Patent Description:
To form gratings with different slant angles on a substrate angled etch systems are used. Angled etch systems include an ion beam chamber that houses an ion beam source. The ion beam source is configured to generate an ion beam, such as a ribbon beam, a spot beam, or full substrate-size beam. The ion beam chamber is configured to direct the ion beam at an optimized angle relative to a surface normal of substrate. Changing the optimized angle requires reconfiguration of the hardware configuration of the ion beam chamber. The substrate is retained on a platen coupled to an actuator. The actuator is configured to tilt the platen, such that the substrate is positioned at a tilt angle relative to an axis of the ion beam chamber. The optimized angle and tilt angle result in an ion beam angle relative to the surface normal.

One example of a device that utilizes gratings with different slant angles is a light field display. Another example of a device that utilizes gratings with different slant angles is a waveguide combiner. A waveguide combiner may require gratings with slant angles that are different depending on the properties required of the augmented reality device. Additionally, a waveguide combiner may require gratings with different slant angles to adequately control the in-coupling and out-coupling of light. Successively fabricating waveguide combiners where the following waveguide combiner may have gratings with a different slant angle than a prior waveguide combiner and fabricating a waveguide combiner to have gratings with different slant angles relative the surface of the waveguide combiner using angled etch systems can be challenging. <CIT> discloses a microfabrication apparatus for fabricating a microstructure on a substrate. The microfabrication apparatus comprises a partitioning system arranged to provide an aperture, a particle source that can generate a beam of particles for patterning the substrate and a substrate holder which supports the substrate Relative motion is effected between the aperture and the substrate over a portion of the substrate's surface so that different points on the surface portion are exposed at different times. Whilst that motion is ongoing. one or more exposure conditions are varied so that the different points are subject to different exposure conditions.

Conventionally, to form gratings with different slant angles on a substrate or from gratings on multiple substrates with gratings having different slant angles, the optimized angle is changed, the tilt angle is changed, and/or multiple angled etch systems are used. Reconfiguring the hardware configuration of the ion beam chamber to change optimized angle is complex and requires reconfiguration time. Adjusting tilt angle to modify the ion beam angle results in non-uniform depths of gratings and using multiple angled etch systems increases the fabrication time and increases costs due the need of multiple chambers.

Accordingly, what needed in the art are methods of forming gratings with different slant angles on a substrate and forming gratings with different slant angles on successive substrates.

In one embodiment, a grating forming method is provided. The method includes positioning a first portion of a first substrate retained on a platen in a path of an ion beam. The first substrate has a grating material disposed thereon. The ion beam is configured to contact the grating material at an ion beam angle ϑ relative to a surface normal of the first substrate and form one or more first gratings in the grating material. The first substrate retained on the platen is rotated about an axis of the platen resulting in a first rotation angle φ between the ion beam and the grating vector of the one or more first gratings. The one or more first gratings have a first slant angle ϑ' relative to the surface normal of the first substrate. The first rotation angle φ selected by an equation φ = cos-<NUM>(tan(ϑ')/tan(ϑ)).

In another embodiment, a grating forming method is provided combiner fabrication method is provided. The method includes positioning a first portion of a first substrate retained on a platen in a path of an ion beam. The first substrate has a grating material disposed thereon. The ion beam is configured to contact the grating material at an ion beam angle ϑ relative to a surface normal of the first substrate and form one or more first gratings in the grating material. The first substrate retained on the platen is rotated about an axis of the platen resulting in a first rotation angle φ between the ion beam and a surface normal of the one or more first gratings. The one or more first gratings have a first slant angle ϑ' relative to the surface normal of the first substrate. The first rotation angle φ selected by an equation φ = cos-<NUM>(tan(ϑ')/tan(ϑ)). A second portion of the first substrate is positioned in the path of the ion beam configured to form one or more second gratings in the grating material. The first substrate is rotated about the axis of the platen resulting in a second rotation angle φ between the ion beam and the surface normal of the one or more second gratings. The one or more second gratings have a second slant angle ϑ' relative to the surface normal of the first substrate. The second rotation angle φ selected by the equation φ = cos-<NUM>(tan(ϑ')/tan(ϑ)). A third portion of the first substrate is positioned in the path of the ion beam configured to form one or more third gratings in the grating material. The first substrate is rotated about the axis of the platen resulting in a third rotation angle φ between the ion beam and the surface normal of the one or more third gratings. The one or more third gratings have a third slant angle ϑ' relative to the surface normal of the first substrate. The third rotation angle φ selected by the equation φ = cos-<NUM>(tan(ϑ')/tan(ϑ));.

In yet another embodiment, a grating forming method is provided. The method includes positioning a first portion and a second portion of a substrate retained on a platen in a path of an ion beam. The substrate having a grating material disposed thereon, the ion beam configured to contact the grating material at an ion beam angle ϑ relative to a surface normal of the substrate and form one or more first gratings and one or more second gratings in the grating material. The substrate retained on the platen is rotated about an axis of the platen resulting in in a first rotation angle φ<NUM> between the ion beam and a grating vector of the one or more first gratings and a second rotation angle φ<NUM> between the ion beam and a grating vector of the one or more second gratings. The one or more first gratings have a first slant angle ϑ'<NUM> and the one or more second gratings have a second slant angle ϑ'<NUM> relative to the surface normal of the substrate. The first rotation angle φ<NUM> and the second rotation angle φ<NUM> are selected by a system of equations ϑ = arctan(tan(ϑ'<NUM>)/cos(φ<NUM>)), ϑ = arctan(tan(ϑ'<NUM>)/cos(φ<NUM>)), and Δφ = φ<NUM>-φ<NUM>.

It is to be noted, however, that the appended drawings illustrate only exemplary embodiments and are therefore not to be considered limiting of its scope, and may admit to other equally effective embodiments.

Embodiments described herein relate to methods of forming gratings with different slant angles on a substrate and forming gratings with different slant angles on successive substrates. The methods include positioning portions of substrates retained on a platen in a path of an ion beam. The substrates have a hardmask disposed thereon. The ion beam is configured to contact the hardmask at an ion beam angle ϑ relative to a surface normal of the substrates and form gratings in the hardmask. The substrates are rotated about an axis of the platen resulting in rotation angles φ between the ion beam and a surface normal of the gratings. The gratings have slant angles ϑ' relative to the surface normal of the substrates. The rotation angles φ selected by an equation φ = cos-<NUM>(tan(ϑ')/tan(ϑ)). In one embodiment, forming gratings with different slant angles on substrate forms a waveguide combiner or a master of a waveguide combiner for nanoimprint lithography processing.

<FIG> is a perspective, frontal view of a waveguide combiner <NUM>. It is to be understood that the waveguide combiner <NUM> described below is an exemplary waveguide combiner. The waveguide combiner <NUM> includes an input coupling region <NUM> defined by a plurality gratings <NUM>, an intermediate region <NUM> defined by a plurality of gratings <NUM>, and an output coupling region <NUM> defined by a plurality of gratings <NUM>. The input coupling region <NUM> receives incident beams of light (a virtual image) having an intensity from a microdisplay. Each grating of the plurality of gratings <NUM> splits the incident beams into a plurality of modes, each beam having a mode. Zero-order mode (T0) beams are refracted back or lost in the waveguide combiner <NUM>, positive first-order mode (T1) beams are coupled though the waveguide combiner <NUM> to the intermediate region <NUM>, and negative first-order mode (T-<NUM>) beams propagate in the waveguide combiner <NUM> a direction opposite to the T1 beams. Ideally, the incident beams are split into T1 beams that have all of the intensity of the incident beams in order to direct the virtual image to the intermediate region <NUM>. One approach to split the incident beam into T1 beams that have all of the intensity of the incident beams is to optimize the slant angle of each grating of the plurality of gratings <NUM> to suppress the T-<NUM> beams and the T0 beams. The T1 beams undergo total-internal-reflection (TIR) through the waveguide combiner <NUM> until the T1 beams come in contact with the plurality of gratings <NUM> in the intermediate region <NUM>. A portion of the input coupling region <NUM> may have gratings <NUM> with a slant angle different than the slant angle of gratings <NUM> from an adjacent portion of the input coupling region <NUM>.

The T1 beams contact a grating of the plurality of gratings <NUM>. The T1 beams are split into T0 beams refracted back or lost in the waveguide combiner <NUM>, T1 beams that undergo TIR in the intermediate region <NUM> until the T1 beams contact another grating of the plurality of gratings <NUM>, and T-<NUM> beams that are coupled through the waveguide combiner <NUM> to the output coupling region <NUM>. The T1 beams that undergo TIR in the intermediate region <NUM> continue to contact gratings of the plurality of gratings <NUM> until the either the intensity of the T1 beams coupled through the waveguide combiner <NUM> to the intermediate region <NUM> is depleted, or remaining T1 beams propagating through the intermediate region <NUM> reach the end of the intermediate region <NUM>. The plurality of gratings <NUM> must be tuned to control the T1 beams coupled through the waveguide combiner <NUM> to the intermediate region <NUM> in order to control the intensity of the T-<NUM> beams coupled to the output coupling region <NUM> to modulate a field of view of the virtual image produced from the microdisplay from a user's perspective and increase a viewing angle from which a user can view the virtual image. One approach to control the T1 beams coupled through the waveguide combiner <NUM> to the intermediate region <NUM> is to optimize the slant angle of each grating of the plurality of gratings <NUM> to control the intensity of the T-<NUM> beams coupled to the output coupling region <NUM>. A portion of the intermediate region <NUM> may have gratings <NUM> with a slant angle different than the slant angle of gratings <NUM> from an adjacent portion of the intermediate region <NUM>. Furthermore, the gratings <NUM> may have slant angles different that the slant angles of the gratings <NUM>.

The T-<NUM> beams coupled through the waveguide combiner <NUM> to the output coupling region <NUM> undergo TIR in the waveguide combiner <NUM> until the T-<NUM> beams contact a grating of the plurality of gratings <NUM> where the T-<NUM> beams are split into T0 beams refracted back or lost in the waveguide combiner <NUM>, T1 beams that undergo TIR in the output coupling region <NUM> until the T1 beams contact another grating of the plurality of gratings <NUM>, and T-<NUM> beams coupled out of the waveguide combiner <NUM>. The T1 beams that undergo TIR in the output coupling region <NUM> continue to contact gratings of the plurality of gratings <NUM> until the either the intensity of the T-<NUM> beams coupled through the waveguide combiner <NUM> to the output coupling region <NUM> is depleted, or remaining T1 beams propagating through the output coupling region <NUM> have reached the end of the output coupling region <NUM>. The plurality of gratings <NUM> must be tuned to control the T-<NUM> beams coupled through the waveguide combiner <NUM> to the output coupling region <NUM> in order to control the intensity of the T-<NUM> beams coupled out of the waveguide combiner <NUM> to further modulate the field of view of the virtual image produced from the microdisplay from the user's perspective and further increase the viewing angle from which the user can view the virtual image. One approach to control the T-<NUM> beams coupled through the waveguide combiner <NUM> to the output coupling region <NUM> is to optimize the slant angle of each grating of the plurality of gratings <NUM> to further modulate the field of view and increase the viewing angle. A portion of the intermediate region <NUM> may have gratings <NUM> with a slant angle different than the slant angle of gratings <NUM> from an adjacent portion of the intermediate region <NUM>. Furthermore, the gratings <NUM> may have slant angles different that the slant angles of the gratings <NUM> and the gratings <NUM>.

<FIG> is a side, schematic cross-sectional view and <FIG> is side, schematic cross-sectional view of an angled etch system <NUM>, such as the Varian VIISta® system available from Applied Materials, Inc. located in Santa Clara, Calif. It is to be understood that the angled etch system described below is an exemplary angled etch system and other angled etch system, including angled etch system from other manufacturers, may be used with or modified to form gratings on a substrate.

To form gratings having slant angles, a grating material <NUM> disposed on a substrate <NUM> is etched by the angled etch system <NUM>. In one embodiment, the grating material <NUM> is disposed on an etch stop layer <NUM> disposed on the substrate <NUM> and a patterned hardmask <NUM> is disposed over the grating material <NUM>. In one embodiment, the materials of grating material <NUM> are selected based on the slant angle ϑ' of each grating and the refractive index of the substrate <NUM> to control the in-coupling and out-coupling of light and facilitate light propagation through a waveguide combiner. In another embodiment, the grating material <NUM> includes silicon oxycarbide (SiOC), titanium dioxide (TiO<NUM>), silicon dioxide (SiO2), vanadium (IV) oxide (VOx), aluminum oxide (Al<NUM>O<NUM>), indium tin oxide (ITO), zinc oxide (ZnO), tantalum pentoxide (Ta<NUM>O<NUM>), silicon nitride (Si<NUM>N<NUM>), titanium nitride (TiN), and/or zirconium dioxide (ZrO<NUM>) containing materials. The grating material <NUM> has a refractive index between about <NUM> and about <NUM>. In yet another embodiment, the patterned hardmask <NUM> is a non-transparent hardmask that is removed after the waveguide combiner is formed. For example, the non-transparent hardmask includes reflective materials, such as chromium (Cr) or silver (Ag). In another embodiment, the patterned hardmask <NUM> is a transparent hardmask. In one embodiment, the etch stop layer <NUM> is a non-transparent etch stop layer that is removed after the waveguide combiner is formed. In another embodiment, the etch stop layer <NUM> is a transparent etch stop layer.

The angled etch system <NUM> includes an ion beam chamber <NUM> that houses an ion beam source <NUM>. The ion beam source is configured to generate an ion beam <NUM>, such as a ribbon beam, a spot beam, or full substrate-size beam. The ion beam chamber <NUM> is configured to direct the ion beam <NUM> at an optimized angle α relative to a surface normal <NUM> of substrate <NUM>. Changing the optimized angle α requires reconfiguration of the hardware configuration of the ion beam chamber <NUM>. The substrate <NUM> is retained on a platen <NUM> coupled to a first actuator <NUM>. The first actuator <NUM> is configured to move the platen <NUM> in a scanning motion along a y-direction and/or a z-direction. In one embodiment, the actuator is further configured to tilt the platen <NUM>, such that the substrate <NUM> is positioned at a tilt angle β relative to the x-axis of the ion beam chamber <NUM>. The optimized angle α and tilt angle β result in an ion beam angle ϑ relative to the surface normal <NUM>. To form gratings having a slant angle ϑ' relative the surface normal <NUM>, the ion beam source <NUM> generates an ion beam <NUM> and the ion beam chamber <NUM> directs the ion beam <NUM> towards the substrate <NUM> at the optimized angle α. The first actuator <NUM> is positions the platen <NUM> so that the ion beam <NUM> contacts the grating material <NUM> at the ion beam angle ϑ and etches gratings having a slant angle ϑ' on desired portions of the grating material <NUM>.

Conventionally, to form a portion of gratings with a slant angle ϑ' than different than the slant angle ϑ' of an adjacent portion of gratings or form gratings having a different slant angle ϑ' on multiple substrates, the optimized angle α is changed, the tilt angle β is changed, and/or multiple angled etch systems are used. Reconfiguring the hardware configuration of the ion beam chamber <NUM> to change optimized angle α is complex and requires reconfiguration time. Adjusting tilt angle β to modify the ion beam angle ϑ results in non-uniform depths of gratings at portions of the substrate <NUM> as the ion beam <NUM> contacts the grating material <NUM> at a different energy levels. For example, a portion positioned closer to the ion beam chamber <NUM> will have gratings with a greater depth than gratings of an adjacent potion positioned further away from the ion beam chamber <NUM>. Using multiple angled etch systems increases the fabrication time and increases costs due the need of multiple chambers. To avoid the reconfiguring the ion beam chamber <NUM>, adjusting the tilt angle β to modify the ion beam angle ϑ, and using multiple angled etch systems, the angled etch system <NUM> includes a second actuator <NUM> coupled to the platen <NUM> to rotate the substrate <NUM> about the x-axis of the platen <NUM> to control the slant angle ϑ' of gratings.

<FIG> is a schematic perspective view of a portion <NUM> of a substrate <NUM>. The tilt angle β and optimized angle α of the ion beam <NUM> are fixed such that the ion beam angle ϑ relative a surface normal <NUM> of the substrate <NUM> is constant. The optimized angle α is between about <NUM>° and about <NUM>° and the tilt angle β is between about <NUM>° and about <NUM>°. The resulting ion beam angle ϑ is between about <NUM>° and about <NUM>°. The ion beam angle ϑ is preferably between about <NUM>° and about <NUM>° as a ion beam angle ϑ close to about <NUM>° or about <NUM>° will result in gratings <NUM> having a slant angle ϑ' of about <NUM>° or about <NUM>°such that the gratings <NUM> are not slanted. The substrate <NUM> is rotated about the x-axis of the platen <NUM> resulting in rotation angle φ between the projection of the ion beam on the substrate <NUM>' and a grating vector <NUM> of the gratings <NUM>. The rotation angle φ is selected to control the slant angle ϑ' without reconfiguring the ion beam chamber <NUM>, without adjusting the tilt angle β to modify the ion beam angle ϑ, and without using multiple angled etch systems. To determine the resulting slant angle ϑ' with a fixed ion beam angle ϑ one of the following equivalent slant angle ϑ' equations are implemented: sin(ϑ') = sin(ϑ)/sqrt(<NUM>+tan<NUM>(φ)*cos<NUM>(ϑ)) and tan(ϑ') = tan(ϑ)*cos(φ). Solving for φ, the rotation angle φ is cos-<NUM>(tan(ϑ')/tan(ϑ). For example, if the ion beam angle ϑ is <NUM>°and the desired slant angle ϑ' is <NUM>° the rotation angle φ is about <NUM>° as cos-<NUM>(tan(<NUM>)/tan(<NUM>) = <NUM>. <FIG> is a graph of the results of the equivalent slant angle ϑ' equations for ion beam angles ϑ of <NUM>°, <NUM>°, <NUM>°, <NUM>°, and <NUM>° as a function of rotation angle φ.

In one embodiment, gratings <NUM> having a slant angle ϑ' can be formed with the angled etch system <NUM>. In another embodiment, gratings <NUM> having a slant angle ϑ' can be formed with an ion beam etch system, also known as full wafer, immersive, or gridded etch system, having a ion beam source <NUM> housed in a ion beam chamber <NUM> that generates an ion beam <NUM> having a geometry corresponding to the geometry of the surface of the substrate <NUM> at an optimized angle α of about <NUM>°. The platen <NUM> of the ion beam etch system is configured to position the substrate <NUM> at a tilt angle β so that the ion beam <NUM> contacts the substrate <NUM> at an ion beam angle ϑ between about <NUM>° and about <NUM>°. The rotation angle φ is selected to control the slant angle ϑ' as described herein.

<FIG> is a schematic top view of a substrate <NUM> having a first portion <NUM> of gratings <NUM> and a second portion <NUM> of gratings <NUM>. The tilt angle β and optimized angle α of the ion beam <NUM> are fixed such that the ion beam angle ϑ relative a surface normal of the substrate <NUM> is constant. The optimized angle α is between about <NUM>° and about <NUM>° and the tilt angle β is between about <NUM>° and about <NUM>°. The resulting ion beam angle ϑ is between about <NUM>° and about <NUM>°. The ion beam angle ϑ is preferably between about <NUM>° and about <NUM>° as a ion beam angle ϑ close to about <NUM>° or about <NUM>° will result in the gratings <NUM> having a slant angle ϑ', and the gratings <NUM> having a slant angle ϑ'<NUM> of about <NUM>° or about <NUM>° such that the gratings <NUM> and the gratings <NUM> are not slanted. The substrate <NUM> is rotated about the x-axis of the platen <NUM> resulting in a rotation angle φ<NUM> between the ion beam <NUM> and a grating vector <NUM> of the gratings <NUM> and a rotation angle φ<NUM> between the ion beam <NUM> and a grating vector <NUM> of the gratings <NUM>. The rotation angle φ<NUM> is selected to form gratings <NUM> having slant angle ϑ', and the rotation angle φ<NUM> is selected to form gratings <NUM> having slant angle ϑ'<NUM> with by moving the platen <NUM> in the scanning motion with a single pass traversing the ion beam chamber <NUM> such that the first portion <NUM> and second portion <NUM> are positioned in the path of the ion beam <NUM>. To form two or more portions of gratings with a single pass of the platen <NUM> traversing the ion beam chamber <NUM> the following system of equations is implemented: <MAT> <MAT> <MAT>.

In one embodiment, the slant angle ϑ'<NUM>, the slant angle ϑ'<NUM>, and the Δφ are known. Solving the system of equations for the rotation angle φ<NUM>, the rotation angle φ<NUM>, and ion beam angle ϑ will allow for the formation of the gratings <NUM> having the slant angle ϑ'<NUM> and the gratings <NUM> the having slant angle ϑ'<NUM> with a single pass of the platen <NUM> traversing the ion beam chamber <NUM>. <FIG> is a graph of the results of the system of equations for the rotation angle φ<NUM>, the rotation angle φ<NUM>, and the ion beam angle ϑ. To form gratings <NUM> having a slant angle ϑ'<NUM> of <NUM>° and gratings <NUM> having a slant angle ϑ'<NUM> of <NUM>° with a Δφ of <NUM>° a rotation angle φ<NUM> of <NUM>° and the rotation angle φ<NUM> of <NUM>° will from the first portion <NUM> and second portion <NUM> with a single pass of the platen <NUM> traversing the ion beam chamber <NUM>. In another embodiment, the ion beam angle ϑ, the slant angle ϑ'<NUM>, the slant angle ϑ'<NUM>, and the Δφ are known and the system of equations is solved for the rotation angle φ<NUM> and the rotation angle φ<NUM>. Thus, the gratings <NUM> having the slant angle ϑ'<NUM> and the gratings <NUM> having slant angle ϑ'<NUM> are formed with a single pass of the platen <NUM> traversing the ion beam chamber <NUM> without reconfiguring the ion beam chamber <NUM>, without adjusting the tilt angle β to modify the ion beam angle ϑ, and without using multiple angled etch systems. Additionally, the system of equations may be extended to form three or more portions of gratings.

<FIG> is a flow diagram of a method <NUM> for forming gratings with different slant angles. In one embodiment, the method <NUM> is performed by the angled etch system <NUM>. In another embodiment, the method <NUM> is performed by an ion beam etch system. The angled etch system <NUM> includes an ion beam source <NUM> that generates the ion beam <NUM>, such as a ribbon beam or a spot beam, housed in a ion beam chamber <NUM>. The ion beam chamber <NUM> is configured to direct the ion beam <NUM> at an optimized angle α relative to the surface normal <NUM> of substrate <NUM>. A first actuator <NUM> coupled to the platen <NUM> is configured to move the substrate <NUM> in a scanning motion and tilt the platen <NUM>, such that the substrate <NUM> is positioned at a tilt angle β relative to an axis of the ion beam chamber <NUM>. The first actuator <NUM> is configured to move the platen <NUM> in the scanning motion along the y-direction and/or the z-direction. The optimized angle α and tilt angle β result in an ion beam angle ϑ relative to the surface normal <NUM>.

At operation <NUM>, a first portion of a first substrate having a grating material <NUM> disposed thereon is positioned in a path of an ion beam <NUM>. The ion beam <NUM> contacts the grating material <NUM> at an ion beam angle ϑ relative to a surface normal <NUM> of the first substrate and forms one or more first gratings in the grating material <NUM>. The first substrate is retained on a platen <NUM> configured to position the first portion in the path of the ion beam <NUM> and to rotate the first substrate about an axis of the platen <NUM> resulting in a first rotation angle φ between the ion beam <NUM> and a grating vector <NUM> of the one or more first gratings. The first rotation angle φ is selected to result in the one or more first gratings having a first slant angle ϑ' relative to the surface normal <NUM> of the substrate. The first rotation angle φ is selected by the rotation angle φ equation of φ = cos-<NUM>(tan(ϑ')/tan(ϑ)). In one embodiment, the first portion corresponds to the input coupling region <NUM> of the waveguide combiner <NUM>.

To form one or more second gratings on a second portion of the first substrate or a portion of a second substrate with a second slant angle ϑ' different than the first slant angle ϑ' without reconfiguring the ion beam chamber <NUM> to change the optimized angle α, adjusting the tilt angle β to modify the ion beam angle ϑ, and using multiple angled etch systems, the optimized angle α and tilt angle β remain constant while the first substrate or second substrate is rotated by a second actuator <NUM> coupled to the platen <NUM> configured to rotate a substrate about the axis of the platen <NUM>.

At operation <NUM>, a second portion of the first substrate having the grating material <NUM> disposed thereon is positioned in the path of the ion beam <NUM>. The ion beam <NUM> contacts the grating material <NUM> at the ion beam angle ϑ relative to the surface normal <NUM> of the first substrate and forms one or more second gratings in the grating material <NUM>. The second portion is positioned in the path of the ion beam <NUM> and the first substrate is rotated about the axis of the platen <NUM> resulting in a second rotation angle φ between the ion beam <NUM> and a grating vector <NUM> of the one or more second gratings. The second rotation angle φ is selected to result in the one or more second gratings having a second slant angle ϑ' relative to the surface normal <NUM> of the substrate. The second rotation angle φ is selected by the rotation angle φ equation of φ = cos-<NUM>(tan(ϑ')/tan(ϑ)). In one embodiment, the second portion corresponds to the intermediate region <NUM> of the waveguide combiner <NUM>.

At operation <NUM>, a third portion of a first substrate having the grating material <NUM> disposed thereon is positioned in the path of the ion beam <NUM>, the ion beam <NUM> contacts the grating material <NUM> at the ion beam angle ϑ relative to the surface normal <NUM> of the first substrate and forms one or more third gratings in the grating material <NUM>. The third portion is positioned in the path of the ion beam <NUM> and the first substrate is rotated about the axis of the platen <NUM> resulting in a third rotation angle φ between the ion beam <NUM> and a grating vector <NUM> of the one or more third gratings. The third rotation angle φ is selected to result in the one or more third gratings having a third slant angle ϑ' relative to the surface normal <NUM> of the substrate. The third rotation angle φ is selected by the rotation angle φ equation of φ = cos-<NUM>(tan(ϑ')/tan(ϑ)). In one embodiment, the third portion corresponds to the output coupling region <NUM> of the waveguide combiner <NUM>.

At operation <NUM>, the first substrate is removed and a second substrate is retained on the platen. At operation <NUM>, operations <NUM>-<NUM> are repeated to form on a second substrate one or more first gratings having a first slant angle ϑ', one or more second gratings having a second slant angle ϑ' different than the first slant angle ϑ', and one or more third gratings having a third slant angle ϑ' different than the first slant angle ϑ' and the second slant angle ϑ'.

<FIG> is a flow diagram of a method <NUM> for forming portions of gratings having different slant angles with a single pass of the platen <NUM> traversing the ion beam chamber <NUM>. At operation <NUM> a first portion <NUM> and a second portion <NUM> of a substrate <NUM> having a grating material <NUM> disposed thereon is positioned in a path of an ion beam <NUM> with a single pass of the platen <NUM> traversing the ion beam chamber <NUM>. The ion beam <NUM> contacts the grating material at an ion beam angle ϑ relative to a surface normal <NUM> of the substrate <NUM> and forms one or more gratings <NUM> and one or more gratings <NUM> in the grating material. The substrate <NUM> is retained on a platen <NUM> configured to position the first portion <NUM> and second portion <NUM> in the path of the ion beam <NUM> and to rotate the substrate <NUM> about an axis of the platen <NUM> resulting in a rotation angle φ<NUM> between the ion beam <NUM> and a grating vector <NUM> of the one or more gratings <NUM> and a rotation angle φ<NUM> between the ion beam <NUM> and a grating vector <NUM> of the one or more gratings <NUM>. The rotation angle φ<NUM> is selected to result in the one or more gratings <NUM> having a slant angle ϑ'<NUM> relative to the surface normal <NUM> of the substrate. The rotation angle φ<NUM> is selected to result in the one or more gratings <NUM> having a slant angle ϑ'<NUM> relative to the surface normal <NUM> of the substrate. The rotation angle φ<NUM> and the rotation angle φ<NUM> are selected by solving the system of equations: <MAT> <MAT> <MAT>.

In one embodiment, the slant angle ϑ'<NUM>, the slant angle ϑ'<NUM>, and the Δφ are known. Solving the system of equations for the rotation angle φ<NUM>, the rotation angle φ<NUM>, and ion beam angle ϑ will allow for the formation of the gratings <NUM> having the slant angle ϑ'<NUM> and the gratings <NUM> the having slant angle ϑ'<NUM> with a single pass of the platen <NUM> traversing the ion beam chamber <NUM>. In another embodiment, the ion beam angle ϑ, the slant angle ϑ'<NUM>, the slant angle ϑ'<NUM>, and the Δφ are known and the system of equations is solved for the rotation angle φ<NUM> and the rotation angle φ<NUM>. Thus, the gratings <NUM> having the slant angle ϑ'<NUM> and the gratings <NUM> the having slant angle ϑ'<NUM> are formed with a single pass of the platen <NUM> traversing the ion beam chamber <NUM> without reconfiguring the ion beam chamber <NUM>, without adjusting the tilt angle β to modify the ion beam angle ϑ, and without using multiple angled etch systems. Additionally, the system of equations may be extended to form three or more portions of gratings. The method <NUM> may be repeated for subsequent substrates.

In summation, methods of successively forming gratings with different slant angles on a substrate and forming gratings with different slant angles on successive substrates using angled etch systems is described herein. The utilization of selecting the rotation angle φ to control the slant angle ϑ' without reconfiguring the ion beam chamber, adjusting the tilt angle β to modify the ion beam angle ϑ, and using multiple angled etch systems allows a singled angled etch system to fabricate waveguide combiners and fabricate a waveguide combiner having gratings with different slant angles ϑ'.

Claim 1:
A grating forming method, comprising:
positioning a first portion of a first substrate retained on a platen (<NUM>) in a path of an ion beam (<NUM>), the first substrate having a grating material (<NUM>) disposed thereon, the ion beam (<NUM>) configured to contact the grating material (<NUM>) at an ion beam angle ϑ relative to a surface normal (<NUM>) of the first substrate and to form one or more first gratings in the grating material (<NUM>); and
rotating the first substrate retained on the platen (<NUM>) about an axis of the platen resulting in a first rotation angle φ between the projection of the ion beam on the substrate (<NUM>') and a grating vector (<NUM>) of the one or more first gratings; and, after rotating, forming the one or more first gratings having a first slant angle ϑ' relative to the surface normal (<NUM>) of the first substrate.