Patent Publication Number: US-8528608-B2

Title: Measuring volume of a liquid dispensed into a vessel

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. application Ser. No. 11/966,654, entitled “MEASURING VOLUME OF A LIQUID DISPENSED INTO A VESSEL,” filed on Dec. 28, 2007, which is incorporated herein by reference in its entirety for all purposes. 
    
    
     GOVERNMENT RIGHTS IN THIS INVENTION 
     This invention was made with U.S. government support under contract number H94003-07-C-0712. The U.S. government has certain rights in this invention. 
    
    
     BACKGROUND 
     1. Field of the Invention 
     Implementations of various technologies described herein generally relate to substrate processing. 
     2. Description of the Related Art 
     The following descriptions and examples do not constitute an admission as prior art by virtue of their inclusion within this section. 
     To achieve the desired performance enhancement for each successive generation of silicon integrated circuits (ICs), semiconductor manufacturing has become increasingly reliant on new materials and their integration into advanced process sequences. Unfortunately, typical semiconductor manufacturing equipment is not well suited for materials exploration and integration. Issues impacting the use of typical semiconductor manufacturing equipment include difficulty in changing process materials and chemicals rapidly, limited ability to integrate and sequence multiple materials or chemicals in a single reactor or process chamber, high equipment cost, large sample size (300 mm wafer) and inflexible process/reactor configurations. To complement traditional manufacturing tools, a need has arisen for process equipment that facilitates fast testing of new materials and materials processing sequences over a wide range of process conditions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Implementations of various technologies will hereafter be described with reference to the accompanying drawings. It should be understood, however, that the accompanying drawings illustrate only the various implementations described herein and are not meant to limit the scope of various technologies described herein. 
         FIG. 1A  illustrates a schematic diagram for implementing combinatorial processing in connection with implementations of various technologies described herein. 
         FIG. 1B  illustrates an exemplary substrate containing multiple regions for combinatorial processing according to implementations of various technologies described herein. 
         FIG. 2  illustrates a schematic diagram of a combinatorial processing tool according to implementations of various technologies described herein. 
         FIG. 3  illustrates a system for measuring a volume of liquid dispensed into a vessel according to implementations of various technologies described herein. 
         FIG. 4  is a flow diagram illustrating a method for measuring a volume of liquid dispensed into a vessel according to implementations of various techniques described herein. 
         FIGS. 5A-5C  illustrate liquid being dispensed into a vessel according to implementations of various technologies described herein. 
     
    
    
     DETAILED DESCRIPTION 
     The following paragraphs generally describe one or more implementations of various technologies and techniques directed to measuring a volume of liquid dispensed into a vessel. In one implementation, the vessel into which the liquid is to be dispensed may have a constant volume. Furthermore, the vessel may contain a gas at an initial pressure as measured by a pressure gauge or pressure transducer coupled to the vessel. As a volume of liquid is dispensed into the vessel, the gas may be compressed, thereby increasing the pressure within the vessel. The volume of liquid dispensed into the vessel may be calculated using the volume of the vessel, the initial pressure of the gas within the vessel, and the final pressure of the gas within the vessel. This calculation allows dispensing of liquids into multiple vessels to occur in parallel, thereby increasing throughput of combinatorial processing tools. 
     One or more implementations of various techniques for measuring a volume of liquid dispensed into a vessel will now be described in more detail with reference to  FIGS. 1A-5C  in the following paragraphs. 
     The discussion below is directed to certain specific implementations. It is to be understood that the discussion below is only for the purpose of enabling a person with ordinary skill in the art to make and use any subject matter defined now or later by the patent “claims” found in any issued patent herein. 
     Combinatorial processing may include any processing, including semiconductor processing, which varies the processing conditions across one or more substrates. As used herein, a substrate may be, for example, a semiconductor wafer, a portion of a semiconductor wafer, solar photovoltaic circuitry, or other semiconductor substrate. The term “substrate” includes a coupon, which is a diced portion of a wafer, or any other device on which semiconductor processes are performed. The coupon or substrate may optionally contain one die, multiple dice (connected or not through the scribe), or portion of die with useable test structures. In some implementations, multiple coupons, or die can be diced from a single wafer and processed combinatorially. 
     Combinatorial processing is performed by varying processing conditions across multiple substrates, multiple regions of a single substrate, or a combination of the two. Processing conditions may include, for example, chemical formulation, fluid flow rates, temperatures, reaction times, concentrations, agitation or stirring, and the like. For example, a first region of a substrate may be processed using a first process condition (e.g., applying a chemical at a first temperature) and a second region of the substrate may be processed using a second process condition (e.g., applying the chemical at a second temperature). The results (e.g., the measured characteristics of the processed regions) are evaluated, and none, one, or both of the process conditions may be selected as suitable candidates for larger scale processing (e.g., further combinatorial processing or deposition on a full wafer). Techniques for combinatorial processing are described in U.S. patent application Ser. No. 11/352,077, entitled “Methods For Discretized Processing and Process Sequence Integration of Regions of a Substrate,” which is incorporated herein by reference. 
     Several combinatorial processing tools can be used. One type of tool may include a reactor block that has several openings (e.g., cylindrical openings) that define individual reactors on a single substrate. Each of the openings may further include a sleeve that creates a seal with the substrate to contain processing fluids or chemicals within a single reactor. For example, a reactor block may include 28 openings that define 28 regions on a substrate. Each of the 28 regions can be processed using varying process conditions, or multiple regions can have the same processing conditions. For example, seven sets of processing conditions can be performed across four regions each. Each region can then be characterized using various techniques (e.g., electrical test, microscopy), and useful or beneficial techniques and/or conditions can be selected. 
     Other combinatorial processing may be performed in a manner that is not site isolated. For example, a wafer can be divided into many small coupons, each of which can be processed using different conditions. Using another example, a wafer can be processed using a gradient approach, where the processing varies over the substrate. 
       FIG. 1A  illustrates a schematic diagram  100  for implementing combinatorial processing in connection with implementations of one or more technologies described herein. The schematic diagram  100  illustrates that the relative number of combinatorial processes that run with a group of substrates decreases as certain materials and/or processes are selected. Generally, combinatorial processing includes performing a large number of processes during a first screen, selecting promising candidates from those processes, performing the selected processing during a second screen, selecting promising candidates from the second screen, and so on. In addition, feedback from later stages to earlier stages can be used to refine the success criteria and provide better screening results. 
     For example, thousands of materials are evaluated during a materials discovery stage  102 . Materials discovery stage  102  is also known as a primary screening stage performed using primary screening techniques. Primary screening techniques may include dividing wafers into coupons and depositing materials using varied processes. The materials are then evaluated, and promising candidates are advanced to the secondary screen, i.e., materials and process development stage  104 . Evaluation of the materials may be performed using metrology tools such as electronic testers and imaging tools, e.g., microscopes. 
     The materials and process development stage  104  may evaluate hundreds of materials (i.e., a magnitude smaller than the primary stage) and may focus on the processes used to deposit or develop those materials. Promising materials and processes are again selected, and advanced to the tertiary screen or process integration stage  106 , where tens of materials and/or processes and combinations are evaluated. The tertiary screen or process integration stage  106  may focus on integrating the selected processes and materials with other processes and materials. 
     The most promising materials and processes from the tertiary screen are advanced to device qualification stage  108 . In device qualification, the materials and processes selected are evaluated for high volume manufacturing, which normally is conducted on full wafers within production tools, but need not be conducted in such a manner. The results are evaluated to determine the efficacy of the selected materials and processes. If successful, the use of the screened materials and processes can proceed to the manufacturing stage  110 . 
     The schematic diagram  100  is an example of various techniques that may be used to evaluate and select materials and processes for the development of semiconductor devices. The descriptions of primary, secondary, etc. screening and the various stages  102 - 110  are arbitrary and the stages may overlap, occur out of sequence, be described and be performed in many other ways. 
       FIG. 1B  illustrates a substrate  120  including multiple regions for combinatorial processing. A substrate  120  includes several regions  122  on which semiconductor processes can be performed. For example, the regions  122   a ,  122   b , and  122   c  may each have an electroless layer deposited on them. The region  122   a  may use a first chemical formulation, the region  122   b  a second chemical formulation, and the region  122   c  a third chemical formulation. The resulting layers can be compared to determine the relative efficacy of each of the formulations. None, one, or more of the formulations can then be selected to use with further combinatorial processing or larger scale processing (e.g., manufacturing). Any process variable (e.g., time, composition, temperature) can be varied using combinatorial processing. 
     As discussed above, each of the regions  122  may or may not be site isolated. Site isolation refers to a condition where the regions  122  can be processed individually and independently without interference from neighboring regions. For example, one or more of the regions  122  may include a sleeve having an end that forms a fluid seal with the substrate  120 . The sleeve is configured to contain processing fluids (e.g., chemicals), and is made from a material (e.g. polytetrafluoroethylene (PTFE)) that does not react with the processing chemicals used. The chemicals do not leak out of the region into which they were dispensed, and each region  122  can be processed and evaluated individually. 
     Each of the regions  122  may be processed using a cell of a combinatorial processing tool, as described in  FIG. 2 . The tool is calibrated so that processing in each of the regions  122  is consistent and comparable. Using the technologies described herein to measure the volume of liquids dispensed into a container, more precise control over chemical mixtures and the volume of fluid dispensed into portions of a combinatorial processing tool may be achieved. Flow cells within the combinatorial processing tool may be calibrated such that a consistent application of chemicals across regions of a substrate is achieved. Furthermore, accurate measurement of volumes of liquids dispensed into vessels within the combinatorial processing tool may improve consistency from experiment to experiment, such that the results of one experiment will mirror those of a subsequent experiment, and will be comparable. 
     Combinatorial Processing Tool 
       FIG. 2  illustrates a schematic diagram of a combinatorial processing tool  200  according to implementations of one or more technologies described herein. The combinatorial processing tool  200  illustrated in  FIG. 2  may be a wet processing tool and may be a portion of a larger combinatorial processing tool. Portions of the combinatorial processing tool  200  may be replicated several times within a larger combinatorial processing tool such that a larger number of variations in substrate processing conditions may be achieved. 
     The combinatorial processing tool  200  illustrated in  FIG. 2  may be divided into four parts. A chemical supply portion  202  may supply chemicals to a chemical mixing portion  204  and a reactor portion  206 . The chemical mixing portion  204  may be used for mixing various chemicals, e.g., liquid chemicals, into solutions which may be applied to various locations on a substrate in the reactor portion  206 . The reactor portion  206  may contain a site isolated reactor and may apply the solutions to the substrate or portions of the substrate and may subject the substrate or portions thereof to various processing conditions. The reactor portion  206  may be coupled to a waste portion  208  of the combinatorial processing tool  200 . The waste portion  208  may be used to capture waste chemicals after substrate processing. A multiple of the portions  202 ,  204 ,  206 ,  208 , or their individual components can be included in the combinatorial processing tool. For example, a combinatorial processing tool  200  may include multiple chemical mixing portions  204 . Using techniques described herein for measuring amounts of liquids dispensed into the chemical mixing portions  204  allows the liquids to be dispensed in a parallel fashion. 
     The supply portion  202  of the combinatorial processing tool  200  may include a bottle  210  containing a liquid chemical. The chemical may be applied to the substrate or may be mixed with another chemical to form a solution which is to be applied to the substrate. As illustrated in  FIG. 2 , a pressure source PS 1  and a pressure regulator Pn 1  may be coupled to the bottle  210  via a pressure supply line  212 . Together the pressure source PS 1  and the pressure regulator Pn 1  may provide a pressurized gas, such as Nitrogen, at a regulated pressure to the bottle  210  via the supply line  212 . In this manner, the pressurized gas may be used to push the liquid chemical out of the bottle  210  and into a line  214  connecting the bottle  210  to a supply manifold Vd 1 . A flow meter  216  and a pressure transducer Pd may be coupled to the line  214 . The flow meter  216  may monitor the flow rate of liquids through the line  214  and the pressure gauge Pd may monitor the pressure within the line  214 . The flow rate of fluids in the combinatorial processing tool  200  is measured to ensure desired processing characteristics. For example, in some combinatorial processing operations, chemicals may need to be flowed past a processed region of a substrate at a desired rate. The desired rate can be maintained by monitoring output of the flow meter. 
     The supply manifold Vd 1  may contain a plurality of two-way and/or multi way valves connecting the bottle  210  to a plurality of mixing cells/vessels within the combinatorial processing tool  200 . Furthermore, in lieu of a single bottle  210 , a plurality of bottles containing various chemicals may be coupled to the supply manifold Vd 1  such that the supply manifold Vd 1  may supply various chemicals to multiple mixing portions or multiple site isolated reactor portions of the combinatorial processing tool  200 . Additionally, in lieu of a single supply manifold Vd 1 , a plurality of supply manifolds Vd 1  may be present in the combinatorial processing tool  200 . Together the plurality of bottles, valves, and supply manifolds may enable the supply of various chemicals and chemical mixtures to the mixing portion  204  and the site isolated reactor portion  206  of the combinatorial processing tool  200 . 
     The line  214  coupling the bottle  210  to the supply manifold Vd 1  may be coupled to a valve, e.g., a multi-way valve, within the supply manifold Vd 1  such that the supply manifold Vd 1  may control the flow of chemicals from the bottle  210  to the mixing portion  204  or the reactor portion  206  of the combinatorial processing tool  200 . 
     The output of the valve in the supply manifold Vd 1  may be coupled via a line  218  to a valve Vp 2 . The valve Vp 2  may be a multi-way valve which controls the flow of fluids/chemicals from the supply manifold Vd 1  into either the mixing portion  204 , site-isolated reactor portion  206 , or both. 
     The mixing portion  204  of the combinatorial processing tool  200  is provided to allow thorough solution mixing of chemicals provided by supply portions. In order to form a solution, a plurality of chemicals may flow from the supply portion  202 , e.g., the bottle  210 , into different mixing vessels in the mixing portion  204 . The mixing vessel  220  may then mix the chemicals to form solutions. The mixing portion  204  may also provide accurate temperature and pH control of a solution being mixed in the mixing portion  204 . 
     A pressure source Ps 2  and a pressure regulator Pn 2  may be coupled to the mixing vessel  220  via a valve Vr and a supply line  222 . Together the pressure source PS 2  and the pressure regulator Pn 2  may provide a pressurized gas, e.g., Nitrogen, at a regulated pressure to the mixing vessel  220  via the valve Vr and the supply line  222 . An outlet of the valve Vr may be coupled to another valve Vg to vent pressure within the supply line  222 . The pressure in the supply line  222  may be measured by a pressure transducer Pg. 
     The pressurized gas provided by the pressure source Ps 2  and the pressure regulator Pn 2  may push the mixed chemicals in the mixing vessel  220  through a line  224  and into the site-isolated reactor portion  206  of the combinatorial processing tool  200 . The mixed chemicals may flow through a valve Vf 1  and into a flow cell  226 . The flow cell  226  may be one portion of a site isolated reactor, and may be used to apply the mixed chemicals to a portion or portions of a substrate under processing in the site-isolated reactor portion  206  of the combinatorial processing tool  200 . The flow cell  226  may have a series of parallel cells forming site-isolated reactors which may be configured to effect site-isolated processing on proximate regions on the substrate. Chemicals may also be provided to the flow cell  226  and, consequently, to a substrate via the supply manifold Vd 1 . 
     After exposing the substrate to the desired amount of chemicals, excess or waste chemicals may exit the flow cell  226  through valve Vf 1  and waste line  228  or through valve Vf 2  and waste line  230 . Waste line  228  may be coupled to a waste manifold Vd 2 , and waste line  230  may be coupled to waste manifold Vd 3 . The waste manifolds may be coupled to waste sumps (e.g., waste sump Ws 1  and waste sump Ws 2 ) and the waste manifolds may be used to divert chemicals into specific waste sumps. A waste line  232  may couple a waste manifold Vd 2  to a waste sump Ws 1 . Furthermore, a waste flow meter  234  may be coupled to the waste line  232  to measure a flow rate of waste liquids flowing into the waste sump Ws 1 . 
     The flow meters (e.g., flow meter  216  and flow meter  234 ) may be any type of flow meter available. For example, the flow meters may be ultrasonic flow meters which measure the travel time of ultrasonic waves through a liquid and calculates a flow rate of the liquid based on the measured travel time of the ultrasonic waves. The flow meters may also be magnetic flow meters which measure changes in a magnetic field applied to a liquid to determine a rate of liquid flow. 
     Measuring Volume of Liquid Dispensed into a Vessel 
     When processing semiconductor substrates it may be desirable to know how much of a liquid has been dispensed into a vessel. For example, in the combinatorial processing tool  200  illustrated in  FIG. 2  it may be desirable to know a volume of a liquid chemical which has been dispensed into a mixing vessel  220  in order to ensure formation of precise solutions in the mixing vessel  220 . Using techniques described herein, for example, precise mixing of solutions can improve combinatorial processing by providing consistent application across regions of a substrate, across regions on different substrates, and across different experiments. These techniques improve the results of combinatorial processing and additionally can help to maintain the calibration of flow cells used in combinatorial processing tools. 
     Determining a volume of liquid which has been dispensed into a vessel may be accomplished using a flow meter. A flow meter may measure the rate at which a liquid is flowing through the flow meter. If the flow meter is coupled to a line through which a liquid flows into the vessel, the volume of liquid dispensed into the vessel may be calculated using the flow rate measured by the flow meter and the amount of time the liquid has been flowing into the vessel. 
     This technique of measuring the amount of liquid dispensed into the vessel in one implementation may use flow meters coupled to each vessel into which the volume of liquid is to be dispensed and measured. Thus, a large number of flow meters may be necessary in a combinatorial processing tool with multiple mixing vessels. The large number of flow meters may add to the cost of producing a combinatorial processing tool. 
       FIG. 3  illustrates a system  300  which may be used to measure a volume of liquids dispensed into a vessel in accordance with various technologies described herein. The system  300  may be a portion of the combinatorial processing tool  200  illustrated in  FIG. 2 , for example incorporated into the chemical mixing portion  204 . Additionally, the system  300  can be used with any system to measure flow rates or volumes of liquid dispensed. The system  300  includes a bottle  305  containing a liquid chemical. A pressurized gas may be provided to the bottle from a pressure source  310  via a supply line  315  which is coupled to the bottle  305 . A liquid chemical supply line  320  may also be coupled to the bottle  305 , and a first end of the supply line  320  may be located within the bottle  305  such that the first end of the liquid chemical supply line  320  is immersed in the liquid chemical. The bottle  305  may be pressurized by the pressure source  310  such that the liquid chemical may be pushed out of the bottle through the supply line  320  when a downstream valve  322  coupled to the supply line  320  is opened. 
     A second end of the supply line  320  may be coupled to an inlet of the valve  322  which is located within a supply manifold  325 . The supply manifold  325  may contain a plurality of multiple-way valves for routing liquid chemicals into mixing vessels and/or reactors within a combinatorial processing tool. An outlet of the valve  322  to which the supply line  320  is coupled may be coupled to a first end of a second supply line  330 . The second end of the second supply line  330  may be coupled to a mixing vessel  335 . The mixing vessel  335  may be the destination vessel into which the liquid chemical in the bottle  305  is to be dispensed. The mixing vessel  335  may have a constant volume V 0 . Furthermore, the mixing vessel  335  may contain a gas having an initial pressure P 0  and may be able to maintain an isothermal state (constant temperature). With the exception of the second supply line  330  coupled to the mixing vessel  335 , the mixing vessel  335  may be sealed while liquid chemical is dispensed into the vessel. In one embodiment, liquid may be dispensed into the mixing vessel  335  and other mixing vessels  335  using the volume measuring techniques described herein. For example, with calibrated mixing vessels (i.e., when the empty volume of the vessel is known), a combinatorial processing tool can dispense liquid from a bottle and into multiple mixing vessels in parallel, since these techniques allow computation of the volume of liquid dispensed into each mixing vessel. Some other techniques for measuring the amount of liquid dispensed can only be used with serial dispensing of liquid into multiple mixing vessels. 
     A pressure gauge  340  or pressure transducer may be coupled to the mixing vessel  335  and may be configured to measure a pressure (e.g., gas pressure) within the mixing vessel  335 . The pressure gauge  340  may also be coupled to a controller or a control device  345  such that the pressure gauge  340  provides the measured pressure within the mixing vessel  335  to the control device  345 . 
     The control device  345  may be, for example, a computer system containing one or more processors, application specific integrated circuits (ASICs), systems on a chip (SOCs), programmable logic, memory (e.g., hard disk drive(s), random access memory, etc.), devices for receiving input from a user (e.g., keyboard, mouse, etc.), communication devices (e.g., network controllers, serial ports, etc.), and/or devices for outputting data (e.g., printers, monitors, data storage, etc.). 
     The control device  345  may be configured to receive as input a recipe for processing a substrate or substrates within the combinatorial processing tool  200 . The control device  345  may also be configured to control the operation of the combinatorial processing tool  200  such that the substrate or substrates are processed in a manner specified by the recipe. For example, a recipe may specify how much of a liquid chemical is to be dispensed into the mixing vessel  335  from the bottle  305 . Consequently, the control device  345  may be coupled to the supply manifold  325  and may be configured to place the valve  322  in the supply manifold  325  in a first or an open position to allow liquid chemicals to flow into the mixing vessel  335 . Furthermore, as described further below with respect to  FIG. 4 , the control device  345  may be configured to calculate the amount of liquid dispensed into the mixing vessel  335 , and configured to place the valve  322  in a second or closed position, thereby stopping the flow of liquid into the mixing vessel  335  when the amount of liquid specified by the recipe has been dispensed into the mixing vessel  335 . 
       FIG. 4  illustrates a method  400  for measuring the volume of liquid dispensed into the mixing vessel  335  using the system  300  illustrated in  FIG. 3  in accordance with implementations of various techniques described herein. 
     In one implementation, the method  400  may begin at step  405  when the control device  345  determines that a liquid chemical is to be dispensed into the mixing vessel  335 . At step  410 , the control device  345  may determine an initial pressure of the gas within the mixing vessel  335 . The initial pressure within the mixing vessel  335  may be determined by checking the pressure measurement provided to the control device  345  by the pressure gauge  340 . The initial pressure within the mixing vessel  335  may be determined before the liquid chemical has been dispensed into the mixing vessel  335 . 
     For example,  FIG. 5A  illustrates the system  300  before the liquid chemical has been dispensed into the mixing vessel  335 . As illustrated in  FIG. 5 , the mixing vessel  335  may have an initial pressure of P 0  as measured by the pressure gauge  340  coupled to the mixing vessel  335 . Furthermore, the mixing vessel  335  may have a constant volume of V 0 . 
     Referring back to method  400 , after the initial pressure within the mixing vessel  335  has been determined, at step  415  the control device  345  may move the valve  322  in the supply manifold  325  to a first or an open position, which may allow the pressurized gas in the bottle  305  to push the liquid chemical in the bottle  305  through the line  320 , through the supply manifold  325 , through the line  330  and into the mixing vessel  335 . As the liquid chemical flows into the mixing vessel  335 , it may compress the gas within the mixing vessel  335 , thereby increasing the pressure of the gas within the mixing vessel  335 . The new or increased pressure in the mixing vessel  335  may be measured by the gauge  340  coupled to the mixing vessel  335 . 
       FIG. 5B  illustrates the system  300  as the liquid chemical is flowing into the mixing vessel  335 . As the liquid chemical flows into the mixing vessel  335 , a volume of liquid chemical VL 1  may accumulate within the mixing vessel  335 . Furthermore, as the liquid chemical flows into the mixing vessel  335 , the pressure within the mixing vessel  335  increase as a result of the new liquid displacing and compressing the gas within the vessel  335 . The increased or new pressure P 1  is measured by the pressure gauge  340  coupled to the mixing vessel  335 . 
     At step  420 , the control device  345  may again determine the pressure within the mixing vessel  335 . The control device  345  may determine the pressure within the mixing vessel  335  by checking the measured pressure provided to the control device  345  by the pressure gauge  340 . 
     At step  425 , the control device  345  may calculate the volume of liquid which has been dispensed into the mixing vessel  335 . The control device  345  may calculate the volume of the liquid dispensed into the mixing vessel  335  using the initial pressure within the mixing vessel  335  (i.e., P 0  determined during step  410 ), the volume of the vessel (i.e., V 0 ), and the increased or new pressure within the mixing vessel  335  (i.e., P 1  determined during step  420 ). 
     If the gas within the mixing vessel  335  is an ideal gas, the control device  345  may calculate the volume of liquid dispensed into the mixing vessel  335  using the following equation: 
     
       
         
           
             
               
                 
                   
                     V 
                     L 
                   
                   = 
                   
                     
                       
                         V 
                         0 
                       
                       ⁡ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               P 
                               0 
                             
                             P 
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
           
         
       
     
     In Equation 1, VL is the volume of liquid within the mixing vessel  335 , V 0  is the volume of the mixing vessel  335 , P 0  is the initial pressure of the mixing vessel  335 , and P is the measured pressure of the mixing vessel  335  after an amount of liquid chemical has been dispensed into the mixing vessel  335  (e.g., P 1  determined during step  420 ). Since V 0 , P 0 , and P are known, the control device  345  may calculate the volume of liquid which has been dispensed into the mixing vessel  335  (VL). 
     The control device  345  may be configured to dispense a predetermined volume of liquid chemical into the mixing vessel  335 . For example, a recipe for substrate processing may specify the volume of liquid chemical to be dispensed into the mixing vessel  335 . Consequently, after determining the volume of liquid which has been dispensed into the mixing vessel  335 , the control device  345  may proceed to step  430  to determine if a sufficient volume of liquid chemical has been dispensed into the mixing vessel  335 . The control device  345  may determine if the predetermined volume of liquid chemical has been dispensed into the mixing vessel  335  by comparing the predetermined volume of liquid with the volume of liquid which has been dispensed into the vessel. 
     If the volume of liquid dispensed into the mixing vessel  335  is equal to the predetermined amount of liquid, the control device  345  may proceed to step  430  where the control device  345  may move the valve  322  within the supply manifold to a second or closed position such that the flow of liquid chemical from the bottle  305  to the mixing vessel  335  is stopped. Then, the control device  345  may proceed to step  435  where the method  400  may end. 
     However, if during step  425  the control device  345  determines that the volume of liquid chemical dispensed into the mixing vessel  335  is less than the predetermined amount of liquid chemical, the control device  345  may return to step  420  to again determine the pressure within the mixing vessel  335 . By returning to step  420 , the control device  345  may allow more liquid chemical to dispense into the mixing vessel  335  and, thus, the volume of liquid chemical in the mixing vessel  335  may approach or reach the predetermined volume of liquid chemical which is to be dispensed into the mixing vessel  335 . 
       FIG. 5C  illustrates the final volume of liquid chemical VL 2  dispensed into the mixing vessel  335 . The final volume of liquid chemical VL 2  may be the predetermined volume of liquid chemical specified by the recipe.  FIG. 5C  also illustrates how the control device  345  has closed the valve  322  in the supply manifold  325  (i.e., in step  430  of method  400 ) thereby stopping the flow of the liquid chemical from the bottle  305  to the mixing vessel  335 . In  FIG. 5C , the final pressure P 2  has been measured by the pressure gauge  340  and consequently, the control device  345  may calculate the final volume of liquid VL 2  using the initial pressure (i.e., P 0 ), the volume of the mixing vessel  335  (i.e., V 0 ), the final pressure of the mixing vessel (i.e., P 2 ) and Equation 1 which results in the following equation: 
     
       
         
           
             
               
                 
                   
                     V 
                     
                       L 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         V 
                         0 
                       
                       ⁡ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               P 
                               0 
                             
                             
                               P 
                               2 
                             
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
           
         
       
     
     After completing method  400 , the control device  345  may flow a second liquid chemical into the mixing vessel  335  and may determine the volume of the second liquid chemical dispensed into the mixing vessel  335  using Equation 1, the volume of the mixing vessel  335  (i.e., V 0 ), the initial pressure of the mixing vessel  335  before the second liquid chemical is flowed into the mixing vessel  335  (e.g., P 2 ), and the pressure of the vessel after some volume of the second liquid chemical has been dispensed into the vessel. The method  400  may be used with the second and subsequent liquid chemicals for mixing and other purposes. 
     Furthermore, the liquid chemicals which flow into the mixing vessel  335  may be mixed to form a solution. After mixing the liquid chemicals into a solution within the mixing vessel  335 , the control device  345  may direct the combinatorial processing tool to flow the solution out of an outlet of the mixing vessel and into a reactor portion  206  of the combinatorial processing tool where the solution may be applied to a portion or portions of a substrate or substrates under processing in the reactor portion  206  of the combinatorial processing tool  200 . These techniques therefore can provide more precisely mixed chemical solutions to the reactor portion  206 , resulting in more consistent results across regions, substrates, and different experiments. The combinatorial results are therefore more comparable to each other and other combinatorial experiments. Additionally, precise mixing of chemical solutions and application of those solutions to the reactors and flow cells helps maintain calibration of the flow cells. 
     While the foregoing is directed to implementations of various technologies described herein, other and further implementations may be devised without departing from the basic scope thereof, which may be determined by the claims that follow. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.