Patent Number: 
Section: description

Reference is now made to FIG. 6, which is a schematic diagram of a scanning probe apparatus (SPA) 70, according to a preferred embodiment of the present invention. SPA 70 is most preferably implemented from a scanning force microscope, by methods which will be apparent to those skilled in the art. In some preferred embodiments of the present invention, SPA 70 is implemented so as to be convertible to a scanning force microscope, so that the one apparatus may be used to form domain-engineered structures (DESs) or as a microscope which is able to read the DESs formed. SPA 70 is used to generate DESs in a ferroelectric sample 86. SPA 70 comprises a tip-electrode 72 connected to a conducting cantilever 74. Tip-electrode 72 ends in an extremely sharp point, the point being sharp enough to generate extremely high electric fields in its region, and thus initiate the process of domain formation, as is known in the art. Cantilever 74 is grounded, i.e., the potential of the cantilever is set to zero. The grounding of the cantilever and consequently of tip-electrode 72 serves to prevent damage from high voltages, utilized as explained below, to the cantilever and to any instrumentation physically connected to the cantilever. Tip-electrode 72 is preferably held substantially in contact with upper surface 94 of sample 86, by one or more methods known in the art. Alternatively, tip-electrode 72 is held at a substantially constant distance, typically less than one nanometer, from upper surface 94. Most preferably, a laser beam is reflected from an upper surface of cantilever 74 onto a 2-quadrant photo-detector 76. A signal from the photo-detector is used as an input signal to an amplifier 78, which in turn provides a feedback signal to a piezoelectric positioner 90. Piezoelectric positioner 90 supports an electrically insulated sample holder 88, which holds ferroelectric sample 86. The feedback signal acts as an input to positioner 90, which in response to the signal moves holder 88 and sample 86 in a vertical z-direction. In addition to z-direction motion, positioner 90 is most preferably implemented for both horizontal x-direction and y-direction motion. Positioner 90 is thus able to position sample 86 at substantially any desired horizontal position relative to tip-electrode 72. Preferably, positioner 90 also operates to move sample 86 in substantially any horizontal direction, so that tip-electrode 72 is able to be scanned at a substantially fixed predetermined velocity across and relative to surface 94. Alternatively or additionally, one or more piezoelectric scanners 91 are attached to cantilever 74, to scan the cantilever horizontally. Thus, positioner 90 and/or scanners 91 act as scanning instrumentation 92 for scanning tip-electrode 72 relative to sample 86. Ferroelectric sample 86 is most preferably in the form of a wafer, having an overall thickness up to approximately 10 mm, although some preferred embodiments of the present invention may be operative with greater thicknesses than 10 mm. Preferably, sample 86 is positioned on a solid or liquid counter-electrode 84, which in turn is mounted on holder 88. Alternatively or additionally, counter-electrode 84 comprises a conductive coating applied to a lower surface 98 of sample 86. Counter-electrode 84 is connected to a high voltage DC source 82. Source 82 may be set at substantially any fixed voltage, most preferably in an approximate range of +15 kV to xe2x88x9215 kV. In some preferred embodiments of the present invention, the voltage range of source 82 may be larger. Source 82 is adapted to provide steady or pulsed DC voltages to counter-electrode 84. Thus, a potential difference between counter-electrode 84 and tip-electrode 72 may be set to be approximately 150 V or more, in contrast to SPA systems known in the art wherein the potential difference between the electrodes is significantly less than 150 V. Thus, as described in more detail below, stable DESs may be formed in bulk ferroelectric materials using SPA 70. In order to generate a specific DES in sample 86, the sample is first pre-positioned by positioner 90. A high voltage is applied by source 82 to electrode 84. The voltage is set to be high enough to overcome a coercive field of the sample, so that a minimum voltage URmin set depends on the composition of the sample and on the thickness of the sample. For example, for a sample comprising 350 micron thick RbTiOPO4 (RTP), which has a coercive field of 30 kV/cm, the voltage is set to a minimum of 1.05 kV. It will be understood that values for the voltage URmin applied to counter-electrode 84, in order to form a DES in sample 86, are given by URminxe2x89xa7Ecxc2x7d xe2x80x83xe2x80x83(3)  wherein Ec is the coercive field of sample 86, and d is a thickness of the sample. In some preferred embodiments of the present invention, in order to form the DES, instrumentation 92 moves sample 86 at a substantially fixed velocity V, while voltage URmin is applied to electrode 84. As described in the Background of the Invention, for a sample which is spontaneously polarized, domains are formed by a three stage process comprising primary domain nucleation, domain forward growth, and secondary domain nucleation at the walls of the primary domain. Preferably, the tip-electrode terminates at one extremely sharp point having a size of about 10-100 nm, which is close to domain nuclear size. Therefore, a switching time xcfx84sw is defined by a time xcfx84nucl needed for domain nucleation. Thus equation (1) reduces to xcfx84sw≈xcfx84nucl xe2x80x83xe2x80x83(4)  FIG. 7 is a schematic diagram showing formation of a primary domain 100, according to a preferred embodiment of the present invention. Primary domain 100 is assumed to be a spherical domain, having a nuclear radius R, which is formed as tip-electrode 72 passes over sample 86. The nuclear radius of a sample may be measured experimentally by methods which are known in the art. A critical velocity Vcrit of tip-electrode 72, relative to sample 86, may be defined as                               V          crit                ≈                  R                      τ            nucl                                              (        5        )             Equation (5), and equations derived from it, apply when counter-electrode 84 is maintained at a substantially constant high voltage difference with respect to tip-electrode 72. Substituting equation (4) in equation (5) gives                               V          crit                ≈                  R                      τ            sw                                              (        6        )             A relative velocity V of tip-electrode 72 can be in one of three regions defined by the equations below V greater than Vcrit xe2x80x83xe2x80x83(7a)  V less than Vcrit xe2x80x83xe2x80x83(7b)  V≈Vcrit xe2x80x83xe2x80x83(7c)  At relative velocities defined by equation (7a) wherein tip-electrode 72 moves faster than the critical velocity, Vcrit, relative to sample 86, the speed of movement causes primary nucleus 100 to be unstable. The instability results in nucleus 100 either not forming at all, or at least some nuclei such as nucleus 100 forming then collapsing. Thus at relative velocities defined by equation (7a) any domains generated tend to be unstable and/or partly formed and/or to exhibit narrowing effects. Furthermore domains formed at these velocities tend not to penetrate through sample 86, i.e., they are predominantly surface domains. At relative velocities defined by equation (7b), wherein tip-electrode 72 moves slower than the critical velocity, Vcrit, relative to sample 86, the speed of movement is slow enough to allow more than one primary nucleus 100 to form. Multiple primary nuclei lead to many secondary nuclei forming, which in turn leads to domains which are formed being stable, but exhibiting undesirable domain broadening effects, including widening of the domains at surface 94 and further widening through the bulk of sample 86. At relative velocities defined by equation (7c), wherein tip-electrode 72 moves approximately at the critical velocity, Vcrit, relative to sample 86, the speed of movement enables one primary nucleus 100 to form. As a result, at these velocities the process of domain formation leads to formation of well-defined domains throughout the bulk of the sample. The domains formed by tip-electrode 72 being scanned at velocities approximately equal to the critical velocity, Vcrit, do not exhibit domain broadening or narrowing effects throughout the bulk of the sample, i.e., a cross-section of each domain is substantially invariant as measured through the sample. FIG. 8 is a set of schematic diagrams showing results obtained by scanning at velocities defined by equations (7a), (7b), and (7c), according to a preferred embodiment of the present invention. The diagrams show schematic outlines of domain walls, as seen looking at samples of RTP along the z direction. The inventors measured the results on spontaneously polarized samples of RTP having a thickness of approximately 340 microns, the samples being scanned to form periodic DESs. A voltage of approximately 1 kV was applied to counter-electrode 84. Measurements on the sample using an atomic force microscope operating in a topography mode gave a nuclear radius R approximately equal to 0.23 microns, and a switching time xcfx84sw was evaluated, as described in the Background of the Invention, as equal to 2.5 ms. Thus, from equation (6)                                           V            crit                    ≈                      0.23            2.5                          =                  92          ⁢                      xe2x80x83                    ⁢          µm          ⁢                      /                    ⁢          s                                    (        8        )             Dark lines in the diagrams indicate walls between oppositely polarized domains. Diagram 120 shows structures formed when the sample and the tip-electrode moved with a relative velocity of 130 microns/s, corresponding to equation (7a). As seen in diagram 120, there are regions 126 where substantially no domains form. Diagram 122 shows structures formed for a tip-sample velocity of 10 micron/s, corresponding to equation (7b), and region 128 shows strong domain broadening. Diagram 124 shows structures formed for a tip-sample velocity of 80 micron/s, corresponding to equation (7c) The DES shows periodically formed domains, demonstrating that relative velocities defined by equations (6) and (7c) generate DESs of good quality. FIG. 9 is a graph of a pulsed DC voltage applied to counter-electrode 84, according to an alternative preferred embodiment of the present invention. In contrast to the above description for generation of DESs with SFM 70 wherein substantially steady DC voltages are applied to counter-electrode 84, in the alternative preferred embodiment a pulsed DC voltage Vp is applied to counter-electrode 84, as sample 86 is scanned relative to tip-electrode 72. The pulsed DC voltage has an xe2x80x9conxe2x80x9d time of xcfx84dur. As stated in the Background of the Invention, equation (2), xcfx84dur greater than xcfx84sw xe2x80x83xe2x80x83(2)  needs to hold for any DES formed by pulsed DC to be stable. During formation of a new domain a depolarizing field is screened by external and/or internal charge flow. External screening is caused by external charge flow occurring via tip-electrode 72 and counter-electrode 84. Internal screening of the depolarizing field may be caused by internal charge motion, within sample 86, of mobile ions, electrons, and/or holes present in the sample. Thus, internal screening is significant for ferroelectric samples having an intermediate to high conductivity. A characteristic dielectric relaxation time xcfx84rel for internal screening is defined as follows                               τ          rel                =                              ϵ            ·                          ϵ              0                                σ                                    (        9        )             wherein xcex5 and "sgr" are respectively a dielectric permittivity and a conductivity of sample 86, and xcex50 is the permittivity of free space. A domain-broadening effect occurs in ferroelectrics to which pulsed fields are applied, due to nucleation in the bulk of the ferroelectric, similar to the nucleation described with reference to equation (7b) above. The domain-broadening effect occurs when xcfx84dur is greater than xcfx84rel, i.e., when xcfx84dur greater than xcfx84rel xe2x80x83xe2x80x83(10)  The converse xcfx84dur less than xcfx84rel xe2x80x83xe2x80x83(11)  holds for domain-broadening not to occur. It will be appreciated that in practice the domain-broadening effect described herein applies to conductive ferroelectrics, with relatively high "sgr", since for ferroelectrics with low values of "sgr", xcfx84rel is larger than any practical pulse length applied. Combining inequalities (2) and (11) leads to a condition that is preferably satisfied for generation of DESs using pulses: xcfx84sw less than xcfx84dur less than xcfx84rel xe2x80x83xe2x80x83(12)  Pulses having an xe2x80x9conxe2x80x9d time xcfx84dur which satisfies condition (12) avoid instabilities associated with inequality (2) and domain-broadening effects associated with inequality (10). The RTP samples described above with reference to FIG. 8 had a relaxation time xcfx84rel (calculated from the conductivity and dielectric permittivity of the sample) of approximately 2 s. Thus, pulse durations lying in the range 2.5 ms less than xcfx84dur less than 2 s xe2x80x83xe2x80x83(13)  provide stable, well-defined, DESs in RTP. FIG. 10 is a schematic diagram showing results of producing one-dimensional DESs, according to a preferred embodiment of the present invention. Diagram 130 and diagram 132 illustrate domain walls 133 produced in two samples of RTP having thicknesses substantially equal to 350 microns, as seen by optically imaging a top surface of the samples. For both samples, counter-electrode 82 was set to be substantially constant at approximately +0.85 kV or xe2x88x920.85 kV. The samples were produced by scanning at one of these voltages, repositioning the sample, toggling to the second voltage, then scanning at the toggled voltage. In the first sample, the DES illustrated by diagram 130 was produced by scanning tip-electrode 72 at approximately 36 microns/s, in directions 134. After each scan, performed substantially as described above with reference to FIG. 7, the first sample was repositioned in a direction 138 by positioner 90, and a further scan in direction 134 was performed. A period of the resultant one-dimensional DES was evaluated at 8.45 microns. In the second sample, the DES illustrated by diagram 132 was produced by scanning tip-electrode 72 at approximately 40 microns/s, in directions 136. After each scan the second sample was repositioned in a direction 140, and a further scan in direction 136 was performed. For the second sample, a period of the resultant one-dimensional DES was evaluated at 2.2 microns. Using similar procedures to those described hereinabove for the first and second samples, the inventors have produced one-dimensional DESs having periods as small as 1.1 microns. It will be appreciated that periods of this magnitude have not been fabricated by prior art systems operating on bulk ferroelectrics. The inventors checked both samples after fabrication, and substantially similar results to those shown in diagrams 130 and 132 were seen when the opposite faces of the respective samples were optically imaged, showing that the ferroelectric domains produced were well-defined and substantially rectilinear. Furthermore, optical imaging of both samples after periods greater than 30 days showed substantially no change in the images, demonstrating that the samples produced are stable. FIG. 11 is a schematic illustration of a two-dimensional DES 150, according to a preferred embodiment of the present invention. DES 150 comprises a sample of RTP, and has domain walls which are represented in the figure as dark lines 152. Initially a periodic one-dimensional DES in the x-direction was implemented, substantially as described above with reference to FIG. 10, by counter-electrode 84 being set substantially equal to +1 kV, and tip-electrode 72 being scanned in a y-direction along lines 154. Counter-electrode 84 was then set to approximately xe2x88x921 kV, and the sample was then scanned along x-direction lines 156. The resultant DES 150 consists of rectangular domains 158 having one direction of polarization, set in a matrix 160 having a polarization in the opposite direction. FIG. 12 is a schematic illustration of a multi-dimensional tip-electrode 170, according to a preferred embodiment of the present invention. Multi-dimensional tip-electrode 170, herein termed MDTE 170, is used in place of tip-electrode 72. In contrast to methods of producing DESs as described above, where tip-electrode 72 is scanned across upper surface 94 of sample 86, MDTE 170 forms a DES by being held over upper surface 94 in a substantially stationary position. Unlike tip-electrode 72, which terminates in a sharp point, MDTE 170 terminates in a generally flattened face 172, the face having a shape corresponding to the DES to be formed in sample 86. Most preferably, multi-dimensional tip-electrodes similar to MDTE 170 are implemented by using focussed ion beam shaping techniques. By way of example, face 172 is assumed to be square in shape, having sides of the order of 1 micron, thus forming square domains, but it will be appreciated that multi-dimensional tip-electrodes can be terminated in substantially any shape, so that substantially any shape domain can be generated. In order to form a domain using MDTE 170, the MDTE is positioned over upper surface 94 of sample 86, substantially as described above for tip-electrode 72 with reference to FIG. 6. Also, as described therein, cantilever 74, and consequently MDTE 170, are grounded. A high-voltage pulse is applied to counter-electrode 84, the pulse being of a sufficiently high voltage to generate a field, greater than a coercive field of the sample, within the sample. A duration of the pulse is preferably set to agree with condition (12). MDTE 170 thus acts to xe2x80x9cbrandxe2x80x9d sample 86 with a DES in the form of a square. It will be understood that a DES similar to that shown in FIG. 11 can be produced by a process of scanning MDTE 170 rectilinearly, stopping the scanning, and branding at positions corresponding to domains 158. FIG. 13 is a schematic diagram showing formation and erasure of DESs, according to a preferred embodiment of the present invention. An RTP sample 180 was initially polarized in a mono-domain state. The inventors then formed linear DESs 182 in RTP sample 180, along lines parallel to a y-axis of the sample. The DESs were formed by linearly scanning sample 180, as described above with reference to FIG. 8, in SPA 70, using sample 180 in place of sample 86. DESs 182 were formed with counter-electrode 84 set at approximately +1 kV, and were formed by reversal of the initial polarization. After formation of DESs 182, counter-electrode 84 was reset to approximately xe2x88x921 kV. Sample 180 was then scanned along lines 184 parallel to an x-direction of sample 180. Regions 186 are regions which were originally poled as DES 182, and then their polarization was restored to the initial direction, demonstrating both erasure and correction in DESs 182. Referring back to FIG. 6, in some preferred embodiments of the present invention, scanner sample holder 88 comprises a heater 89. Heater 89 most preferably comprises a feedback source, so that it is able to maintain sample 86 at a substantially constant temperature above an ambient room temperature. Maintaining sample 86 at an elevated temperature reduces the coercive field of the sample, compared to the coercive field at room temperature, as is known in the art. For example, the inventors have found that a LiTaO3 crystal having a coercive field of 150 kV/cm at room temperature had a reduced coercive field of 37 kV/cm at a temperature of the order of 58xc2x0 C. Operating SPA 70 with a LiTaO3 crystal 300 microns thick in place of sample 86, and maintaining the crystal above 58xc2x0 C., the inventors were able to form linear domains in the crystal by scanning tip-electrode 72, with counter-electrode 84 set at approximately 1.2 kV. It will be appreciated that domain production may be possible in 300 micron LiTaO3 at room temperature, but from equation (3) a minimum applied potential for production is 4,500 V. In some preferred embodiments of the present invention, scanner sample holder 88 comprises a cooler 91 in place of heater 89. Cooler 91 most preferably comprises a container in which a coolant such as liquid nitrogen may be placed. As described above with reference to equations (10) and (11), domain broadening occurs in ferroelectric samples having high values of conductivity "sgr". By using cooler 91 to cool sample 86 to temperatures of the order of 170 K, SPA 70 may be operated to produce stable, well-defined DESs in ferroelectric materials which have high conductivity at room temperature. For example, KTP crystals have "sgr"≈10xe2x88x926 xcexa9xe2x88x921 cmxe2x88x921 at room temperature, so that strong domain broadening occurs when SPA 70 generates DESs in a KTP sample at room temperature. However, reducing the temperature of the KTP sample to 170 K reduces the conductivity to approximately 10xe2x88x9212 xcexa9xe2x88x921 cmxe2x88x921. Thus, operating SPA 70 on samples of KTP at 170 K generates stable, well-defined DESs. Preferred embodiments of the present invention are implemented so that a high potential difference of up to approximately 15 kV can be applied between tip-electrode 72 and counter-electrode 84. Preferably, as described hereinabove, tip-electrode 72 is grounded, and the high (or low) potential is applied to counter-electrode 84. It will be appreciated that other arrangements for the electrodes may be implemented. For example, both electrodes may be maintained at potentials different from ground, by insulating each electrode from the ground. In such a case, different potentials are applied to each electrode in order to form the required high potential difference between the two electrodes. Alternatively, counter-electrode 84 may be grounded, and the high (or low) potential is applied to tip-electrode 72. In preferred embodiments where tip-electrode 72 is not grounded, any instrumentation attached to cantilever 74, such as scanners 91 if implemented, is insulated from the ground so that voltages applied to the tip-electrode do not adversely affect the instrumentation. It will be appreciated that the scope of the present invention includes all such arrangements enabling a high potential difference to be maintained between the tip-electrode and the counter-electrode. It will further be appreciated that tip-electrode 72 may be implemented as a plurality of separated sharp points coupled together electrically. Each of the separate points is able to generate substantially similar but separate electric fields in sample 86, and the plurality of separate points improves the overall field distribution generated by each of the points. By implementing tip-electrode 72 as a multiple point electrode, SPA 70 is thus able to produce DESs in parallel. In addition to being able to implement periodic DESs, as described above, it will be appreciated that preferred embodiments of the present invention may be used to construct aperiodic DESs, as well as DESs of substantially any regular or irregular form, or combination of such forms. For example, a ferroelectric crystal may be utilized as an optical waveguide, and within such a ferroelectric waveguide a DES may be implemented to form a monolithic optical waveguide device such as a periodic or an aperiodic grating. It will be appreciated that the preferred embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.