Classifications

• • G—PHYSICS
  • G05—CONTROLLING; REGULATING
  • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
  • G05D7/00—Control of flow
  • G05D7/06—Control of flow characterised by the use of electric means
  • G05D7/0617—Control of flow characterised by the use of electric means specially adapted for fluid materials
  • G05D7/0629—Control of flow characterised by the use of electric means specially adapted for fluid materials characterised by the type of regulator means
  • G05D7/0635—Control of flow characterised by the use of electric means specially adapted for fluid materials characterised by the type of regulator means by action on throttling means
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
  • Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
  • Y10T137/00—Fluid handling
  • Y10T137/7722—Line condition change responsive valves
  • Y10T137/7758—Pilot or servo controlled
  • Y10T137/7761—Electrically actuated valve

Definitions

• a recipe may require more than one gas species.
• the gas species become mixed and reach an equilibrium pressure state ⁇ e.g., set pressure) within a processing chamber at the same time.
• an equilibrium pressure state e.g., set pressure
• several factors may cause the gas species to have different time scales (i.e., delivery time).
• O ne factor that may impact the gas delivery time is the mass of gas species.
• gas species with heavier molecular mass may travel slower than gas species with lighter molecular mass.
• the mass difference between gas species may impact the flow rate of each gas specie in a low pressure environment.
• the gas flow may become molecular and each gas specie may become virtually independent of each other.
• separation of the gas species may occur resulting in gas composition drift at the chamber.
• the gas species may reach the equilibrium state at different time.
• the time scale e.g., delivery time
• gas line geometry Another factor that may impact the gas delivery time scale is the gas line geometry.
• a recipe may require more than one gas species to perform substrate processing.
• Each gas may flow from a gas line into a mixing manifold (main gas line).
• the geometry of each gas line may impact the flow of the gas.
• the delivery time will be greater for the gas flowing through the longer gas line.
• Some recipes may have low-flow gas mixing with high-flow gas.
• This type of gas delivery is known as a carrier gas-driven delivery, where the high-flow gas (carrier gas) drives the flow of the low-flow gas (process gas) via molecular collision.
• the process gas In order for the process gas to enter the mixing manifold where the carrier gas is flowing, the process gas needs to build up a pressure comparable to the pressure at the mixing manifold.
• the carrier gas is flowing at a much higher flow rate than the process gas, it could take a prohibitively long time for the process gas to build up enough pressure and then mix with the carrier gas. In this case, the carrier gas will reach the processing chamber without carrying the process gas. Thus, the carrier will reach an equilibrium state before the process gas resulting in gas composition drift.
• substrate processing may begin when pressure stabilization has been reached within the processing chamber, regardless of gas composition drift. Performing substrate processing without the proper gas mixture may cause substandard devices to be created. Other recipes may require each gas specie within the processing chamber to reach the required equilibrium state before processing may begin. However, the additional time required may result in longer processing time and less substrate to be processed.
• the invention relates, in an embodiment, to a method for establishing a mass flow controller (MFC) control scheme for a recipe, wherein the MFC control scheme is configured for reducing a time scale for gas delivery into a processing chamber of a plasma processing system.
• the method includes identifying a set of delayed gas species utilized during execution of the recipe with a set of delivery time slower than a target delivery time scale.
• the method also includes establishing an initial overshoot strength for each gas specie of the set of delayed gas species, wherein the initial overshoot strength is a factor by which an MFC flow rate is increased.
• the method further includes determining an initial overshoot duration for each gas specie of the set of delayed gas species.
• the initial overshoot duration is a time duration for applying the initial overshoot strength to the MFC flow rate.
• the method yet also includes verifying the MFC control scheme by executing the recipe by adjusting an MFC hardware for each gas specie of the set of delayed gas species, wherein adjusting the MFC hardware includes applying the initial overshoot strength for the initial overshoot duration to determine if the MFC control scheme provides for each gas specie of the set of delayed gas species a pressure profile within a target accuracy of an equilibrium pressure for the processing chamber.
• Fig. IA shows a simple diagram of a partial view of a gas delivery system.
• Fig. I B shows a simple block diagram illustrating the flow of gas in a carrier gas- driven flow environment.
• FIG. 2 shows, in an embodiment of the invention, a simple flow chart illustrating steps for implementing a pressure control scheme.
• Fig. 3 shows, in an embodiment of the invention, a simple plot illustrating several overshoot strengths.
• FIG. 4 shows, in an embodiment, a simple flow chart illustrating the steps for performing a multiple steps overshooting process.
• inventions are described herein below, including methods and techniques. It should be kept in mind that the invention might also cover articles of manufacture that includes a computer readable medium on which computer-readable instructions for carrying out embodiments of the inventive technique are stored.
• the computer readable medium may include, for example, semiconductor, magnetic, opto-magnetic, optical, or other forms of computer readable medium for storing computer readable code.
• the invention may also cover apparatuses for practicing embodiments of the invention. Such apparatus may include circuits, dedicated and/or programmable, to carry out tasks pertaining to embodiments of the invention.
• a general-purpose computer and/or a dedicated computing device when appropriately programmed and may include a combination of a computer/computing device and dedicated/programmable circuits adapted for the various tasks pertaining to embodiments of the invention.
• As aforementioned, in the prior art, delivery delay may occur when one or more gas species flows into a processing chamber after the processing chamber has reached an equilibrium pressure state (i.e., set pressure point). Since different gas species may reach the chamber at different time, gas composition drift may occur.
• Fig. 1 A shows a simple diagram of a partial view of a gas delivery system.
• 0018j Processing tool 100 may include a gas delivery system that delivers gas into a processing chamber 1 14.
• the gas delivery system may include a main gas line 102 (i.e., mixing manifold) and one or more gas lines (104 and 106).
• the flow of gas through each gas line may be controlled by a mass flow controller (MFC), such as MFC 1 10 and MFC 1 12.
• MFC mass flow controller
• the gas flow into processing chamber 1 14 is driven by a pressure differential from the high pressure gas mixture and the low pressure processing chamber 1 14.
• the pressure of processing chamber 1 14 is monitored by a sensor. Based on the reading of the sensor, a vacuum pump 1 18 may adjust a throttle valve 130, which is positioned at the vacuum pump inlet. By adjusting throttle valve 130, vacuum pump 1 18 may control the pressure within processing chamber 114.
• throttle valve 130 controls the gas conductance (volumetric gas flow rate) from processing chamber 1 14 to vacuum pump 1 18, thereby maintaining the pressure within processing chamber 1 14 to be at a specified equilibrium pressure. Equation 1 below shows that at an equilibrium state, the partial pressure (P 2 ) of a given gas species at the chamber reaches the equilibrium pressure (p c ), which is equal to the ratio of the gas flow controlled by the MFC (Q) and the conductance of the chamber to the pump (k 2 ).
• a gas conductance curve may be empirically determined for each gas at a given flow rate and pressure. Once the pressure within processing chamber 1 14 has reached a set pressure point, substrate processing may be initiated.
• Equation 2 above shows that the partial pressure t ⁇ ) at a specific time (t) depends upon the gas flow time scale through the gas line ( r, ), the gas flow time scale from the processing chamber to the pump (r 2 ), the MFC gas flow rate (Q), and the conductance between the chamber and the pump (k ⁇ ).
• the time scale ( r, ) and the flow conductance (k 2 ) are usually unchanged since both of them are a function of the processing chamber geometry and the pumping speed.
• the partial pressure (p ⁇ ) at time t depends primarily on the time scale of the gas line ( T 1 ) and the MFC flow rate (Q) of the given gas.
• the time scale of the gas line ( r, ) is determined by the gas line geometry and is inversely proportional to the square root of the mass of the gas species, as shown in Equation 3. For ease of discussion, assume that the mass of the gas is not a factor. In an example, the gas flowing through gas line 104 and gas line 106 is the same. If the mass of the gas is not a factor, the time scale of the gas line (r, ) is a factor of the gas line geometry, as shown in Equation 4 above.
• the time scale of the gas line ( r, ) is a function of the gas line volume (Vi) and the gas line conductance (ki). Since both the volume and the flow conductance of a gas line are a function of the length and/or diameter of the gas line, the time scale of the gas line ( r, ) is also a function of the length and/or diameter of the gas line.
• gas line 106 has a shorter length than gas line 104. Based on Equation 4 above, the volume of gas line 104 is greater than the volume of gas line 106 and the flow conductance of gas line 104 is less than gas line 106.
• the gas delivery time scale for gas line 104 is greater than the gas delivery time scale of gas line 106.
• Referring back to Equation 3, besides the gas line geometry, the time scale of the gas line ( r, ) is also a function of the molecular mass of the gas.
• the gas species required by a recipe may usually be of different molecular mass.
• the mass of a gas is especially important in a low pressure environment. In a low pressure environment, the gas flow may become molecular. In other words, the gas flow may become independent of one another (i.e., collisional momentum transfer may become minimal between the gas molecules).
• the mass of the gas may determine the delivery time of the gas.
• a heavier gas species flows at a slower velocity than a lighter gas species.
• the delivery time for Hi will be about three times faster than C 4 Fs.
• the lighter gas species may reach the equilibrium pressure within a processing chamber before the heavier gas specie.
• the gas species may separate and each gas may reach the state of equilibrium at different time.
• pressure stabilization within processing chamber 114 may be reached even though the correct gas mixture has not been delivered into the processing chamber.
• substrate processing may begin even though the proper gas mixture may not be present, thereby resulting in substandard devices being created.
• substrate processing may be delayed until the proper gas mixture is present; however, the delay time may result in higher cost of production due to longer process time.
• Fig. I B shows a simple block diagram illustrating the flow of gas in a carrier gas-driven flow environment.
• a carrier gas such as Argon
• main gas delivery line 102 e.g., mixing manifold
• the process gas is usually carried into processing chamber 114 by the carrier gas via collisional momentum transfer.
• the process gas may be unable to mix with the carrier gas.
• the process gas is "stuck" at intersection 150 until the process gas pressure (pi) reaches the carrier gas pressure (p c ).
• a sufficient pressure may have to be built up in the gas line (e.g., gas line 104) before the process gas in gas line 104 may be able to mix with the carrier gas flowing through main gas line 102.
• At least one parameter - gas line conductance, MFC flow rate, or pump speed - may have to be modified.
• the inventors herein realized that by increasing the MFC flow rate for a short burst, the gas delivery time scale may be controlled without requiring hardware changes.
• a mass flow control (MFC) scheme to reduce the time scale of gas delivery to a processing chamber.
• Embodiments of the invention include overshooting the MFC to reduce the effective gas delivery rime scale.
• Embodiments of the invention also include a multiple steps process for performing the overshooting to reduce delivery time during a carrier gas-driven flow environment.
• a single step overshooting method is provided for overshooting the MFC to reduce the delivery delay into a processing chamber for a gas.
• an optimal overshoot strength may be determined.
• the optimal overshoot strength is a factor by which the MFC flow rate may be increased by to ensure minimize gas composition drift within processing chamber. Since reducing delivery delay increases the quality of substrate processing, optimal overshoot strength is desirable.
• initial overshoot strength may be calculated. The initial overshoot strength is a function of the overshoot duration and the time scale of the delayed gas species ( ⁇ i).
• an overshoot duration refers to the time elapsed period during which an overshoot strength may be applied to an MFC flow rate.
• 0037j the overshoot duration is set to the response time of an MFC (e.g., the speed at which the MFC can respond to a set of instructions).
• a response delay may exist when an MFC setting is changed. In other words, when an MFC setting is changed a few second may elapse before the gas flow rate is changed. In an example, assume that an MFC has response delay of 2 seconds.
• the MFC may release gas at 20 seem for 2 seconds before releasing the gas at 10 seem.
• the delay is due to the MFC response time and not due to the deliberate intention of the tool operator. Since, the intention is to minimize the time scale of gas delivery into a processing chamber, the overshoot duration set at the MFC response time may add little or no additional time to the overall delivery time, thereby enabling the overshoot strength to be utilized as a method for controlling the time scale of gas delivery while minimizing the time required to apply the overshoot duration.
• the response time may be specific to an MFC.
• the initial overshoot strength for the first gas species associated with the first MFC may differ from the initial overshoot strength for the second gas species associated with the second MFC.
• the overshoot duration is limited by the MFC response time.
• the overshoot strength is also a function of the time scale of a delayed gas species ( ⁇ ). Since the time scale ⁇ i depends on the gas line geometry and the molecular mass of the gas, the overshoot strength may have to be increased to account fora longer gas line. Similarly, the overshoot strength may also have to be increased for a gas with heavier molecular mass.
• a test run may be conducted with the MFC flow rate being increased by a factor of the initial overshoot strength. In an example, if the set MFC flow rate is 20 seem and the initial overshoot strength is 1.5, then the MFC will be initially set to 30 seem.
• the chamber pressure profile may be observed for a predetermined period of time (e.g., 10 seconds). By analyzing the chamber pressure profile, the initial overshoot strength may be adjusted to identify the optimal overshoot strength.
• an overshoot strength may be determined by adjusting the initial overshoot strength until the overshoot strength creates a chamber pressure profile in which the chamber pressure at a pre-defined target time period (e.g., 2 seconds) is within a target accuracy rate (e.g., 1 percent of the set pressure point). Since limited time is usually provided for establishing a stabilized pressure environment, the pre-defined target time period may have to be set at a time period that is less than the time allotted for stabilizing the processing chamber pressure.
• a pre-defined target time period e.g. 2 seconds
• a target accuracy rate e.g. 1 percent of the set pressure point
• the overshoot duration may be adjusted if the initial overshoot strength is not within the MFC capacity.
• the overshoot duration may be set to the response time of the MFC to minimize additional time due to overshooting.
• the modified MFC flow rate i.e., mass flow rate increased by a factor of the overshoot strength
• the overshoot duration may have to be increased in order to reduce the overshoot strength.
• the overshoot duration may be modified if the modified mass flow rate is not less than a pre-determined percentage (such as 95 percent) of the maximum MFC flow rate.
• the pre-determined percentage is less than 100 percent to account for potential hardware inaccuracy that may exist in the MFC. Since each MFC may have different specification, the maximum MFC flow rate may vary depending upon the MFC. [0042] In an embodiment, factors and/or physical conditions (e.g., gas line geometry, molecular mass of a gas, momentum of a gas, and the like) that may have caused delivery delay may now be managed by overshooting the MFC flow rate for an certain time duration (overshoot duration). Thus, the time scale of a gas into processing chamber may be modified to minimize the time differences between gas species for reaching an equilibrium pressure. (0043] In an embodiment, a multiple steps overshooting method may be applied in a carrier gas-driven flow environment.
• the single step overshooting method may be applied to decrease the delivery delay in a carrier gas-driven flow environment
• the multiple steps overshooting method may provide an alternative method for reducing delivery delay.
• a low-flow process gas may have to build up sufficient pressure before it can mix with the high-flow carrier gas.
• an initial overshoot may be applied to the MFC flow rate of the low-flow process gas.
• the build-up overshoot duration may be a function of the ratio of the time scale of the build-up time period and the initial overshoot strength.
• the build-up overshoot duration is less than the build-up time period, in an embodiment.
• the build-up overshoot duration is set to be at least the MFC response time, in an embodiment.
• the initial overshoot strength may be a function of the overshoot duration and the time scale of the low-flow process gas.
• the MFC flow rate may be modified by a second overshoot strength for a period of time.
• the second overshoot duration for the second overshoot strength may be set to the MFC response time. Similar to the single step overshooting method, the second overshoot strength may be determined empirically. In other words, the second overshoot strength may be adjusted until an optimal overshoot strength is identified.
• the multiple steps overshooting method enable multiple overshoot strength to be applied to accommodate the different processing conditions that may exist due to the differences in the flow rates between gas species. Similar to the single step overshooting method, the multiple steps overshooting method enables a faster gas delivery while minimizing the time required for applying the overshoot scheme.
• FIG. 2 shows, in an embodiment of the invention, a simple flow chart illustrating steps for implementing a pressure control scheme.
• a slow gas delivery situation is identified.
• Slow gas delivery may be due to many reasons.
• slow gas delivery may be due to a condition known as gas composition drift in which gas species are reaching an equilibrium state within a processing chamber at different time.
• gas composition drift may occur in a low pressure environment and/or in a carrier gas driven-flow environment.
• Those skilled in the art may have different techniques for identifying when the situation occurs.
• One method may include measuring a pressure time profile. By employing metrology tools positioned within the processing chamber, pressure within the processing chamber may be measured for each gas. If the time period for a gas species to reach the set pressure point takes longer than other gas species, gas composition drift may be occurring.
• Gas composition drift in a carrier gas driven-flow environment may also be identified by observing the configuration of the plasma tool.
• Some plasma tools may have the gas line for the carrier gas positioned at the downstream of the gas line for the process gas. Since the carrier gas is located downstream, the carrier gas is unable to carry a process gas to the downstream processing chamber unless the process gas is able to reach the pressure of the carrier gas.
• Gas composition drift may also occur due to the gas line configuration.
• a long gas line may usually add to the gas delivery time.
• the prior art shows that a heavier gas may reach an equilibrium state within the processing chamber at a slower rate since a heavier gas tends to flow at a slower speed than a lighter gas.
• the gas line configuration may also require a large number of process gas molecules to be accumulated within the gas line volume in order for the process gas to build up enough pressure to mix properly with a carrier gas, which is usually flowing at a higher flow rate.
• the longer the gas line the larger the delivery delay may be for a given gas species.
• the gas species with a delivery time slower than a target delivery time may be identified.
• the target delivery time is usually specific to a recipe, it is not uncommon for the target delivery time to be less than 10 seconds.
• a set of partial pressure profiles may be analyzed to identify the set of gas species that may have a slow delivery time.
• the MFC flow rate (Q) for a given gas species at a set pressure point ⁇ i.e., equilibrium pressure) may be determined.
• the MFC flow rate may be determined by referring to a conductance curve.
• the conductance curve for a gas species may be determined by measuring the chamber pressure for a given flow rate.
• the flow rate for a given gas species at a given set pressure may already be pre-measured and may be easily retrieved. From the conductance curve and/or flow rate chart, the flow rate at a given set pressure may be determined for each gas specie that may have a slow delivery time.
• a time scale ( ⁇ i) for each gas specie identified as slow delivery gas is calculated.
• One method for determining the time scale ( ⁇ ) is by tracing the pressure rise in the processing chamber for a given MFC flow rate (Q) with a fixed throttle valve position ⁇ i.e., constant pump speed).
• overshoot strength ( ⁇ ) may be initially set for a specific gas species at a specific MFC.
• the initial overshoot strength ( ⁇ ) may be set by employing Equation 6 below.
• the overshoot strength ( ⁇ ) is a function of the overshoot duration (to) and the time scale of a delayed gas species ( ⁇ i).
• overshoot duration (to) for a gas species may be dependent upon the MFC that controls the gas flow rate.
• an MFC may have a delayed response time.
• an MFC control may be switched to a flow rate of 40 seem.
• the processing tool may experience a few seconds delay before the MFC may begin flowing gas at the new flow rate. Typically, the delay is about 0.5 — 2 seconds; however, the delay may vary depending upon the specific MFC.
• the overshoot duration (to) may change depending upon the MFC specification.
• the overshoot duration (to) may vary depending upon the time scale of the delayed gas species ( ⁇ i).
• the time scale of a gas species ( ⁇ i) may depend upon the gas line geometry and the mass of the gas species.
• the time scale of a gas species (ii) may also depend on the flow rate of the carrier gas. Since the carrier gas is usually flowing at a higher rate than the process gas, the process gas may have to build up sufficient pressure before being able to successfully mix with the carrier gas. The additional time delay is thereby a function of the time required by the process gas to build up sufficient pressure as previously discussed in Equation 5 above.
• a test run may be performed by modifying the MFC flow rate (Q) by the initial overshoot strength ( ⁇ ). While the test run is being performed, the gas composition within the processing chamber may be measured.
• the overshoot strength ( ⁇ ) may be sufficient or optimal for minimizing delivery delay for the gas. Since limited time is usually provided for establishing a stabilized pressure environment, the pre-defined target time period may have to be set less than the time allotted for stabilizing the processing chamber pressure.
• Fig. 3 shows, in an embodiment of the invention, a simple plot illustrating several overshoot strengths ( ⁇ ). Consider the situation wherein, for example, the equilibrium pressure is set at 1.00.
• the overshoot strength ( ⁇ ) is considered to be optimal if the chamber pressure is within the target accuracy (i.e., 1 percent) at a pre-defined target time period.
• the target accuracy i.e., 1 percent
• the pre-defined target time period is twice of the overshoot duration (i.e., 2 seconds).
• the overshoot strength ( ⁇ ) of 2.52 (curve 302) is considered as optimal since the pressure reaches the set pressure ( 1.00) within the target accuracy at the target time (2 seconds).
• the target pressure accuracy is set such that the pressure profile for a gas is within close proximity to the set pressure point and the pressure profile of the gas reaches equilibrium before the pre-determined period of time.
• the overshoot strength ( ⁇ ) may be adjusted, as shown in Equation 7 below, for the target equilibrium pressure (p e ) and the pressure (p) at time to attained by the overshoot strength ( ⁇ ). Steps 212-216 are iterative and may be repeated until an optimal overshoot strength is determined.
• the gas is run again with the optimal MFC overshoot strength ( ⁇ »).
• ⁇ the optimal overshoot strength
• inaccuracy may occur if the optimal overshoot strength causes the MFC flow rate to be set too high.
• hardware e.g., MFC
• the desired modified MFC flow rate may be less than the maximum MFC flow rate.
• One method for performing the analysis is to calculate if the modified MFC flow rate (i.e., Q * ⁇ ») is less than a pre-determined percentage of the (e.g., 95 percent) of the maximum MFC flow rate.
• the pre-determined percentage is set at less than 100 percent. Since the maximum MFC flow rate may vary depending upon MFC specification, the acceptable range is set as a percentage of the maximum MFC flow rate instead of as an actual constant.
• the overshoot duration may be increased.
• the overshoot duration may be set to the MFC response time to minimize the possibility of increasing the time for delivering a gas to the processing chamber.
• the overshoot duration may have to be increased, in an embodiment, in order to reduce the optimal overshoot strength, thereby reducing the modified MFC flow rate.
• Steps 208 - 224 may be iterative until an optimal overshoot strength has been determined.
• the optimal overshoot strength ( ⁇ ») may be determined for a specific gas. By identifying the optimal overshoot strength ( ⁇ »), the delivery delay may be significantly reduced. Thus, the optimal overshoot strength (a * ) may be employed to minimize gas composition drift by manipulating the MFC flow rate of one or more gas species.
• the method described in Fig. 2 may reduce the time scale associated with a gas. However, due to the additional time delay that may occur due to the time scale associated with the built-up pressure (t t ), the method described in Fig.2 may be adjusted to allow for a multiple steps overshooting process that may further reduce the delivery delay.
• Fig. 4 shows, in an embodiment, a simple flow chart illustrating the steps for performing a multiple steps overshooting process.
• the initial overshoot strength ( ⁇ ) is determined.
• the delivery delay for a low-flow process gas may also depend on the time scale required for the low-flow gas to build up sufficient pressure to mix with the high-flow carrier gas.
• the first overshoot strength may be set to the maximum MFC flow rate.
• the first overshoot duration is calculated.
• the first overshoot duration (i.e., build-up overshoot duration) may be a function of the ratio of the pressure build-up time period and the initial overshoot strength. In an embodiment, the build-up overshoot duration is less than the build-up time period since the initial overshoot strength is applied to minimize the build-up time period.
• the overshoot duration for the first overshooting step may be calculated using Equation 8 below. To minimize uncontrolled pressure profile (such as spiking) the first overshoot duration (t x ⁇ ) may be set at a value at greater than or equal to the MFC response time (to), in an embodiment.
• the MFC flow rate may be modified to manage the time scale related to the gas line geometry and/or the molecular mass of the gas.
• a second overshoot duration may be determined similar to the single step overshooting. Since the second overshoot duration is the time required to manage the time associated with the gas line geometry and/or the molecular mass of a gas, the second overshoot duration may be set to the MFC response time (same as the overshoot duration of Fig.2), in an embodiment, to minimize additional time being added to the overall pressure stabilization time.
• the second overshoot strength is determined.
• the second overshoot strength may be determined by performing a test run.
• the test run may include increasing the MFC flow rate (Q) by the initial overshoot strength (i.e., first overshoot strength).
• the second overshoot strength may be determined empirically.
• the second overshoot strength may be adjusted until an optimal overshoot strength ( ⁇ «) is identified (such that the chamber pressure at a predefined target time period is within the target accuracy of the equilibrium pressure).
• Step 406 is similar to step 212-216 of Fig. 2.
• test run may include the multiple overshoot strength and overshoot duration.
• Steps 406-416 may be iterative until the optimal MFC scheme has been determined.
• the multiple steps overshooting method enable multiple overshoot strength to be applied to accommodate the different time scales that may affect the overall delivery time for a gas. Similar to the single step overshooting method, the multiple steps overshooting method provide a method for determining a modified MFC flow rate that reduces delivery delay while minimizing the time required for applying the overshoot strength. Both the methods described in Figs. 2 and 4 may be manually performed by a technician. In an embodiment, the MFC scheme, as illustrated by Figs. 2 and 4 may also be automatically applied (e.g., software application), thereby reducing labor cost and minimizing the risk of human error.

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