WO2007040488A1 - Microscope probe for investigation of semiconductor structures - Google Patents
Microscope probe for investigation of semiconductor structures Download PDFInfo
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- WO2007040488A1 WO2007040488A1 PCT/US2005/034127 US2005034127W WO2007040488A1 WO 2007040488 A1 WO2007040488 A1 WO 2007040488A1 US 2005034127 W US2005034127 W US 2005034127W WO 2007040488 A1 WO2007040488 A1 WO 2007040488A1
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- 239000000523 sample Substances 0.000 title claims description 21
- 238000011835 investigation Methods 0.000 title abstract description 3
- 239000004065 semiconductor Substances 0.000 title description 4
- 238000001069 Raman spectroscopy Methods 0.000 claims abstract description 21
- 230000003287 optical effect Effects 0.000 claims abstract description 21
- 230000005855 radiation Effects 0.000 claims abstract description 16
- 230000010287 polarization Effects 0.000 claims description 16
- 230000005284 excitation Effects 0.000 claims description 7
- 238000003841 Raman measurement Methods 0.000 claims description 5
- 239000000463 material Substances 0.000 claims description 4
- 238000000034 method Methods 0.000 claims description 4
- 230000003595 spectral effect Effects 0.000 claims description 4
- 230000000903 blocking effect Effects 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 claims description 3
- 229910003460 diamond Inorganic materials 0.000 claims description 2
- 239000010432 diamond Substances 0.000 claims description 2
- 238000001228 spectrum Methods 0.000 claims 2
- 238000001237 Raman spectrum Methods 0.000 claims 1
- 238000004891 communication Methods 0.000 claims 1
- 238000012937 correction Methods 0.000 claims 1
- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 abstract description 9
- 229910052710 silicon Inorganic materials 0.000 abstract description 9
- 239000010703 silicon Substances 0.000 abstract description 9
- 235000012431 wafers Nutrition 0.000 abstract 1
- 239000013598 vector Substances 0.000 description 10
- 238000005259 measurement Methods 0.000 description 8
- 239000013078 crystal Substances 0.000 description 7
- 238000002474 experimental method Methods 0.000 description 7
- 239000011159 matrix material Substances 0.000 description 6
- 238000012886 linear function Methods 0.000 description 2
- 230000001902 propagating effect Effects 0.000 description 2
- 230000005483 Hooke's law Effects 0.000 description 1
- 229910021419 crystalline silicon Inorganic materials 0.000 description 1
- 238000000295 emission spectrum Methods 0.000 description 1
- 238000005286 illumination Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000005624 perturbation theories Effects 0.000 description 1
- 238000012827 research and development Methods 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/62—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light
- G01N21/63—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light optically excited
- G01N21/65—Raman scattering
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/02—Details
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/02—Details
- G01J3/0205—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows
- G01J3/021—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows using plane or convex mirrors, parallel phase plates, or particular reflectors
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/02—Details
- G01J3/0205—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows
- G01J3/0229—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows using masks, aperture plates, spatial light modulators or spatial filters, e.g. reflective filters
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/28—Investigating the spectrum
- G01J3/44—Raman spectrometry; Scattering spectrometry ; Fluorescence spectrometry
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
- G01L5/0047—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes measuring forces due to residual stresses
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/62—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light
- G01N21/63—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light optically excited
- G01N21/65—Raman scattering
- G01N2021/653—Coherent methods [CARS]
- G01N2021/656—Raman microprobe
Definitions
- Loechelt et al. [2] demonstrate that by conducting an experiment in an off axis
- the present device and method of using this invention allows convenient measurement of off-axis Raman emissions without the need to realign the excitation and collection optics, and without the need to rotate the wafer during measurement (as it is described by Lomül [1,2]).
- the present invention is compact and easy to implement in an industrial metrology tool.
- Figure 1 depicts the geometry of a typical Raman measurement.
- Figure 2 depicts the geometry of a beam focused on a wafer by means of a microscope
- Figure 3 depicts a definition of the angle coordinates ⁇ and ⁇ defining collection
- Figure 4 depicts a device for the control of an incidence angle.
- Figure 5 depicts a device for control of both incidence and collection angles.
- Figure 6 depicts a device for the fine control of the position of an excitation spot.
- FIG. 1 we present an experimental arrangement usually used for off-axis Raman measurements.
- a laser 1 is emitting a laser beam which is filtered by a spectral filter 2, polarization of the beam merging from spectral filter 2 is rotated by a half wave plate 3, ellipticity of the polarization state of the beam is controlled subsequently by a quarter wave plate 4.
- the radiation emerging from the quarter wave plate 4 is focused using an optional focusing lens 400 impinging a silicon wafer 5 and is collected by a collection lens 6, and filtered by a spectral filter 60.
- the polarization state of the beam is analyzed by combination of quarter- wave plate 7 and polarizer 8. Subsequently beam is spectrally analyzed by spectrometer 9 and detected by array detector 10.
- Apertures 301,302 can be mounted on motorized filter wheels, such as described in Thorlabs catalog [7], or other suitable moving stages allowing their easy automated positioning of said apertures.
- the polarization state of the incident and emitted radiation can be controlled and analyzed by standard optical tools such as polarizers, quarter- wave and half- wave plates mounted on suitable rotational stages.
- Loechelt et al [1, 2] teaches that by measuring Raman emission from silicon wafer oriented in 100 a crystallographic direction at various incidence angles with respect to crystallographic orientation of the wafer and at various polarization angles, one can establish all six independent components of stress tensor of the material. Loechelt et al [1, 2]
- Loecht et al [1,2] define a procedure in which they specify which combination of incidence, emission angles and polarization states for incidence and emission angle should be used in order to accurately measure all the components of stress tensor.
- TOl, TO2 , and LO denote phonon modes polarized in the [100],
- Ik is the intensity from the Mh phonon mode (TOl, TO2, or LO)
- ⁇ is a constant related to the Raman scattering cross section
- p' is the polarization vector of the scattered light
- Ok is one of the polarizability tensors given above
- p is the polarization vector of the incident light inside the sample
- /o is the intensity of the incident light
- T denotes transposed vector.
- the signal line shape ⁇ * for a given phonon mode with a frequency of vfc is given by a Lorentzian function of the form [2]:
- Equation 3 where ⁇ is the difference in frequency between the incident and scattered light (Raman frequency), and T is the half width at half maximum of the signal.
- the total signal line shape ⁇ ( ⁇ ) is the sum of the signals from the three contributing phonon modes,
- the Raman polarizability tensors are the derivatives of the system's electronic polarizability relative to the phonon normal coordinates, and the normal coordinates under stress are linear combinations of the normal coordinates for the unstressed material, as is apparent from Eq. (5), the Raman polarizability tensors for the perturbed phonons can be easily written as linear combinations of the tensors, in the first order approximation in Eq. (1) as
- Equation 7 In the preceding equations, ⁇ ( ⁇ ) is a 3x3 secular matrix whose components are linear functions of the strain tensor ⁇ e, which is ultimately related to the stress tensor ⁇ through the compliance tensor s.
- the parameters p, q, and r are deformation potential constants [2].
- s For crystalline silicon, s has only three different components.
- (d k )z represents the /th component of the Mh normalized eigenvector. The approximations in Eq. (6) are valid since CD ⁇ are close to ⁇ 0 .”
- the four angle combination ( ⁇ , ⁇ , a, ⁇ ) describe configuration of off- axis Raman measurement,
- the calculation of model vector parameter x is performed by means of fitting predicted line shapes given by equation 4 to experimentally observed line shapes for every experiment j. This is accomplished by minimizing parameter ⁇ 2 as a function of of its arguments (x, and ⁇ ):
- ⁇ t is frequency at which observation is performed and corresponds to one point of
- n points comprising Raman emission spectrum.
- the steering mirror angle is controlled by piezo-electric actuators (for example, a mirror mounted on a mirror mount KC-IPZ [8]). Since the focal length of the typical microscope objective described above is of the order of 1-3 mm, and resolution of this mirror mount is 6 arc sec, this arrangement permits positioning the center of the optical beam with a resolution of the order of 20 nm. It is possible to construct a mirror stage having a resolution one order of magnitude higher and achieve control of the position of the center of the optical beam with a resolution of the order of 20 nm. This allows us to further enhance the spatial resolution of our optical system. Resolution is achieved by modulation of the position of center of the optical beam, which can be at least an order of magnitude higher than the waist of the beam.
Abstract
A device (300-302) is described allowing simultaneous control of angles at which an optical beam is impinging a sample (5) and at which radiation emitted by the sample (5) is collected. The device (300-302) can be applied in the field of Raman spectroscopy for investigation, which can be used to identify tensor components of stress in silicon wafers. An embodiment of the invention allows scanning optical beams on the sample surface with 80 nanometer and below resolutions.
Description
MICROSCOPE PROBE FOR INVESTIGATION OF SEMICONDUCTOR STRUCTURES
BACKGROUND OF THE INVENTION
The selection rules used in Raman spectroscopy of semiconductor structures often require control of the angle at which an optical beam and control of the angle at which Raman emission is collected. Often certain resonances are manifested only at particular incidence and collection angle combinations. In research and development laboratory environments this is often accomplished using separate optics for control of excitation and collecting emitted radiation [I].
In a commercially important case of Raman spectroscopy of a silicon surface [100], commonly used backscattering geometry allows observation of only one longitudinal optical (LO) phonon [I]. Bonera et al. [3], [4] notice that by using a high numerical aperture, one can break the selection rules for pure backscattering geometry and one can excite vibration modes forbidden in pure backscattering geometry, and observe the presence and characteristics of other phonons. Furthermore, they discuss angular distribution and application of the polarization control to analyze and determine independently, up to three components of out of six independent strain components in silicon. Bonera et al. [3], [4] points out that the exact values of measured stress tensor components depend upon model assumptions (in particular depend on assumed vanishing elements of the stress tensor).
Loechelt et al. [2] demonstrate that by conducting an experiment in an off axis
configuration and by controlling the incident angle and polarization state of the incident
and collected radiation, it is possible to determine all six independent components of a stress tensor for [100] ([100] crystallographic direction) cut surface of silicon. These types of arrangements are quite complicated and difficult to implement in a commercial tool. Furthermore, this type of lateral resolution of a spectroscopic system deteriorates, and cannot be implemented in a micro - Raman tool [3, 4].
In this disclosure we describe a novel optical probe allowing wide control of the incidence and collection angles of the excitation beam and Raman emission respectively, while preserving relatively high spatial resolutions.
Furthermore, we describe modifications of this probe allowing measurements and imaging of the features significantly smaller than the spot size of the excitation beam on the sample surface.
The present device and method of using this invention allows convenient measurement of off-axis Raman emissions without the need to realign the excitation and collection optics, and without the need to rotate the wafer during measurement (as it is described by Loechtel [1,2]). The present invention is compact and easy to implement in an industrial metrology tool.
Brief description of drawings
Figure 1 depicts the geometry of a typical Raman measurement.
Figure 2 depicts the geometry of a beam focused on a wafer by means of a microscope
objective.
Figure 3 depicts a definition of the angle coordinates α and θ defining collection and
incidence angles. Figure 4 depicts a device for the control of an incidence angle.
Figure 5 depicts a device for control of both incidence and collection angles. Figure 6 depicts a device for the fine control of the position of an excitation spot.
DETAILED DESCRIPTION OF THE INVENTION
In Figure 1 we present an experimental arrangement usually used for off-axis Raman measurements. A laser 1 is emitting a laser beam which is filtered by a spectral filter 2, polarization of the beam merging from spectral filter 2 is rotated by a half wave plate 3, ellipticity of the polarization state of the beam is controlled subsequently by a quarter wave plate 4. The radiation emerging from the quarter wave plate 4 is focused using an optional focusing lens 400 impinging a silicon wafer 5 and is collected by a collection lens 6, and filtered by a spectral filter 60. The polarization state of the beam is analyzed by combination of quarter- wave plate 7 and polarizer 8. Subsequently beam is spectrally analyzed by spectrometer 9 and detected by array detector 10.
Similar experimental arrangement was used by Loechelt et al their work [1,2]. In their work, Loechelt et. al., [1,2] were using an incidence angle approximately equal to 60 degrees. We propose using a device, based upon a microscope objective, to reproduce the off axis geometry. Let us consider a microscope objective (focusing lens) 200 presented in Figure 2 focusing laser beam on wafer 5 by means of microscope objective 200. The angle between the marginal ray 201 and the chief ray 202 defines the Numerical Aperture (NA) of the system. All rays emerging from the microscope objective 200 are
propagating inside a cone defined by the angle between the marginal ray and the chief ray.
The angle between the chief ray 202 and the marginal ray 201, in case of typical commercial 6OX microscope objective, is often in the range of 58 - 71 degrees (which corresponds to NA = 0.85 - 0.95) [5, 6]. This angle is essentially the same as the incidence angle of 60 degrees used by Loechelt et al [1, 2].
It is straightforward that one can define the angular coordinates α and θ of rays
propagating from a focal point of a microscope objective 200 by introducing suitable a aperture restricting the spherical angle as shown in Figure 3. Every ray collected by the objective 200 and emerging from a focal point of the objective can be described by a pair
of angles α and θ.
As presented in Figure 3, it is possible to select a portion of the spherical angle within the cone, defined by marginal rays, which will correspond to the same or essentially the same geometry of measurement as that described in [2]. This can be accomplished by means of a suitable aperture partially blocking a potion of the incident radiation as described in Figure 4. As seen in Figure 4, the aperture 210 partially blocks the incident beam 501 so only portion of the beam within the well defined spatial position
is impinging lens 200 and is focused at well defined angles α and θ on the sample 5.
It is straightforward to extend this idea to the geometry encountered in a typical micro Raman experiment, where the exciting laser beam and the Raman emission are passing through the same beam splitter as presented in Figure 5. As shown in Figure 5, the incident beam 501 is partially blocked by aperture 301 and directed by beam-splitter
300 to microscope objective 200 and focused at incident angle defined by the aperture
301 on sample 5. The sample emits radiation, which is collected by a microscope objective 200, passes through the beam-splitter 300 and is partially blocked by the aperture 302. The radiation transmitted through the aperture 302 was emitted by the sample 5 at an emission angle defined by the opening in the aperture 302.
It is important to notice that in this case, by choosing suitable apertures 301,302, we can fully reproduce all the geometries of all measurements necessary to calculate all six independent components of stress tensor described in [2], Apertures 301,302 can be mounted on motorized filter wheels, such as described in Thorlabs catalog [7], or other suitable moving stages allowing their easy automated positioning of said apertures. Furthermore the polarization state of the incident and emitted radiation can be controlled and analyzed by standard optical tools such as polarizers, quarter- wave and half- wave plates mounted on suitable rotational stages.
Loechelt et al [1, 2] teaches that by measuring Raman emission from silicon wafer oriented in 100 a crystallographic direction at various incidence angles with respect to crystallographic orientation of the wafer and at various polarization angles, one can establish all six independent components of stress tensor of the material. Loechelt et al [1,
2] provides an explicit prescription for the stress tensor calculation.
It is straightforward to anyone skilled in the arts that the results presented by Loechelt et al [1, 2] can be generalized to any material possessing the same (diamond) crystal structure.
Loecht et al [1,2] define a procedure in which they specify which combination of incidence, emission angles and polarization states for incidence and emission angle should be used in order to accurately measure all the components of stress tensor. Here are the main findings presented in the Loechelt [2] patent:
"In a diamond-structure semiconductor like silicon, there are three Raman-active optical phonon modes: two transverse optical (TO) phonon modes (TOl and TO2) and one longitudinal optical (LO) phonon mode. Because unstrained silicon has cubic
symmetry, these three phonons are degenerate in frequency at k = 0 Non-hydrostatic crystal strain destroys this symmetry and lifts the degeneracy The splitting in phonon frequencies and the mixing of the phonon modes contain complete information about the stress that destroyed the symmetry However, if only one of these three phonons is observed, as in conventional backscattering Raman spectroscopy, only partial information can be obtained about the stress
The intensity of a phonon mode for a given scattering geometry can be determined by examining the Raman polarizability tensors For phonons with a wave number of k=0 appropriate for Raman scattering, one can choose the polarizations of the three degenerate optical phonons to be any set of three mutually perpendicular vectors If the three cubic axes are chosen, the Raman polarizability tensors are given by [2]
0 0 0
IO — Λ* = 0 0 d G A' C
Equation 1
In this notation, TOl, TO2 , and LO denote phonon modes polarized in the [100],
[010], and [001] directions, respectively, and d represents a nonzero number This particular choice of phonon basis and nomenclature is useful for interpreting the results of backscattering experiments from a [001] crystal surface
The Raman polarizability tensors determine the intensity of the scattered light from the sample according to
/fc=S|p'rΔ*p|2/», Equation 2
where Ik is the intensity from the Mh phonon mode (TOl, TO2, or LO), Ξ is a constant related to the Raman scattering cross section, p' is the polarization vector of the scattered light, Ok is one of the polarizability tensors given above, p is the polarization vector of the incident light inside the sample, /o is the intensity of the incident light, and the superscript T denotes transposed vector. The signal line shape Λ* for a given phonon mode with a frequency of vfc is given by a Lorentzian function of the form [2]:
Equation 3 where ω is the difference in frequency between the incident and scattered light (Raman frequency), and T is the half width at half maximum of the signal. The total signal line shape Λ(ω) is the sum of the signals from the three contributing phonon modes,
k- l
Equation 4
For unstrained silicon, all three phonon modes are degenerate with a frequency of ωk= ω0 = 520.3 cm) at room temperature (22 0C).
In the presence of strain τ the phonon frequencies Ok shift from their unstrained value α>o. Using degenerate perturbation theory, the new phonon frequencies and polarizations follow from the eigenvalues and eigenvectors of the following secular matrix. [2]
P €γ i + q{ €-i-i + €y. ' 2 ff^ 2ren <
Equation 5
These eigen values and eigenvectors are related to the shifted phonon frequencies α>k in the following fashion:
"" ' δ Equation 6
Since the Raman tensors are the derivatives of the system's electronic polarizability relative to the phonon normal coordinates, and the normal coordinates under stress are linear combinations of the normal coordinates for the unstressed material, as is apparent from Eq. (5), the Raman polarizability tensors for the perturbed phonons can be easily written as linear combinations of the tensors, in the first order approximation in Eq. (1) as
[2]
Equation 7
In the preceding equations, Ψ(τ) is a 3x3 secular matrix whose components are linear functions of the strain tensor ε e, which is ultimately related to the stress tensor σ through the compliance tensor s. The parameters p, q, and r are deformation potential constants [2]. The strain tensor ε is related to the stress tensor σ by Hooke's law, which states that ε = s σ. For crystalline silicon, s has only three different components. Also, (dk)z represents the /th component of the Mh normalized eigenvector. The approximations in Eq. (6) are valid since CD^ are close to ω0."
Further, it has been demonstrated by Loechtel in [2] that the incident light is tilted away from the normal axis, the scattered light is collected normally, and both beams are polarized. By allowing the incident light to deviate from normal incidence, all three active optical phonon modes are accessible for measurement. Furthermore, the polarizers enable the experimenter to vary the relative contribution of these three modes to the measured signal intensity. This combination of off-axis illumination with polarization is more powerful and general than polarized backscattering methods, which can only determine the in-plane stress components for special crystal orientations. If one judiciously selects the various angles of the apparatus, a given phonon mode can be selectively studied. By analyzing the results of several selective measurements, all six components of the stress tensor can be determined.
As it is shown in [2] further simplification can be achieved by efficiently relating
the secular matrix to the components of the stress tensor σ. First, the symmetry of Ψ( σ) implies that there are only six independent components and said matrix has form
j
Equation 8
where vector ψ is given by ψ = I7sσ Equation 9 where π is a matrix of deformation potential constants s in compliance matrix, and σ is a stress tensor expressed in six component vector form convention. In a linear model stress σ is given as a linear form with vector of adjustable parameters (model parameters) x. σ - Tx Equation 10
From Eq. 9 and Eq. 10 we see that ψ is also a linear function of vector x. Loechtel in [2] at all has shown that it is possible to find all relevant stress components from the experiment in which incidence θ angle is constant, the angle between the [100] axis of the crystal (in plane of the surface) and the projection of the incidence beam direction on the surface of crystal φ, and angles α, β describing direction of linear polarizers inserted in the incident and scattered beam paths and defined in [2], Angles are α, β varied by rotating said polarizers, angle φ can be changed by means of rotating crystal with respect to axis normal or by means of selecting suitable aperture proposed in this invention 301. The four angle combination (θ, φ, a, β) describe configuration of off- axis Raman measurement, The full measurement comprises of series of experiments in r configurations defined by angles (θ, (pj, % βj) where r =1,..., r. Specific examples of such angles combinations are presented in [2]. The calculation of model vector parameter x is performed by means of fitting predicted line shapes given by equation 4 to experimentally observed line shapes for every experiment j. This is accomplished by minimizing parameter χ2 as a function of of its arguments (x, and Ξ):
χ2 (x, Ξ) = ]T χ2 (x, Ξ, θ, apφpβ)) Equation 11
where we implicitly assumed that all experiments j =l,...,r have been performed under the same or similar experimental conditions (same apparatus, same exposure times etc), where
where ωt is frequency at which observation is performed and corresponds to one point of
n points comprising Raman emission spectrum.
By finding absolute minimum of the function χ2 (x, Ξ) we find value of x vector
optimizing fit, and stress tensor components in the sample using Equation 10. Furthermore, we present a second embodiment of the invention where the angle of the incident beam is controlled by means of a steering mirror as shown in Figure 6 where shoes how the incident beam 501 is deflected by steering mirror 600, subsequently is partially blocked by aperture 301 and directed by the beam-splitter 300 to a microscope objective 200 and focused at an incident angle defined by the aperture 301 on the sample 5. The sample emits radiation, which is collected by the microscope objective 200 passes through the beam-splitter 300 and is partially blocked by the aperture 302. The radiation transmitted through the aperture 302 was emitted by the sample 5 at an emission angle defined by the opening in the aperture 302. The exact position of the focal spot is defined by the angle of steering mirror. The steering mirror angle is controlled by piezo-electric actuators (for example, a mirror mounted on a mirror mount KC-IPZ [8]). Since the focal length of the typical microscope objective described above is of the order of 1-3 mm, and resolution of this
mirror mount is 6 arc sec, this arrangement permits positioning the center of the optical beam with a resolution of the order of 20 nm. It is possible to construct a mirror stage having a resolution one order of magnitude higher and achieve control of the position of the center of the optical beam with a resolution of the order of 20 nm. This allows us to further enhance the spatial resolution of our optical system. Resolution is achieved by modulation of the position of center of the optical beam, which can be at least an order of magnitude higher than the waist of the beam.
References:
[1] G. H .Loechelt, N. G. Cave, and Menendez, Appl. Phys. Lett., Vol. 66, No. 26, 26
June 1995 [2] GH. Loechelt, N. G. Cave, and J. Menendez, J. of Applied Physics, 86, 6164-80
(1999).
[3] E. Bonera, M. Fanciulli, and D. N. Batchelder, Appl. Phys. Lett., Vol. 81, No. 18, 28
October 2002
[4] E. Bonera, M. Fanciulli, and D. N. Batchelder, J. Appl. Phys., Vol. 94, No. 4, 15 August 2003
[5] Edmund Optics OBJECTIVE MICRO 6OX JIS http ://www. edmundoptics. com/onlinecatalog/DisplayProduct. cfm?productid=l 720 (2 of
3)7/18/2005 6:40:29 AM, Copyright 2005, Edmund Optics Inc. 101 East Gloucester
Pike, Barrington, NJ/USA 08007-1380 Phone: (800) 363-1992, Fax: (856) 573-6295
[6]Nikon: http://www.microscopyu.com/articles/optics/objectiveproperties.html (3 of
8)7/19/2005 10:55:25 AM
[7] httρ://www.thorlabs.com/Visual/Nav.cfm?Guide_ID=80&Visual_ID=:91
[8] Thorlabs mirror KCl-PZ http://www.thorlabs.com/NewGroupPage9.cfm?Category_ID=26&ObjectGroup_ID=231
Claims
1. An optical device for exciting a sample surface by an optical beam at a predetermined and controlled angle for collecting radiation emitted by a sample at other than, but not necessarily, the same angle comprising: an entrance aperture partially blocking exciting radiation, and being mounted in front of, and to, an optical beam-splitter directing exciting radiation towards the focusing element and being mounted in front of a focusing element, directing focused exciting radiation on the surface of a sample being in optical communication with the focusing element and the sample is mounted to a wafer chuck mechanically connected to the focusing element, at an incidence angle predetermined by the opening in the aperture, and a second aperture mounted on another side of the optical beam splitter in such way that said aperture is partially blocking the radiation emitted by the sample, which was collected and collimated by the focusing element, where the opening of the second aperture defines the collection angle.
2. The device described in claim 1 where the apertures are replaceable.
3. The device described in claim 1 where the apertures are positioned by motion
stages and positioning devices.
4. The device described in claim 3 where the positioning devices are filter wheels.
5. The device described in claim 1 where the polarization state, of the incident and emitted radiation, is controlled by quarter wave plates and polarizers mechanically connected to the apertures.
6. The device described in claim 1 used as an optical probe incorporated in a Raman spectrometer.
7. The device described in claim 1 where the exciting beam is directed to the entrance aperture by a steering mirror which is optically with the entrance aperture, which deflects the exciting beam at a user controlled angle which defines the position of the spot where the exciting beam is impinging the measured sample.
8. A method of measuring stress tensor components in materials possessing crystallographic diamond structure using the apparatus described in claim 1 comprising: performing a series of off-axis Raman measurements with different configurations defined by an excitation incidence angle, a polarization angle of an excitation beam, a collection angle, and a polarization of collection emission conditions in the spectral proximity of (LO) phonon, calculation of the root mean square sum of the deviation of the spectra observed in each of the off-axis Raman measurements and spectra calculated using a model assuming the presence of three nearly degenerate phonons and taking into account linear corrections to the phonon frequencies due to the presence of stress, where stress is a model fitting parameter, calculating the sum of the mean square sum of the deviations for all spectra, minimizing said sum by changing the value of an assumed stress model fitting
parameter by iterating the last two steps until the value of the stress model fitting parameter does not change more than a prescribed tolerance, and reporting the value of the model fitting parameter minimizing the sum as a stress tensor.
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US20020039184A1 (en) * | 2000-10-03 | 2002-04-04 | Sandusky John V. | Differential numerical aperture methods and device |
US20020080357A1 (en) * | 2000-11-15 | 2002-06-27 | Dana Kristin J. | Apparatus and method for measuring spatially varying bidirectional reflectance distribution function |
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US20020039184A1 (en) * | 2000-10-03 | 2002-04-04 | Sandusky John V. | Differential numerical aperture methods and device |
US20020080357A1 (en) * | 2000-11-15 | 2002-06-27 | Dana Kristin J. | Apparatus and method for measuring spatially varying bidirectional reflectance distribution function |
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