Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01Q—SCANNING-PROBE TECHNIQUES OR APPARATUS; APPLICATIONS OF SCANNING-PROBE TECHNIQUES, e.g. SCANNING PROBE MICROSCOPY [SPM]
  • G01Q60/00—Particular types of SPM [Scanning Probe Microscopy] or microscopes; Essential components thereof
  • G01Q60/18—SNOM [Scanning Near-Field Optical Microscopy] or apparatus therefor, e.g. SNOM probes
  • G01Q60/22—Probes, their manufacture, or their related instrumentation, e.g. holders

Definitions

• This invention relates generally to scanning probe microscopy and more specifically to scanning evanescent near field microwave and electromagnetic spectroscopy.
• Scanning probe type microscopes have typically been used to create visual images of a sample material.
• the image obtained may reflect any of a number of distinct electrical or magnetic properties of the sample material, depending on the parameter measured by the probe tip.
• the tip may image electron tunneling, atomic force, absorption and refraction of propagating or evanescent electromagnetic waves, or other parameters.
• the tip may be in contact with the sample or it may be a short distance above the sample.
• SPMs Scanning Probe Microscopes
• microscopy signals as obtained from SPMs often are a combined function of topography and physical properties of the material. Separating them requires measuring at least two independent signals. For example, in scanning tunneling microscopy, the tunneling current is a function of both the tip to sample distance and the density of states. A recently developed scanning near-field optical microscope can measure optical signals such as luminescent spectra or optical index of refraction in addition to shear force, which can be used to determine the distance between tip and sample. Second, to obtain quantitative information regarding the physical sample being imaged, complicated electromagnetic field equations in the region of the tip and sample must be solved. A review of this work is discussed by C. Girard and A. Dereux in Rep. Prog. Phys., vol. 657, 1996.
• the invention comprises a near field scanning evanescent-wave microscope wherein a probe tip primarily emits an evanescent wave and wherein interfering propagating wave emissions are minimized. Propagating waves have low resolution while evanescent waves have high resolution. This feature is crucial for quantitative measurements, where only the near-field evanescent wave is modeled.
• a high resolution image is generated by scanning a sample with a novel evanescent wave probe on the inventive microscope.
• the inventive microscope provides complex electrical impedance values that are calculated from measured data and which are associated with the resolved image features.
• the complex impedance, including dielectric constant, loss tangent and conductivity can be measured for materials having properties that range from insulators to superconductors.
• the inventive microscope is capable of quantitative measurements of dielectric properties and surface resistance with submicron resolution.
• the electrical properties of the sample are measured.
• One embodiment of the SEMM comprises a ⁇ /4 coaxial resonator operating at frequency ( of roughly 1 GhZ coupled to a sharp tip protruding from a narrow hole.
• frequency of roughly 1 GhZ coupled to a sharp tip protruding from a narrow hole.
• the inventive microscope is capable of converting the measured ⁇ and Q shifts to electrical parameters of the sample. Since the extremely small tip radius determines the extent of the field distribution, this microscope is capable of submicron resolution.
• the interaction between the probe tip and the sample is dependent on the dielectric constant and tangent loss of the nearby sample.
• the interaction depends on the surface resistance of the sample.
• the probe itself comprising either a resonator or a conventional coaxial body, is a key inventive feature of the microscope.
• An important novel feature of the probe tip is a conducting endwall having an aperture, through which the center conducting element of the coaxial cable or resonator extends without shorting to the endwall.
• Another key feature of the inventive microscope is the computing element programed to convert measured changes in resonant frequency (or reflected electromagnetic wave) and measured changes in the quality factor to quantitative electrical parameters of the sample.
• An additional important feature of the inventive microscope is a means to maintain a constant separation distance between the tip and the sample while measurement scans of the sample are performed.
• Figure 1 is a diagrammatic view of the various components which comprise the imaging evanescent near field microscope system.
• Figure 2 is a diagrammatic view of the various components which comprise the quantitative evanescent near field microscope system.
• Figure 3 shows the image charge distribution for a thick sample in contact with the end of the probe tip.
• the q tire series represents the charge redistribution on the tip;
• the q n ' series represents the effect of polarization of the dielectric sample;
• the q terme" is the effective value of q admiration inside the sample.
• Figure 4 shows the image charge distribution for the configuration with an air gap between a thick sample and the end of the probe tip. Symbols q terme, q vessel', and q termed.
• Figure 5 shows a graph of measured and fitted resonant frequency as a function of the distance between the end of the probe tip and the sample for a MgO single crystal.
• Figure 6 shows distribution of image charges for a tip-sample configuration in which the sample comprises a thin film (e-j) on a thick substrate (e t ) and in which there is an air gap (g) between the probe tip and the film surfaces.
• Symbols q terme, q terme', and q termed have the same meaning as in Figure 3.
• the q lake' series represents the effect of polarization of the dielectric film induced by the field of the tip.
• the q,,” series represents the reaction on the film from the polarized substrate.
• Figure 10 shows the radial distribution for the magnetic field on the surface of a conducting material surrounding the proximity of the probe tip, for different probe tip radii, a,,.
• Figure 11 shows measured data points (triangles) and a best fit calculated curve from SEMM signals as a function of gap size between the probe tip and a copper sample using the resonant frequency equation 12.
• Figure 12 shows measured data points (triangles) and a best fit calculated curve from SEMM signals as a function of gap size between the probe tip and a copper sample using the quality factor equation 19.
• Figure 13 shows the spatial frequency spectra of the magnetic field on the surface of a conducting material for five different values of a,,.
• Figure 14 shows the power dissipated, S, in a conducting sample as a function of a fertiliz, the ratio of the gap distance to the radius of the probe tip.
• Figure 15 shows on the left, a topographic image of a LiNb0 3 sample having periodically poled domains. The image on the right is of a simultaneously obtained first harmonic image in which the contribution from sample-probe geometry has been excluded. These images were obtained using the inventive feed back control component to control sample to tip distance.
• Figure 16 shows an embodiment of the inventive probe tip comprising a coaxial cable instead of a resonator.
• Figure 17 shows a change in frequency as a function of gap distance for a known metal, the curve being useful as a calibration curve for the gap distance controller.
• Figure 18 shows results obtained using the SEMM to image conducting silver sections having differing heights but constant conductivity.
• Figure 19 shows results obtained using the SEMM to image conducting metal sections having differing heights and differing conductivity.
• the present invention improves the visual image resolution of the scanning evanescent electromagnetic microscope and extends its utility to essentially simultaneous measurement of quantitative microscopy.
• the microscope is referred to as a SEMM, originally for Scanning Evanescent Microwave Microscope, and alternatives, because the microscope is not limited to the microwave region, for "Scanning Evanescent electroMagnetic Microscope".
• SEMM quantitative microscopy can be used to obtain the complex electrical impedance of dielectric, ferroelectric, and conducting materials with submicron resolution.
• Use of the SEMM is not limited to the microwave region.
• the electromagnetic frequency of the inventive microscope is limited on the high end by the electron mobility in the sample being measured (that is the plasma frequency of the material) and on the low end by the practicality of the physical dimension of the resonant cavity portion of the probe tip.
• frequencies ranging from the infrared region of the electromagnetic spectrum to the microwave region can be used on the scanning evanescent wave microscope. If the resonation is replaced by a coaxial cable having an end wall connected to the coaxial shielding element, the low end of the measurement frequency is essentially d.c.
• the evanescent-waves in this context refer to electromagnetic waves with wave- vectors of imaginary number not originating from dissipation.
• the evanescent electromagnetic waves are the photon equivalent of quantum mechanic electron waves in the classically forbidden region (within a barrier).
• an orthogonal eigenfunction set of Hubert space is chosen as the plane waves whose wave vectors are any real number satisfying Helmholtz equation (as a consequence, these plane waves are propagating waves).
• propagating wave for example, a propagating spherical wave from a point source
• These waves only have resolving power on the order of ⁇ .
• these plane waves can not be used to reconstruct, for example, a spherical wave whose wave front has a radius less than the wavelength ⁇ .
• a true complete set of Hilbert space should include plane waves whose wave-vectors are any complex number satisfying the Maxwell equation to construct such a spherical wave. Since imaginary wave vectors are allowed, the components k ⁇ , k y , and kj can then be any value and still satisfy the Maxwell equation.
• these waves are "evanescent" and can not propagate much more than a wavelength ⁇ .
• evanescent- wave microscopy uses different means to obtain strong evanescent waves and strong interaction between the evanescent wave and the substance under inspection.
• a metal sphere or tip fed by a wave source with a radius of r will generate evanescent waves (to form a spherical wave on the metal surface satisfying the boundary conditions) whose wave vectors range up to l ⁇ . ⁇ 1/r and resolving power up to ⁇ r.
• the inventive scanning evanescent microscope uses an evanescent wave to image the surface with high resolution and to obtain a quantitative measurement of the complex electrical impedance associated with detail resolved in the image.
• the inventive apparatus uses the near-field interaction between the evanescent waves around the tip and the samples under scan.
• Figure 1 shows the inventive near field microscope system utilizing the novel evanescent probe structure comprising a microwave resonator such as illustrated microwave cavity 10 having generator 30 electrically connected to cavity 10 to feed an input signal, through a coaxial line 32, into a coupled loop input 12 on cavity 10.
• a coupled loop output 14 of cavity 10 is connected to a detector 40 through a second coaxial line 42.
• Detector 40 feeds the output signal to a data acquisition unit 50.
• the data from data acquisition unit 50 is then fed into a computer 60 which converts the data into an image viewable at image display 70 connected to computer 60.
• Other means besides coupled loops or tuned loops can be used to couple energy to and from the resonant cavity, as described in detail in the text "Microwave Engineering" by D. M.
• the present inventors developed a configuration in which the center wire was sharpened and extended a distance beyond the shielding, or a sharpened tip was mechanically and electrically connected to the center wire.
• additional inventive shielding element was added to the bottom edge of the coaxial cable in order to minimize any electromagnetic fields created between the sharpened end of the probe and the end of the external shielding, which when left open can allow far-field propagating wave to reach the sample and dominate the near-field evanescent wave.
• the present inventors added a resonator which was located immediately above or near the probe tip so that evanescent waves could be generated and sensed with greater efficiency and sensitivity, although the resonator is not a necessary component for every application.
• the inventive SEMM tip limits the creation of propagating waves so that high resolution evanescent wave measurements can be made effectively.
• One feature of the inventive tip that limits creation of far-field propagating waves is a conductive shielding element that extends over the portion of the coaxial cable that otherwise would have been open. Referring to Figures 1 and 2, at the end from which the probe tip 20 extends, a new electrically conducting shielding element 16 is located so that its outer edge connects to the exterior coaxial shield 1 7 and its inner edge circles, or surrounds, the probe tip without electrically shorting to it.
• the conducting shielding element 32 is preferably thin, on the order of 1 ⁇ m, to avoid causing excess loss. It is preferably physically supported by a low loss insulator like sapphire.
• the outer shield 32 is brought around the end portion 16 of the insulator but has an opening, or aperture 22 through which the probe can extend without electrically shorting to the shield.
• the aperture is conveniently circular but does not have to be circular.
• the aperture is smaller than either the coaxial cable or a resonator that is used to generate the evanescent wave.
• the end portion of the insulator forms a plane that is approximately normal to the line of the probe portion, however a tapered surface could span part of the distance between the outer shield and probe as long as the sensitivity of the probe remains acceptable and degradation of the Q factor is avoided.
• Q 2 ⁇ E tot E diS! ⁇ fated .
• a sharpened metal tip 20 which, in accordance with the invention acts as a point-like evanescent field emitter as well as a detector, extends through a cylindrical opening or aperture 22 in endwall 16 of cavity 10, as will be described in more detail below.
• Mounted immediately adjacent sharpened tip 20 is a sample 80.
• Sample 80 is mounted to a movable target mount or stepper mechanism 90 which can be moved in either the X, or Y or Z axis by an X-Y-Z scanning controller 100 which, in turn, is controlled by signals from computer 60.
• Microwave generator 30, detector 40, data acquisition unit 50, computer 60, display 70, movable target mount 90, and X-Y-Z scanning control 100 all comprises commercially available equipment.
• microwave generator 30 is available from the Programmed Test Source Company as model PTS1000
• detector 40 is available from Pasternack Enterprises as model PE800-50
• data acquisition unit 50 is available from National Instruments as model PC-TIO02150
• computer 60 may comprises any standard programmable computer
• display 70 may comprise any commercially available monitor
• movable target mount or stepper mechanism 90 is available from the Ealing Company as model 61-0303
• X-Y scanning control 100 is available from the Ealing Company as model 37-1039.
• Design principles for a quarter wave cavity, such as cavity 10 may be found in "Radio Engineer Handbook" by F.E. Terman.
• Cavity 10 comprises a standard quarter or half wave cylindrical microwave cavity resonator having a central metal conductor 18 with a tapered end 10 to which is attached sharpened metal tip or probe 20.
• An optional spacer made of an insulation material such as Teflon, may be used to assist in maintaining the central positional of central conductor 18 coaxially within cavity 10.
• probe tip 20 extends through and beyond aperture 22 formed in endwall 16.
• Metal probe tip 20 has a sharpened end thereon which may be as find as about 100 .Angstroms in diameter.
• the sharpened end of tip 20 will usually vary in diameter from as small as about 100 -Angstrom (10 nm) to as large as about 100 ⁇ m, and preferably ranges from about 200 -Angstroms (20nm) to about 20 ⁇ m.
• Sharpened metal probe tip 20 may be formed, for example, by electrochemically etching one section of a wire which might have an initial diameter of from about 1 ⁇ m to about 0.2 millimeters (mm) prior to the electrochemical etch.
• Sharpened metal probe tip 20 may be connected to tapered end 19 of central conductor 18 by welding or any other suitable means which will provide a secure mechanical and electrical connection between tip 20 and tapered probe end 19.
• the minimum diameter of aperture 22 has been determined to be the minimum diameter which maintains the high Q and sensitivity of the resonator.
• the aperture opening must be small enough that a propagating wave is not emitted that will interfere with the evanescent wave measurement.
• the minimum diameter of aperture 22 should be greater than the thickness of endwall 16. That is, endwall thickness t divided by aperture diameter d must be much less than unity (t d «1) to maintain high Q (or low loss) of the resonator.
• the endwall should be made by plating a good conducting film (silver or copper) of about 1-2 ⁇ m thick on a low loss insulating plate ( ⁇ 1 mm thick), such as sapphire or LaA103 to reduce the thickness t while maintaining rigidity (mechanical vibration is not desired).
• the aperture diameter is also related to the diameter of the metal probe tip which passes through and beyond aperture 22. The minimum aperture diameter, therefore, will usually be at least about 200 Angstroms (20 nm). If the diameter of aperture 22 is too large, however, the resolution will be reduced. It has been found, however, that the diameter of aperture 22 may be as large as 3 mm while still maintaining satisfactory resolution.
• the diameter of aperture 22 will range from about 500 -Angstroms (50 nm) to about 1 mm.
• sharpened metal probe tip 20 extends through and beyond cylindrical aperture 22 in endwall 16 of resonator 10.
• the reason why probe tip 20 must extend beyond aperture 22 a distance comparable to the diameter of aperture 22, in accordance with the invention, is to reduce the effect of the size of the aperture on the resolution. That is, the reason probe tip 20 extends through and beyond aperture 22, instead of terminating at aperture 22, as in prior art structure, is to provide increased spacial resolution, dependent dimensionally on the radius of probe tip 20 rather than the diameter of aperture 22.
• the extension of probe tip 20 beyond aperture 22 also is helpful and convenient for the scanning of the sample.
• the length of the portion of sharpened metal probe tip 20 which extends through and beyond aperture 22 is related to the diameter of aperture 22. This length of probe tip 20 extending through and beyond aperture 22 will range from about Vb of the diameter of aperture 22 to about 3 times the diameter of aperture 22.
• the preferred ratio of extension length to aperture diameter has been found to be about 1.
• the extension length should be further selected to be the length that does not give rise to a large background signal (caused by radiation from the aperture which interacts with the sample) while still giving rise to a strong signal by the tip-sample interaction.
• cavity 10, including shielding 32 and endwall 16 is formed of metal but preferably comprises a diamagnetic material such as copper or silver, rather than a ferromagnetic material, so that a modulating magnetic field can be used in connection with cavity 10.
• cavity diameter should be large enough and the diameter ratio of cavity 10 to central electrode 18 should be about 3.6 to provide an optimum Q.
• the Q of a microwave cavity or resonator may be defined as the quality factor of the cavity, and should be kept as high as possible.
• the sensitivity of the near field microscope can be improved by increasing the input microwave power and unloaded Q, denoted Q u , of the resonator with an optimal coupling which is achieved by adjusting the coupling strength so that the loaded Q, denoted Q,, is 2/3 of Q u .
• the resonator cavity volume is filled with a dielectric material, preferably one having low loss.
• the relative dielectric constant is proportion al to the dielectric constant of a vacuum.
• Sample dielectric materials that can be advantageously used to fill the resonator cavity include air, Strontium Titanate (SrTiO 3 ), and sapphire (Al 2 O 3 ).
• the resonator height is in integral multiples of ⁇ /4, that is n ⁇ /4 where n is an integer. If the resonator is an open resonator n is an even integer; if the resonator is closed n is an odd integer.
• the resonator can be replaced with a standard coaxial cable.
• Figure 16 shows an embodiment of the inventive probe tip using a conventional coaxial cable in place of a resonator.
• -An electromagnetic energy source 40 delivers electromagnetic energy to the cable.
• the coaxial cable has an outer electric shielding element 52 that surrounds an insulator element 44 and a central conducting element 48.
• the central conducting element extends beyond the end of the coaxial cable and is either sharpened into a tip or a fine sharp tip is attached to it 20.
• a thin metal endwall 46 is attached to the insulator that is interposed between the shielding 52 and the center conductor 48. The endwall thickness is guided by the same consideration as for the conductive endwall 16 at the end of the resonator.
• the endwall 46 located at the end of the coaxial cable, has an orifice of sufficient size to allow the center cable 48 to pass through it without electrically shorting the center probe to the endwall.
• the inventive probe comprising a coaxial cable, additionally has a directional coupler 42 located between the endwall 46 and the source 40.
• the directional coupler 42 couples the source electromagnetic wave to the cable.
• the electromagnetic wave propagates down the cable to the end and is reflected back by the end wall. Interaction between the probe tip 60 and the sample being scanned modifies the properties of the reflected wave.
• the reflected wave is coupled to a detector by directional coupler 42 and the amplitude and phase of the reflected wave are measured by the detector.
• Quantitative values of the physical properties of the sample such as complex conductivity, dielectric constant, tangent loss, conductivity, and other electrical parameters are determined using equations programed into the SEMM. Quantitative Measurement of the Complex Electrical Impedance of a Dielectric or Ferromagnetic
• dielectric materials have been imaged having a spatial resolution of 100 nm and sensitivity of 1 x 10 '3 . Furthermore, using a computation of an analytic expression of the field distribution around the probe tip, a quantitative measurement was taken of the complex electrical impedance dielectric material. Thus a map of electrical impedance values was constructed that matched resolution and sensitivity of the image, and wherein the measured complex electrical impedance values were correlated to features visualized on the image.
• the coaxial resonator has a height of ⁇ /4.
• a sapphire disk 21 with a center hole only slightly larger than that of the tip wire was located in the end plate.
• the tip diameter was between about 50 ⁇ m and about 100 ⁇ m.
• a metal layer of about 1 ⁇ m was coated on the outside surface of the sapphire disk to shield the tip from far-field propagating components. The metal coating thickness is determined by the skin-depth to avoid the formation of a micro-transmission line, which would have heavy loss near the aperture.
• the sapphire disk serves to minimize vibration and is bonded to the probe tip using insulating glue.
• insulating glue having low energy loss may be used to fix the tip wire with respect to the endwall shielding so that the tip does not vibrate against the shielding.
• the entire resonant cavity is filled with a dielectric material such as SrTi0 3 .
• a dielectric material such as SrTi0 3 .
• the height of the resonant cavity is greatly reduced as the resonant wavelength is inversely proportional to the square root of the relative dielectric constant of the material that fills the cavity.
• an image is obtained by placing the tip of the resonator in direct physical contact with the sample to be imaged, and scanning the tip across the surface of the sample.
• the resonator is driven at a frequency that is slightly higher or lower than the resonant frequency of the resonator.
• the change in the resonant frequency is then measure by recording the output power at the input frequency (measured as the detector output voltage).
• the resonant frequency of the resonator is reduced as a function of the relative conductivity of different regions of the sample.
• very fine niobium wires coated on, say, silicon dioxide can be successfully imaged to a spatial resolution of about
• the present invention in addition to detecting relative differences in conductivity of the surface of the sample, a quantitative measurement is obtained of the complex electrical impedance. This is possible because the resonant frequency, f ⁇ and the quality factor, Q, shifts as functions of the dielectric constant and loss tangent of any material, such as the sample material, located near the probe tip. In the past this functional relationship was not well enough known, however, to obtain quantitative information about the dielectric constant, loss tangent, or complex electrical impedance, from a measured shifts in ⁇ . or Q.
• the present invention comprises a scanning evanescent wave resonant-probe microscope having a computing element capable of correctly relating a series of measured shifts in fj.
• the computing element is programmed to calculate values of e and tangent losses (tan ⁇ ) at a series of different frequencies.
• the frequency versus power curve in the proceedure above can be determined using a Lorentz line type fit to obtain f 0 , and Q 0 .. Soft Contact Measurements of Dielectrics
• the electromagnetic wave can be treated as quasi-static, that is, the wave nature of the field can be ignored.
• the sample material in the vicinity of the small probe tip is reasonably considered as homogeneous and isotropic in its dielectric properties.
• e e' + j e" and e is »esammlung, and e' » e", where e is the complex dielectric constant, e' is the real component of the dielectric constant, e" is imaginary component of the dielectric constant, and e 0 is the dielectric constant of free space.
• ⁇ ⁇ ' + j ⁇ " and ⁇ ⁇ ⁇ 0 ;
• ⁇ is the complex magnetic permeability of the sample;
• ⁇ ' is the real component of the magnetic permeability, and
• ⁇ " is the imaginary component of the magnetic permeability, and
• ⁇ 0 is the magnetic permeability of free space.
• Figure 3 shows a diagram of the measurement geometry.
• the probe tip 20 is in soft contact with the surface of a dielectric material 80 having a thickness much larger than the tip radius.
• the sample thickness may be more than 2 times as thick as the tip radius. More preferably it is 5 times as thick.
• the probe tip is represented as a charged conducting sphere under the same potential as the end point or tip of the center conductor in the endwall of the resonator, since the tip only extends out a length several orders of magnitude smaller than the wavelength beyond the cavity.
• the dielectric sample under the tip is polarized by the electric field of the tip and thus acts electrically on the tip causing a redistribution of charges on the tip to maintain the equipotential surface of the conducting sphere.
• the action on the tip is represented by an image charge q,' located in the sample; the redistribution of charge in the probe tip is represented by another image charge q-, inside the spherically modeled tip end.
• This action and redistribution repeats itself, that is it is iterative until equilibrium is attained.
• Three series of image point charges are formed that meet the boundary conditions at both tip and dielectric sample surfaces as shown in Figure 3.
• the peak value of the field distribution inside the sample can be expressed as a superposition of contributions from the series of point charges q cauliflower", the effective value of qbie in the sample.
• This field distribution satisfies Coulomb's law and the boundary conditions on the surfaces of both the dielectric sample and the conducting sphere terminus of the probe tip. In this model the majority of the electromagnetic energy is concentrated in the cavity and the field distribution inside the cavity is not disturbed by any tip-sample interaction.
• perturbation theory for electromagnetic resonators where the frequency is perturbed slightly to find the resonant frequency or the amplitude of the energy deposited in the cavity is perturbed, can be used to calculate the ⁇ . and Q shifts that would result from a particular dielectric material, as noted in equations (2) and (3).
• E 0 , H 0 , and E,, H 1; refer to the electric and magnetic field before and after the perturbation, respectively
• ⁇ is the wavelength
• N 0 is the voltage on the probe tip.
• Equation (2) shows that the shift in resonant frequency is proportional to the radius Ro of the probe tip. This is because the electric field near a conducting sphere, which is how the probe tip is modeled, at a given voltage is inversely proportional to the sphere radius and the total contribution to the signal is the integration of the square of the electrical field magnitude divided by the volume of the sample.
• the shift in quality factor Q the extra current required to support a charge redistribution on the spherical probe tip end when it is brought near a dielectric induces resistivity loss. This results in a shift in Q that is expressed as,
• the tan d is referred to as the loss tangent.
• the sample thickness may be at least about two times as thick as the probe tip radius. Preferably the sample thickness is at least five times as thick as the probe tip radius. Even more preferably the sample thickness is at least 10 times greater than the probe tip radius.
• the constants A and B are found by calibration against a standard sample such as sapphire that has a known dielectric constant and loss tangent. Table I lists relative dielectric constants e r and loss tangents for a number of materials measured using the inventive SEMM. The relative dielectric constants are relative to measurements taken in a vacuum or air.
• t. l + a' + a ⁇ ' " ⁇ l
• MgO Magnesium Oxide
• Equation 7 shows that even if the tip to sample distance is maintained within 1 nm (for example a' ⁇ 10 "2 for an 100 nm probe
• One application of the inventive SEMM is measuring the dielectric constant of thin
• the penetration depth of the field is
• inventive SEMM and a conventional inter-digital contact electrode at 1 GHZ are inventive SEMM and a conventional inter-digital contact electrode at 1 GHZ.
• Table II Measured dielectric constants and tangent losses of various thin films By SEMM and interdigital electrode technique, both measured at 1 GHZ.
• Intrinsic spatial resolution is an important figure of merit for microscopes.
• the instrinsic resolution of the inventive microscope was estimated using equation 2 to calculate numerically the contribution to ( ⁇ /Q from small vertical columns as a function
• the estimated resolution was about two orders of magnitude smaller than the tip
• the field distribution inside the sample is concentrated in a very small region just below the tip apex with the polarization pe ⁇ endicular to the
• the resonant system can be analyzed using an equivalent lumped series resonant
• R 0 is the internal resistance of the source, and , is the resonant
• the output signal of the phase detector can be expressed as:
• N QJ(Q U -QJ is the insertion loss
• k B Bolzmann's constant
• B is the
• the estimated sensitivity is about 1 x 10 "5 for R 0 - 1 ⁇ m
• the inventive SEMM is based on a high quality factor (Q) microwave coaxial
• resonator with a sha ⁇ ened metal tip mounted on the center conductor.
• the tip extends beyond an aperture formed on a thin metal shielding end-wall of the resonator.
• the first order field redistribution can be obtained by treating the material as an ideal conductor with
• the surface of the conducting material is a
• charge mirror and the tip-sample interaction can be represented as a multiple image charge
• the electric field in the tip-sample region can be calculated as
• e r and ⁇ z are the unit vectors along the directions of the cylindrical coordinates
• a corpus and 7 n are the position and charge of the nth image inside the tip, respectively.
• a corpus and q bis have the following iterative relations:
• FIG.10 The figure indicates that the size of caster (a measure of spatial resolution of the microscope) decreases and the intensity of the field increases with decreasing tip-sample distance, respectively.
• the tip is represented as a small capacitor, C ', whose capacitance depends on the tip-
• k c represents the refracted wave vector of ⁇ o .
• incident wave is a propagating wave, the pe ⁇ endicular component of its wave vector in
• ⁇ ⁇ kor k c because k 0r j s negligible compared to ⁇ k c
• the conducting material has a unique surface impedance (or
• corresponding k 0r can De any value, comparable or even larger than
• H s (K r ) ⁇ H s (r)exp(ik ⁇ r - r)ds
• the field intensity increase associated with the decrease of the tip-sample distance is mainly concentrated in the high spatial frequency region.
• the corresponding electromagnetic field inside the conducting material has the form of:
• H c k 0r H,(*. r ) exp[/(*;,z + k 0r r) - k versatility' z]
• the electric field configuration solved here is identical to the static electric field configuration in various SPMs, such as scanning
• the capacitance can be expressed very
• SEMM scanning evanescent electromagnetic microscope
• the shift in f r corresponds to the dielectric constant of the
• the separation by maintaining the separation so as to induce a constant frequency shift.
• the surface topography can be imaged.
• the conductivity of the metal can be imaged
• the frequency response can be measured. -After calibration of the cavity to determine the geometrical
• a frequency f ⁇ is chosen to correspond to some tip-sample
• connection 31 on Fig. 2 is open.
• a constant RF frequency f ⁇ is input into the cavity and
• the cavity output is mixed with a signal coming from a reference path.
• the length of the reference path is adjusted so that the output of the mixer is zero when fj. matches f ⁇ .
• tip-sample separation is chosen for the cavity.
• the resonance frequency chosen is fed into
• the cavity and the output of the phase defector is used to regulate the applied voltage to the piezoelectric actuator.
• Sample topography is measured by monitoring the variation in voltage applied to the actuator.
• This sample consists of 100 nm, 200 nm, and 400 nm Ag squares on a 2J ⁇ m Ag substrate on a
• image is essentially featureless.
• Poled Single Crystals For materials in which the frequency shift is constant (i.e.
• the tip-sample distance (d) can be controlled by adjusting the
• Sample topography is measured by monitoring the variation in voltage applied to the actuator.
• Variations in the transmitted power correspond to variations in tangent loss or surface
• the first order nonlinear dielectric constant ( ⁇ ijk ) can also be measured.
• Figure 15 This image was taken of a periodically poled single-crystal LiNbO 3 wafer. The topographic image is essentially featureless, with the exception of a constant
• the nonlinear image features a reversal in phase by the reversal of polarization in the
• Apertureless reflectance-mode near-field optical microscopy (apertureless
• NSOM can also be used for distance regulation of a SEMM.
• waveguide can either confine or sample light from a region near an aperture with size
• a vertical dither may be used to reduce the effects of a far-field background. This dither should
• This method allow for control the tip-sample separation in an SEMM with high resolution over a broad range of substrates in combination with simultaneous measurements of the sample's electrical properties.
• the tip-sample distance may also be regulated by differential measurement of the
• the microscope signal and can be used for distance control.
• the frequency shift and harmonic intensity are independent functions of the dielectric constant and the tip-sample distance, g, and give raise to two independent
• Equation 5 is then solved for ⁇ and used as equation 20.
• Equation 21 is the first derivative taken with respect to g. The equations 20 and 21 are solved simultaneously to yield the dielectric

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• Length Measuring Devices By Optical Means (AREA)

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• 1998
  • 1998-09-22 JP JP2000513305A patent/JP4431273B2/ja not_active Expired - Fee Related
  • 1998-09-22 EP EP98953178A patent/EP1018138A4/en not_active Withdrawn
  • 1998-09-22 WO PCT/US1998/019764 patent/WO1999016102A1/en not_active Application Discontinuation
  • 1998-09-22 AU AU10615/99A patent/AU1061599A/en not_active Abandoned

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