Patent Description:
As background, <CIT> describes ultrasonic inspection method and ultrasonic inspection device; <CIT> describes non-destructive wafer-scale sub-surface ultrasonic microscopy employing near field AFM detection; XP011311943 describes probing buried defects in extreme ultraviolet multilayer blanks using ultrasound holography <CIT>, which is relevant for Article <NUM>(<NUM>) EPC only, describes an ultrasonic inspection method and an ultrasonic inspection device wherein an absorption layer contacting a side of a sample is excited by a pulsed laser beam, thus generating ultrasonic shear waves.

In semiconductor applications, alignment, overlay, metrology, and defect detection are challenging subjects. For example, 3D NAND is now introduced as the next generation of memory applications. These chips may consists of hundreds of layers with a total thickness of few micrometers. Since semiconductor components may by opaque, the alignment of the wafers and sublayers cannot always rely on optical methods.

Atomic force microscopy (AFM), empowered by the use of ultrasound excitation can give information of the subsurface. For example, ultrasound can be delivered through the bottom of the substrate (chip) while the dynamic response of the AFM cantilever and tip in contact with the sample is monitored through the measurement of the contact resonance frequency or the measurement of the amplitude or phase change close to contact resonance. However, the propagation of ultrasound waves from the bottom may be difficult to control and predict through the many layers of the substrate, thus affecting the imaging particularly when the substrate comprises multiple sublayers each having nanostructures.

Accordingly there remains a need for improving reliability and control over subsurface imaging of nanostructures buried at ever greater depths below the substrate surface.

Claim <NUM> of the invention provides a method for subsurface imaging of nanostructures buried inside a 3D substrate, e.g. chip. An atomic force microscope is provided with an AFM tip at a top surface of the substrate. An ultrasonic generator is provided at a side face of the substrate, i.e. transverse to the top surface. The ultrasonic generator is thus used to couple ultrasound waves via the side face into the substrate, or into a selected part of the substrate. The interior of the substrate comprise or form a waveguide for propagating the ultrasound waves in a direction along a length of the substrate transverse to the side face. To behave as guided waves, a wavelength of the ultrasound waves propagating in the waveguide is selected to be larger than a thickness of the waveguide transverse to the direction of propagation. The nanostructures are imaged using the AFM tip to measure an effect at the top surface caused by direct or indirect interaction of the guided ultrasound waves with the buried nanostructures.

It will be appreciated that relatively thin, e.g. plate shaped structures such an integrated chips, or circuit layers inside the chip may typically have sufficiently small dimensions with respect to a wavelength of the ultrasound waves so that they may act as wave guides. By injecting the ultrasound waves from the side and using the substrate or sublayer as waveguides, the propagation of the waves can be accurately predicted, e.g. depending on a selected wave mode. For example, an injected wave may act as a moving sound source propagating from the side over a length of the sample. In some embodiments, ultrasound waves are injected in a limited time window. In other or further embodiments, ultrasound waves are injected continuously. In some embodiments, the ultrasound waves are reflected between side faces of the substrate. In such embodiments, the ultrasound waves may form standing waves in the substrate. In other embodiments, ultrasound waves may be absorbed or transmitted e.g. to a (block of) material, e.g. disposed at a side face of the substrate opposite the actuation side face.

Ultrasound waves in a MHz range may benefit from elasticity contrast while ultrasound waves in in a GHz range may benefit from scattering contrast or a combination of scattering and elasticity. In elasticity contrast regime (MHz frequencies) the substrate (chip) or the cantilever is typically actuated at ultrasound frequencies above the contact resonance of the cantilever. In scattering contrast regime (GHz frequencies) the substrate or the cantilever is typically actuated at ultrasound frequencies such that the acoustic wavelength is comparable/shorter than the critical dimensions of nanostructures in the sample.

In one embodiment, the ultrasound waves interact with the nanostructures by scattering, typically in a GHz frequency range between <NUM> - <NUM>, or higher. In another or further embodiment, the ultrasound waves interact with the nanostructures by elastic interaction, typically in a MHz frequency range between <NUM> - <NUM>, or lower.

In some embodiments, the ultrasound waves may traverse a region with the nanostructures to be imaged, i.e. the nanostructures are comprised in the substrate or sublayer forming the waveguide. For example, elastic interaction in the MHz range typically occurs in the whole substrate including a region with the nanostructures to be imaged. For example, scattering interaction in the GHz range may occur when the whole substrate acts as waveguide or with nanostructures comprised in a sublayer acting as waveguide.

In other or further embodiments, the nanostructures may be outside of a sublayer forming the waveguide and interact e.g. with secondary waves leaked from the sublayer forming the waveguide. For example, secondary waves can be emitted from the waveguide into the surrounding sample with a wave front at an angle with respect to a length of the waveguide, or as evanescent waves. The angle and/or character of the secondary waves may depend on the relative difference between the speed of sound outside the waveguide and the phase velocity inside the waveguide which can be tuned depending on the wave mode or frequency. In some embodiments, secondary waves are emitted and then propagate from bottom to top, i.e. the waveguide is below the nanostructures, and the secondary waves interact with the nanostructures by scattering transmission there through. In other or further embodiments, secondary waves are emitted and then propagate from top to bottom, i.e. the waveguide is above the nanostructures, and the secondary waves interact with the nanostructures by scattering reflection there off.

Claim <NUM> is about an AFM system for subsurface imaging of buried nanostructures.

The description of the exemplary embodiments is intended to be read in connection with the accompanying drawings, which are to be considered part of the entire written description.

<FIG> schematically illustrate an embodiment for subsurface imaging of nanostructures 10n buried inside a plate shaped substrate <NUM>.

In a preferred embodiment, an atomic force microscope <NUM> is provided with an AFM tip <NUM> disposed at a top surface 10a of the substrate <NUM> while at least one ultrasonic generator <NUM> is disposed at a side face 10b of the substrate <NUM>, i.e. transverse to the top surface 10a. The ultrasonic generator <NUM> directly or indirectly contacts the side face 10b with an actuating element, e.g. piezoelectric or electrostatic transducer.

Alternatively, the ultrasonic generator <NUM> couples to the side face 10b via a coupling medium 30c there between, e.g. water. Preferably, the coupling medium 30c comprises material such as wax that is able to transmit transversal vibration between the ultrasonic generator <NUM> and the side face 10b, e.g. vibrations in a direction "Z" parallel to the side face 10b and/or transverse to the top surface 10a.

The ultrasonic generator <NUM> is used to couple ultrasound waves "W" via the side face 10b into an interior of the substrate <NUM>. As described herein, the interior comprises or forms a waveguide <NUM> for propagating the ultrasound waves "W" in a direction "X" along a length of the substrate <NUM> or transverse to the side face 10b. When one dimension of an object in which elastic waves are generated is thin compared to the wavelength, guided waves can be generated. Accordingly, a (minimum) wavelength "λ" of at least one wave mode of the guided ultrasound waves "W" propagating in the waveguide <NUM> is larger than a thickness "d" of the waveguide <NUM> transverse to the direction of propagation "X". For example, the wavelength "λ" is larger than the thickness "d" by a factor of at least two, five, or ten.

According to the invention, the nanostructures 10n are imaged by using the AFM tip <NUM> to measure an effect "E" at the top surface 10a caused by direct or indirect interaction of the ultrasound waves "W", e.g. in a particular wave mode, with the buried nanostructures 10n. In one embodiment, the nanostructures 10n are imaged based on a vibrational characteristic of an AFM cantilever <NUM> comprising the AFM tip <NUM>. For example, the vibrational characteristic comprises one or more of a measured frequency "fe", amplitude "Ae" and/or phase "Φe" of the dynamic response of the vibrating AFM cantilever <NUM> at, or close to, contact resonance.

In some embodiments, the vibrational characteristic is compared to a reference value, e.g. based on an input value for driving an actuator of the system such as the ultrasonic generator <NUM>, an actuator of the AFM cantilever <NUM> and/or other actuators, e.g. actuating the bottom or other side surfaces of the substrate <NUM>, or actuating the tip. In a preferred embodiment, the effect "E" is measured as a function of an input parameter for driving the ultrasonic generator <NUM>, e.g. a comparative measurement with and without the ultrasound waves "W", or with ultrasound waves "W" having different input characteristics such as driving frequency "fw", amplitude "Aw" and/or phase "Φw" of the ultrasonic generator <NUM>.

In some embodiments, the measurement comprises lock-in amplification or selection of a measured signal as a function of an input parameter for generating the ultrasound waves "W". In one embodiment, the measurement comprises homodyne detection using the ultrasonic generator <NUM> to actuate the side face 10b with an input frequency "fw", and amplifying that frequency in an output signal measured via the vibrating AFM cantilever <NUM>. In another or further embodiment, the measurement comprises heterodyne detection using one or more ultrasonic generators to generate signals comprising two or more frequencies, wherein a difference frequency signal is amplified, e.g. corresponding to a contact resonance frequency of the AFM cantilever <NUM> with the tip <NUM> contacting the top surface 10a.

In one embodiment, the AFM tip <NUM> is scanned over different locations (X,Y) of the top surface 10a. In another or further embodiment, the subsurface nanostructures 10n are imaged based on a contrast of a measured signal, e.g. contrast between areas with and without buried nanostructures and/or nanostructures having different acoustoelastic properties such as different elastic modulus, speed of sound, etcetera.

Typically, the substrate or sublayer forming the waveguide <NUM> has a plate shape with a height that is lower than its length and/or width by a factor of at least ten, hundred, or even thousand. For example, the waveguide has a thickness "d" less than hundred micrometers, less than ten micrometers, or even less than one micrometer. For example, the substrate has a length and width more than one millimeter, typically several millimeters or centimeters for a chip, or up to three hundred or four hundred fifty millimeter, or more for a wafer. In case the waveguide <NUM> is formed by a sublayer of the substrate <NUM>, the sublayer preferably has different acoustic properties than the surrounding medium of the substrate. For example the waveguide <NUM> comprises or essentially consists of material having a different speed of sound (e.g. bulk or phase velocity) for the guided ultrasound waves W than that of the surrounding layers, e.g. a speed of sound that is different by at least ten percent, twenty percent, fifty percent, or more.

Typically the buried nanostructures 10n to be detected inside the substrate <NUM> may comprise elements, materials, and/or substructures (e.g. circuit parts) being acoustically or elastically distinguishable from the surrounding substrate medium and having typical dimensions e.g. between <NUM> - <NUM> nanometer, or between <NUM> - <NUM> nanometer. For example the nanostructures 10n comprise or essentially consist of material having a different speed of sound (bulk velocity) than the surrounding medium (waveguide or substrate), e.g. a speed that is different by at least ten percent, twenty percent, fifty percent, or more. The nanostructures may be buried below the top surface 10a with at least one sublayer of the substrate <NUM> there between, e.g. at depths below the top surface 10a of at least ten, twenty, fifty, hundred nanometers, or even deeper, e.g. up to several micrometers.

<FIG> schematically illustrate guided waves with different orientations of oscillation.

In a preferred embodiment, the ultrasound waves are shear or transverse guided waves having a main component of oscillation in a direction "Y" or "Z" transverse to their direction of propagation "X". Accordingly, the ultrasonic generator <NUM> is configured to actuate the side face of the substrate <NUM> in a direction along its surface, For example, the ultrasonic generator <NUM> is configured to expand and contract in a direction "Z" transverse to the top surface 10a. For example, the ultrasonic generator <NUM> comprises a piezo crystal powered by electrodes, wherein the crystal orientation dimensions, and placement of the electrodes are configured to have the crystal resonate in the direction "Z" for a given actuation frequency.

In the embodiment of <FIG>, the transverse guided waves oscillate in a direction "Z" transverse to the top surface 10a. This may be preferred for the atomic force microscope <NUM> to pick up vibrations "Vz" of the top surface 10a resulting from the transverse guided waves "Wz", e.g. by up- and-down, out-of-plane, movement the AFM cantilever.

In the embodiment of <FIG>, the transverse guided waves oscillate in a direction "Y" along the top surface 10a. For example, the atomic force microscope <NUM> is configured to pick up vibrations "Vy" along the top surface 10a resulting from the transverse guided waves "Wy", e.g. torsional or in-plane movement of the AFM cantilever. Alternatively, or additionally, in guided wave mode excitation, the actuator may vibrate laterally, but can also result in a normal displacement of the top surface 10a. Also in this mode, an AFM tip may thus indent in the substrate. How the normal displacement is coupled from the designated layer to the sample surface depends for example on the excitation frequency. Tuning of the frequency can be used to e.g. tune the angle of leakage (described in detail later with reference to <FIG>), and the normal component of indentation can be tuned accordingly.

In the embodiment of <FIG>, the ultrasound waves are compressional or longitudinal guided waves having a main component of oscillation in a direction "X" of propagation. In one embodiment, the atomic force microscope <NUM> is configured to pick up vibrations "Vx" along the top surface 10a resulting from the longitudinal guided waves "Wx", e.g. torsional or in-plane movement of the AFM cantilever. Also vibrations "Vz" and/or "Vy" may be present. In some embodiments, a length of the AFM cantilever extends in a direction transverse to the vibration of the transverse or longitudinal guided waves "Wx" or "Wy" having a main component of oscillation in a direction "X" or "Y" along the top surface 10a to pick up in-plane movement of the top surface 10a resulting in torsional vibration Vy,Vz of the cantilever.

<FIG> schematically illustrate embodiments for selectively coupling ultrasound waves in a specific sublayer forming a waveguide <NUM> inside the substrate <NUM>.

Preferably, the sublayer comprises distinct wave guiding properties compared to adjacent layers, e.g. the sublayer comprises a distinct material or combination of materials. Accordingly, the ultrasound waves "W" can propagate inside the waveguide <NUM> formed by the sublayer. In the embodiment shown, the ultrasonic generator <NUM> is configured to selectively inject the ultrasound waves "W" at a specific height H in a sublayer of the substrate <NUM>, wherein the sublayer forms the waveguide <NUM>.

The present embodiment may be compared to another embodiment wherein the waveguide <NUM> is formed by an entire thickness of the plate shaped substrate <NUM> (e.g. <FIG>). In such embodiment, the ultrasound waves "W" are coupled over an entire thickness of the substrate <NUM>. In some embodiments, the ultrasound waves "W" propagate inside a waveguide <NUM> formed by the entire substrate <NUM>, or multiple layers of the substrate (not shown).

In the embodiment of <FIG>, the ultrasonic generator <NUM> comprises a plurality of actuation elements arranged in a stacked formation to selectively actuate the side face of the substrate <NUM> at a selected one or more heights H. In another or further embodiment, the ultrasonic generator <NUM> is controlled by a plurality of controlled elements <NUM>, e.g. electrodes interposed between piezo elements as shown; or electrodes attached to a side face of a piezo element in stacked formation (not shown).

In the embodiment of <FIG>, the ultrasonic generator <NUM> comprises a single actuation element with a control element <NUM> configured to selectively control parts of the actuation element to actuate at a selected one or more heights H. For example, a different voltage "V" can be applied at by apodization of different heights of the generator <NUM>.

In some embodiments (not shown) the ultrasonic generator <NUM> is configured to generate ultrasound waves "W" in the waveguide <NUM> at two or more different wave modes, e.g. a first wave mode at a first frequency range and a second wave mode in a second frequency range. In one embodiment, a first guided wave is generated in a specific sublayer, e.g. in a GHz scattering domain, and a second guided wave is generated over the entire substrate, e.g. in a MHz elastic domain. In some embodiments, multiple wave modes are generated by a single ultrasonic generator, e.g. exciting the thickness mode or one of the lateral modes different resonance frequencies can be generated to vibrate the substrate. In other or further embodiments, a first generator is stacked between a second generator and the side face of the substrate <NUM>, wherein the first generator is configured to pass ultrasound waves "W" generated by the second generator to the side face of the substrate <NUM>. For example, the first generator is configured to inject a GHz wave in a particular sublayer of the substrate <NUM> while the second generator is configured to generate MHz waves for actuating the entire substrate.

In the embodiments of <FIG>, the nanostructures 10n to be imaged are comprised in a sublayer of the substrate <NUM> wherein the sublayer forms the waveguide <NUM>. For example, the substrate <NUM> comprises a plurality of layers with a designated layer comprising one or more nanostructures 10n to be imaged. In another or further embodiment, the sublayer comprises nanostructures 10n forming an alignment marker to be imaged for alignment of other layers. For example, in a three-dimensional chip structure, one or more circuit layers or other layers comprise respective alignment markers used for relative alignment of new layers. Alternative to imaging nanostructures 10n inside a waveguide <NUM>, also features outside the waveguide <NUM> can be imaged as will be discussed with reference to <FIG>. In some embodiments, the waveguide <NUM> is formed by a dedicated waveguide layer e.g. interposed between circuit layers.

<FIG> schematically illustrate embodiments for imaging nanostructures outside the waveguide <NUM> using secondary waves "W2".

In the embodiments shown, the nanostructures 10n to be imaged are arranged between the top surface 10a and a deeper laying waveguide <NUM> formed by a sublayer of the substrate <NUM>. For example, secondary waves "W2" emitted from the waveguide <NUM> and propagating towards the top surface 10a interact with the nanostructures 10n on the path there between. In another embodiment (not shown), the sublayer forming the waveguide <NUM> can be arranged between the top surface 10a and the nanostructures 10n beneath, e.g. wherein secondary waves "W2" reflect off the nanostructures 10n through the waveguide <NUM> back towards the top surface 10a.

In the embodiment of <FIG>, the phase velocity of waves in the waveguide <NUM> is higher than a speed of sound in the adjacent layers (bulk velocity of surrounding medium). This may lead to a situation wherein the ultrasound waves "W" traversing the waveguide <NUM> cause emission of leaky or secondary waves "W2" towards the top surface 10a. As shown, the secondary waves "W2" can be emitted at an angle "θw" with respect to a length of the waveguide <NUM>. For example, the angle "θw" can be calculated as being dependent on the relative difference between the phase velocity of the guided wave "W" in the waveguide <NUM> and the speed of sound in the adjacent medium (above or below the waveguide <NUM>).

As shown, the effect "E" of interaction by the secondary waves "W2" with the nanostructures 10n, sensed at the top surface 10a, can be displaced in a direction dXn along a propagation direction "X" of the ultrasound waves "W". For example, the displacement can be calculated from the angle "θw" of the secondary waves "W2" and a depth "dZn" of the nanostructures 10n below the top surface 10a. For example, the depth "dZn" of the nanostructures 10n is known or calculated, e.g. based on a time of arrival of the ultrasound waves "W" and/or secondary waves "W2".

Conversely, in the embodiment of <FIG>, the phase velocity of the waves "W" in the waveguide <NUM> is lower than a speed of sound in the adjacent layers. This may lead to a situation wherein the ultrasound waves "W" traversing the waveguide <NUM> cause emission of an evanescent secondary wave W2 e.g. wherein the angle of leakage is imaginary. Typically, the interaction of evanescent secondary wave W2 decreases exponentially away from the waveguide <NUM>. This may lead to a relatively short interaction range making it more suitable for detecting nanostructures 10n close to the waveguide <NUM>.

<FIG> schematically illustrates an embodiment for guided ultrasound waves in a waveguide <NUM> according to an asymmetric wave mode "Wa", also referred to as flexural wave mode. Flexural modes are non-axially symmetric bending modes. For example, in a plate the fundamental flexural mode F(<NUM>,<NUM>) is a pure bending mode at zero frequency.

<FIG> schematically illustrates an embodiment for guided ultrasound waves in a waveguide <NUM> according to a symmetric (with respect to a neutral plane) wave mode "Ws".

<FIG> schematically illustrates various neutral lines "Zn" that may particularly occur in symmetric wave modes "Ws". In some embodiments, one or more wave modes of the ultrasound waves comprises one or neutral lines or planes "Zn" in the waveguide <NUM> with minimal or no oscillation. In one embodiment, one or more depths are selectively not actuated at the neutral lines Zn of the wave mode, e.g. "Ws". In another or further embodiment, the wave mode is varied to select neutral lines at specific layers not being imaged. For example, the entire substrate <NUM> is actuated by a symmetric wave mode "Ws", e.g. in a MHz domain, wherein imaging comprises varying the interaction at different depths by selecting the neutral lines of the wave mode. In this way selective probing at particular depths can be effected even using MHz waves spanning the entire substrate height.

<FIG> schematically illustrates different wavelengths "λs" and "λa" depending on the wave mode "Ws" or "Wa", respectively at the same excitation frequency (f*) for the same sample. In some embodiments, the ultrasound waves "W" comprise multiple wave modes such as "Ws" and "Wa" at a particular actuation or measurement frequency "f*". The wave modes can act simultaneously on the AFM probe e.g. if the ultrasound generator is not designed to enhance one particular mode. In some embodiments, particular wave modes can be suppressed or enhanced e.g. by suitable actuation. In some embodiments, imaging of the subsurface nanostructures is adapted to be sensitive to a particular wave mode, e.g. at a distinct wavelength, wave velocity, or other characteristic.

<FIG> schematically illustrates an embodiment for an AFM probe with a tip width adjusted to a wavelength "λ" to be detected. <FIG> schematically illustrates another embodiment for an AFM probe with a multiple tips placed apart with a distance adjusted to a wavelength to be detected;.

In some embodiments, the AFM cantilever <NUM> comprises one or more AFM tips 21a,21b,21c contacting the substrate top surface 10a at one or more contact points spanning a distance across the top surface 10a, wherein the spanned distance along the propagation direction "X" of the ultrasound waves "W" equals an integer times a half wavelength "½ λ" of one of the wave modes at an actuation or measurement frequency "f*" of the AFM cantilever <NUM>. In other or further embodiments, one of the multiple wave modes is isolated (enhanced or suppressed) by taking a linear combination of measurements at multiple locations across the top surface 10a. For example, as shown with reference to <FIG>, two measurements are taken at a half wavelength distance "½ λs" of the symmetric wave mode "Ws". By adding the measurements, the symmetric wave mode "Ws" may cancel while another wave mode having another wavelength at the same frequency "f*", e.g. the asymmetric wave mode Wa does not cancel and may even be amplified, e.g. when the distance equals the wavelength "λa" of the asymmetric wave mode Wa.

<FIG> schematically shows an embodiment of an AFM system <NUM> comprising an ultrasonic generator <NUM> configured to generate guided ultrasound waves (W) via a side face 10b of a substrate <NUM>.

In one embodiment, the system <NUM> comprises a substrate holder <NUM> configured to hold a plate shaped substrate <NUM> with the nanostructures 10n to be imaged. In another or further embodiment, the system comprises an AFM tip <NUM> configured to scan a top surface 10a of the substrate <NUM>. Typically the AFM tip <NUM> and/or substrate holder <NUM> are configured for relative movement to scan the substrate <NUM>.

An ultrasonic generator <NUM> is configured to couple ultrasound waves "W" via a side face 10b of the substrate <NUM> into an interior of the substrate <NUM>. The interior comprises or forms a waveguide <NUM> for propagating the ultrasound waves "W" in a direction "X" along a length of the substrate <NUM> transverse to the side face 10b. The ultrasonic generator <NUM> is configured to actuate the side face 10b with a frequency corresponding to a wavelength "λ" of the ultrasound waves "W" propagating in the waveguide <NUM> that larger than a thickness "d" of the waveguide <NUM> transverse to the direction of propagation "X".

In the embodiment shown, the system <NUM> comprises a sensor system configured to image the nanostructures 10n by using the AFM tip <NUM> and/or cantilever <NUM> to measure an effect "E" at the top surface 10a caused by direct or indirect interaction of the ultrasound waves "W" with the buried nanostructures 10n. In some embodiments, an element <NUM> is placed on an opposite side of the substrate <NUM> with respect to the ultrasonic generator <NUM> to block the substrate such that waves can be more efficiently coupled in the medium. For example, the substrate <NUM> is pressed against the ultrasonic generator <NUM>, e.g. by a pressing tool <NUM>.

In the shown embodiment of the AFM, a probe is attached to a scan head <NUM>. The scan head <NUM> enables scanning of the probe relative to a top surface 10a of substrate <NUM>. The probe consists of a cantilever <NUM> and a probe tip <NUM>. During scanning, the probe tip <NUM> is brought in contact with the top surface 10a of the substrate <NUM>. For example the probe tip <NUM> may be scanned across the surface of the substrate <NUM> in contact mode (continuous contact between the probe tip <NUM> and the surface of the substrate <NUM>) or tapping mode (periodic contact between the probe tip <NUM> and the surface of the substrate <NUM> during each cycle of a vibration applied to the cantilever <NUM>).

According to the invention, the AFM is configured to measure subsurface nanostructures 10n below the top surface 10a. In one embodiment, the AFM tip <NUM> is brought in contact with an area under investigation. In another or further embodiment, a subsurface parameter Sn is calculated based on measurement of a contact stiffness Kc of the atomic force microscope AFM at the exposure area 1a. Typically, ultrasound waves "W" in the substrate <NUM> may be coupled via the AFM tip <NUM> to the AFM cantilever <NUM> causing vibration of the AFM cantilever <NUM>. For example, a vibrational amplitude "Ae" of the AFM cantilever <NUM> may depend on a contact stiffness Kc of the AFM tip <NUM> contacting the substrate <NUM>. Contact stiffness Kc may be quantified e.g. as the combined stiffness of the tip contacting the substrate, e.g. derivate of a force experienced by the tip as a function of displacement of the tip. It will be appreciated that the contact stiffness Kc may depend on material properties of the nanostructures (10n) below the substrate surface 10a. In turn, the contact stiffness may determine vibrational modes in the AFM cantilever <NUM>.

In some embodiments a contact resonance frequency "fcr" of the AFM cantilever <NUM> may depend on the contact stiffness Kc. Accordingly, a contact resonance frequency "fcr" of the AFM cantilever <NUM> while the AFM tip <NUM> contacts the substrate <NUM> can be a measure for the effect "E" of the interaction between the ultrasound waves "W" with the nanostructures 10n below the top surface 10a. The contact resonance frequency "fcr" may be probed e.g. by including a modulation frequency "fm" in the ultrasound waves "W" through the substrate <NUM>. Alternatively, or in addition, ultrasound waves may be generated at the tip (not shown), or both at the tip and the sample simultaneously (not shown). For example, the ultrasound waves "W" can be modulated by a modulation frequency "fm" near a contact resonance frequency "fcr" of the AFM. The closer the modulation frequency "fm" is to the contact resonance frequency "fcr", the higher the amplitude "A" of the resulting vibration in the AFM cantilever <NUM> at that frequency. Accordingly, in some embodiments, the imaging of subsurface nanostructures 10n may be based on a measurement of a vibrational amplitude "Ae" of the AFM cantilever <NUM>. Also other parameters such as the frequency "fe" and/or phase of the cantilever vibration can be used as measure for the nanostructures 10n.

In addition to the modulation frequency "fm", the ultrasound waves "W" may comprise other signal components, e.g. a carrier frequency "fc". For example, the carrier frequency "fc" can be a relatively high frequency determining scattering interaction with the nanostructures 10n while the modulation frequency "fm" is at a relatively low frequency near a contact resonance frequency of the cantilever. For example, the carrier frequency "fc" is between <NUM> and <NUM>. For example, the modulation frequency "fm" is lower than the carrier frequency "fc", e.g. by a factor of at least ten, e.g. between <NUM> and <NUM>. Of course also other frequencies, e.g. for heterodyne detection, can be envisaged depending on the particulars of the system under investigation and/or intrinsic properties of the cantilever.

Preferably, the ultrasound waves "W" comprise a wavelength in the waveguide which is higher than its thickness. In case of multiple frequencies, it is preferred that the wavelength corresponding to the highest frequency is still relatively long compared to the waveguide thickness so that the waves act as guided waves. For example, in an acoustic wave at a frequency of <NUM> (<NUM><NUM> s-<NUM>) and velocity of <NUM>/s, the expected wavelength is <NUM> (<NUM><NUM>/<NUM><NUM>=<NUM>-<NUM> m = <NUM> ). Accordingly the waveguide in such cases preferably has a thickness of a fraction of one micrometer. For example, a substrate such as a chip or a substrate layer such as a circuit layer has a thickness of less than one micrometer. The thickness can be higher for lower frequencies, e.g. in a MHz range below <NUM> or for higher wave velocities. For example in a waveguide structure formed by a silicon layer, the speed of sound can be between <NUM> - <NUM>/s depending on the wave mode (longitudinal, transversal, extensional). Accordingly, one or more silicon circuit layers with a (combined) thickness up to <NUM> could be used as waveguide for a wave at a frequency up to <NUM> - <NUM>.

Ultrasonic force microscopy may for example be performed by applying an ultrasonic signal to side face of the substrate and modulating the ultrasonic wave with a modulation frequency "fm" of approximately the cantilever resonance frequency. By sensing the output signal at the modulation frequency and analyzing the amplitude and/or phase, subsurface structures can be imaged. Without being bound by theory, this may be explained by the fact that the high frequency (fc) ultrasonic signal may be perturbed by the subsurface structures. Information on the subsurface structures is conveyed via these perturbations and becomes measurable in the deflection of the probe tip, i.e. the output sensor signal at or near the cantilever resonance frequency.

In the embodiment shown, a signal generation and analysis system <NUM> is used to generate and extract signals. A first signal generator <NUM> provides a first signal at the carrier frequency "fc". A second signal generator <NUM> provides a second signal at the modulation frequency "fm". The frequencies may serve as input for a mixer <NUM> which generates mixed signals e.g. providing three frequency components: the carrier frequency fc, the carrier frequency fc lowered by the modulation frequency "fm" to obtain a frequency component fc-fm, and the carrier frequency fc increased by the modulation frequency "fm" to obtain a frequency component fc+fm. For example, offering these frequency component signals in a favorable signal component ratio (e.g. fc : (fc-fm) : (fc+fm) = <NUM> : <NUM> : <NUM>) may yields an amplitude modulated wave having a frequency "fc" wherein the amplitude modulates at a frequency "fm".

In the embodiment shown, a single ultrasonic generator <NUM> (transducer) is shown to generate ultrasound waves "W" at a particular set of frequencies. Alternatively, or in addition, multiple ultrasonic generators (not shown) can be used in homodyne or heterodyne configuration. For example an additional frequency may be applied directly to the AFM probe, e.g. by a modulated laser beam L or otherwise. Furthermore, signals may be generated at alternative or additional frequencies than shown or only at a single (modulation) frequency. In some embodiments, the signals may be amplified in a power amplifier (not shown) before being provided to the generator <NUM>. In the shown embodiment, a coupling medium 30c (e.g. wax) is used to provide for acoustic coupling between the generator <NUM> and the substrate <NUM>. In alternative embodiments this may be omitted.

In the embodiment shown, the laser <NUM> sends a light beam "L" at a position on the AFM cantilever <NUM>. Vibrational movement of the AFM cantilever <NUM> causes deflection of the reflected beam which is measure by sensor <NUM> which is sensitive to the position of the impinging beam, e.g. a quadrant detector. The sensor <NUM> results in a measurement signal Se.

In one process path, high frequency components of the signal Se are extracted by a high pass filter <NUM> to the analysis system <NUM>. In particular, the passed signal comprises a frequency component with a certain amplitude "A" at the modulation frequency "fm". The amplitude "A" may be retrieved e.g. by a demodulator <NUM> using the original modulation frequency "fm" as reference. For example, the demodulator <NUM> may comprise a lock-in amplifier. The amplitude "A" may be processed by a processor <NUM> to calculate the contact stiffness Kc. The contact stiffness may be used by processor <NUM> to calculate subsurface parameter Sn for imaging the nanostructures 10n. Of course the processors <NUM> and <NUM> may also be integrated. Alternatively, or in addition, the step of calculating the contact stiffness Kc may omitted and the subsurface parameter Sn directly calculated from the vibrational amplitude "Ae" or any other measured characteristics such as fe and Φe. Alternatively, or in addition, the contact stiffness Kc may be directly equated to the subsurface parameter Sn.

In another process path, low frequency components of the signal Se are extracted by a low pass filter <NUM> as a measure of a distance or height "Z" between the AFM tip <NUM> over the substrate surface 10a. The measured distance may be fed into a comparator <NUM> together with a desired distance "Z0", e.g. corresponding to a desired average force/deflection of the probe. The output signal of the comparator may be used to control a height of the scan head <NUM> to which the probe is attached.

While the present embodiment shows ultrasound waves being applied via the substrate, ultrasound AFM can be additionally done via tip, e.g. by optional transducer <NUM>. Accordingly, various embodiments can be envisaged such as heterodyne force microscopy, atomic force acoustic microscopy, waveguide ultrasonic force microscopy, force modulation microscopy. The ultrasonic generator <NUM> contacts the side face 10b of the substrate <NUM> directly, or indirectly via a coupling medium 30c. The generator comprises an electro-acoustic transducer, e.g. based on piezo transducers, electrostatic actuation etc. In some embodiments, additional ultrasound in the AFM cantilever <NUM> can be generated in various ways such as using piezo transducers, electrostatic actuation, photo thermal actuation via the light beam "L", etc..

In the embodiment shown, a laser source <NUM> provides a laser beam L that impinges on the cantilever <NUM> and reflects towards an optical detector <NUM>. Using the optical detector <NUM>, vibrations in the cantilever <NUM> can be sensed due to small deflections of the reflected beam L under influence of such vibrations. This provides an output signal Se for further analysis, e.g. by a processor to calculate an image of subsurface nanostructures 10n. In some embodiments, the processor may comprise a memory to store previous measurements or reference values for comparison.

Alternative or in addition to measuring beam deflection also other ways may be envisaged for measuring the cantilever deflection and/or vibration frequency/amplitude. Alternative sensing techniques for example include the application of a piezo-resistive layer, the electrical resistance of which vary with probe deflection. Probe deflection may in that case be detected by detecting voltage differences in an electric signal applied to the piezo-resistive layer. As another alternative, probe deflection may be detected using a piezo-electric element or layer, the potential of which changes dependent on cantilever motion. Alternatively, capacitive measurements may be applied in an electrostatic sensing technique. As some further alternatives, one may also apply an interferometer to measure probe deflection or perform a heat flux measurement in a thermal method by using a temperature difference between probe and substrate. The skilled person will be familiar with such techniques and is able to apply them in embodiments of the present disclosure.

<FIG> schematically shows curves indicative of a vibrational amplitude "A" depending on a proximity between the modulation frequency "fm" and the contact resonance frequency "fcr".

As shown, the modulation frequency "fm" near the contact resonance frequency "fcr" causes an amplitude increased of the AFM cantilever vibrations. For example the amplitude may increase by a factor of two or more compared to an off-resonant vibration of the AFM cantilever. In one embodiment, a position of the contact resonance frequency shifts depending whether the AFM tip contacts an area affected by interaction of the ultrasound waves with a buried nanostructures ("fcr,on") or an areas of the substrate without nanostructures ("fcr,off"). As shown in the bottom curve, at certain modulation frequencies, such shifting of the contact resonance frequency "fcr" causes an amplitude difference "dA" of the (cantilever) vibrations caused by the ultrasound waves between the areas with and without buried nanostructures. Alternatively, or in addition to shifting, an overall amplitude of the curve may increase or decrease (not shown here) depending on the presence or absence of buried nanostructures. In one embodiment, the amplitude difference "dA" is used for calculating an image of the subsurface nanostructures. Alternative, or in addition to a change in amplitude "dA", also other changes can be used as parameter for subsurface imaging, e.g. a phase and/or frequency shift (not shown).

Claim 1:
A method for subsurface imaging of nanostructures (10n) buried inside a three dimensional substrate (<NUM>), the method comprising
- providing an atomic force microscope (<NUM>) with an AFM tip (<NUM>) continuously or periodically contacting a top surface (10a) of the substrate (<NUM>);
- providing an ultrasonic generator (<NUM>) comprising an actuating element directly or indirectly contacting a side face (10b) of the substrate (<NUM>), transverse to the top surface (10a), wherein the actuating element comprises an electro-acoustic transducer, or the ultrasonic generator (<NUM>) couples to the side face (10b) via a coupling medium (30c) there between;
- using the ultrasonic generator (<NUM>) to couple ultrasound waves (W) via the side face (10b) into an interior of the substrate (<NUM>), wherein the interior comprises or forms a waveguide (<NUM>) for propagating the ultrasound waves (W) in a direction (X) along a length of the substrate (<NUM>) transverse to the side face (10b), wherein a wavelength (λ) of the ultrasound waves (W) propagating in the waveguide (<NUM>) is larger than a thickness (d) of the waveguide (<NUM>) transverse to the direction of propagation (X); and
- imaging the nanostructures (10n) by using the AFM tip (<NUM>) to measure an effect (E) at the top surface (10a) caused by direct or indirect interaction of the ultrasound waves (W) with the buried nanostructures (10n).