Devices and methods for in-situ control of mechanical or chemical-mechanical planarization of microelectronic-device substrate assemblies

Planarizing machines and methods for endpointing or otherwise controlling mechanical and/or chemical-mechanical planarization of microelectronic-device substrates. In one embodiment of the invention, a method for planarizing a microelectronic substrate assembly includes removing material from the substrate assembly during a planarizing cycle by contacting the substrate assembly with a planarizing medium and moving the substrate assembly and/or the planarizing medium relative to each other. The method can also include controlling the planarizing cycle by predicting a thickness of an outer film over a first region on the substrate assembly and providing an estimate of an erosion rate ratio between the first region and a second region. The endpointing procedure continues by determining an estimated value of an output factor, such as a reflectance intensity from the substrate assembly, by modeling the output factor based upon the thickness of the outer film over the first region and the erosion rate ratio between the first region and the second region. The endpointing procedure continues by ascertaining an updated predicted thickness of the outer film over the first region by measuring an actual value of the output factor during the planarizing cycle without interrupting removal of material from the substrate, and then updating the predicted thickness of the outer film according to the actual value of the output factor and the estimated value of the output factor. The updated predicted thickness can be determined using an Extended Kalman Filter. The planarizing process is controlled according to the updated predicted thickness of the outer film.

TECHNICAL FIELD
 The present invention relates to devices and methods for estimating
 selected parameters for controlling mechanical and/or chemical-mechanical
 planarization of microelectronic-device substrate assemblies. More
 particularly, the present invention relates to in-situ optical endpointing
 methods and devices.
 BACKGROUND OF THE INVENTION
 Mechanical and chemical-mechanical planarizing processes (collectively
 "CMP") are used in the manufacturing of electronic devices for forming a
 flat surface on semiconductor wafers, field emission displays and many
 other microelectronic device substrate assemblies. CMP processes generally
 remove material from a substrate assembly to create a highly planar
 surface at a precise elevation in the layers of material on the substrate
 assembly. FIG. 1 schematically illustrates an existing web-format
 planarizing machine 10 for planarizing a substrate 12. The planarizing
 machine 10 has a support table 14 with a top-panel 16 at a workstation
 where an operative portion (A) of a planarizing pad 40 is positioned. The
 top-panel 16 is generally a rigid plate to provide a flat, solid surface
 to which a particular section of the planarizing pad 40 may be secured
 during planarization.
 The planarizing machine 10 also has a plurality of rollers to guide,
 position and hold the planarizing pad 40 over the top-panel 16. The
 rollers include a supply roller 20, idler rollers 21, guide rollers 22,
 and a take-up roller 23. The supply roller 20 carries an unused or
 pre-operative portion of the planarizing pad 40, and the take-up roller 23
 carries a used or post-operative portion of the planarizing pad 40.
 Additionally, the left idler roller 21 and the upper guide roller 22
 stretch the planarizing pad 40 over the top-panel 16 to hold the
 planarizing pad 40 stationary during operation. A motor (not shown)
 generally drives the take-up roller 23 to sequentially advance the
 planarizing pad 40 across the top-panel 16, and the motor can also drive
 the supply roller 20. Accordingly, clean pre-operative sections of the
 planarizing pad 40 may be quickly substituted for used sections to provide
 a consistent surface for planarizing and/or cleaning the substrate 12.
 The web-format planarizing machine 10 also has a carrier assembly 30 that
 controls and protects the substrate 12 during planarization. The carrier
 assembly 30 generally has a substrate holder 32 to pick up, hold and
 release the substrate 12 at appropriate stages of the planarizing process.
 Several nozzles 33 attached to the substrate holder 32 dispense a
 planarizing solution 44 onto a planarizing surface 42 of the planarizing
 pad 40. The carrier assembly 30 also generally has a support gantry 34
 carrying a drive assembly 35 that can translate along the gantry 34. The
 drive assembly 35 generally has an actuator 36, a drive shaft 37 coupled
 to the actuator 36, and an arm 38 projecting from the drive shaft 37. The
 arm 38 carries the substrate holder 32 via a terminal shaft 39 such that
 the drive assembly 35 orbits the substrate holder 32 about an axis B--B
 (arrow R.sub.1). The terminal shaft 39 may also rotate the substrate
 holder 32 about its central axis C--C (arrow R.sub.2).
 The planarizing pad 40 and the planarizing solution 44 define a planarizing
 medium that mechanically and/or chemically-mechanically removes material
 from the surface of the substrate 12. The planarizing pad 40 used in the
 web-format planarizing machine 10 is typically a fixed-abrasive
 planarizing pad in which abrasive particles are fixedly bonded to a
 suspension material. In fixed-abrasive applications; the planarizing
 solution is a "clean solution" without abrasive particles. In other
 applications, the planarizing pad 40 may be a non-abrasive pad that is
 composed of a polymeric material (e.g., polyurethane) or other suitable
 materials. The planarizing solutions 44 used with the non-abrasive
 planarizing pads are typically CMP slurries with abrasive particles and
 chemicals.
 To planarize the substrate 12 with the planarizing machine 10, the carrier
 assembly 30 presses the substrate 12 against the planarizing surface 42 of
 the planarizing pad 40 in the presence of the planarizing solution 44. The
 drive assembly 35 then 30 translates the substrate 12 across the
 planarizing surface 42 by orbiting the substrate holder 32 about the axis
 B--B and/or rotating the substrate holder 32 about the axis C--C. As a
 result, the abrasive particles and/or the chemicals in the planarizing
 medium remove material from the surface of the substrate 12.
 The CMP processes should consistently and accurately produce a uniformly
 planar surface on the substrate to enable precise fabrication of circuits
 and photo-patterns. During the fabrication of transistors, contacts,
 interconnects and other features, many substrates develop large "step
 heights" that create highly topographic surfaces across the substrates.
 Such highly topographical surfaces can impair the accuracy of subsequent
 photolithographic procedures and other processes that are necessary for
 forming sub-micron features. For example, it is difficult to accurately
 focus photo patterns to within tolerances approaching 0.1 micron on
 topographic surfaces because sub-micron photolithographic equipment
 generally has a very limited depth of field. Thus, CMP processes are often
 used to transform a topographical surface into a highly uniform, planar
 surface at various stages of manufacturing the microelectronic devices.
 In the highly competitive semiconductor industry, it is also desirable to
 maximize the throughput of CMP processing by producing a planar surface on
 a substrate as quickly as possible. The throughput of CMP processing is a
 function, at least in part, of the ability to accurately stop CMP
 processing at a desired endpoint. In a typical CMP process, the desired
 endpoint is reached when the surface of the substrate is planar and/or
 when enough material has been removed from the substrate to form discrete
 components on the substrate (e.g., shallow trench isolation areas,
 contacts, damascene lines, etc.). Accurately stopping CMP processing at a
 desired endpoint is important for maintaining a high throughput because
 the substrate assembly may need to be re-polished if it is
 "under-planarized," or components on the substrate may be destroyed if it
 is "over-polished." Thus, it is highly desirable to stop CMP processing at
 the desired endpoint.
 In one conventional method for determining the endpoint of CMP processing,
 the planarizing period of a particular substrate is estimated using an
 estimated polishing rate based upon the polishing rate of identical
 substrates that were planarized under the same conditions. The estimated
 planarizing period for a particular substrate, however, may not be
 accurate because the polishing rate and other variables may change from
 one substrate to another. Thus, this method may not produce accurate
 results.
 In another method for determining the endpoint of CMP processing, the
 substrate is removed from the pad and then a measuring device measures a
 change in thickness of the substrate. Removing the substrate from the pad,
 however, interrupts the planarizing process and may damage the substrate.
 Thus, this method generally reduces the throughput of CMP processing.
 U.S. Pat. No. 5,433,651 issued to Lustig et al. ("Lustig") discloses an
 in-situ chemical-mechanical polishing machine for monitoring the polishing
 process during a planarizing cycle. The polishing machine has a rotatable
 polishing table including a window embedded in the table. A polishing pad
 is attached to the table, and the pad has an aperture aligned with the
 window embedded in the table. The window is positioned at a location over
 which the workpiece can pass for in-situ viewing of a polishing surface of
 the workpiece from beneath the polishing table. The planarizing machine
 also includes a device for measuring a reflectance signal representative
 of an in-situ reflectance of the polishing surface of the workpiece.
 Lustig discloses terminating a planarizing cycle at the interface between
 two layers based on the different reflectances of the materials. In many
 CMP applications, however, the desired endpoint is not at an interface
 between layers of materials. Thus, the system disclosed in Lustig may not
 provide accurate results in certain CMP applications.
 Another endpointing system disclosed in U.S. Pat. No. 5,865,665 issued to
 Yueh ("Yueh") determines the end point in a CMP process by predicting the
 removal rate using a Kalman filtering algorithm based on input from a
 plurality of Linear Variable Displacement Transducers ("LVDT") attached to
 the carrier head. The process in Yueh uses measurements of the downforce
 to update and refine the prediction of the removal rate calculated by the
 Kalman filter. This downforce, however, varies across the substrate
 because the pressure exerted against the substrate is a combination of the
 force applied by the carrier head and the topography of both the pad
 surface and the substrate. Moreover, many CMP applications intentionally
 vary the downforce during the planarizing cycle across the entire
 substrate, or only in discrete areas of the substrate. The method
 disclosed in Yueh, therefore, may be difficult to apply in some CMP
 application because it uses the downforce as an output factor for
 operating the Kalman filter.
 SUMMARY OF THE INVENTION
 The present invention is directed toward planarizing machines and methods
 for endpointing or otherwise controlling mechanical and/or
 chemical-mechanical planarization of microelectronic-device substrates. In
 one aspect of the invention, a method for planarizing a microelectronic
 substrate assembly includes removing material from the substrate assembly
 during a planarizing cycle by contacting the substrate assembly with a
 planarizing medium and moving the substrate assembly and/or the
 planarizing medium relative to each other. The method can control a
 process parameter of a planarizing cycle, such as endpointing the
 planarizing cycle or determining the status of the surface of the
 substrate. For example, the method can endpoint the planarizing cycle by
 predicting a thickness of an outer film over a first region on the
 substrate assembly and providing an estimate of an erosion rate
 relationship based on a first erosion rate over the first region and a
 second erosion rate over a second region. The erosion rate relationship
 can be the first and second erosion rates or an erosion rate ratio between
 the first and second erosion rates. The first region can be an array at a
 first elevation and the second region can be a periphery area at a second
 elevation.
 The endpointing procedure continues by determining an estimated value of an
 output factor, such as a reflectance intensity from the substrate
 assembly. The output factor can be estimated by modeling the output factor
 based upon the thickness of the outer layer over the first region and the
 erosion rate ratio between the first region and the second region. The
 endpointing procedure continues by ascertaining an updated predicted
 thickness of the outer film over the first region by measuring an actual
 value of the output factor during the planarizing cycle without
 interrupting removal of material from the substrate, and then updating the
 predicted thickness of the outer film according to the variance between
 the actual value of the output factor and the estimated value of the
 output factor. The endpointing process also continues by repeating the
 determining procedure and the ascertaining procedure using the revised
 predicted thickness of the outer layer of an immediately previous
 iteration to bring the estimated value of the output factor to within a
 desired range of the actual value of the output factor. The planarizing
 process is terminated when the updated predicted thickness of the outer
 layer over the first region is within a desired range of an endpoint
 elevation in a substrate assembly.
 Several embodiments of methods in accordance with the invention can be
 performed with a planarizing machine having an endpointing system
 including a computer having an optical module and a Kalman module. The
 optical module can be programmed with optical algorithms for modeling a
 total reflectance from the substrate based upon the proportionate
 reflectances from the arrays and the periphery areas. The Kalman module
 can be programmed with an Extended Kalman Filtering ("EKF") algorithm for
 estimating a number of operating variables ("state variables") of the CMP
 process based upon the estimated reflectance and the measured reflectance.
 The Kalman module updates the estimates of the operating variables and the
 optical module revises the estimate of the reflectance based on the
 updates of the operating variables until the estimated values of the
 reflectance converge with the measured values of the reflectance. At this
 point, the estimated operating variables should approximately equal the
 actual operating variables. Therefore, when one of the operating variables
 is the thickness of the outer film over the arrays, the planarizing cycle
 can be endpointed when the estimated thickness of the outer film is
 approximately equal to a desired endpoint thickness.

DETAILED DESCRIPTION
 The present invention is directed toward planarizing machines and methods
 for endpointing or otherwise controlling mechanical and/or
 chemical-mechanical planarization of microelectronic-device substrates.
 Many specific details of the invention are described below with reference
 to web-format planarizing applications to provide a thorough understanding
 of such embodiments. The present invention, however, can be practiced
 using rotary planarizing machines, such as the Mirra planarizing machine
 manufactured by Applied Materials Corporation. A person skilled in the art
 will thus understand that the invention may have additional embodiments,
 or that the invention may be practiced without several of the details
 described below.
 A. CMP Machines With Optical Control Systems
 FIG. 2 is an isometric view of a web-format planarizing machine 100
 including an optical reflectance system 107 and an end pointing system 200
 in accordance with one embodiment of the invention. The planarizing
 machine 100 has a table 102 including a stationary support surface 104, an
 opening 105 at an illumination site in the support surface 104, and a
 shelf 106 under the support surface 104. The planarizing machine 100 also
 includes an optical emitter/sensor 108 mounted to the shelf 106 at the
 illumination site. The optical sensor 108 projects a light beam 109
 through the hole 105 and the support surface 104. The optical sensor 108
 can be a reflectance device that emits the light beam 109 and senses a
 reflectance 109a to determine the surface condition of a substrate 12
 in-situ and in real time. Reflectance and interferometer endpoint sensors
 that may be suitable for the optical sensor 108 are disclosed in U.S. Pat.
 Nos. 5,865,665; 5,648,847; 5,337,144; 5,777,739; 5,663,797; 5,465,154;
 5,461,007; 5,433,651; 5,413,941; 5,369,488; 5,324,381; 5,220,405;
 4,717,255; 4,660,980; 4,640,002; 4,422,764; 4,377,028; 5,081,796;
 4,367,044; 4,358,338; 4,203,799; and 4,200,395; and U.S. application Ser.
 Nos. 09/066,044 and 09/300,358; all of which are herein incorporated by
 reference.
 The planarizing machine 100 can further include a pad advancing mechanism
 having a plurality of rollers 120, 121, 122 and 123 that are substantially
 the same as the roller system described above with reference to the
 planarizing machine 10 in FIG. 1. Additionally, the planarizing machine
 100 can include a carrier assembly 130 that is substantially the same as
 the carrier assembly 30 described above with reference to FIG. 1.
 FIG. 3 is a cross-sectional view partially illustrating a web format
 polishing pad 150 on the support surface 104, and the optical sensor 108
 in greater detail. Referring to FIGS. 2 and 3 together, the polishing pad
 150 has a planarizing medium 151 with a first section 152a, a second
 section 152b, and a planarizing surface 154 defined by the upper surfaces
 of the first and second sections 152a and 152b. The planarizing medium 151
 can be an abrasive or a non-abrasive material. For example, an abrasive
 planarizing medium 151 can have a resin binder and abrasive particles
 distributed in the resin binder. Suitable abrasive planarizing mediums 151
 are disclosed in U.S. Pat. Nos. 5,645,471; 5,879,222; 5,624,303; and U.S.
 patent application Ser. Nos. 09/164,916 and 09/001,333, all of which are
 herein incorporated by reference. In this embodiment, the polishing pad
 150 also includes an optically transmissive backing sheet 160 under the
 planarizing medium 151 and a resilient backing pad 170 under the backing
 sheet 160. The planarizing medium 151 can be disposed on a top surface 162
 of the backing sheet 160, and the backing pad 170 can be attached to an
 under surface 164 of the backing sheet 160. The backing sheet 160, for
 example, can be a continuous sheet of polyester (e.g., Mylar.RTM.) or
 polycarbonate (e.g., Lexan.RTM.). The backing pad 170 can be a
 polyurethane or other type of compressible material. In one particular
 embodiment, the planarizing medium 151 is an abrasive material having
 abrasive particles, the backing sheet 160 is a long continuous sheet of
 Mylar, and the backing pad 170 is a compressible polyurethane foam.
 The polishing pad 150 also has an optical pass-through system to allow the
 light beam 109 to pass through the pad 150 and illuminate an area on the
 bottom face of the substrate 12 irrespective of whether a point P on the
 pad 150 is at position I.sub.1, I.sub.2. . . or I.sub.n (FIG. 2). In this
 embodiment, the optical pass-through system includes a first view port
 defined by a first elongated slot 180 through the planarizing medium 151
 and a second view port defined by a second elongated slot 182 (FIG. 3
 only) through the backing pad 170. The first and second elongated slots
 180 and 182 can extend along the length of the polishing pad 150 in a
 direction generally parallel to a pad travel path T--T. The first and
 second slots 180 and 182 are also aligned with the hole 105 in the support
 surface 104 so that the light beam 109 and the reflectance 109a can pass
 through any view site along the first and second slots 180 and 182. When
 the point P is at intermediate location I.sub.1, for example, a view site
 184 along the first and second elongated slots 180 and 182 is aligned with
 the hole 105. After the polishing pad 150 has moved along the pad travel
 path T--T so that the point P is at intermediate position I.sub.2, another
 view site 185 along the first and second elongated slots 180 and 182 is
 aligned with the hole 105.
 The embodiment of the polishing pad 150 shown in FIGS. 2 and 3 allows the
 optical sensor 108 to detect the reflectance 109a from the substrate 12
 in-situ and in real time during a planarizing cycle on the web-format
 planarizing machine 100. In operation, the carrier assembly 130 moves the
 substrate 12 across the planarizing surface 154 as a planarizing solution
 144 flows onto the polishing pad 150. The planarizing solution 144 is
 generally a clear, non-abrasive solution that does not block the light
 beam 109 or the reflectance 109a from passing through the first elongated
 slot 180. As the carrier assembly 130 moves the substrate 12, the light
 beam 109 passes through both the optically transmissive backing sheet 160
 and the clean planarizing solution in the first elongated slot 180 to
 illuminate the face of the substrate 12 (FIG. 3). The reflectance 109a
 returns to the optical sensor 108 through slot 180. The optical sensor 108
 thus detects the reflectance 109a from the substrate 12 throughout the
 planarizing cycle.
 The planarizing machine 100 also includes an endpointing system 200 (shown
 schematically) coupled to the optical sensor 108. The endpointing system
 200 can include a computer 210 having an optical module 220 and a Kalman
 module 230. The optical module 220 is programmed with optical algorithms
 for modeling the total reflectance from the substrate 12 based upon the
 proportionate reflectances from the arrays and the periphery areas on the
 substrate 12. The Kalman module 230 is programmed with an Extended Kalman
 Filtering (EKF) algorithm for estimating a number of state variables of
 the CMP process based on the measured reflectance 109a. A "state variable"
 is an operating variable of the CMP process related to the status of the
 surface of the substrate 12 and/or the reflectance 109a. As explained
 below, the Kalman module 230 refines the estimates of the state variables,
 and then the computer 210 uses the refined estimates of the state
 variables to estimate the endpoint of the CMP process.
 B. Particular State Variables For Endpointing CMP Processing
 One aspect of several embodiments of the invention is determining the
 appropriate state variables for estimating the endpoint of CMP processing.
 The state variables generally cannot be observed during a planarizing
 cycle, but at least some of the state variables can be modeled by an
 algorithm using an output factor of the CMP process. The output factor
 preferably provides an accurate indication of the status of the substrate,
 and it should be able to be determined in-situ during a planarizing cycle.
 One particularly useful output factor is the measured reflectance 109a
 from the substrate assembly, which can be related to certain state
 variables by optical algorithms programmed in the optical module 220 and
 the EKF algorithm programmed in the Kalman module 230. Therefore, to
 provide an accurate estimate of the endpoint or other aspects of a
 planarizing cycle, one embodiment of the endpointing system 200 is
 operated by selecting the appropriate state variables for determining the
 endpoint when the reflectance is the output factor.
 FIG. 4 is a schematic cross-sectional side view of a portion of a
 microelectronic-device substrate assembly 300 having a plurality of arrays
 312 and a plurality of periphery areas 314 that illustrates several state
 variables related to the surface of the substrate assembly. The substrate
 assembly 300 has a film stack 320 with an outer film or top layer 324. The
 film stack 320 can also have several other configurations with one or more
 underlying layers 322. Before planarizing the substrate assembly 300, the
 top layer 324 initially has a thickness (depth) d.sub.0 over the arrays
 312 and an initial depth d.sub.P0 over the periphery areas 314. The
 erosion rate of the top layer 324 is initially much greater over the
 arrays 312 than over the periphery areas 314 because the planarizing pad
 exerts more pressure against the arrays 312. As such, the thickness of top
 layer 324 decreases much faster over the arrays 312 than over the
 periphery areas 314. The contour of the top surface 326 at an intermediate
 stage of the planarizing cycle can change to a surface 326a (shown in
 phantom) in which the change in thickness of the top layer 324 over the
 arrays 312 (d.sub.0 -d.sub.1) is significantly greater than the change in
 thickness over the periphery areas 314 (d.sub.P0 -d.sub.P1). At the
 endpoint of the planarizing cycle, however, the finished surface 326b
 (also shown in phantom) of the top layer 324 is substantially planar such
 that the erosion rate over the arrays 312 is approximately equal to the
 erosion rate over the periphery areas 314.
 Still referring to FIG. 4, one state variable is the depth or thickness of
 the top layer 324 over the arrays 312. The CMP process is generally
 endpointed in the portion of the top layer 324 over the arrays 312 or at
 the interface between the top layer 324 and the conformal layer 322. The
 depth of the top later 324 over the arrays 312 at an elapsed time kT
 during a planarizing cycle is defined by the term d(kT), and the erosion
 rate over the arrays 312 is defined by the term er(kT). As such, at the
 next point in time ((k+1)T), the depth d is decreased by Ter(kT) in which
 the erosion rate er is a negative value. The depth of the top layer 324
 over the arrays 312 is accordingly defined by the equation
EQU d((k+1)T)=d(kT)+Ter(kT).
 The erosion rate er(kT) of the top layer 324 over the arrays 312 is another
 state variable because the erosion rate varies during a planarizing cycle
 and it affects the depth of the top layer 324 over the arrays 312. The
 erosion rate over the arrays 312 changes as a function of time according
 to the following equation
EQU er(kT)=er(kT)+w.sub.er (kT)+u(kT).
 In this equation, w.sub.er is a zero mean white Gaussian sequence of the
 signal noise and u is a known reference signal of the trajectory of the
 erosion rate. The value of w.sub.er varies over the planarizing cycle, and
 it can be determined by analyzing reflectance data from test planarizing
 cycles and comparing the reflectance data with the actual measured erosion
 rates taken ex-situ in the test planarizing cycles to estimate the noise
 in the signal. Similarly, the variance in u over the planarizing cycle can
 also be estimated from the trajectory of the erosion rate over the test
 planarizing cycles. The variables w.sub.er and u accordingly incorporate
 known information about the noise and the expected erosion rate over the
 planarizing cycle of a particular substrate design. The determination of
 w.sub.er and u are known to a person skilled in the art and can be
 programmed in data files in the optical module 220 and/or the Kalman
 module 230 (FIG. 2).
 Another state variable for estimating the endpoint of CMP processing in
 accordance with several embodiments of the invention is the erosion rate
 ratio ("L") of the periphery erosion rate over the periphery areas 314 and
 the array erosion rate over the arrays 312. The periphery erosion rate
 over the periphery areas 314 affects the array erosion rate over the
 arrays 312 because the array erosion rate generally decreases as the
 planarizing cycle progresses. Referring again to FIG. 4, the array erosion
 rate over the arrays 312 is initially greater than the erosion rate over
 the periphery areas 314, but the erosion rate ratio L approaches 1.0 as
 the surface of the substrate assembly becomes planar. Depending upon the
 architecture of the substrate 12, the erosion rate ratio L is generally
 about 0.3-0.4 at the start of a planarizing cycle. Therefore, the erosion
 rate ratio L between the array erosion rate and the periphery erosion rate
 is another state variable that affects endpointing the CMP process.
 When the reflectance 109a (FIG. 3) of the light beam is the output factor
 of the CMP process for operating the Kalman module 230, an additional
 state variable is the gain h of the optical system. During a planarizing
 cycle, the optical system is also subject to fluctuations that affect the
 reflectance signal generated by the light sensor 108. The signal generated
 by the sensor 108, for example, can be affected by the depth and clarity
 of the planarizing solution 144 over the light beam 109, or the clarity of
 the optically transmissive sheet 160. The gain h of the light sensor 108
 accordingly compensates for changes in these variables. The equation for
 modeling the optical gain h is as follows:
EQU h((k+1)T)=h(kT)+w.sub.h (kT).
 In this equation, w.sub.h is another Gaussian sequence independent of
 w.sub.er. The value of w.sub.h varies over the planarizing cycle, and it
 can be determined by analyzing reflectance data from test planarizing
 cycles and comparing the actual reflectance data with a theoretical
 reflectance signal based upon known optical equations for reflectance from
 a film stack to estimate the noise in the signal. The determination of
 w.sub.h is also known to a person skilled in the art and can be programmed
 as a function time into data files in the optical module 220 and/or the
 Kalman module 230.
 The state variables d, er, L and h cannot be directly measured in-situ
 during a planarizing cycle, but one aspect of a preferred embodiment is to
 accurately model the reflectance based on the depth "d" over the arrays.
 Additionally, the etch rate er can then be determined by the change in the
 depth over time. Therefore, when the output factor for the Kalman module
 230 is the reflectance from the substrate, an aspect of several
 embodiments of the invention is to provide optical algorithms that
 accurately correlate the depth of the top layer 324 over the arrays 312
 with the reflectance from the substrate.
 C. Optical Algorithms
 The intensity of the reflectance from a film stack having a flat surface
 can be modeled by determining a reflectance coefficient r that relates the
 intensity of the reflected light to the incident light intensity. Simple
 models to determine the reflectance coefficient r for smooth, thin films
 are well-known to persons skilled in the art. In a film stack having "n"
 separate films, the reflection coefficient r is related to the depth of
 the top layer of the film stack by the equation
 ##EQU1##
 In the above equation, "a" and "c" are variables that relate the
 propagation of the light through the separate films to the propagation of
 the light through air, and a* and c* denote the complex conjugates of a
 and c, respectively. The values for a and c are determined according to
 the following matrix equation:
 ##EQU2##
 In this equation, r.sub.1. . . r.sub.m are the reflectance coefficients for
 each layer in the film stack an .delta. is the change in thickness of each
 layer. In CMP applications, only the thickness of the top layer 324
 changes, and thus the matrix values of the underlying layers are a
 constant. The determination of a and c for a planar film stack is well
 known to a person skilled in the art.
 The reflectance for a planar film stack, however, does not accurately model
 the reflectance from a topographical substrate having arrays and periphery
 areas because the reflectance from the arrays varies differently than the
 reflectance from the periphery areas. FIG. 5, for example, is a graph
 illustrating the constituent components of the reflectance including the
 array reflectance (R.sub.A) from the arrays 312 (FIG. 4) and the periphery
 reflectance (R.sub.P) from the periphery areas 314 (FIG. 4). The
 difference in the period of the sinusoidal waveforms for the array
 reflectance R.sub.A and the periphery reflectance R.sub.P is caused, at
 least in part, by the difference in the thickness of the top layer over
 the arrays 312 and the periphery areas 314 that occurs during
 planarization. Therefore, one aspect of a preferred embodiment of the
 invention is to provide optical algorithms that model the reflectance
 based on the proportionate array reflectance and the proportionate
 periphery reflectance.
 The array reflectance R.sub.A at a given depth d of the top layer 324 (FIG.
 4) over the arrays 312 is given by the following equation:
 ##EQU3##
 In this equation, .delta.=d.sub.o -d, d.sub.o is the original thickness of
 the top layer 324, and d is an estimate of the current thickness. The
 periphery reflectance R.sub.P at the same moment is given by the following
 equation:
 ##EQU4##
 In this equation, .delta.=d.sub.o -L.multidot.(d.sub.o -d), and L is the
 erosion rate ratio of the periphery erosion rate over the array erosion
 rate. Thus, by estimating the depth d of the top layer 324 over the arrays
 312, both the array and periphery reflectances can be estimated.
 The total reflectance r at any given point in time is the sum of a
 proportionate value of the array reflectance R.sub.A and a proportionate
 value of the periphery reflectance R.sub.P. The array reflectance R.sub.A
 generally dominates the periphery reflectance R.sub.P because the arrays
 312 occupy more surface area of the substrate assembly 300 in a typical
 application (e.g., approximately 75%). The periphery reflectance R.sub.P
 accordingly modulates the array reflectance R.sub.A to produce a generally
 sinusoidal wave for the total reflectance r.
 To address the different reflectances from the arrays and the periphery
 areas, a preferred embodiment of an optical algorithm correlates the array
 reflectance R.sub.A, the periphery reflectance R.sub.P, and the relative
 surface area ("v") covered by the arrays 312 and the periphery areas 314
 as a function of the thickness of the top layer 324 over the arrays 312.
 The optical algorithms determine the individual reflectances from both the
 arrays 312 and the periphery areas 314 at both a current thickness d and a
 subsequent thickness d-i of the top layer. The increment "i" for the
 subsequent thickness can be selected so that it provides good resolution.
 The increment "i," for example, is generally 5-20 .ANG.. For the increment
 i=5 .ANG., the total present reflectance r and the instantaneous slope of
 the change in reflectance relative to the change in the thickness of the
 top layer .differential.r/.differential.d, are as follows:
 ##EQU5##
 Based on these equations for estimating the total reflectance r and the
 change of the reflectance with depth .differential.r/.differential.d, the
 EKF algorithm programmed in the Kalman module 230 can provide a control
 procedure that iteratively estimates the state variables based upon an
 estimated total reflectance and a measured actual reflectance from the
 substrate assembly. As explained below, the estimates of the state
 variables are used to estimate the endpoint and other aspects of CMP
 processing.
 D. End Pointing CMP Processing Using the Estimates of the State Variables
 Based on the Array/Periphery Reflectance Algorithms and an Extended Kalman
 Filtering Algorithm
 FIG. 6 is a flowchart of a method 400 for estimating the endpoint of a CMP
 cycle using the state variables and the array/periphery optical algorithms
 described above in sections B and C. The first series of routines 410-440
 estimates the state variables of the planarizing cycle, and the second
 series of the routines 450-470 estimates the endpoint of the planarizing
 cycle based upon the estimates of the state variables. As explained above
 with respect to FIG. 2, the computer 210 calculates the estimates of the
 state variables using the signals from the optical sensor 108 along with
 the algorithms and data files programmed in the optical module 220 and the
 Kalman module 230.
 The embodiment of the endpointing process shown in FIG. 6 begins with a
 start routine 410 that includes providing an initial estimate of the state
 variables related to the endpoint of the planarizing cycle. The state
 variables for this embodiment can include the following: (a) the depth or
 thickness d of the top layer 324 over the arrays 312 (FIG. 4); (b) the
 etch rate er of the top layer 324 over the arrays 312; (c) the gain h of
 the optical reflectance system; and (d) the erosion rate ratio L between
 the array erosion rate and the periphery erosion rate. As explained below,
 the state variable can also include other parameters of the planarizing
 cycle. The initial estimates of the state variables for the start routine
 410 can be obtained using data from previous runs of identical substrates
 or from actual measurements from runs of test substrates. The state
 variables are specific to the particular architecture of a substrate, and
 thus the initial estimates of the state variables must be determined for
 each CMP process of a particular substrate architecture. For the purposes
 of using the EKF algorithm for this embodiment of the invention, the state
 variables are mathematically represented by the following column vector.
 ##EQU6##
 The embodiment of the endpointing process shown in FIG. 6 continues with a
 reflectance estimating routine 420 including calculating an estimated
 total reflectance based upon the estimated depth of the top layer 324
 above the arrays 312 provided in the start routine 410. The reflectance
 routine 420 is preferably performed by the computer 210 and the optical
 module 220 using the optical algorithm for r set forth above based upon
 both the proportional array reflectance and the proportional periphery
 reflectance. The software for performing the total reflectance routine 420
 using the computer 210 and the optical module 220 can be developed by a
 person skilled in the art.
 The process continues with a change of reflectance routine 422 including
 calculating an instantaneous change in reflectance relative to the depth
 of the top layer. The computer 210 and the optical module 220 preferably
 perform the change in reflectance routine 422 based on the optical
 algorithm for .differential.r/.differential.d set forth above. The
 software for performing the change in reflectance routine 422 can also be
 programmed in computer 210 and the optical module 220 by a person skilled
 in the art.
 After performing the total reflectance routine 420 and the change in
 reflectance routine 422, the process continues with a measuring routine
 430 including measuring the actual reflectance output of the reflectance
 109a (FIG. 2) using the optical sensor 108. The measured reflectance 109a
 inherently has the proportionate array reflectance from the arrays 312
 (FIG. 4) and the proportionate periphery reflectance from the periphery
 areas 314 (FIG. 4). The optical sensor 108 generates a signal
 corresponding to the actual total reflectance and sends the signal to the
 computer 210.
 The embodiment of the method shown in FIG. 6 continues with an Extended
 Kalnan Filtering (EKF) routine 440 for refining the estimates of the state
 variables in the state vector x. The EKF routine 440 involves determining
 a Kalman gain matrix K, a conditional covariance matrix P, and correlating
 the equations for the state variables d, er, h and L. When the dynamic
 equations for the state variables are combined with the optical output,
 the equations for the update of the state variables x((k+1)1T) and the
 measured output of the reflectance y(kt) are as follows:
 ##EQU7##
 The EKF update equations are given below. In this description, y is the
 measured reflectance, y is the estimated reflectance based upon the total
 reflectance routine 420 and the change in reflectance routine 422, and x
 is a refined estimate of the state variables according to the difference
 between the measured reflectance y and the estimated reflectance y. The
 EKF routine performs a measurement update after a new measurement has been
 acquired, and calculates a time update to determine the new mean and
 covariance between measurements. Variables with a super-minus (e.g.,
 x.sup.-) are results of the time update, and the absence of a super-minus
 indicates the result is from the measurement update.
 The equations for the measurement update are as follows.
EQU K(kT)=P(kT).sup.- C.sub.k.sup.T (C.sub.k P(kT).sup.- C.sub.k.sup.T
 +R.sub.k).sup.-1
EQU y(kT)=g(x(kT).sup.-,u(kT),0,kT)
EQU P(kT)=(I-K(kT)C.sub.k)P(kT).sup.-
EQU x=x(kT).sup.- +K(kT) (y(kT)-y(kT))
 The time update is set forth by the following equations.
EQU x((k+1)T).sup.- =.function.(x(kT),u(kT),0,kt)
EQU P((k+1)T).sup.- =A.sub.k P(kT)A.sub.k.sup.T +Q.sub.k
 and
 ##EQU8##
 Based upon the equations for r and .differential.r/.differential.d
 described above, these values are set forth below.
 ##EQU9##
 The components of C.sub.k (e.g., the total estimated reflectance r and
 instantaneous change in reflectance .differential.r/.differential.d) need
 to be computed for each value of d that will be encountered during the
 estimation. It is generally sufficient to compute r.sub.(d) once at each
 time step, and then use this and a past value for a slightly different d
 to approximate .differential.r/.differential.d as a first difference.
 Thus, one aspect of this embodiment of the method 400 is that optical
 algorithms account for the reflectances from the arrays and the periphery
 areas on a topographical substrate.
 The EKF algorithm programmed in the Kalman module 230 and the computer 210
 refine the estimates of the state variable from a present estimate x(kT)
 to the next time increment x((k+1)T) based upon the measured reflectance y
 and the estimated reflectance y. The basic equations for the EKF are known
 to persons skilled in the art and have been applied to endpoint and etch
 rate control of planar film stacks on substrates as set forth in the
 following references, all of which are herein incorporated by reference:
 Vincent et al., End Point and Etch Rate Control Using Dual-Wavelength
 Laser with a Nonlinear Estimator, J. ELECTROCHEMICAL SOC'Y, v. 144 (1997);
 Vincent et al., An Extended Kalman Filtering-Based Method of Processing
 Reflectometry Data for Fast In-Situ Etch Rate Measurements, IEEE
 TRANSACTIONS ON SEMICONDUCTOR nMANUFACTURING, v. 10, No. 1, (Feb., 1997);
 Vincent et al., An Extended Kalman Filter Based Method for Fast In-Situ
 Etch Rate Measurements, MAT. RES. SOC. SYS. PROC., Vol. 406, 1996. As
 such, the Extended Kalman Filtering routine 440 and the databases for
 operating the routine can be programmed into the computer 210 and the
 Kalman module 230 by a person skilled in the art.
 After the estimates of state variables in the state vector x have been
 refined for the next iteration x((k+1)T) using the Kalman routine 440, the
 process continues with a comparing routine 450 in which the estimated
 reflectance based upon the previous estimate of the state variables is
 compared with the actual reflectance to determine whether the estimated
 reflectance is within an acceptable variance. If the estimated reflectance
 is not within an acceptable variance, the process continues with a
 repeating routine 442 in which the routines 420-450 are repeated with the
 refined estimates of the state variables x((k+1)T) from the Kalman routine
 440.
 The refined estimates of the state variables in the state vector x((k+1)T)
 from the Kalman routine 440 should cause the value of the estimated
 reflectance from the total reflectance routine 420 to approximate the
 measured reflectance. The EKF routine 440 has a high sampling rate and
 performs several iterations of estimating the state variables to refine
 the estimates of the state variables before the actual state variables
 change. The estimated reflectance r from the total reflectance routine 420
 accordingly converges with the measured reflectance and then tracks the
 measured reflectance throughout the planarizing cycle.
 When the estimated reflectance is within an acceptable variance of the
 measured reflectance at the comparing routine 450, the process continues
 with an endpoint routine 460 in which the time remaining in the
 planarizing cycle to reach the desired endpoint d.sub.e is calculated
 using the most recent estimates of the depth d and erosion rate er from
 the Kalman routine 440. The process then continues with a time routine 462
 in which the elapsed time is compared to the estimated time to the
 endpoint. Before the elapsed time equals the estimated endpoint time, the
 process continues by repeating the routines 420-462. Once the elapsed time
 equals the estimated endpoint time, the depth d of the top layer 324 over
 the arrays 312 should be at the endpoint depth. The process then proceeds
 to a terminating routine 470 in which the substrate is removed from the
 planarizing pad.
 FIG. 7 is a graph illustrating the actual reflectance and the estimated
 reflectance based upon estimates of the state variables d, er, h and L
 using the optical algorithms for r and
 ##EQU10##
 programmed in the computer 210, the optical module 220, and the Kalman
 module 230. FIG. 7 shows that the estimated reflectance tracks the actual
 reflectance. The state variables based upon the estimated reflectance are
 thus approximately equal to the actual values for the state variables
 during the planarizing cycle. FIG. 7 accordingly indicates that the method
 400 accurately estimates the state variables in-situ without interrupting
 the planarizing cycle.
 One advantage of the embodiment of the method illustrated in FIG. 6 is that
 it is expected to provide accurate estimates of the endpoint of a
 planarizing cycle. The accuracy of the method 400 is enhanced by providing
 optical algorithms that model the reflectance based upon both the
 reflectance from the arrays 312 and the periphery areas 314. Unlike
 conventional models for reflectance that treat the reflectance from the
 periphery areas as noise, the method 400 uses the proportionate value of
 the array reflectance and the proportionate value of the periphery
 reflectance to provide an accurate algorithm for modeling the estimated
 reflectance. Several embodiments of the method illustrated in FIG. 6 are
 expected to provide accurate in-situ and real time estimates of the
 endpoint for a planarizing cycle.
 Several embodiments of the methods in accordance with FIG. 6 are also
 expected to provide information regarding other aspects of CMP processing.
 For example, when the estimated reflectance does not converge with the
 value of the actual reflectance, it is apparent that the planarizing
 process is not proceeding in an expected manner. In a typical application,
 for example, the planarizing process may not proceed as expected because
 the condition of the polishing pad, the effectiveness of the planarizing
 solution, the downforce exerted by the carrier assembly and other factors
 may not be within a desired range. Therefore, unexpected variances between
 the estimated reflectance and the measured reflectance provide a
 diagnostic tool for indicating that a planarizing parameter is not within
 an acceptable range.
 The method 400 illustrated in FIG. 6 and the planarizing machine 100
 illustrated in FIG. 2 set forth several embodiments of determining the
 endpoint of CMP processing in accordance with the invention. It will be
 appreciated that the invention is not limited to these embodiments, but
 the invention also includes other ways of iteratively refining the
 estimates of the state variables, other combinations of state variables,
 and other output factors that can be used to measure the performance of
 the particular planarizing cycle. The output factor, for example, can be
 the reflectances of a plurality of wavelengths of light or the drag force
 between the substrate and the polishing pad. Additionally, instead of
 using an EKF algorithm for refining the estimates of the state variables,
 it is expected that the state variables can be refined using extrema
 counting or a least squares fit routine. The EKF algorithm, however, is
 preferred over other processes for iteratively determining a plurality of
 state variables using dynamic equations.
 FIG. 8 is a flowchart of another method in accordance with another
 embodiment of the invention. In this embodiment, the method includes the
 routines 410-450 described above with reference to FIG. 6, a substrate
 status routine 560, and a control routine 570. The substrate status
 routine 560 estimates the status of the substrate surface according to the
 estimated values of the state variables. The substrate status, for
 example, can be the thickness of the outer film over either the array
 areas or the periphery areas, the array erosion rate, the periphery
 erosion rate, or several other of the state variables. The control routine
 570 changes or maintains one or more parameters of the planarizing cycle
 according to the estimated status of the substrate surface.
 The status routine 560 and the control routine 570 are useful, for example,
 to predict the endpoint of a planarizing cycle for constructing
 Shallow-Trench-Isolation (STI) structures on the substrate assembly. FIGS.
 9A-9C are schematic partial cross-sectional views of a substrate assembly
 580 at various stages of a method for forming STI structures 595 (FIG.
 9C). Referring to FIG. 9A, the substrate assembly 580 initially has a
 substrate 582 with a top surface 584 and a plurality of trenches 586
 extending along the top surface 584. The substrate assembly 580 also
 includes a thin conformal layer 590 (e.g., a silicon nitride layer) that
 covers the top surface 584 of the substrate 582 and conforms to the
 trenches 586, and a fill layer 596 (e.g., a silicon dioxide, BPSG or TEOS
 layer) over the conformal layer 590 that fills the trenches 586.
 FIG. 9B illustrates the substrate assembly 580 after it has been-planarized
 to expose the conformal layer 590 over the top surface of the substrate
 582. In one embodiment of a method for planarizing the substrate assembly
 580, the exposure of the conformal layer 590 over the top surface 584 of
 the substrate 582 is estimated using the EKF method described above with
 reference to FIG. 6. But, instead of calculating the endpoint time for the
 planarizing cycle and comparing the elapsed time with the endpoint time
 according to the method 400 of FIG. 6, this method calculates the time for
 removing the fill layer over the top portions of the conformal layer 590.
 When the elapsed time equals the calculated time of exposure of the
 conformal layer 590, the control routine 570 of this method then uses
 another process for determining the final endpoint of the planarizing
 cycle. FIG. 9C illustrates the final endpoint for the STI structure 595 in
 which the conformal layer 590 has been removed from the top surface 584 of
 the substrate 582. In one embodiment, the other process for determining
 the final endpoint involves periodically measuring the actual thickness of
 the conformal layer using an interferometer or other technique (e.g.,
 diagnostic machines manufactured by Nova). In another embodiment, the
 other process for determining the endpoint involves sensing or monitoring
 the drag force between the substrate assembly 580 and a planarizing medium
 using the motor current for the planarizing machine or a load cell.
 Suitable planarizing machines that monitor the drag force are disclosed in
 U.S. Pat. Nos. 5,036,015 and 5,069,002, and U.S. application Ser. No.
 09/386,648, all of which are herein incorporated by reference.
 The control routing 570 can also control other aspects of the planarizing
 cycle. In one embodiment, for example, the control routine 570 can
 terminate the planarizing cycle if the erosion rate over either the array
 areas or the periphery areas is not within an acceptable range, or if the
 predicted thickness is not within an expected range. In still another
 embodiment, the control routine can change the type or volume of the
 planarizing solution according to the estimates of the erosion rates or
 the predicted thickness.
 From the foregoing it will be appreciated that, although specific
 embodiments of the invention have been described herein for purposes of
 illustration, various modifications may be made without deviating from the
 spirit and scope of the invention. For example, the EKF algorithm can be
 based on a direct calculation of the thickness of a layer over the array
 areas and/or the periphery areas, and/or a calculation of the array
 erosion rate and the periphery erosion rate. The state variable for the
 state vector x can also alternatively include: (a) the thickness of a
 layer over the array areas; (b) the thickness of a layer over the
 periphery areas; (c) the array erosion rate; (d) the periphery erosion
 rate; and (e) the sensor gain. Additionally, the terms array areas and
 periphery areas as used herein mean "high density" areas and "low density"
 areas, respectively, without being limited to a particular geographic
 region on the substrate or relative to each other. Accordingly, the
 invention is not limited except as by the appended claims.