;

[0097] FIG. 8a illustrates the ferroelectric nanoparticle capacitor-device according to an embodiment wherein a channel of a transistor forms a conductive element of the ferroelectric nanoparticle capacitor-device;

[0098] FIG. 8b illustrates an equivalent electric circuit of the ferroelectric nanoparticle capacitor-device of FIG. 8a;

[0099] FIG. 9a illustrates the ferroelectric nanoparticle capacitor-device according to another embodiment, wherein the ferroelectric nanoparticles provide four polarization states;

[0100] FIG. 9b illustrates the four polarization states of the ferroelectric nanoparticles of FIG. 9a;

[0101] FIG. 9c illustrates the ferroelectric nanoparticle capacitor-device according to another embodiment, wherein the ferroelectric nanoparticles provide four polarization states;

[0102] FIG. 9d illustrates the four polarization states of the ferroelectric nanoparticles of FIG. 9c;

[0103] FIG. 10a illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to an embodiment corresponding to FIG. 9a or FIG. 9c, and routes for addressing and/or switching the polarization states;

[0104] FIG. 10b illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to another embodiment corresponding to FIG. 9a or FIG. 9c, and routes for addressing and/or switching the respective polarization states;

[0105] FIG. 10c illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to another embodiment corresponding to FIG. 9a or FIG. 9c, and routes for addressing and/or switching the respective polarization states;

[0106] FIG. 10d illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to another embodiment corresponding to FIG. 9a or FIG. 9c, and routes for addressing and/or switching the respective polarization states;

[0107] FIG. 10e illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to another embodiment corresponding to FIG. 9a or FIG. 9c, and routes for addressing and/or switching the respective polarization states;

[0108] FIG. 10f illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to another embodiment corresponding to FIG. 9a or FIG. 9c, and routes for addressing and/or switching the respective polarization states;

[0109] FIG. 10g illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to another embodiment corresponding to FIG. 9a or FIG. 9c, and routes for addressing and/or switching the respective polarization states;

[0110] FIG. 10h illustrates a charge-voltage hysteresis loop associated with the polarization states of the ferroelectric nanoparticles according to another embodiment corresponding to FIG. 9a or FIG. 9c, and routes for addressing and/or switching the respective polarization states; and

[0111] FIG. 11 illustrates a method according to an embodiment.

DETAILED DESCRIPTION OF THE INVENTION

[0112] FIG. 1 is a schematic illustration of a ferroelectric nanoparticle capacitor-device 100 according to a first embodiment. The ferroelectric nanoparticle capacitor-device 100 comprises two conductive elements 102, 112 in the form of conductive layers 102, 112, and ferroelectric nanoparticles 104a, 104b between them.

[0113] The conductive layers 102, 112, or their respective surfaces 108, 118, respectively, each extend along the horizontal, lateral directions x, y, and are thus parallel to each other along those directions x, y.

[0114] Along the perpendicular, vertical direction z the conductive layers 102, 112 or their respective surfaces 108, 118, respectively, are spaced apart from each other by a distance d of 1 nm to 100 nm.

[0115] The conductive layers comprise a noble metal (such as Cu or Au) as well as tantalum and/or titanium or its respective nitride and/or may comprise other metallic or semiconducting materials.

[0116] The ferroelectric nanoparticles 104a, 104b are composed of respective ferroelectric materials. In the depicted embodiments, the ferroelectric nanoparticles 104a, 104b are composed of the same ferroelectric material.

[0117] The ferroelectric material is a material characterized by the nonlinear dependence of its polarization on the electric field, P=?P.sub.s+?.sub.0?.sub.fE, where ?P.sub.s is the spontaneous polarization, directed parallel or antiparallel to the electric field E respectively, ?.sub.0 is the vacuum permittivity, and ?.sub.f is the dielectric constant of the ferroelectric material. The switching between the different directions of spontaneous polarization in ferroelectric material occurs at the coercive electric field E.sub.c. For the sake of brevity, the coercive electric field is also referred to as the coercive field.

[0118] The ferroelectric material of the ferroelectric nanoparticles comprises Pb(Zr,Ti)O.sub.3, PbTiO.sub.3, or other ferroelectric oxides, HfO.sub.2, in particular doped HfO2, comprising, e.g., zirconium, BaTiO.sub.3, Ba(Sr,Ti)O.sub.3, or other ferroelectric oxides, P(VDF-TrFE. Alternatively, or in addition, it comprises a hyperferroelectric material, LiZnAs, LiBeSb, NaZnSb, LiBeBi. In the hyperferroelectric materials, the coercive field can achieve values substantially larger than the depolarization electric field, which enable an easy selection of the desirable relative strengths of Qc and Qs, for example, while temperature and strain are controlled to tune the system.

[0119] Each of the ferroelectric nanoparticles 104a, 104b is sufficiently small to support a monodomain ferroelectric state. For this purpose, the ferroelectric nanoparticles 104a, 104b are formed with their maximum extensions (namely, bulk diagonals) no larger than 100 nm, 50 nm, 30 nm, 20 nm or 10 nm, depending on the ferroelectric material of the ferroelectric nanoparticles 104a, 104b. Typical sizes of the ferroelectric nanoparticles 104a, 104b are 1 nm, 5 nm, 10 nm, 50 nm, or 100 nm.

[0120] The depicted ferroelectric nanoparticles 104a, 104b are in one of three possible ferroelectric polarization states 106, in the following also referred to as polarization states 106 for the sake of brevity.

[0121] The polarization state 106 refers to the overall polarization state 106 of the ferroelectric nanoparticles 104a, 104b, i.e., to the combination of the individual (i.e., ferroelectric) polarization states of the ferroelectric nanoparticles 104a, 104b.

[0122] More specifically, the polarization state 106 refers to the projection of the total (net, overall) polarization of the total (i.e., ferroelectric) polarization of the ferroelectric nanoparticles 104a, 104b onto the axis z. In other words, the polarization state 106 refers to the z-component of the total polarization.

[0123] Correspondingly, the individual polarization states refer to the projections of the individual polarizations of the ferroelectric nanoparticles 104a, 104b onto the axis z.

[0124] The depicted polarization state 106 is characterized by antiparallel individual polarization states of the ferroelectric nanoparticles 104a, 104b, with the individual polarization of the ferroelectric nanoparticle 104a along (i.e., parallel to) the axis z, and the individual polarization of the ferroelectric nanoparticle 104b antiparallel to the axis z. The same polarization state, i.e., with a same z-component of the total polarization, is realized when the individual polarization of the ferroelectric nanoparticle 104b is along the axis z, and the individual polarization of the ferroelectric nanoparticle 104a is antiparallel to the axis z. In the depicted embodiment, these two configurations are equivalent as the ferroelectric nanoparticles 104a are equivalent, i.e., with the same individual polarizations. The two configurations therefore establish a first one of the polarization states 106.

[0125] A second polarization state 106 is realized when the individual polarizations of the ferroelectric nanoparticles 104a, 104b are both along the axis z.

[0126] A third polarization state 106 is realized when the individual polarizations of the ferroelectric nanoparticles 104a, 104b are both antiparallel to the axis z.

[0127] The ferroelectric nanoparticle 104a is sandwiched between the first-first sections 110a, 120a of the conductive layers 102, 112. Vice versa, the first-first sections 110a, 120a of the conductive layers 102, 112, or of their corresponding surfaces, respectively, correspond to projections of the ferroelectric nanoparticle 104a onto the conductive layers 102, 108.

[0128] The first-first sections 110a, 120a of the conductive layers 102, 112 and the ferroelectric nanoparticle 104a form a first ferroelectric capacitor 124.

[0129] Correspondingly, second first sections 110b, 120b of the conductive layers 102, 112 are associated with the ferroelectric nanoparticle 104b. The second first sections 110b, 120b of the conductive layers 102, 112 and the ferroelectric nanoparticle 104b form a second ferroelectric capacitor 126.

[0130] The first sections 110a, 110b of the first conductive layer 102 have a total area 110 which corresponds to the projection of the ferroelectric nanoparticles 104a, 104b onto the first conductive layer 102, or onto its surface 118, respectively. In the context of this disclosure, this area 110 is referred to as the overall surface-projected area of the ferroelectric nanoparticles 104a, 104b.

[0131] The overall surface-projected area 110, 120 of the ferroelectric nanoparticles 104a, 104b is alternatively defined by the projection 120 of the ferroelectric nanoparticles 104a, 104b onto the second conductive layer 112. Alternatively, the surface-projected area 110, 120 of the ferroelectric nanoparticles 104a, 104b is defined by the sum of the areas of the ferroelectric capacitors 124, 126 defined by the ferroelectric nanoparticles 104a, 104b.

[0132] The area of each of the conductive layers 102, 122 exceeds the overall surface-projected area 110, 120 of the ferroelectric nanoparticles 104a, 104b. Consequently, excess portions 102, 112 of the conductive layers 102, 122 extend beyond the first sections 110a, 110b, 120a, 110b.

[0133] These excess portions 102, 112 form a dielectric capacitor 130, i.e. a capacitor with linear charge-voltage characteristics or without a (significant) hysteresis.

[0134] In the depicted embodiment, the dielectric capacitor 130 comprises a dielectric material 122 arranged between second portions 102, 112 of the conductive layers 102, 112. In the depicted embodiment, the dielectric material 122 fills the entire space between the excess portions 102, 112 of the conductive layers 102, 112, such that the second portions 102, 112 are identical to the excess portion 102, 112 of the conductive layers 102, 112.

[0135] The dielectric material 122 is characterized by a linear dependence of its polarization on an applied electric field, P=?.sub.0?.sub.dE, where ?.sub.d is the dielectric constant of the dielectric material 122. According to embodiments, the dielectric material comprises a high-? dielectric such as Al.sub.2O.sub.3, Li.sub.2O, HfSiO.sub.4, Sc.sub.2O.sub.3, SrO, ZrO.sub.2, Y.sub.2O.sub.3, BaO, Ta.sub.2O.sub.5, BaO, WO.sub.3, MoO.sub.3, TiO.sub.2, SrTiO.sub.3, DyScO.sub.3. A dielectric material 122 may also comprise a low-? dielectric such as SiO.sub.2 or an organic dielectric. In alternative embodiments, the dielectric material 122 is implemented as an air gap, which may be filled with a substitutional gas or vacuum.

[0136] In the depicted embodiment, the dielectric material 122 serves as a dielectric separator material 122 to separate the ferroelectric nanoparticles 104a, 104b from one another. For this purpose, the dielectric material 122 is arranged between the ferroelectric nanoparticles 104a, 104b and encircles the ferroelectric nanoparticles 104a, 104b individually in the horizontal/lateral plane x, y.

[0137] The ferroelectric nanoparticle capacitor-device 100 is manufactured using existing nano-manufacturing procedures, in particular nano-manufacturing procedures developed in the context of semiconductor industries. These procedures allow to fabricate complex designs with precision and reliability. For example, advances in fabrications enable the creation of three-dimensional design of the ferroelectric nanoparticle capacitor-device 100 on a suitable substrate support. An exemplary single crystal semiconducting substrate of a selected type doping, or conductivity, respectively (for example, n-conductivity) is available commercially from various sources. A proper geometric design is achieved by the appropriate lithography and etching techniques, for example, electron beam lithography and ion etching. The conductive elements 102, 112 are created by CVD and PVD methods and/or other suitable processes. After deposition of a first conductive element 102, 112, a ferroelectric layer is disposed, thereover, using, for example, an ALD approach and/or other suitable processes. The constitutive ferroelectric nanoparticles 104a, 104b are structured individually or together from the ferroelectric layer, e.g., in a single structuring step. In the former case, the geometric configuration at each stage is designed using appropriate lithography techniques, for example, extreme ultraviolet or electron beam lithography. The dielectric material 122 is optionally grown over the first conductive element 102, 112 by the, for example, ALD technique. A second conductive element 102, 112 is deposited. Optional interconnecting structures are formed on or in the substrate to form gate, source and drain wire connection, for example by CVD and PVD methods. The patterning and architecture of the device 100 is to be implemented by the, for example, Cadence Allegro software package and/or other suitable packages.

[0138] To illustrate the working mechanism of the ferroelectric nanoparticle capacitor-device 100, FIG. 2a, FIG. 2b refer to the situation of a single ferroelectric nanoparticle 104a between conductive elements 102, 112, with a charge control device 114 electrically connected 114a to one of the conductive elements 102, 112.

[0139] As shown in FIG. 2a, the ferroelectric nanoparticle 104a is uniformly polarized and is confined between the two conductive elements 102, 112 carrying the electric charge 132. It can stay in either of two individual (ferroelectric) polarization states 106a: a state (+1), having the polarization directed up along the z-axis, and a state (?1) having the polarization directed down. The single ferroelectric nanoparticle 104a between conductive elements 102, 112 thus implements two corresponding logical levels, l+1) and l?1).

[0140] Consequently, the individual polarization state 106a may be controlled by the charge applied to the conductive elements 102, 112. The single ferroelectric nanoparticle 104a of FIG. 2a, confined between the conductive elements 102, 112, therefore implements a binary (i.e., two-level) logic device with the logical levels l+1) and mL+1).

[0141] Here, and in the following, a charge control device 114 with an electrical connection 114a to at least one of the conductive elements 102, 112 is used to control the charge of the respective conductive element(s) 102, 112 and thus the individual polarization state 106a of the ferroelectric nanoparticle 104a or the polarization state 106 of FIG. 1. This approach is distinct from conventional techniques, which control the voltages at conductive elements. Advantageously, through the charge control and the charge control device 114, the nanoparticle 104a or the nanoparticles 104a, 104b of FIG. 1 and their respective polarization states 106a, 106 are addressed much more reliably than in conventional techniques based on the voltage control.

[0142] Importantly, the effective electric field, E, operating the polarization of the ferroelectric nanoparticle 104a includes not only the field induced by the charge 132 on the conductive plates, but also by the depolarization field, induced by the bound charge, Q.sub.s=SP.sub.s, emerging at the polarization field lines' termination points located at the interface between the ferroelectric nanoparticle 104a and the conductive elements 102, 112. Herein, P.sub.s refers to the spontaneous polarization of the ferroelectric nanoparticle associated with the polarization state 106a. The voltage-charge relation for the single ferroelectric nanoparticle capacitor is given by C.sub.fV=Q?Q.sub.s, where V is the voltage and C.sub.f=?.sub.0?.sub.fS/d is the capacitance of the ferroelectric material and the sign ? corresponds to the up (+1) or down (?1) orientation of the polarization 106a.

[0143] FIG. 2b exemplifies the electrostatic energies, W.sub.?=(Q?Q.sub.s).sub.2/2C.sub.f corresponding to the (+1) and (?1) polarization states 106a of FIG. 2a, as functions of the applied charge Q. They are shifted over ?Q, with respect to Q=0, and the minima correspond to situations where the charge on the conductive elements 102, 112 precisely compensates the bound charge resulting in the zero internal field. The terminal points N.sub.0 (corresponding to the critical charges Q.sub.1,2) of parabolas correspond to the situation where a polarization states 106a with a given polarization direction becomes unstable with respect to switching to the polarization states 106a with the opposite polarization direction. The critical charges N.sub.0 corresponding to the switching (?1).fwdarw.(+1) and (+1).fwdarw.(?1) are given by Q.sub.1,2=?(Q.sub.s?Q.sub.c) respectively, where Q.sub.c=C.sub.fE.sub.cd. This energy profile results in the charge-voltage two-branch switching hysteresis loop V(Q) with upper and lower branches V.sub.?(Q)=C.sub.f.sup.?1(Q?Q.sub.s) corresponding to the polarization states 106a, or logical levels l+1) and l?1), respectively.

[0144] FIG. 3 shows an effective electric circuit of the ferroelectric nanoparticle capacitor-device 100 of FIG. 1. The ferroelectric nanoparticle capacitor-device 100 includes the two ferroelectric capacitors 124, 126, each with a capacitance Cf. It further comprises a dielectric capacitor 130 with a capacitance Cd, connected in parallel to the ferroelectric capacitors 124, 126.

[0145] The effective electric circuit further comprises a charge-control element 114 in electrical contact 114a with at least one of the conductive elements 102, 112. The charge-control element 114 is adapted to apply a charge Q to the conductive element(s) 102, 112 it is connected to.

[0146] Importantly, the charge Q applied to the conductive elements 102, 112 can be distributed nonuniformly over the conductive elements 102, 112, forming the charge Q.sub.a in the region of the first ferroelectric nanoparticle 104a (or on first first sections 110a, 120a of the conductive elements 102, 112 corresponding to the first ferroelectric capacitor 124, respectively), the charge Q.sub.b in the region of the second ferroelectric nanoparticle 104b (or on sections 110b, 120b of the conductive elements 102, 112 corresponding to the second ferroelectric capacitor 126, respectively), and the charge Q.sub.d in the region of the dielectric material 130 (or on the second portions or the excess portions 102, 112 of the conductive layers 102, 112, respectively, corresponding to the dielectric capacitor 130).

[0147] The charges Q.sub.a, Q.sub.b, and Q.sub.d of the corresponding capacitors 124, 126, 130 are determined by the equality of the potential at the plates of the capacitors and are determined by the condition: C.sub.f.sup.?1(Q.sub.a?Q.sub.s)=C.sub.f.sup.?1(Q.sub.b?Q.sub.s)=C.sub.d.sup.?1Q.sub.d, taking into account that Q.sub.a+Q.sub.b+Q.sub.d=Q. Here every particular combination of pluses and minuses corresponds to a polarization state 106 of the system, C.sub.f=?.sub.0?.sub.fS.sub.f/d is the capacitance of the ferroelectric material and C.sub.d=?.sub.0?.sub.d(S?2S.sub.f)/d is the capacitance of the dielectric spacer. From the above condition, one obtains Q.sub.a,b=(C.sub.f/C.sub.eff)Q?Q.sub.s, Q.sub.d=(C.sub.d/C.sub.eff)Q, where C.sub.eff.sup.?1=2C.sub.f.sup.?1+C.sub.d.sup.?1 is the effective capacitance of the entire system.

[0148] FIG. 4a illustrates the emerging polarization states 106 and their total energies W.

[0149] In the following, the term level refers to a logical level, the two terms are used equivalently.

[0150] The levels are represented by the polarization states 106 of the ferroelectric nanoparticles 104a, 104b, and vice versa. In other words, the polarization states 106 provide the levels. For this reason, the terms level and polarization states may be used equivalently.

[0151] The polarization states 106 are preferentially discrete polarization states 106, e.g., in a sense that a switching between two different polarization states 106 is characterized by a subtle, abrupt change of the ferroelectric polarization. In other words, the ferroelectric nanoparticles 104a, 104b are adapted to not assume any stable ferroelectric polarization between the one of the discrete polarization states 106.

[0152] The polarization states 106 are determined by minimization of the total energy W=Q.sub.a.sup.2/2C.sub.f+Q.sub.b.sup.2/2C.sub.f+Q.sub.d.sup.2/2C.sub.d, that gives the energies corresponding to either of three above states 106 defining logic levels, l?1), l0), and l+1). Namely, W.sub.?1=(Q?2Q.sub.s).sup.2/2C.sub.eff, W.sub.0=Q.sup.2/2C.sub.eff, and W.sub.+1=(Q+2Q.sub.s).sup.2/2C.sub.eff. The switching between the logical levels takes place when the field inside the corresponding ferroelectric nanoparticle 104a, 104b exceeds the coercive field Ec. It occurs at four distinct values of the total charge of the capacitor Q.sub.1,4=?Q.sub.c for level l0), Q.sub.2=2Q.sub.s?Q.sub.c for level l?1), and Q.sub.3=?2Q.sub.s+Q.sub.c for level l+1), where Q.sub.c=C.sub.effE.sub.cd.

[0153] FIG. 4a, FIG. 5a, and FIG. 6a present the abovementioned energy profiles, W.sub.+1(Q), W.sub.0(Q), W.sub.?1(Q) for the polarization states 106, l?1), l0), and l+1). FIG. 4b, FIG. 5b, and FIG. 6b present corresponding three-branch hysteresis loops, and routes for addressing the polarization states 106, l?1), l0), and l+1), or switching between them, respectively. The polarization states 106, l?1), l0), and l+1) are associated with three branches of the charge-voltage characteristics V.sub.?(Q)=C.sub.eff.sup.?1(Q?2Q.sub.s), V.sub.0(Q)=C.sub.eff.sup.?1Q and V.sub.+(Q)=C.sub.eff.sup.?1(Q+2Q.sub.s).

[0154] FIG. 4a, FIG. 4b, FIG. 5a, FIG. 5b, FIG. 6a, and FIG. 6b represent the three existing distinct regimes of topology of the hysteresis loops, determined by the relative strength of the effective charge parameters Q.sub.c and Q.sub.s.

[0155] The energy profile of polarization states 106, l?1), l0), and l+1) and transition sequence are exemplified in FIG. 4a, FIG. 4b for the case 3Q.sub.s>Q.sub.c>2Q.sub.s. The terminal points, N.sub.0, correspond to the switching instability of one of the ferroelectric nanoparticles 104a, 104b towards the lowest-energy state with the opposite polarization 106. The corresponding hysteresis loop with sequential switching between the logical levels l?1), l0), and l+1) at the said critical charges Q.sub.1, Q.sub.2, Q.sub.3, and Q.sub.4 is demonstrated in FIG. 4b.

[0156] FIG. 5a, FIG. 5b present the energy profile and charge-voltage characteristics realized under the condition Q.sub.c>3Q.sub.s. Although it has three logic levels l?1), l0), and l+1) realized at Q=0, the intermediate-ferroelectric-polarization state, l0), is topologically unstable in a sense that once the switching from this logical level to either l?1) or l+1) has occurred, the system can never be switched back to the l0) logical level, and a two-branch hysteresis loop with switching between the minimum-ferroelectric-polarization state l?1) and the maximum-ferroelectric-polarization state l+1) becomes the only effective regime. The switching of the system to the hidden logical level, l0), can be achieved, however, by variation of external parameters, different from the charge, for instance by thermal cycling, involving passing through a high temperature paraelectric state.

[0157] FIG. 6a and FIG. 6b present the energy profiles and charge-voltage characteristics realized under the condition Q.sub.c<2Q.sub.s. There is only one logic level, l0), at zero charge, but hysteretic switching occurs at finite charges, implementing, thus, a three-position relay element, also known as the Schmitt trigger.

[0158] Importantly, the hysteresis loops shown in FIG. 4b (FIG. 4a), FIG. 5b (FIG. 5a) and FIG. 6b (FIG. 6a) realize all the topologically possible sets of switching in the 3-levels logic [Baudry, L., Lukyanchuk, I., and Vinokur, V. Sci. Rep. 7, 42196 (2017)]. In our embodiment, it is the relation of the material-depended critical parameters, Qs and Qc that determine which type of the logic is realized. The specific switching properties/protocols can be achieved by the selection of the desirable ratio between parameters, Qs and Qc, or by appropriately selecting the size and material composition of the ferroelectric nanoparticles 104a, 104b, respectively.

[0159] FIG. 7a presents an embodiment of a ferroelectric nanoparticle capacitor-device 100 similar to the one of FIG. 1, alternatively implementing the hysteresis loops shown in FIG. 4b (FIG. 4a), FIG. 5b (FIG. 5a) and FIG. 6b (FIG. 6a).

[0160] As compared to FIG. 1, the ferroelectric nanoparticle capacitor-device 100 of FIG. 7a is formed with various modifications: It comprises a charge control device 104, consisting of an additional conductive element 202 and a dielectric spacer 204. In addition, the ferroelectric nanoparticle capacitor-device 100 of FIG. 7a comprises a temperature-control element 206. It also comprises a force-control element 210. According to various embodiments (not shown), the ferroelectric nanoparticle capacitor-device 100 is formed with any, any combination, or all of the described modifications (charge control device 104 and/or temperature-control element 206 and/or force-control element 210).

[0161] The charge control device 104 comprises an additional conductive element 202 arranged below the first conductive element 102, opposite to the second conductive element 112 which is arranged above the first conductive element 102.

[0162] The charge control device 104 further comprises a dielectric spacer 204, formed as a layer 204 of dielectric material between the first conductive element 102 and the additional conductive element 202 to electrically insulate them from each other. The dielectric spacer 204 is composed of one of the dielectric materials described above, and preferentially contains SrTiO3, SiO2, Si3N4, or HfO2.

[0163] The charge control device 104 is operated by applying a voltage between the additional conductive element 202 and the second conductive element 112 while the first conductive element 102 is kept at a fixed charge (e.g., electrically floating), resulting in the application of a charge to the second conductive element 112.

[0164] The temperature-control element 206 is implemented as a heater 206, more specifically as an Ohmic heater 206. The heater 206 is arranged below a conductive element 102, 112, to heat the respective conductive element 102, 112 and thus the ferroelectric nanoparticles 104a, 104b. A temperature variation of the ferroelectric nanoparticles 104a, 104b can be of the range 10-300 Kelvin.

[0165] The ferroelectric nanoparticle capacitor-device 100 of FIG. 7a further comprises a substrate 208 to support the ferroelectric nanoparticle capacitor-device 100.

[0166] The substrate is arranged below the conductive elements 102, 112, and below the additional conductive element 202 if present. The substrate is in thermal contact with one of the (first, second, or additional) conductive elements 102, 112, 202; e.g. via a direct physical contact or an indirect contact via a heat-conducting material such as a metal or a sufficiently thin (<100 nm or <20 nm) intermediate layer.

[0167] Heating the substrate 208 using the heater 223 leads to a mechanical deformation 212 in the form of an expansion 212, that generates strains in the ferroelectric nanoparticles 104a, 104b. Alternatively, the strain can also be induced by the piezoelectric effect developing when the electric field is applied to the substrate 208. For example, the generated strain can lie in the range of 0.001-0.1% of the crystal lattice constant.

[0168] The temperature-control element 206 and/or the force-control element 210 permit to tune the interrelation between the parameters Qs and Qc by the external stimuli temperature and/or strain. They thus allow for an on-the-fly modification of the switching logic of the said device 100. This tuning can be done by accounting for different temperature and strain dependences of these parameters. The so-called hyper-electric materials, for example, LiZnAs, LiBeSb, NaZnSb, and LiBeBi, present the particular interest for implementation of the ferroelectric nanoparticles 104a, 104b, because in these materials the coercive field can achieve values substantially larger than the depolarization electric field, and the relative strengths of the parameters, Qs and Qc can vary over fairly wide ranges.

[0169] FIG. 7b shows an equivalent electric circuit of the ferroelectric nanoparticle capacitor-device 100 of FIG. 7a. The additional conductive element 202 and the dielectric spacer 204 form an additional capacitor 214 with the capacitance Ci. The additional capacitor 214 shares the first conductive element 102 with the capacitors 124, 126, 130. The equivalent electric circuit therefore comprises the capacitors 124, 126, 130 (defined by the conductive elements 102, 112) and the additional capacitor 214 (defined by the conductive elements 102, 202) connected in series. The second conductive element 112 and the additional conductive element 202 receive the incoming voltage Vin between them. The charge at the conductive elements 102, 112 induced by the voltage Vin is given by the equation Vin=Q/Ci+V(Q), where V(Q) is the voltage determined by the chargevoltage characteristics such as exemplified in FIG. 4b, FIG. 5b, FIG. 6b. This relation becomes particularly simple and transforms to Q?Ci Vin when the effective capacitance of the parallel arrangement of the capacitors 124, 126, 130 substantially exceeds the capacitance of the additional capacitor 214. The charge that controls the polarization state 106 of the ferroelectric nanoparticles 104a, 104b is directly tuned by the voltage Vin applied to the second conductive element 112 and the additional conductive element 202.

[0170] FIG. 8a illustrates the integration of the ferroelectric nanoparticle capacitor-device 100 into a field-effect transistor 300, alternatively implementing the hysteresis loops shown in FIG. 4b (FIG. 4a), FIG. 5b (FIG. 5a) and FIG. 6b (FIG. 6a). FIG. 8b shows an equivalent electric circuit of the device 100 of FIG. 8a.

[0171] The field-effect transistor 300 comprises source/drain regions 304, 306, a channel 302 extending between the source/drain regions 304, 306, and a gate stack 308 arranged over the channel 302. The field-effect transistor 300 further comprises a body electrode 312, which is grounded.

[0172] The channel 302 serves as the additional conductive element 202 described in the context of FIG. 8a.

[0173] The gate dielectric 204 is a high-k dielectric layer, preventing a charge leakage between the first conductive element 102 and the channel 302.

[0174] The gate stack comprises the gate dielectric 204, provided by the dielectric spacer 204, and at least one electrode. In the depicted embodiment, the at least one electrode of the gate stack 308 is provided by a ferroelectric nanoparticle capacitor-device 100 similar to the one of FIG. 1. More specifically, the second conductive element 112 of the ferroelectric nanoparticle capacitor-device 100 serves as a gate electrode of the transistor 300 and is connected to an external voltage source to receive the driving voltage V.sub.in. Preferably, the driving voltage V.sub.in is applied between the second conductive element 112 and the additional conductive element (channel) 202, 302, implementing the charge control device 114 described above in the context of FIG. 7a.

[0175] As described above in the context of previous embodiments, the first conductive element 102 is kept at a constant charge, e.g., kept electrically isolated and floating. It thus serves to stabilize the polarization 106 of the ferroelectric nanoparticles 104a, 104b. Furthermore, the floating first conductive element 102 makes the potential along the interface between the ferroelectric nanoparticles 104a, 104b and the first conductive element 102 even, maintaining, therefore, a uniform electric field across the gate stack 308 and the substrate 304.

[0176] The stepwise switching of the voltage, Vout, operating the current in the channel 302, under the appropriate protocol for the variation of the driving voltage Vi, realizes the multilevel logic switching sequence corresponding to the one of the topologically possible hysteresis loops (see FIG. 4a to FIG. 6b). The logic levels switching order can be modified by the external stimuli, for example, by the temperature or strain, as described above in the context of FIG. 7a, FIG. 7b, allowing for the on-fly modification of the switching logics of the ferroelectric nanoparticle capacitor-device 100.

[0177] According to different embodiments, the ferroelectric nanoparticle capacitor-device 100 is formed with the temperature-control element 206 and/or the force-control element 210 described above in the context of FIG. 7a, e.g., instead of the substrate 312, integrated into the substrate 312 or below the substrate 312. In the latter embodiments, a substrate 312 with a high heat conductivity is applied.

[0178] FIG. 9a, FIG. 9c present embodiments of the ferroelectric nanoparticle capacitor-device 100 for implementing a topologically configurable 4-level logical unit. FIG. 9b, FIG. 9d show the respective polarization states 106 representing the 4 logical levels.

[0179] FIG. 9a shows a ferroelectric nanoparticle capacitor-device 100 with three identical, for example, cylindrical ferroelectric nanoparticles 104a, 104b, 104c between the conductive elements 102, 112. The ferroelectric nanoparticles 104a, 104b, 104c provide equal coercive fields and equal cross-sections.

[0180] In the depicted embodiment, a dielectric separator material 122 fills the residual space between the conductive elements 102, 114.

[0181] The system is driven and controlled by an electric charge, Q, placed onto at least one of the conductive elements 102, 114, using a charge control element 114 as described above.

[0182] As illustrated in FIG. 9b, the ferroelectric nanoparticle capacitor-device 100 of FIG. 9a provides the polarization states, (+++), (++?) (or equivalently, (+?+) and (?++)), (+??), or equivalently, (?+?) and (??+), and, finally, (???), wherein arrows down (or up) in FIG. 9b represent negative ? or positive + polarization with respect to the z axis.

[0183] Consequently, the ferroelectric nanoparticle capacitor-device 100 of FIG. 9a realizes a 4-level logic, characterized by the logic levels l+2), l+1), l?1), and l?2), respectively.

[0184] FIG. 9c shows another embodiment of a ferroelectric nanoparticle capacitor-device 100 for implementing a 4-level logic device. Here, two non-equivalent ferroelectric nanoparticles 104a, 104b are disposed between the conductive elements 102, 112 and coated by a dielectric separator material 122. The ferroelectric nanoparticles 104a, 104b can be made from different ferroelectric materials and may have different sizes.

[0185] FIG. 9d illustrates the polarization states 106 of the ferroelectric nanoparticles 104a, 104b of FIG. 9c, which are similar to the polarization states 106 of FIG. 4a associated with the ferroelectric nanoparticles 104a, 104b, 104c of FIG. 1. However, in FIG. 9d, since the states (+?) and (?+) are not equivalent, the four polarization states 106 implement the logical levels of a 4-level logic unit, namely, (??).Math.l?2), (?+).Math.l?1), (+?).Math.l+1), and (++).Math.l+2).

[0186] Except for the number or the size/material composition of the ferroelectric nanoparticles 104a, 104b, 104c, the embodiments of FIG. 9a, FIG. 9c are similar to the embodiment of FIG. 1. In alternative embodiments (not depicted), the ferroelectric nanoparticles 104a, 104b, 104c described in the context of FIG. 9a or FIG. 9c (i.e., with the respective number or with the respective size/material composition) are applied in a ferroelectric nanoparticle capacitor-device 100 similar to the embodiment of FIG. 7a or FIG. 8a.

[0187] FIG. 10a, FIG. 10b, FIG. 10c, FIG. 10d, FIG. 10e, FIG. 10f, FIG. 10g, and FIG. 10h illustrate charge-voltage hysteresis loops associated with the polarization states 106 of ferroelectric nanoparticle capacitor-devices 100 similar to the ones of FIG. 9a or FIG. 9c.

[0188] Considerations similar to those given above for the 3-level logic units, show that the hysteresis loops V(Q) for the said 4-level configurations of the ferroelectric nanoparticles 104a, 104b have four branches corresponding to the logical levels 116, l+2), l+1), l?1), and l?2). FIG. 10a, FIG. 10b, FIG. 10c, FIG. 10d, FIG. 10e, FIG. 10f, FIG. 10g, and FIG. 10h present all possible hysteresis loops with different switching sequences in 4-level logic [Baudry, L., Lukyanchuk, I., and Vinokur, V. Sci. Rep. 7, 42196 (2017)].

[0189] FIG. 10a shows a charge-voltage hysteresis loop with the sequential switching between the logical levels/polarization states 106, l+2), l+1), l?1), and l?2), driven by changing the charge Q at the conductive elements 102, 112.

[0190] The charge-voltage hysteresis loops in FIG. 10a, FIG. 10b, FIG. 10c, and FIG. 10d correspond to different switching sequences between logical levels/polarization states 106, 1+2), l+1), l?1), and l?2) that can be used or the design of the four-level logic memories or other processing protocols with different topological ways of accessing the information stored at these logical levels/polarization states 106, l+2), l+1), l?1), and l?2).

[0191] The charge-voltage hysteresis loops of FIG. 10e and FIG. 10f comprise hidden logical levels l?1), l1). Such protocols can be used if the information, stored at the hidden levels l?1), l1) needs to be protected from undesirable change and other interferences. Any attempt to access these levels l?1), l1) will immediately switch the corresponding information unit to another level l?2), l2) with no possibility of the back restoring. Therefore, the said charge-voltage hysteresis loops provide the security protection of the ferroelectric nanoparticle capacitor-device 100, which is an especially novel feature of our disclosure.

[0192] The charge-voltage hysteresis loops of FIG. 10g and FIG. 10h implement the multilevel Schmitt trigger, required for multiple applications in electronics.

[0193] The ferroelectric nanoparticle capacitor-device 100 of FIG. 9a or 9c, via selection of appropriate sizes and material compositions of the ferroelectric nanoparticles 104a, 104b, 104c, enables the implementation of any preselected charge-voltage hysteresis loop of the charge-voltage hysteresis loops represented in FIG. 10a, FIG. 10b, FIG. 10c, FIG. 10d, FIG. 10e, FIG. 10f, FIG. 10g, and FIG. 10h.

[0194] Controlling external stimuli, for instance, the temperature or strain, as described above in the context of FIG. 7a, FIG. 8b, the charge-voltage hysteresis loop and the switching sequence between the logical levels/polarization states 106, l+2), l+1), l?1), and l?2) can be selected and modified on-the-fly, i.e. after fabrication of the ferroelectric nanoparticle capacitor-device 100 with given sizes and material compositions of the ferroelectric nanoparticles 104a, 104b, 104c.

[0195] Similarly, the charge-voltage hysteresis loop can be controlled for a ferroelectric nanoparticle capacitor-device 100 comprising more than three, for example, four, five, or any larger number of ferroelectric nanoparticles 104a, 104b, 104c. The charge-voltage hysteresis loop can be controlled initially via selection of an appropriate number of appropriate ferroelectric nanoparticles 104a, 104b, 104c and their sizes and material compositions. A later, on-the-fly control is achieved by incorporating a temperature-control element 206 or a force-control element as described above. To ensure a sufficient spacing between the polarization states 106 in terms of total energy W, voltage V and/or charge Q, a smaller number of ferroelectric nanoparticles 104a, 104b, 104c such as up to 10, 5, 4 or three ferroelectric nanoparticles 104a, 104b, 104c is preferable. In other words, the number of polarization states 106 should be limited, e.g., to up to 64, 32, 16, 8, or 5 polarization states 106. A smaller number of ferroelectric nanoparticles 104a, 104b, 104c and/or number of polarization states 106 improves the reliability of the switching and of the readout of the polarization state 106.

[0196] Embodiments with more than three ferroelectric nanoparticles 104a, 104b, 104c use the (ferroelectric and/or dielectric) materials described above, as well as the temperature and/or strain ranges described above; also, the remaining device parameters are similar to the ones described above. Devices comprising any other number of the nanoparticles and their configuration realize multilevel logic units possessing more complicated routes for the charge-voltage hysteresis loops enabling, therefore, even higher levels of the neuromorphic computing.

[0197] FIG. 11 illustrates a method 400 for operating the ferroelectric nanoparticle capacitor-device 100.

[0198] The ferroelectric nanoparticle capacitor-device 100 is similar to one of the ferroelectric nanoparticle capacitor-devices 100 described above in the context of FIG. 1, FIG. 7a, FIG. 8a, FIG. 9a, or FIG. 9c. Any of those ferroelectric nanoparticle capacitor-devices 100 provides a maximum-ferroelectric-polarization state (and a minimum-ferroelectric-polarization state) with a maximum (and a minimum) ferroelectric polarization, such that no polarization state of the at least three polarization states has a ferroelectric polarization larger (or smaller, respectively) than the maximum-ferroelectric-polarization state (or the minimum-ferroelectric-polarization state). Moreover, any of those ferroelectric nanoparticle capacitor-devices 100 provides an intermediate-ferroelectric-polarization state with a polarization between the minimum ferroelectric polarization and the maximum ferroelectric polarization.

[0199] At step 402, the method 400 comprises selecting an intermediate-ferroelectric-polarization state.

[0200] At step 404, the method 400 comprises selecting a first voltage or charge according to the selected intermediate-ferroelectric-polarization state.

[0201] At step 406, the method 400 comprises applying the first voltage or charge to a conductive element 102, 112 of the pair to set the ferroelectric nanoparticles 104a, 104b, 104c to the selected intermediate-ferroelectric-polarization state.

[0202] Preferentially, the current polarization state 106 of the ferroelectric nanoparticles 104a, 104b, 104c is detected based on a voltage of at least one of the conductive elements 102, 112. For this purpose, the voltage between the conductive elements 102, 112 is measured, which corresponds to the voltage in the charge-voltage hysteresis loop described above. For a given device, the measured voltage is thus directly associated with the polarization state 106.

[0203] Alternatively, the current polarization state 106 of the ferroelectric nanoparticles 104a, 104b, 104c is detected based on a change of the voltage of at least one of the conductive elements 102, 112, such as by counting jumps of the voltage of at least one of the conductive elements 102, 112. For this purpose, the voltage measurement is performed continuously to identify the change of the voltage.

[0204] Amongst the two options of selecting a first voltage or charge, the selecting the first charge is preferred. Correspondingly, applying the first charge is preferred.

[0205] The other conductive element 102, 112 of the pair is kept at a constant electrical charge.

[0206] Preferably, the first voltage or charge is applied between one of the conductive elements (i.e., the second conductive element 112 described above) and the additional conductive element 202, 302 described above, preferably using the charge control device 114 described above.

[0207] When applied to a ferroelectric nanoparticle capacitor-device 100 with a charge-voltage hysteresis loop as illustrated in FIG. 10a, the voltage or charge applied to the conductive element 102, 112 is continuously increased until the first voltage or charge is reached. To reach a polarization state 106 with a larger or smaller (i.e., more negative) polarization, a larger or smaller voltage or charge is applied to the conductive element 102, 112.

[0208] Thereafter, the voltage or charge applied to the conductive element 102, 112 may be reduced to zero whereupon the polarization state 106 remains preserved. The ferroelectric nanoparticle capacitor-device 100 thus implements a non-volatile memory, which can be used to store information without external power, voltage, or charge support.

[0209] When applied to a ferroelectric nanoparticle capacitor-device 100 with a charge-voltage hysteresis loop as illustrated in FIG. 10b, to reach the intermediate-ferroelectric-polarization state l+1), the voltage or charge applied to the conductive element 102, 112 first needs to be increased to a positive value sufficient to reach state l+2). Thereafter, the applied voltage is decreased until the negative first voltage or charge is reached, setting the polarization to state l+1). An inverse voltage or charge sequence is applied to the conductive element 102, 112 to reach the intermediate-ferroelectric-polarization state l?1).

[0210] When applied to a ferroelectric nanoparticle capacitor-device 100 with a charge-voltage hysteresis loop as illustrated in FIG. 10c, to reach the intermediate-ferroelectric-polarization state l+1), the voltage or charge applied to the conductive element 102, 112 first needs to be increased to a positive value sufficient to reach state l+2). Thereafter, the applied voltage is decreased to a negative value until the ferroelectric nanoparticles 104a, 104b, 104c switch to the state l?1). Thereafter, the applied voltage is increased until the positive first voltage or charge is reached, setting the polarization 106 to state l+1). An inverse voltage or charge sequence is applied to the conductive element 102, 112 to reach the intermediate-ferroelectric-polarization state l?1).

[0211] In a ferroelectric nanoparticle capacitor-device 100 with a hidden state, such as illustrated in the context of FIG. 5b, FIG. 10e, FIG. 10f, heating the ferroelectric nanoparticles 104a, 104b, 104c and/or applying a mechanical force to the ferroelectric nanoparticles 104a, 104b, 104c can be used to set the polarization state 106 of the ferroelectric nanoparticles 104a, 104b, 104c to the hidden state.

[0212] Alternatively, heating the ferroelectric nanoparticles 104a, 104b, 104c and/or applying a mechanical force to the ferroelectric nanoparticles 104a, 104b, 104c is used to modify the charge-voltage hysteresis loop of the ferroelectric nanoparticle capacitor-device 100.

[0213] The description of the embodiments and the figures merely serve to illustrate the techniques of the present disclosure and the beneficial effects associated therewith but should not imply any limitation. The scope of the disclosure is to be determined from the appended claims.

[0214] All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein.

[0215] The use of the terms a and an and the and at least one and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The use of the term at least one followed by a list of one or more items (for example, at least one of A and B) is to be construed to mean one item selected from the listed items (A or B) or any combination of two or more of the listed items (A and B), unless otherwise indicated herein or clearly contradicted by context. The terms comprising, having, including, and containing are to be construed as open-ended terms (i.e., meaning including, but not limited to,) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., such as) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.

[0216] Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations of those preferred embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.