The disclosed subject matter relates to sensors for determining surface topographies, nano-scale scanning probes, and techniques.
Atomic force microscopy (“AFM”) is a scanning probe technique with spatial resolution that can be as low as fractions of a nanometer. AFM is ubiquitous in nanoscience, where it can be used to measure and manipulate structures and surfaces far below the diffraction limit of light and indeed below the spatial resolution of most scanning electron microscopes, especially in the vertical dimension. Certain AFM devices use a cantilever with a small tip that physically scans across a surface in contact or scanning mode. The tip's deflection can be measured by monitoring the reflection of a laser beam from the tip surface. This optical setup can require a precisely engineered mechanical assembly for the laser source, alignment optics, and the split-photodiode detection, and can be large, complicated, and expensive.
Accordingly, there is a need for improved devices and methods for nanoscale scanning.
In accordance with one aspect of the disclosed subject matter, a device for measuring the topography of a surface is disclosed. In an exemplary embodiment, a device includes a semiconductor slab having a distal end and a base region. An air-slot can be cut into the semiconductor slab. The air-slot can have a proximal end and a distal end. The device can also include a sensor tip, coupled to the semiconductor slab, below the air-slot. The device can further include a photonic crystal. The phonic crystal, which can be integrated into the slab above and below the air-slot, can have a lattice pattern and a cavity region defined by a local perturbation in the lattice pattern. The air-slot can run through the cavity region, thereby splitting the cavity region and providing a split-cavity photonic crystal resonator integrated into the semiconductor slab.
In some embodiments, the device can further comprise a holder. The holder can be coupled to the base region and configured to couple with a piezo scanning device. The sensor tip can have a nm-scale radius of curvature.
In some embodiments, the semiconductor slab can be planar. Additionally, the slab can include either of a drop-filter or a detector. In some embodiments, the air-slot can function as a waveguide and can functionally couple the cavity to the drop-filter. The detector can be coupled to the drop-filter. The slab can also include a light source configured to emit light through the air-slot, which can function as a wave-guide, functionally coupling the light source and the cavity.
In some embodiments the light source can be further configured to emit light through the scanning tip, which can have a nano-scale tip (e.g., a plasmonic tip). The light can be directed into the surface and allows the device to be used as a component in a scanning near-field optical microscope.
In some embodiments the distal end of the air-slot can be contiguous with the distal end of the semi-conductor slab, creating a cantilever region below the air-slot. The sensor tip can be coupled to the semiconductor slab proximate the distal end of the semiconductor slab. In some embodiments either or both of the proximate and distal ends of the air-slot can comprise a cut-out region, increasing flexibility of the slab. In some embodiments the semiconductor slab can comprise one or more cut-out regions, increasing flexibility of the semiconductor slab in a first axis and decreasing flexibility of the semiconductor slab in a second axis.
In accordance with another embodiment, methods of determining the topography of a surface are provided. An exemplary method includes placing a tip of a semiconductor slab having a photonic crystal resonator with a split-cavity region, split by an air-slot, at a first location proximate the surface. An initial resonance frequency of the split-cavity of the optical resonator can be determined, and can correspond with a first level of compression of the cavity. The slab can be advanced across the surface to at least a second location proximate the surface. At least one additional resonance frequency of the split-cavity of the optical resonator corresponding to at least one additional level of compression of the cavity can be determined. A deflection of the tip based on the change from the initial resonance frequency to the at least one additional resonance frequency can be determined.
In some embodiments, the resonance frequency of the split-cavity of the optical resonator can be determined by coupling a resonant optical field into the cavity and measuring the cavity spectrum. In some embodiments, at least one additional resonance frequency of the split-cavity of the optical resonator can be determined by measuring a leakage metric of the cavity with a spectrum analyzer.
In some embodiments, a method of determining the topography of a surface can further include scanning the slab across the surface to a plurality of locations proximate the surface, determining a plurality of resonance frequencies of the split-cavity of the optical resonator, calculating a plurality of deflections of the tip based on the change in resonance frequency from the initial resonance frequency to the plurality of resonance frequencies, and determining the topography of the surface based on the plurality of deflections.
Other aspects and advantages of the subject matter will become apparent from the following description.
a-7d are schematic diagrams of various tip configurations according to certain embodiments of the disclosed subject matter.
Throughout the drawings, the same reference numerals and characters, unless otherwise stated, are used to denote like features, elements, components or portions of the illustrated embodiments. Moreover, while the disclosed subject matter will now be described in detail with reference to the Figs., it is done so in connection with the illustrative embodiments.
The disclosed subject matter provides methods and devices for measuring the topography of a surface, which can include a semiconductor slab with an optical resonator including a split-cavity photonic crystal resonator (SCPCR) integrated on the semiconductor slab. A sensor tip can be coupled to the slab below the SCPCR. If the sensor tip is deflected during sensing, the SCPCR can be compressed, changing the SCPCR's resonance frequency. This change can be measured and used to calculate the tip's deflection.
When the SCPCR is compressed (shortened), the cavity resonance frequency can increase from a value of wc0 to a value of wc. In one embodiment, for example, the change can be measured by observing the cavity leakage on a spectrometer or a spectrum analyzer. Alternatively, resonant light from the cavity can be transmitted via one or more waveguides to a spectrometer or spectrum analyzer. A strong change in the cavity intensity at frequency wc0 can be observed if the cavity center line width has changed by more than a cavity line width, Dw. The efficiency of the device, which can be given by a figure of merit, FOM, can be given by abs(wc0-wc)/Dw. The FOM, for example, can be proportional to the cavity's quality factor (Q) to volume (V) ratio, Q/V. Photonic crystal cavities can have high Q/V ratios and therefore can be suited for nanometer scale sensing applications. The deflection of the tip can thus be monitored, enabling sub-nm precision, as described in greater detail below.
Particular embodiments of a device for measuring the topography of a surface are described below, with reference to
In accordance with certain embodiments of the disclosed subject matter, device 10 includes a semiconductor slab 20. The semiconductor slab 20 includes a proximal end 21, a distal end 22, and a base region 23. The device 10 can also include a photonic crystal 30 integrated onto the semiconductor slab 20. In one embodiment, the photonic crystal 30 can include a lattice pattern of holes through the semiconductor slab 20. The holes can have a diameter of approximately 50 to approximately 400 nm. A suitable hole diameter can depend on the resonance wavelength λ of the cavity. For example, in a triangular lattice of holes in a high-index membrane such as silicon, the fundamental bandgap can exist from approximately a/λ=0.25 to a/λ=0.33 for a hole radius r=0.3*a, where a is the lattice constant (i.e., distance between holes). The cavity resonance frequency can be anywhere within the bandgap. The hole radius can be calculated from these relations. The photonic crystal 30 can have a cavity region 31, defined by a local perturbation in the lattice pattern.
The cavity region 31 can, for example, be a split-cavity region. For example, the semiconductor slab 20 can be at least partially bisected by an air-slot 40, such that the photonic crystal 30 and the cavity region 31 are integrated into the slab both above and below the air-slot 40. This configuration can result in a SCPCR located within the semiconductor slab 20. In some embodiments, one or both of the photonic crystal 30 and the cavity region 31 can be symmetric about the air-slot 40. The air-slot 40 can be, for example approximately 20 nm to approximately 60 nm wide. The depth of the air-slot 40 can extend through the membrane. The width of the air-slot 40 can be, for example, greater than ten lattice constants, i.e., over 10 a.
A holder 60 can be coupled, for example using adhesives such as UV-curable glue, to base region 23, and adapted to integrate with a conventional AFM device. For example, the holder can be attached to a commercial AFM scanner, or an AFM ‘blank’ which includes the mechanism for mounting the scanner into the commercial AFM holder and a membrane, but can lack the sharp AFM tip. In some embodiments, discussed in greater detail below, the holder 60 can be adapted to integrate with other scanning or sensing devices, including for example, a scanning near-field optical microscope. The holder 60 can be a piezo controlled holder. If sensing tip 50 is brought into contact with surface 70, the cavity region 31 can be deflected (compressed), causing a measurable change in the resonant frequency of the cavity region 31. The term “contact,” as used herein, can include physical interactions between the sensing tip 50 and the surface 70 or other force interactions between the sensing tip 50 and the surface 70, e.g., electromagnetic forces.
With reference to
In some embodiments, and with reference to
In certain embodiments, and with reference to
In certain embodiments of the disclosed subject matter, and with reference to
The input grating 120 can, for example, include small perturbations on the existing grating of the photonic crystal, at a desired location. For example, in a W1 photonic crystal waveguide in a holey photonic crystal membrane, the grating can include only small dielectric index perturbations to a set of holes near the waveguide region, in such a way as to scatter vertical light into the high-index slab, as disclosed, for example, in M. Toishi, D. Englund, A. Faraon, and J. Vuckovic, High-brightness single photon source from a quantum dot in a grating-integrated nanocavity, Optics Express, Vol 17, pp 14618-14626 (2009). In some instances extra holes adjacent to the existing holes can be introduced, which can reduce fabrication challenges that may be associated with electron beam fabrication of non-circular or very small, isolated perturbations.
Input grating 120 can direct light through waveguide 80 and into cavity region 31. Light emitted from cavity region 31 can travel through waveguide 81 and into filter 90. From filter 90, light can travel along another waveguide to detector 100.
Light source 110 can be a broadband, such as a light emitting diode, supercontinuum laser, fluorescent, or incandescent light source, or narrowband, such as a laser light source. Alternatively the light source can be internal to the photonic crystal, for example the material can be made of a fluorescent material (such as GaAs—InAs quantum wells), or it can have some fluorescent dye or quantum dots deposited on the semiconductor slab 20. The light source 110 can be pumped by electrical carrier injection or by shining a pump laser at the device. For example, with reference to
Waveguides 80 and 81 can be, for example, regions of the air-slot 40 within the photonic crystal 30, but generally outside the cavity region 31. Waveguides 80 and 81 can be configured to behave as such by, for example, surrounding the desired regions of the air-slot 40 with mirrors.
Filter 90 can be a drop filter or a transmission filter and can be used to convert the frequency of light resonated from the cavity into an intensity, which can then be measured by detector 100. Detector 100 can be a photodiode or other known light detectors.
a-d show schematic diagrams of various sensing tip 50 configurations. Sensing tip 50 can have a nm-scale radius of curvature. In some embodiments, the tip can be fabricated using electron beam lithography. Additionally, for example, anisotropic chemical etching can be used, e.g., potassium hydroxide for silicon substrates. Such etching can be directional with the crystal direction and can lead to clear crystal facets that focus at one points, which can be sub-nm in size.
These techniques can allow for fabrication of a planar AFM tip and a variety of other different shapes. The sensing tip 50 can have a variety of geometries, for example a triangle (
The device, including the semiconductor chip and the SCPCR, can be fabricated by a variety of known techniques, including, for example, chemical etching or reactive ion etching. Chemical etching involves applying reactive ions, for example hydrofluoric acid, to selected regions of the surface of the semiconductor chip to dissolve away material providing the desired pattern. In some embodiments, a substrate can be chosen with regard to its propensity to be selectively etched. For example, for a silicon membrane, the substrate can be silicon dioxide, which can be selectively removed with hydrofluoric acid.
In accordance with another aspect of the disclosed subject matter, a method for sensing the topography of a surface will now be described in detail. In one embodiment, for example, the devices described herein can be positioned tip-down over a surface. When the tip is retracted from the surface, the cavity resonance frequency can have an initial value of wc0. When the tip approaches the surface, the cavity can be compressed (shortened), such that that the cavity resonance frequency increases to a value of wc. This change can be monitored with a detector, such as a photodetector, and measured with an AFM control system, providing information about the topography of the surface. With a feed-back loop controlling the cavity height, the tip is scanned relative to the surface, enabling the acquisition of a plurality of values for wc. This can be used to determine a topographical image or can be used for other functions of AFM devices.
In accordance with another embodiment of the presently disclosed subject matter, methods of determining the topography of a surface are provided. Referring to
In some embodiments, determining a first resonance frequency of the split-cavity of the optical resonator (1210) can include coupling a resonant optical field into the cavity and measuring a first cavity spectrum (1211). In some embodiments, determining at least one additional resonance frequency of the split-cavity of the optical resonator (1230) can include coupling a resonant optical field into the cavity and measuring at least one additional cavity spectrum (1231). In some embodiments, determining at least one additional resonance frequency of the split-cavity of the optical resonator (1230) can include measuring a leakage metric of the cavity (1212).
In some embodiments, a method of determining the topography of a surface can further include scanning the slab across the surface (1260) to a plurality of locations proximate the surface, determining a plurality of resonance frequencies of the split-cavity of the optical resonator, calculating a plurality of deflections of the tip based on the change in resonance frequency from the initial resonance frequency to the plurality of resonance frequencies, and determining the topography of the surface based on the plurality of deflections.
For purposes of illustration, and not limitation, the devices disclosed herein can be characterized in accordance with the following description. Additionally, for purposes of illustration, the following cavity parameters can be given as follows: l is the length of the cavity, t is the thickness of the slab, and δ is the shift in the air slot size
The frequency shift induced in the harmonic modes of a system by small changes in the dielectric function of the system can be found through first-order perturbation theory and can be given by:
Δωs/ω0 can be proportional to −Δλs/λ0i, where ω0 and λ0 represent the mode's unperturbed frequency. In the case where Δωs is cavity line width limited, Δωs/ω0 can also proportional to the inverse of the quality factor Q. Owing to a strong confinement of light in the cavity, it can be assumed that the electric field strength is the highest in the cavity region. As such, the lower integral of equation 1 can assume its maximum in the cavity, and the upper integral of equation 1 can assume its maximum where the dielectric function changes (i.e. the cavity moves). Accordingly, for small δ(<<λ0/2n),
From Equation 2, the smallest (cavity line width limited) displacement that can be detected for a given Q can be identified as follows:
Equations 2 and 3 can satisfy the small δ criteria imposed earlier, and can hold if,
Accordingly, the assumptions hold for even moderate Q's. For example, for a silicon cavity at 1.5 μm with a Q of 103, δmin can provide a sub-angstrom resolution of:
However, equations 1-3 can be inaccurate for shifting boundaries as the normal component of the electric field to the boundary is discontinuous across it. Considering such discontinuities, the proper perturbation theory result can be given by:
accounting for high-index contrast boundaries. The following assumptions can be used to evaluate the integrals of equation 4: (1) in the plane of the cavity, it can be assumed that Ez is small compared to Ex and Ey and can be ignored; (2) the length of the region where maximum field intensity exists in the cavity is given by cl and the fraction of that region in the air is given by θ; (3) Ex=ηEy, ExSi=ExAir and DySi=DyAir. Ex and Ey are uniform throughout the cavity region (with Ey satisfying the boundary condition); (4) h(α) is the function that describes how the boundary of the leaves shifts parameterized by α (e.g., h(α)=x0+α); and (5) Δ∈12=∈1−∈2=∈0 (∈r−1) and Δ(∈12−1)=∈1−1−∈2−1=−(∈r−1)/∈r∈0 since ∈1=∈Si and ∈2=∈0.
Accordingly, the integral in the numerator can be given by:
The integral in the denominator can be given by:
Combining the above representation of the integral in the numerator and the integral in the denominator, and using the relation that ∈r=n2 can yield the following:
While equation 5 is significantly more complex than equation 2, the two are similar when the appropriate values for equation 5 are entered. For example, inserting cl=λ0/2n, η=1, and θ=1 provides
Equation 5 can provide a more accurate representation of reality as compared to equation 2. The minimum absolute shift can thus be given by:
when η=n−1. From
which is maximized when θ=0 or
minimizes it to give
Similarly, in the limit where there is only Ey, η→0 and
which is maximized when θ=1 to give
minimizes it to give
Q∝G and can be applied to the above results. For a mode with Ex only, Q is maximized when θ=0. This situation can be interpreted as the mode requiring a node at the air slot. For a mode with only Ey, Q is maximized when θ=1 or when there is an antinode in the slot.
The small δ criteria for equation 6 can also be satisfied as follows:
This holds for moderate Q (assuming that n is within a reasonable range, as the index contrast becomes smaller, achieving a high Q becomes much harder). The minimum detection limit can thus be bounded, and for cl=λ0/2n:
When evaluated with the previous parameters, there can be a large range for the minimum detection limit: 0.038 nm≦δmin≦0.467 nm
For purpose of illustration and not limitation, cavity performance in detecting shifts can be evaluated using a dimensionless figure of merit (FOM). An appropriate figure of merit can measure how well a cavity can shift its resonance for a given change in cavity length. Taking detection limitations into considerations, the shift is defined in terms of the original cavity line width:
where Δλs is the shift in the cavity resonance, λ0 is the resonant wavelength, and Δλ0 is the original cavity line width. Thus, the FOM can be bound for known maximum and minimum values of G:
While the presently disclosed subject matter has been particularly described with reference to exemplary embodiments thereof, it will be understood by those skilled in the art that various modifications and alterations may be made without departing from the spirit and scope of the invention. Accordingly, the disclosed embodiments are considered merely illustrative, and the disclosed subject matter is limited in scope only as specified in the appended claims.
This application is a continuation of International Patent Application No. PCT/US2012/048837 filed Jul. 30, 2012, which is related to U.S. Provisional Application Ser. No. 61/513,818, filed Aug. 1, 2011, each of which is incorporated herein by reference in its entirety and from which priority is claimed.
This invention was made with government support under Grant No. PECASE # FA9550-12-1-0045, awarded by the Air Force Office of Scientific Research. The government has certain rights in the invention.
Number | Date | Country | |
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61513818 | Aug 2011 | US |
Number | Date | Country | |
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Parent | PCT/US2012/048837 | Jul 2012 | US |
Child | 14150389 | US |