Patent Publication Number: US-2023143437-A1

Title: Vapor cells and related systems and methods

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit under 35 U.S.C. § 119(e) of the priority date of U.S. Provisional Patent Application Ser. No. 63/263,897, filed Nov. 11, 2021, for EMPLOYING PORES FOR CONTROLLING VAPOR PRESSURE IN VAPOR CELLS, AND RELATED VAPOR CELLS, SYSTEMS, AND METHODS, the disclosure of which is incorporated herein in its entirety by this reference. 
    
    
     FIELD 
     This disclosure relates generally to techniques for controlling vapor pressure of subject materials in vapor cells for atomic clocks and other applications. More specifically, disclosed examples relate to structures and materials for controlling vapor pressure, which may improve reliability of operation across broader temperature ranges. 
     BACKGROUND 
     Vapor pressure at a liquid-vapor interface is affected by surface tension according to the Kelvin equation: 
     
       
         
           
             
               
                 P 
                 
                   P 
                   sat 
                 
               
               = 
               
                 e 
                 
                   2 
                   ⁢ 
                   γ 
                   ⁢ 
                   
                     
                       V 
                       m 
                     
                     / 
                     rRT 
                   
                 
               
             
             , 
           
         
       
     
     where P/P sat  is the ratio of the vapor pressure to the saturated vapor pressure, γ is the surface tension, V m  is the molar volume of the liquid, r is the radius of the droplet or meniscus, R is the universal gas constant, and T is the absolute temperature. Vapor pressure is relevant in a variety of operational contexts, including, without limitation, atomic clocks. 
     BRIEF SUMMARY 
     In some examples, vapor cells may include a body defining a cavity within the body. A first substrate may be bonded to a second substrate at an interface. At least one of the first substrate, the second substrate, or an interfacial material between the first substrate and the second substrate may define at least one recess or pore. The at least one recess or pore may have a smallest dimension of about 500 microns or less, as measured in a direction parallel to at least one surface of the first substrate partially defining the cavity. 
     In other examples, methods of using vapor cells may involve providing a vapor cell including a body. The body may include a first substrate bonded to a second substrate at an interface. A cavity may be defined within the body. At least one pore or recess may be formed in at least one of the first substrate, the second substrate, or an interfacial material between the first substrate and the second substrate. The at least one pore or recess may have a smallest dimension of about 500 microns or less, as measured in a direction parallel to at least one surface of the first substrate partially defining the cavity. 
     In other embodiments, a system may include an emitter positioned and oriented to direct radiation through windows of a vapor cell. The system may include a detector positioned and oriented to detect the radiation. The vapor cell may include a body defining a cavity within the body. The body may include a first substrate, a second substrate, or an interfacial material between the first substrate and the second substrate. The first substrate, the second substrate, or the interfacial material between the first substrate and the second substrate may define at least one pore or recess having a smallest dimension of about 500 microns or less, as measured in a direction parallel to at least one surface of the first substrate partially defining the cavity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       While this disclosure concludes with claims particularly pointing out and distinctly claiming specific embodiments, various features and advantages of embodiments within the scope of this disclosure may be more readily ascertained from the following description when read in conjunction with the accompanying drawings. In the drawings: 
         FIGS.  1 A and  1 B  are schematic cross-sectional side views of examples of vapor cells; 
         FIGS.  2 A,  2 B,  2 C, and  2 D  are schematic cross-sectional side views of other examples of vapor cells; 
         FIGS.  3 A and  3 B  are flowcharts depicting illustrative methods of making a vapor cell; and 
         FIGS.  4 A and  4 B  are schematics of illustrative systems including a vapor cell in accordance with this disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Disclosed examples relate generally to designs for structural features that allow for control of vapor pressure in vapor cells for, as a nonlimiting example, atomic clocks. Such designs and structural features may, as a nonlimiting example, increase the temperature range over which reliable operation may be achieved. More specifically, disclosed examples relate to structures and methods for forming recesses and or pores in vapor cells for controlling (e.g., suppressing) vapor pressure. For example, at least one surface in a vapor cell may include one or more recesses or pores sized, shaped, positioned, and configured to control (e.g., suppress) vapor pressure of a subject material in the vapor cell. The recess or recesses may be formed by, for example, selectively etching certain material of a stacked structure of a portion of a body of the vapor cell, thereby recessing certain portions of the stacked structure relative to other portions of the stacked structure to form one or more recesses. As another illustrative technique for forming the pore or pores, a material of a portion of a substrate, or the material of portions of multiple substrates in a stacked structure forming a portion of a body of the vapor cell, may be rendered porous, and certain portions of the porous material and of any relevant non-porous material may be removed to form a portion of a cavity of the vapor cell, and the substrate or substrates may be oriented, stacked, and bonded to one another to form at least a portion of the body of the vapor cell with the porous material exposed to, and placed in a predetermined location relative to, the cavity. Disclosed methods of controlling vapor pressure may provide volumes of capillaries for holding subject material in a liquid state therein and for inducing an exposed surface of the subject material in the liquid state to be concave. 
     As used herein, the terms “substantially” and “about” in reference to a given parameter, property, or condition means and includes to a degree that one of ordinary skill in the art would understand that the given parameter, property, or condition is met with a degree of variance, such as within acceptable manufacturing tolerances. For example, a parameter that is substantially or about a specified value may be at least about 90% the specified value, at least about 95% the specified value, at least about 99% the specified value, or even at least about 99.9% the specified value. 
     The term “pore,” as used herein, means and includes surface features having an average dimension less than 500 microns, as measured in at least one direction parallel to a major surface defining a cavity to which the pore is exposed. For example, “pores” include interconnected, three-dimensional networks of voids within a material that may be occupied by environmental fluids (e.g., air, inert gas, subject material). “Pores” also include, for example, depressions, divots, dimples, and other surface features having average dimensions less than 500 microns, which may be measurable as surface roughness. 
     The term “interface” as used herein, means and includes a point or region of attachment between two materials or structures. For example, an “interface” may include direct contact between two adjacent surfaces, or may include an interfacial material interposed between, and attaching, two adjacent surfaces on opposite sides of the interfacial material. 
     Unless the context indicates otherwise, removal of materials or surface modifications described herein may be accomplished by any suitable technique including, but not limited to, etching (e.g., dry etching, wet etching, vapor etching, reactive ion etching, stain etching), ion milling, abrasive planarization (e.g., chemical-mechanical planarization (CMP)), anodization, or other known methods. 
     The upper operating temperature limit of vapor-cell atomic clocks, such as chip scale atomic clocks (CSACs), without limitation, may be limited by excessive optical absorption, collisional line broadening, and/or heating of a trapped sample due to the high density of alkali metal vapor at elevated temperatures. The vapor pressure above a liquid may be suppressed by containing the liquid within a recess, recesses, pore, or pores. Such structures may enable depressing the alkali metal vapor pressure. In accordance with the Kelvin equation mentioned above, if the curvature of a droplet of subject liquid is convex, r&gt;0, then P&gt;P sat . If the curvature is concave, r&lt;0, then P&lt;P sat . Maintaining control over the vapor pressure of the metal vapor requires the holding capacity (e.g., volume) of the pores to be equal to or greater than a volume required to hold a mass of the metal vapor in a liquid or solid state. 
     Reducing subject material vapor pressure within vapor cells of atomic clocks may be achieved by introducing at least one recess or pore that affects the surface shape of masses of the subject material in the pores. Stated another way, the interaction between the subject material and the size and shape of a pore causes a shape of a surface of the subject material to change in a desired manner (introduces a disturbance) as compared to a shape of the surface of the subject material when on a generally flat surface. 
     When forming vapor cells, top and bottom windows may be bonded to opposite surfaces of a remainder of a body of the vapor cell having cavities formed in the remainder, each cavity corresponding to a respective vapor cell to be singulated from a wafer. The cavities may be formed, by way of example, by etching or micromachining through a material of the remainder of the body of the vapor cell (e.g., a substrate, a wafer, a stacked structure). By way of example, the geometry of a cylindrical cavity may be described by height and diameter, wherein the height of the cavity may be defined as the distance from the at least one window to another window located at an opposite side of the cavity, and the diameter of the cavity may be defined as the distance between sidewalls defining the cavity, as measured in a direction perpendicular to the sidewalls and along a line intersecting a central geometric axis of the cavity. The height and diameter of the cavity may be used to describe geometric differences along the sidewalls of the cavity of the vapor cell. In other examples, the cavity may have a shape other than cylindrical (e.g., ovoid, rectangular prism, rectangular prism having one or more rounded and/or chamfered edges and/or corners). A subject material may be introduced into the cavity of each vapor cell, and the cavities may be enclosed to contain the subject material. For example, each cavity may be enclosed using anodic bonding to bond the top and bottom windows to major surfaces of the remainder of a body of the vapor cell. In embodiments where the body of the vapor cell comprises a wafer or stacked wafers, individual vapor cells may be diced from the wafer or stacked wafers. 
     In one or more examples, surface modification may include generation of one or more recesses in the walls of a body of a vapor cell, with the recesses partially defining a cavity of the vapor cell. By way of example, a recess may be formed by bonding two wafers or substrate with an interfacial material therebetween and subsequently removing a portion of the interfacial material to form a recess cooperatively defined by the adjacent substrates and the interfacial material. As a specific example, an oxide layer may be grown on a first silicon wafer, and a second silicon wafer may be surface bonded to the first silicon wafer with the oxide layer therebetween. Holes to define sidewalls of the vapor cell cavities may be formed through the first and second wafers and the oxide layer, either before or after bonding, by, for example, masking and etching, drilling, selectively growing the oxide layer only on those portions of the wafers that will not be removed to form the cavities, or performing any combination of these. The recess may then be formed by selectively etching the oxide layer, forming a recess with a depth controlled by the time of exposure to the etchant material (e.g., HF etching) and a height controlled by the growth of the oxide layer. In some examples, the body of the vapor cell may include more than two bonded substrates, such as, for example, by stacking three or more wafers bonded together with an interfacial material between each pair of wafers, and a series of recesses, one for each interfacial material. 
     By way of additional example, recesses may be formed by providing a substrate or wafer with alternating regions of oxide material between regions of non-oxide material, the oxide material being recessed relative to the non-oxide material to form a recess. This may be accomplished by, for example, alternately growing the oxide and non-oxide materials on a wafer. For example, silicon oxide may be alternately grown with silicon nitride or polysilicon materials on a silicon wafer through epitaxy, providing selective control of the height of the pores to be formed by partial removal of the regions of oxide material. Two at least substantially complementary wafers or substrates having the alternating regions of oxide and non-oxide materials facing one another may be bonded to one another by surface bonding techniques. Cavities may be formed by, for example, drilling and/or etching the wafers or substrates and the alternating regions of oxide and non-oxide materials. Recesses in the cavities may be formed utilizing, for example, a selective etch (e.g., HF etch) to remove portions of the oxide material while leaving the non-oxide material, providing selective control over the depth of the recesses. Recesses, as disclosed herein, may also be characterized as “trenches.” 
       FIGS.  1 A and  1 B  are schematic cross-sectional side views of examples of vapor cells  100 . Each vapor cell  100  may include, for example, a body  105  which contains a cavity  110 . For example, the body  105  may include windows  115  forming one or more walls (e.g., boundaries) of the body  105 , with the remaining sidewalls  120  being opaque. More specifically, the windows  115  may include, for example, a transparent or translucent borosilicate or aluminosilicate glass material, enabling the cavity  110  of the vapor cell  100  to be viewable through each of the windows  115 . 
     The body  105  defining the cavity  110  within the body  105  may include a first substrate  155  bonded to a second substrate  160  at an interface, which may be defined by an interfacial material  130  interposed between the first substrate  155  and the second substrate  160 . At least one of the first substrate  155 , the second substrate  160 , or the interfacial material  130  may define at least one recess  145  having a smallest dimension of 500 microns or less. For example, a surface of the interfacial material  130  facing the cavity  110  may be recessed relative to surfaces of the first substrate  155  and the second substrate  160  facing the cavity  110 , such that the first substrate  155 , second substrate  160 , and interfacial material  130  may cooperatively define a recess  145 . The recess  145  may include, for example, an annular recess extending around a circumference of the body  105  and exposed to a remainder of the cavity  110 . The interfacial material  130  may include an oxide material interposed between, and bonded to, the first substrate  155  and the second substrate  160 . The body  105  may include a stack of substrates including at least the first substrate  155  and the second substrate  160  and a respective mass of the interfacial material  130  interposed between each pair of substrates of the stack of substrates. For example, the body  105  may include the first substrate  155 , the second substrate  160  adjacent to the first substrate  155 , and a third substrate  165  located on a side of the second substrate  160  opposite the first substrate  155 , with a mass of the interfacial material  130  between the first substrate  155  and the second substrate  160  and another mass of the interfacial material  130  between the second substrate  160  and the third substrate  165 . Each respective mass of the interfacial material  130  may be recessed relative to each pair of adjacent substrates to define a respective recess  145  between each pair of adjacent substrates. Each of the first substrate  155 , the second substrate  160 , and the third substrate  165  may include a substrate material  125 . For example, the substrate material  125  may include a silicon material. 
     The sidewalls  120  of the vapor cell  100  may include a substrate material  125  defined by respective substrates (e.g., the first substrate  155 , the second substrate  160 , the third substrate  165 ), and the interfacial material  130 . The sidewalls  120  of the cavity  110  may be configured such that the substrate material  125  and the interfacial material  130  cooperatively form a recess  145 , the surface of the recess  145  inside the cavity  110  being inset relative to the substrate material  125 . The substrate material  125  and interfacial material  130  may be formed of, and include, at least one material with specific properties to facilitate chemical processing (e.g., etching). The substrate material  125  may, for example, be selectively etch resistant in comparison to the interfacial material  130  during contemporaneous exposure to an etchant (e.g., hydrofluoric acid (HF)). By way of example only, the substrate material  125  may be selected to include single crystal or polycrystalline silicon or silicon nitride, and the interfacial material  130  may be selected to include silicon oxide. The characteristics of the recesses  145 , including but not limited to number, size, shape, height, depth, and lateral circumference of the recesses  145 , may be configured to induce the vapor pressure of a subject material  140  in the cavity  110  to be within predetermined thresholds in anticipated operating conditions for the vapor cell  100 . The height of the recesses  145  may be defined as the distance along the sidewall  120  that a recess  145  occupies. By way of example, the height of the recesses  145  may be substantially the same as the thickness of interfacial material  130 . The depth of the recesses  145  may be defined as the distance the recess  145  is offset relative to the inner cavity  110  surface. By way of example, the depth of the recesses  145  may be substantially the same as the distance between surface of the substrate material  125  facing the cavity  110  and surface of the interfacial material  130  facing the cavity  110 . By way of example, the height of a given recess  145  may be between about 20 nm and about 500 nm, and the depth of the recess  145  may be between about 10 μm and about 100 μm. By way of example, the recesses  145  may be sized, shaped, positioned, and configured to contain between about 0.01 μg and about 100 μg of a subject material  140 . More specifically, the volume of the recesses  145  may be sized, shaped, positioned, and configured to contain between about 0.25 μg and about 5 μg of a subject material  140 . 
     Regarding  FIG.  1 A , the interfacial material  130  may be selected such that it may be grown directly on the surface of a wafer or substrate of substrate material  125 . By way of example, the interfacial material  130  (e.g., silicon oxide), may result from modification of the substrate surface (e.g. thermal oxidation) or may be controllably grown on the substrate material  125  (e.g., a silicon wafer, a silicon substrate). Growth of the interfacial material  130  on the substrate material  125  may be accomplished by, for example, a vapor deposition process (e.g., chemical vapor deposition or physical vapor deposition). The sidewalls  120  forming the cavity  110  of the vapor cell may be prepared by stacking wafers or substrates on top of one another and bonding the wafers or substrates to one another, with interfacial material  130  between at least some of the wafers or substrates. As a specific, nonlimiting example, the substrate material  125  and interfacial material  130  may be bonded together by means of a contact and anneal bonding process. The sidewall  120  may then include the substrate material  125  and the interfacial material  130 , with the interfacial material  130  at least substantially flush with the substrate material  125 . The height of the sidewall  120  may include the combination of the height of the substrate material  125  and the height of the interfacial material  130 . By way of example, three substrates or wafers of the substrate material  125 , each having a respective height of about 500 μm may be utilized. The substrates or wafers of the substrate material  125  may be oxide bonded to each other utilizing the interfacial material  130  (e.g., silicon oxide) as an interfacial material, each instance of the interfacial material  130  having a height of between about 20 nm and about 500 nm. A total height of the stacked structure, including the masses of the substrate material  125  and the masses of the interfacial material  130 , may be, for example, between about 1,000 μm and about 2,000 μm (e.g., about 1,500 μm). 
     Regarding  FIG.  1 B , the body  105  may include alternating regions of disparate materials, such as, for example, the substrate material  125  (e.g., the substrate material  125  of the first substrate  155 , the second substrate  160 , epitaxially grown regions of the substrate material  125  interposed between the first substrate  155  and the second substrate  160 ) and the interfacial material  130  interposed between adjacent regions of the substrate material  125 . Each region of the interfacial material  130  may be recessed relative to adjacent regions of the substrate material  125  to define respective recesses  145  between adjacent regions of the substrate material  125 . The first substrate  155  may be interposed between the alternating regions of the substrate material  125  and the interfacial material  130  and a first of the windows  115  on a first side of the body  105 , and a second substrate  160  may be interposed between the alternating regions of the substrate material  125  and the interfacial material  130  and another of the windows  115  on an opposite side of the body  105 . By way of example, the substrate material  125  may include polycrystalline silicon or silicon nitride, and the interfacial material  130  may include silicon oxide. Discrete regions of the substrate material  125  and interfacial material  130  may be, for example, iteratively grown to form portions of the sidewalls  120  of the vapor cell  100 . By way of example, each discrete region of the substrate material  125  may have a height of between about 20 nm and about 500 μm. 
     Recesses  145  in the form of trenches may be formed in the sidewall  120  by, for example, selectively removing portions of the interfacial material  130  facing the cavity  110  to recess the interfacial material  130  relative to the substrate material  125 . By way of example only, a series of recesses  145  may be provided in the sidewall  120  by chemical etching (e.g. HF) to remove portions of the interfacial material  130 . In some examples, recesses  145  may be formed in the sidewall  120  in such a way as to expose the recesses  145  to the remainder of the cavity  110  by, for example, selectively etching the interfacial material  130 . Each resulting recess  145  may have, for example, an at least substantially annular shape, extending around and in fluid communication with a remainder of the cavity  110 . By way of example only, the interfacial material  130  (e.g., silicon oxide) may be selectively etched using hydrofluoric acid. The cavity  110  of the body  105  of the vapor cell  100  may be enclosed by adding windows  115  covering the open ends of the cavity and bonding the windows  115  to adjacent regions of the substrate material  125 . In embodiments where an array of vapor cells  100  are formed in a wafer, the individual vapor cell  100  may then be singulated from one another, for example, utilizing a dicing saw. 
     A transparency of the material of the windows  115  may be, for example, about 10% or more within wavelengths of radiation to be directed toward the cavity  110 . More specifically, the transparency of the material of the windows  115  may be, for example, between about 10% and about 99%. As a specific, nonlimiting example, the transparency of the material of the windows  115  may be, for example, between about 20% and about 95% (e.g., about 25%, about 50%, about 75%). 
     In one or more examples, a pore or recess may be introduced into a vapor cell  100  through modification of a material defining the interior vapor cell  100  wall surface. More specifically, a region of at least one of a first substrate or a second substrate partially defining the cavity may include a porous material defining the pore or pores. When a material of a wafer or substrate includes silicon, the silicon material may be rendered porous by, for example, anodization, stain etching, bottom-up synthesis, or other techniques for rendering silicon porous. The regions of the wafer or substrate rendered porous may have a diameter larger or smaller than a diameter of the cavities to be formed or partially formed in the wafer or substrate. Material within the regions of the wafer or substrate rendered porous may be removed (e.g., by drilling, by etching), leaving an annular shaped region of the porous material around each partial cavity formed in the wafer or substrate. The wafer may be bonded to another wafer, before or after formation of the cavities, with the porous region or regions in a specified position and orientation to expose pores to the cavities. 
     For example, a substrate including the porous regions may be interposed between, and bonded to, two other substrates to form a body with the porous material spaced from the windows by the two other substrates. In some such examples, the porous region may be located proximate to the interface between the first substrate and the second substrate. In some examples, a diameter of the cavity proximate to the region of the porous material may be less than a diameter of the cavity distal from the region of the porous material in order to expose pores on the exposed surfaces normal to the principal axis of the cell. For example, the porous material may be located adjacent or proximate to a window of the vapor cell, and transmission of incident radiation through the window may enable application of incident radiation to the subject material with the cavity, despite a restricted aperture for radiation passing through the window to proceed into the cavity due to the narrower diameter of the substrate having the porous material adjacent or proximate to the window. 
       FIGS.  2 A through  2 D  are schematic cross-sectional views of vapor cells  200 . Each vapor cell  200  may include, for example, a body  205  which defines a cavity  210  within the body  205 . For example, the body  205  may include windows  215  forming one or more walls (e.g., boundaries) of the body  205 , with the remaining sidewalls  220  being opaque. More specifically, the windows  215  may include, for example, a transparent or translucent borosilicate or aluminosilicate glass material, enabling the cavity  210  of the vapor cell  200  to be viewable through the windows  215 . 
     As shown in  FIG.  2 A , the body  205  may include a first substrate  255  bonded to a second substrate  260  at an interface including an interfacial material  230  interposed between the first substrate  255  and the second substrate  260 . At least one of the first substrate  255 , the second substrate  260 , or the interfacial material  230  between the first substrate  255  and the second substrate  260  may define at least one pore (e.g. a porous volume  235 ) with a smallest dimension of 500 microns or less. For example, the substrate material  225  of at least a portion of one of the stacked substrates (e.g., the first substrate  255 , the second substrate  260 , a third substrate  265 ) may be porous, and the porous portion of the substrate material  225  may be exposed to the cavity  210 . More specifically, a region of the second substrate  260  proximate a geometric center of the body  205  between the windows  215  may be porous, and the second substrate  260  may be interposed between, and bonded to, the first substrate  255 , at an interface including an interfacial material  230  interposed between the first substrate  255  and the second substrate  260 , and bonded to the third substrate  265  to which the windows  215  are respectively bonded, where the bond to the third substrate  265  is at an interface including an interfacial material  230  interposed between the second substrate  260  and the third substrate  265 . Each of the first substrate  255 , the second substrate  260 , and the third substrate  265  may include, and be defined by, a respective mass of a substrate material  225 . 
     The sidewalls  220  of the vapor cell  200  may include the substrate material  225 , and an interfacial material  230 . By way of example only, the substrate material  225  may include polycrystalline silicon or silicon nitride, and the interfacial material  230  may include silicon oxide. The sidewalls  220  of the cavity  110  may be configured such that at least a portion of the substrate material  225  may be porous, defining a porous volume  235  exposed to and partially defining the cavity  210 . By way of example, the substrate material  225  may be rendered porous by anodization, stain etching, bottom-up synthesis, or other techniques for rendering silicon porous in examples where the substrate material  225  includes silicon (e.g., silicon nitride, polycrystalline silicon). Additionally, the interfacial material  230  may also be rendered porous, allowing for the porous volume  235  to be defined in the substrate material  225 , the interfacial material  230 , or both the substrate material  225  and the interfacial material  230 . The characteristics of the porous volume  235 , including but not limited to surface area, volume of pores, shape, and average porous diameter of pores, may be configured to induce the vapor pressure of a subject material  240  in the cavity  210  to be within predetermined thresholds in anticipated operating conditions for the vapor cell  200 . By way of example, the average diameter of pores within the porous volume  235  may be between about 20 nm and about 500 μm. By way of example, the total volume of pores defined by the porous volume  235  may be sized, shaped, positioned, and configured to contain between about 0.01 μg and about 100 μg of a subject material  240 . More specifically, the volume of pores defined by the porous volume  235  may be sized, shaped, positioned, and configured to contain between about 0.25 μg and about 25 μg of a subject material  240 . 
     Regarding  FIG.  2 A , as an example embodiment, the sidewall  220  of the vapor cell  200  may include three stacked regions of substrate material  225 , bonded to one another by regions of interfacial material  230  interposed between adjacent regions of the substrate material  225  to facilitate bonding of the substrate material. In other examples, the three stacked regions of substrate material  225  may be directly bonded to one another without interfacial material  230  interposed between adjacent regions of the substrate material  225 . By way of example the substrate material  225  (e.g. the first substrate  255  and the second substrate  260 ) may be bonded through direct Si—Si bonding in embodiments where one or more interfaces between adjacent substrates of the body  205  (e.g., between the first substrate  255  and the second substrate  260 , between the second substrate  260  and the third substrate  265 ) lacks the interfacial material  230 . By way of example only a middle region of substrate material  225  may include a porous volume  235 , and overlying and underlying regions of the substrate material  225  may be interposed between the porous volume  235  and the respective windows  215 . 
     Regarding  FIG.  2 B , as another example, the body  205  may include stacked substrates, such as, for example, a first substrate  255  and a second substrate  260 , bonded to one another at an interface by regions of interfacial material  230  interposed between adjacent regions of the substrate material  225  to facilitate bonding of the substrate material. In another example interfacial material is not provided and first substrate  255  and second substrate  260  are bonded to one another at an interface without interfacial material  230 . At least one of the first substrate  255 , the second substrate  260 , or an interfacial material  230  between the first substrate  255  and the second substrate  260  may define at least one pore having a smallest dimension of 500 microns or less. For example, the first substrate  255 , the second substrate  260 , or both may include a porous volume  235 , a portion of the substrate material  225  of the first substrate  255 , the second substrate  260 , or both being porous. More specifically, the first substrate  255  proximate to one of the windows  215  may include the porous volume  235 , and the porous volume  235  may extend around a circumference of the cavity  210 . As a specific, nonlimiting example, the porous volume  235  may occupy an entirety of the surface of the first substrate  255  exposed to the cavity  210 . In such an example, an entirety of a thickness of the first substrate  255  may be rendered porous utilizing chemical treatment before material is removed from the porous volume  235  to define a portion of the cavity  210 . In some examples, the diameter of the cavity  210  as defined by the first substrate  255  may be smaller than the diameter of the cavity  210  as defined by the second substrate  260 . For example, the first substrate  255  may define a restricted aperture  270  proximate to the window  215  through which radiation may be directed toward the subject material  240  within the cavity  210 . Each of the first substrate  255  and the second substrate  260  may include, and be defined by, a region of substrate material  225 , and a mass of the interfacial material  230  may be interposed between, and bonded to, each adjacent pair of substrates. 
     The sidewall  220  of the vapor cell  200  may include two stacked regions of substrate material  225 , bonded together with a region of interfacial material  230  interposed between the regions of substrate material  225 . By way of example only, the two regions of substrate material  225  are displayed as having different heights corresponding to different regions forming different surface areas of the sidewall  220 . For example, the height of the region of substrate material  225  including the porous volume  235  may be less than the height of the other region of substrate material  225  not containing the porous volume  235 . In some examples, the diameter of the cavity  210  may not be constant. By way of example, the diameter of the cavity  210  defined by the region of the substrate material  225  adjacent to the window  215  through which incident radiation is to be received into the cavity  210 , and including the porous volume  235 , may be less than the diameter of the cavity  210  defined by the remainder of the substrate material  225 . Such a configuration may enable the vapor cell  200  to include a larger porous volume  235  without reducing the ability of incident radiation to interact with subject material within the cavity  210 , as beams of radiation may tend to diffuse and expand with distance after passing through the window  215  and beyond the region of substrate material  225  having the smaller diameter. 
     Regarding  FIG.  2 C , as another example, the body  205  may include stacked substrates, such as, for example, a first substrate  255  and a second substrate  260 , bonded to one another an interface. At least one of the first substrate  255 , the second substrate  260 , or an interfacial material  230  between the first substrate  255  and the second substrate  260  may define at least one pore having a smallest dimension of 500 microns or less. For example, the first substrate  255 , the second substrate  260 , or both may include a porous volume  235 , a portion of the substrate material  225  of the first substrate  255 , the second substrate  260 , or both being porous. More specifically, the first substrate  255  proximate to one of the windows  215  may include the porous volume  235 , and the porous volume  235  may extend around a circumference of the cavity  210 . As a specific, nonlimiting example, the porous volume  235  may occupy only a portion of the surface of the first substrate  255  exposed to the cavity  210 , a remainder of the surface of the first substrate  255  exposed to the cavity  210  being nonporous. In such an example, only a portion of a thickness of the first substrate  255  may be rendered porous before material is removed from the porous volume  235  and the remainder of the first substrate  255  to define a portion of the cavity  210 . In some examples, the diameter of the cavity  210  as defined by the first substrate  255  may be smaller than the diameter of the cavity  210  as defined by the second substrate  260 . Each of the first substrate  255  and the second substrate  260  may include a substrate material  225 , and a mass of the interfacial material  230  may be interposed between, and bonded to, each adjacent pair of substrates. 
     One of the regions of substrate material  225  may include a porous volume  235  occupying only a portion of the surface of the region of substrate material  225  defining the cavity  210 . A remainder of the region of substrate material  225  defining the cavity  210  may be nonporous. For example, the porous volume  235  may be spaced from the window  215 , with the remainder of the region of substrate material  225  interposed between the porous volume  235  and the window  215  being nonporous. The porous volume  235  may also have a depth that is not constant within the region of the substrate material  225 , as measured relative to the surface of the substrate material  225  with the interfacial material  230 . For example, the depth of the porous volume  235  may be greatest proximate to the interfacial material  230  and may decrease nonlinearly as distance from the interfacial material  230  increases. In another example, the depth of the porous volume  235  may be greatest proximate to the interfacial material  230  and may decrease linearly as distance from the interfacial material  230  increases. 
     The cross sectional profile of the porous volume  235  may be at least partially defined by the method through which it was prepared. By way of example, the selected region for the porous volume  235  may be prepared by creating a patterned hard mask (e.g., silicon carbide) over a surface of the region of substrate material  225 . Exposed portions of the substrate material  225  may be rendered porous by, for example, anodization, stain etching, bottom-up synthesis, or other techniques for rendering silicon porous. With some such techniques, a depth of the porous volume  235  may be at its maximum proximate to the cavity  210 , and may taper to a minimum depth distal from the cavity  210  (e.g., proximate to the edges of the mask used when rendering the substrate material  225  porous). In some examples, the cross-sectional shape of the porous volume  235  having a non-constant depth may include an at least substantially arcuate portion (e.g., a quarter-circular cross-sectional shape). 
     In some examples, a porous volume  235  may be rendered into multiple separate substrate material  225  segments. For example, two substrate material  225  segments may be bonded together with an interfacial material  230  interposed between the two substrate material  225  segments. Each substrate material  225  may be rendered to have a region within the cavity to include a respective porous volume  235 . The porous volume  235  may cover the entire surface, or a portion of the surface within the cavity  210  of the substrate material  225 . Such a configuration may provide a concentrated region at which the porous volume  235  is concentrated proximate to, or distal from, the bonding interface. 
     Regarding  FIG.  2 D , as another example, the body  205  may include stacked substrates, such as, for example, a first substrate  255  and a second substrate  260 , bonded to one another an interface. At least one of the first substrate  255 , the second substrate  260 , or an interfacial material  230  between the first substrate  255  and the second substrate  260  may define at least one pore having a smallest dimension of 500 microns or less. For example, the first substrate  255 , the second substrate  260 , or both may include a porous volume  235 , a portion of the substrate material  225  of the first substrate  255 , the second substrate  260 , or both being porous. More specifically, each of the first substrate  255  and the second substrate  260  may include a respective porous volume  235 , and the porous volume  235  may extend around a circumference of the cavity  210 . As a specific, nonlimiting example, a first porous volume  235  may occupy only a portion of the surface of the first substrate  255  exposed to the cavity  210 , a remainder of the surface of the first substrate  255  exposed to the cavity  210  being nonporous, and a second porous volume  235  may occupy only a portion of the surface of the second substrate  260  exposed to the cavity  210 , a remainder of the surface of the second substrate  260  exposed to the cavity  210  being nonporous. In such an example, only a portion of a thickness of the substrate material  225  of the first substrate  255  and the second substrate  260  may be rendered porous before material is removed from the porous volume  235  and the remainder of the first substrate  255  and the second substrate  260  to define a portion of the cavity  210 . The porous volumes  235  may be located, for example, adjacent to the windows  215  on opposite sides of the stacked first substrate  255  and second substrate  260 . As another example, the porous volumes  235  may be located proximate to the interfacial material  230  interposed between, and bonded to, the first substrate  255  and the second substrate  260 . Each of the first substrate  255  and the second substrate  260  may include a substrate material  225 , and a mass of the interfacial material  230  may be interposed between, and bonded to, each adjacent pair of substrates. 
     Each discrete region of the substrate material  225  may include a respective porous volume  235 . For example, each of the regions of substrate material  225  may include a porous volume  235  occupying only a portion of the surface of the respective region of substrate material  225  defining the cavity  210 . A remainder of the region of substrate material  225  defining the cavity  210  may be nonporous. For example, at least one porous volume  235  may be located proximate (e.g., adjacent) to the window  215 , with the remainder of the region of substrate material  225  interposed between the porous volume  235  and the interfacial material  230  being nonporous. More specifically, each porous volume  235  may be located proximate (e.g., adjacent) to a respective one of the windows  215 , with the remainder of the corresponding region of substrate material  225  interposed between the porous volume  235  and the interfacial material  230  being nonporous. 
       FIGS.  3 A and  3 B  show a flowchart depicting an illustrative method  300  of making a vapor cell. As specific, nonlimiting examples, the body of the vapor cell may take any of the forms, and may include any of the materials, described previously in connection with  FIGS.  1 A,  1 B,  2 A,  2 B,  2 C, and  2 D . 
     Referring to  FIG.  3   , the method  300  may involve providing a body, the body including a first substrate bonded to a second substrate at an interface, as indicated at act  302 . A cavity may be defined within the body, as indicated at act  304 . In at least one of the first substrate, the second substrate, or an interfacial material between the first substrate and the second substrate, at least one pore or recess having a smallest dimension of about 500 microns or less, as measured in a direction parallel to at least one surface of the first substrate partially defining the cavity, may be formed, as indicated at act  306 . 
     In some examples, forming the at least one pore or recess may involve forming the at least one pore by exposing the at least one of the first substrate, the second substrate, or the interfacial material to chemical processing, as indicated at act  308 . In some examples, forming the at least one pore or recess may involve forming the at least one recess by selectively etching a portion of the interfacial material between the first substrate and the second substrate to recess the interfacial material relative to the first substrate and the second substrate, as indicated at act  310 . In some examples, forming the at least one pore or recess comprises forming the at least one recess by selectively etching regions of oxide material interposed between regions of non-oxide material of at least one of the first substrate or the second substrate to recess each region of the oxide material relative to adjacent regions of the non-oxide material, as indicated at act  312 . In some examples, forming the at least one pore or recess may involve rendering a material of a region of at least one of the first substrate or the second substrate partially defining the cavity porous through chemical treatment or by patterning and selective etching of the substrate, as indicated at act  314 . 
     In some examples, the method  300  may involve placing the second substrate comprising the region between, and bonding the second substrate to, the first substrate and a third substrate of the body, as indicated at act  316 . In some examples, the region may be placed proximate to the interface between the first substrate and the second substrate, as indicated at act  318 . In some examples, forming the cavity may involve rendering a diameter of the cavity proximate to the region less than a diameter of the cavity distal from the region, as indicated at act  320 . In some examples, rendering the material of the region of the at least one of the first substrate or the second substrate partially defining the cavity porous may involve rendering the material of a first region of the first substrate partially defining the cavity porous to form a first mass of the porous material and rendering a material of a second region of the second substrate partially defining the cavity porous to form a second mass of the porous material, as indicated at act  322 . In some examples, the first and the second porous regions may be placed distal from the interface between the first substrate and the second substrate, as indicated at act  324 . 
     The ordering and arrows of the acts in the flowchart of  FIGS.  3 A and  3 B  are not to be interpreted to imply that those acts must or should be performed in a specific order. When it is logically possible to do so, the acts in the flowchart of  FIGS.  3 A and  3 B  may be performed in any order. For example, the cavity may be defined in the body, as stated in act  304 , before the body is provided (i.e., when the cavity has been preformed as part of the body), after the formation of at least one pore or recess, or before or after any of acts  308  through  324 . In addition, the dashed lines indicating acts  308  through  324  are optional in some examples should not be interpreted to mean that any of acts  302 ,  304 , or  306 , or the order in which they are presented, is not optional. 
       FIGS.  4 A and  4 B  are schematics of illustrative systems  402  and  416 , respectively, including a vapor cell  400  in accordance with this disclosure, differing in whether microwaves are applied directly to the vapor cell  400 , as in a microwave-optical double-resonance clock or an Mx magnetometer shown in system  402 , or applied as modulation to a laser bias current, as in a clock based on coherent population trapping or a Bell-Bloom type magnetometer shown in system  416 . The systems  402  and  416  may be configured as, for example, atomic clocks, magnetometers, or gyroscopes. 
     The vapor cell  400  may include an examination region containing vaporized atoms of the subject material, and one or more emitters may be configured to direct electromagnetic radiation of a known type and intensity toward the examination region (e.g., one or more lasers  408 , microwaves  412 , both lasers  408  and microwaves  412 , without limitation). Such a vapor cell  400  may be maintained at near-vacuum pressure or may include a buffer gas. By way of example only, the buffer gas may include a mixture of N 2  and argon. A detector  414  may include a sensor configured to detect the transmitted radiation and therefore determine one or more properties of the vaporized atoms of the subject material in response to the transmitted radiation. For example, the sensor of the detector  414  may be configured to detect the transition of electrons of the subject material between energy levels, responsive to the energy from a first of the emitters (e.g., from the laser  408 ), as measured in variation of signal strengths relative to the spectrum of the radiation, e.g., from the microwave  412 . 
     One or more signals representative of the properties measured by the detector  414  may be provided as feedback to an oscillator  406 . The oscillator  406  may be used to generate a clock output  404 , which may be used as a clock signal itself or may be used to verify or synchronize another clock signal. In other words, the oscillator  406  may generate a clock output  404  whose frequency is determined by energy level differences in the subject material. 
     Providing recesses or pores in a body of a vapor cell may induce one or more exposed surfaces of a subject liquid within the vapor cell to exhibit a concave shape. As a nonlimiting example, the size, shape, position, and configuration of the recesses or pores may have capillary-like characteristics, causing any subject material condensed within the recesses or pores to have a negative meniscus. In accordance with the Kelvin equation, the concave shape of the exposed surfaces of the masses of subject material may cause the vapor pressure to be less than the saturation pressure for the subject material above a flat liquid surface. Such control over the vapor pressure may enable devices utilizing the vapor cells, such as, for example, atomic clocks, to operate reliably over a greater range of operating temperatures. 
     Such a system  402  or  416  may be particularly useful for generating, verifying, or synchronizing clock signals of high accuracy and/or in extreme environmental conditions. Systems  402  and  416  in accordance with this disclosure may find application in the aerospace industry (e.g., to control clock signals in satellites and spacecraft), the automotive industry, the telecommunications and banking industries (e.g., to verify or set clock signals for relevant computing systems), and in standard-setting situations (e.g., to establish timings for relevant standards). By reducing the vapor pressure of the subject material in the vapor cell of the system  402  or  416 , the atomic clock may operate over a larger range of ambient temperatures. 
     Techniques for forming recesses and/or pores, as disclosed herein, may enable formation of recesses and/or pores having selectable sizes, shapes, volumes, and positions in vapor cells. Such techniques may enable selection and variation in the volume of subject material receivable by the recesses and/or pores, and accompanying flexibility in size of the vapor cell, quantity of subject material in the cavity of the vapor cell, and operating parameters for vapor cells. 
     While certain illustrative examples have been described in connection with the figures, the scope of this disclosure is not limited to those examples explicitly shown and described in this disclosure. Rather, many additions, deletions, and modifications to the examples described in this disclosure may be made to produce examples within the scope of this disclosure, such as those specifically claimed, including legal equivalents. In addition, features from one disclosed example may be combined with features of another disclosed example while still being within the scope of this disclosure.