Chemical mechanical polishing apparatus and method

A polisher head of a polishing apparatus includes a membrane and a first local pressure nodule and a second local pressure nodule physically contacting the membrane. The first local pressure nodule is configured to apply a first local force to the membrane and the second local pressure nodule is configured to apply a second local force to the membrane. The first local pressure nodule and the second local pressure nodule are independently controllable.

BACKGROUND

Generally, semiconductor devices comprise active components, such as transistors, formed on a substrate. Any number of interconnect layers may be formed over the substrate connecting the active components to each other and to outside devices. The interconnect layers are typically made of low-k dielectric materials comprising metallic trenches/vias.

As the layers of a device are formed, it is sometimes necessary to planarize the device. For example, the formation of metallic features in the substrate or in a metal layer may cause uneven topography. This uneven topography creates difficulties in the formation of subsequent layers. For example, uneven topography may interfere with the photolithographic process commonly used to form various features in a device. It is, therefore, desirable to planarize the surface of the device after various features or layers are formed.

One commonly used method of planarization is via chemical mechanical polishing (CMP). Typically, CMP involves placing a wafer in a carrier head, wherein the wafer is held in place by a retaining ring. The carrier head and the wafer are then rotated as downward pressure is applied to the wafer against a polishing pad. A chemical solution, referred to as a slurry, is deposited onto the surface of the polishing pad to aid in the planarizing. Ideally, the retaining ring comprises a multitude of grooves to facilitate the even distribution of the slurry over the wafer surface. When retaining rings without any grooves are used during CMP, the resulting wafers tend to suffer topographical unevenness due to irregular slurry disposition. Thus, the surface of a wafer may be planarized using a combination of mechanical (the grinding) and chemical (the slurry) forces.

DETAILED DESCRIPTION

Various embodiments are described with respect to a specific context, namely a chemical mechanical polishing (CMP) apparatus and a method of polishing a semiconductor wafer using the CMP apparatus. Various embodiments include a polisher head having local pressure nodules configured to apply a non-uniform down force to a semiconductor wafer during a CMP process. The local pressure nodules allow for independently controlling the force applied to different regions of a semiconductor wafer and allow for compensating for a thickness asymmetry or a thickness non-uniformity of a polished layer of a semiconductor wafer. The use of local pressure nodules further allows for reducing polishing time and allows for increasing a wafer per hour (WPH) output of a CMP apparatus in some embodiments. Various embodiments further allow for configuring local pressure nodules to apply a non-uniform force to a semiconductor wafer based on a non-uniform thickness of a polished layer of a semiconductor wafer.

FIG. 1illustrates a perspective view of a CMP apparatus100in accordance with some embodiments. In some embodiments, the CMP apparatus100includes a platen101over which a polishing pad103has been placed. In some embodiments, the polishing pad103may be a single layer or a composite layer of materials such as felts, polymer impregnated felts, microporous polymers films, microporous synthetic leathers, filled polymer films, unfilled textured polymer films, or the like. The polymers may include polyurethane, polyolefins, or the like.

In some embodiments, a polisher head105is placed over the polishing pad103. The polisher head105includes a carrier107and a retainer ring109. In some embodiments, the retainer ring109is mounted to the carrier107using mechanical fasteners such as screws or by any other suitable means. During a CMP process, a wafer (not shown inFIG. 1, seeFIG. 3) is placed within the carrier107and is held by the retainer ring109. In some embodiments, the retainer ring109has an annular shape with a hollow center. The wafer is placed in the hollow center of retainer ring109such that the retainer ring109holds the wafer in place during a CMP process. The wafer is positioned so that the surface to be polished faces downward towards the polishing pad103. The carrier107is configured to apply a downward force or pressure and causes the wafer to come in contact with polishing pad103. The polisher head105is configured to rotate and rotates an attached wafer over the polishing pad103during a CMP process.

In some embodiments, the CMP apparatus100includes a slurry dispenser111, which is configured to deposit a slurry113onto the polishing pad103. The platen101is configured to rotate and causes the slurry113to be distributed between the wafer and the platen through a multitude of grooves (not shown) in the retainer ring109, which may extend from an outer sidewall of the retainer ring109to an inner sidewall of the retainer ring109. The composition of the slurry113depends on a type of material to be polished. For example, the slurry may comprise a reactant, an abrasive, a surfactant, and a solvent. The reactant may be a chemical, such as an oxidizer or a hydrolyzer, which will chemically react with a material of the wafer in order to assist the polishing pad103in grinding away the material. In some embodiments in which the material is tungsten, the reactant may be hydrogen peroxide, although any other suitable reactant, such as hydroxylamine, periodic acid, ammonium persulfate, other periodates, iodates, peroxomonosulfates, peroxymonosulfuric acid, perborates, malonamide, combinations of these, and the like, that will aid in the removal of the material may alternatively be utilized. Other reactants may be used in order to remove other materials. For example, in some embodiments in which the material is an oxide, the reactant may comprise HNO3, KOH, NH4OH, or the like.

The abrasive may be any suitable particulate that, in conjunction with the polishing pad103, aids in the polishing of the wafer. In some embodiments, the abrasive may comprise silica, aluminum oxide, cerium oxide, polycrystalline diamond, polymer particles such as polymethacrylate or polymethacryclic, combinations of these, or the like.

The surfactant may be utilized to help disperse the reactant and abrasive within the slurry113and to prevent (or at least reduce) the abrasive from agglomerating during a CMP process. In some embodiments, the surfactant may include sodium salts of polyacrylic acid, potassium oleate, sulfosuccinates, sulfosuccinate derivatives, sulfonated amines, sulfonated amides, sulfates of alcohols, alkylanyl sulfonates, carboxylated alcohols, alkylamino propionic acids, alkyliminodipropionic acids, potassium oleate, sulfosuccinates, sulfosuccinate derivatives, sulfates of alcohols, alkylanyl sulfonates, carboxylated alcohols, sulfonated amines, sulfonated amides, alkylamino propionic acids, alkyliminodipropionic acids, combinations of these, or the like. However, these embodiments are not intended to be limited to these surfactants, as any suitable surfactant may alternatively be utilized as the surfactant.

The remainder of the slurry113may be a solvent that may be utilized to combine the reactant, the abrasive, and the surfactant and allow the mixture to be moved and dispersed onto the polishing pad103. In some embodiments, the solvent of the slurry113may be a solvent such as deionized (DI) water or an alcohol. However, any other suitable solvent may alternatively be utilized.

In some embodiments, the CMP apparatus100includes a pad conditioner119attached to a pad conditioner head117. The pad conditioner head117is configured to rotate and rotates the pad conditioner119over the polishing pad103. In some embodiments, the pad conditioner119is mounted to the pad conditioner head117using mechanical fasteners such as screws or by any other suitable means. A pad conditioner arm115is attached to the pad conditioner head117and is configured to move the pad conditioner head117and the pad conditioner119in a sweeping motion across a region of the polishing pad103. In some embodiments, the pad conditioner head117is mounted to the pad conditioner arm115using mechanical fasteners such as screws or by any other suitable means. In some embodiments, the pad conditioner119comprises a substrate over which an array of abrasive particles, such as diamonds, is bonded using, for example, electroplating. The pad conditioner119removes built-up wafer debris and excess slurry from the polishing pad103during a CMP process. In some embodiments, the pad conditioner119also acts as an abrasive for the polishing pad103to create an appropriate texture (such as, for example, grooves, or the like) against which the wafer may be properly polished.

Referring to further toFIG. 1, in the illustrated embodiment, the CMP apparatus100has a single polisher head (such as the polisher head105) and a single polishing pad (such as the polishing pad103). However, in other embodiments, the CMP apparatus100may have multiple polisher heads and/or multiple polishing pads. In some embodiments in which the CMP apparatus100has multiple polisher heads and a single polishing pad, multiple wafers may be polished at the same time. In other embodiments in which the CMP apparatus100has a single polisher head and multiple polishing pads, a CMP process may be a multi-step process. In such embodiments, a first polishing pad may be used for bulk material removal from a wafer, a second polishing pad may be used for global planarization of the wafer and a third polishing pad may be used to buff a surface of the wafer. In some embodiments, different slurries may be used for different CMP stages. In other embodiments, the same slurry may be used for all CMP stages.

FIG. 2illustrates a top view of the CMP apparatus100in accordance with some embodiments. In some embodiments, the platen101is configured to rotate in a clockwise or a counter-clockwise direction indicated by a double-headed arrow203around an axis extending through a point201, which is a center point of the platen101. The polisher head105is configured to rotate in a clockwise or a counter-clockwise direction indicated by a double-headed arrow207around an axis extending through a point205, which is a center point of the polisher head105. In some embodiment, the axis through the point201is parallel to the axis through the point205. In some embodiment, the axis through the point201is spaced apart from the axis through the point205. In some embodiments, the pad conditioner head117is configured to rotate in a clockwise or a counter-clockwise direction indicated by a double-headed arrow211around an axis extending through a point209, which is a center point of the pad conditioner head117. In some embodiments, the axis through the point201is parallel to the axis through the point209. The pad conditioner arm115is configured to move the pad conditioner head117in an arc as indicated by a double-headed arrow213.

FIG. 3illustrates a cross-sectional view of the polisher head105in accordance with some embodiments. In some embodiments, the carrier107includes a membrane301that interfaces with a wafer303during a CMP process. In some embodiments, the CMP apparatus100includes a vacuum system (not shown) coupled to the polisher head105and the membrane301is configured to pick up and hold the wafer303using vacuum suction on the membrane301. In some embodiments, the wafer303may be a semiconductor wafer comprising, for example, a semiconductor substrate (e.g., comprising silicon, III-V semiconductor materials, or the like), active devices (e.g., transistors) on the semiconductor substrate, and/or various interconnect structures. The interconnect structure may include conductive features, which electrically connect the active devices in order to form functional circuits. In various embodiments, CMP processing may be applied to the wafer303during any stage of manufacture in order to planarize, reduce, or remove features (e.g., dielectric material, semiconductor material, and/or conductive material) of the wafer303. Thus, the wafer303being processed may include any subset of the above features as well as other features. In some embodiments, the wafer303comprises a bottommost layer307to be polished during a CMP process. In some embodiments in which the bottommost layer307comprises tungsten, the bottommost layer307may be polished to form contact plugs contacting various active devices of the wafer303. In some embodiments in which the bottommost layer307comprises copper, the bottommost layer307may be polished to form various interconnect structures of the wafer303. In some embodiments in which the bottommost layer307comprises a dielectric material, the bottommost layer307may be polished to form shallow trench isolation structures on the wafer303.

Referring further toFIG. 3, in some embodiments, the carrier107includes N local pressure nodules3051to305Nthat are configured to independently exert a local force or a local pressure onto the wafer303through the membrane301. For the clarity of presentation only the local pressure nodules3051,3052and305Nare labeled inFIG. 3. The local pressure nodules3051to305Nare configured to be controlled independently and to apply independent local forces F1to FN, respectively, to the membrane301and to the wafer303attached to the membrane301. In what follows the local forces F1to FNmay be collectively referred to as a force field. Through such an independent control, a force field of any desired configuration may be applied to the wafer303. In some embodiments, the force field may be a uniform force field. In other embodiments, the force field may be a non-uniform force field.

In some embodiments, the local pressure nodules3051to305Nmay be electrically controllable and may comprise a piezoelectric material such as quartz, lithium niobate, barium titanate, lead zirconate titanate (PZT), or the like. The local pressure nodules3051to305Nmay further comprise electrical contacts3091to309N, respectively. In such embodiments, through the inverse piezoelectric effect, the local pressure nodules3051to305Nmay be deformed by applying voltages V1to VN, respectively, to the electrical contacts3091to309Nof the local pressure nodules3051to305N. The voltages V1to VNcause the local pressure nodules3051to305Nto stretch towards the membrane301and apply local forces F1to FN, respectively, to the wafer303. In some embodiments, the CMP apparatus100includes a controller (not shown), which is configured to provide voltages V1to VNto the local pressure nodules3051to305N, such that the voltages V1to VNare independent form each other. In some embodiments, by providing independent voltages V, to VNto the local pressure nodules305, to305N, the local pressure nodules305, to305Nmay be independently deformed and may apply independent local forces F, to FNto the wafer303. In some embodiments, for each i=1 to N, the voltage Vibetween about 0 mV and about 30 mV may be applied to the local pressure nodule305i, which in turn applies a local force Fibetween about 0.1 N and about 1 N to the wafer303. In some embodiments, each of the local pressure nodules3051to305Nmay apply a pressure between about 50 hpa and about 500 hpa to the wafer303.

In other embodiments, the local pressure nodules3051to305Nmay be pressure controllable, may comprise flexible sidewalls and may be configured to hold a fluid. In some embodiments, the fluid may comprise a suitable gas or liquid. The CMP apparatus100may include one or more pumps (not shown), which are configured to independently control pressures P1to PNof a fluid held by the local pressure nodules3051to305N, respectively. In such embodiments, the flexible sidewalls of the local pressure nodules3051to305Nare deformed (for example, stretched) in response to the pressures P1to PN. By independently controlling the pressures P1to PN, the flexible sidewalls of the local pressure nodules3051to305Nmay be independently deformed and may apply independent local forces F1to FNto the wafer303.

FIG. 4illustrates a top view of the membrane301with the local pressure nodules305in accordance with some embodiments. In the illustrated embodiment, top-view shapes of the local pressure nodules3051to305Nare circles. In other embodiments, top-view shapes of the local pressure nodules3051to305Nmay be ovals, squares, rectangles, or the like. In some embodiments, the local pressure nodules3051to305Nmay have a width W, between about 1.5 cm and about 3.5 cm, such as about 2.54 cm (1 in). InFIG. 4, a particular number and arrangement of the local pressure nodules3051to305Nare provided for illustrative purposes only. One skilled in the art would appreciate that the number and arrangement of the local pressure nodules3051to305Nmay vary according to design requirements of the CMP apparatus100.

FIG. 5illustrates thicknesses of the bottommost layer307of an exemplary wafer303in accordance with some embodiments. In some embodiments, the bottommost layer307may have a non-uniform thickness, for example, due to process variations during forming the bottommost layer307. In the illustrated embodiment, the bottommost layer307is formed by depositing tungsten using a CVD process. Due to CVD process variations the bottommost layer307has a non-uniform thickness ranging from about 146.8 nm to about 160.1 nm, with a mean value of about 155.4 nm and a standard deviation of about 2.97 nm. Based on the non-uniform thickness of the bottommost layer307, various regions of the bottommost layer307may be identified. In some embodiments, the bottommost layer307may be separated into a plurality of regions, such that each region may have a nearly uniform thickness. In the illustrated embodiment, the bottommost layer307has a first region501, a second region503and a third region505. A thickness of the first region501is similar to the average thickness of the bottommost layer307. A thickness of the second region503is less than the average thickness of the bottommost layer307. A thickness of the third region505is greater than the average thickness of the bottommost layer307. As described below in greater detail, the local pressure nodules3051to305Nare configured such that the local pressure nodules3051to305Napply a non-uniform force field to the wafer303to more efficiently polish the bottommost layer307of the wafer303.

FIG. 6illustrates a top view of the membrane301with the local pressure nodules3051to305N, with the local pressure nodules3051to305Nconfigured to apply a non-uniform force field to the wafer303(seeFIG. 3) in accordance with some embodiments. For the clarity of presentation only the local pressure nodules3051and305Nare labeled inFIG. 6. In some embodiments, the local forces F1to FNto be applied by the local pressure nodules3051to305N, respectively, may be determined independently for each of the local pressure nodules3051to305N. In such embodiments, the local forces F1to FNto be applied by the local pressure nodules3051to305N, respectively, may be determined based on local thicknesses of the bottommost layer307immediately below the respective local pressure nodules3051to305N. In some embodiments, the local forces F1to FNmay be proportional to local thicknesses of the bottommost layer307. In other embodiments, other functional dependencies between the local forces F1to FNand the thicknesses of the bottommost layer307may be used.

Referring further toFIG. 6, in some embodiments, the local forces F1to FNto be applied by the local pressure nodules3051to305N, respectively, may be determined by grouping the local pressure nodules3051to305Ninto a plurality of groups such that each of the local pressure nodules in a group is configured to apply a nearly same local force to the wafer303. For example, to polish the bottommost layer307of the wafer303illustrate inFIG. 5, the local pressure nodules3051to305Nmay be grouped into a plurality of groups that correspond to the regions501,503and505of the bottommost layer307. In the illustrated embodiment, the local pressure nodules3051to305Nare grouped into a first group601, a second group603and a third group605. The first group601corresponds to the first region501(seeFIG. 5) of the bottommost layer307and each local pressure nodule in the first group601is configured to apply a first force to the wafer303. The second group603corresponds to the second region503(seeFIG. 5) of the bottommost layer307and each local pressure nodule in the second group603is configured to apply a second force to the wafer303, with the second force being lower than the first force. The third group605corresponds to the third region505(seeFIG. 5) of the bottommost layer307and each local pressure nodule in the third group605is configured to apply a third force to the wafer303, with the third force being higher than the first force.

FIG. 7is a flow diagram of a method700of polishing a semiconductor wafer in accordance with some embodiments. Referring toFIGS. 5 and 7, the method starts with step701, where a thickness map of the bottommost layer307of the wafer303is determined. The thickness map of the bottommost layer307may be determined by measuring a thickness of the bottommost layer307or using empirical data from previous processes. In some embodiments, the thickness of the bottommost layer307may be measured using ellipsometry, interferometry, reflectometry, picosecond ultrasonics, atomic force microscopy (AFM), scanning tunneling microscopy (STM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), or the like. In the illustrated embodiment, a thickness measurement apparatus (not shown) is external from the CMP apparatus100and the thickness map of the bottommost layer307is determined before loading the wafer330into the CMP apparatus100. In other embodiments, the thickness measurement apparatus may be a part of the CMP apparatus100and the thickness map of the bottommost layer307is determined after loading the wafer330into the CMP apparatus100.

Referring toFIGS. 5-7, in step703, a force field to be applied to the wafer303during a CMP process is determined based on the thickness map of the bottommost layer307. The force field is a collection of local forces F1to FNto be applied to the wafer303using individual local pressure nodules3051to305N. In some embodiments, the force field may be determined using a method as described above with reference toFIG. 6.

Referring toFIGS. 5-7, in step705, voltages V1to VNto be applied to the local pressure nodules3051to305N, respectively, are determined based on the desired force field. In some embodiments, the voltages V1to VNto be applied to the local pressure nodules3051to305Nmay be determined based on the inverse piezoelectric effect. The voltages V1to VNto be applied to the local pressure nodules3051to305Nare voltages that after being applied to the local pressure nodules3051to305Ncause the local pressure nodules3051to305Nto change shape and apply the desired local forces F1to FNto the wafer303during a CMP process.

Referring toFIGS. 1-3 and 7, in step707, the wafer303is loaded into the CMP apparatus100. In some embodiments, the polisher head105may be lowered towards the wafer303placed on a stage (not illustrated). The carrier107may pick up the wafer303from the stage using vacuum suction on the membrane301so that the wafer303is disposed within an opening of the retainer ring109as illustrated inFIG. 3. In some embodiments, the polisher head105may be lowered towards the polishing pad103for polishing the wafer303. The wafer303is positioned so that the layer to be planarized (such as the bottommost layer307) faces towards the polishing pad103. Other methods of disposing the wafer303over the polishing pad103may be used as well. For example, in other embodiments, the wafer303may be placed on the polishing pad103using a different mechanism, and the polisher head105may be lowered onto the wafer303while the wafer303is on the polishing pad103.

Referring toFIGS. 1-3 and 7, in step709, the voltages V1to VNdetermined in step705are applied to the local pressure nodules3051to305N, respectively, such that the local pressure nodules3051to305Napply the desired local forces F1to FNto the wafer303as determined in step703. In some embodiments, the voltages V1to VNdetermined in step705are applied to the local pressure nodules3051to305Nusing a controller (not show) that is configured to apply the desired voltages V1to VNto the local pressure nodules3051to305N, such that the voltages V1to VNare independent from each other.

Referring toFIGS. 1-3 and 7, in step711, the wafer303is polished. During a CMP process the local pressure nodules3051to305Napply the force forces F1to FNdetermined in step703to the membrane301and the membrane301pushes the wafer303onto the polishing pad103as illustrated inFIG. 3. The wafer303is polished by rotating the polisher head105and/or the polishing pad103/platen101as indicated by double-headed arrows207and203, respectively. In some embodiments, the polisher head105and the polishing pad103/platen101may be rotated in a same direction. In other embodiments, the polisher head105and the polishing pad103/platen101may be rotated in opposite directions. By rotating the wafer303against the polishing pad103, the polishing pad103mechanically grinds the bottommost layer307of the wafer303to remove undesirable material of the bottommost layer307.

Referring further toFIGS. 1-3, the slurry113is dispensed over a top surface of the polishing pad103by the slurry dispenser111. In some embodiments, a gap may be disposed between the retainer ring109and the polishing pad103during a CMP process to allow the slurry113to be distributed under the bottommost layer307of the wafer303. In other embodiments, the retainer ring109may contact the polishing pad103and the slurry113may be distributed under the bottommost layer307of the wafer303using one or more groves (not shown) extending from an outer sidewall to an inner sidewall of the retainer ring109.

Referring further toFIGS. 1-3, during a CMP process, the pad conditioner arm115may move the pad conditioner head117and the pad conditioner119in a sweeping motion over a region of the polishing pad103. The pad conditioner119may be used to remove built-up wafer debris and excess slurry from the polishing pad103. The pad conditioner119may also acts as an abrasive for the polishing pad103to create an appropriate texture against which the wafer303may be mechanically ground. In some embodiments, the pad conditioning head117/pad conditioner119may rotate in directions indicated by the double-headed arrow211. In some embodiments, the pad conditioning head117/pad conditioner119and the platen101/polishing pad103may rotate in a same direction. In other embodiments, the pad conditioning head117/pad conditioner119and the platen101/polishing pad103may rotate in opposite directions. In some embodiments, the pad conditioner arm115may move the pad conditioning head117/pad conditioner119in an arc indicated by the double-headed arrow213. In some embodiments, the range of the arc corresponds to the size of the carrier107. For example, the carrier107may be larger than 300 mm in diameter to accommodate 300 mm wafers. Accordingly, the arc would extend from the perimeter of the platen101/polishing pad103to a distance of at least 300 mm inward from that perimeter. This ensures that any portion of polishing pad103that may contact the wafer303is conditioned appropriately. One skilled in the art would recognize that the numbers given in this paragraph are exemplary. The actual dimensions of the carrier107and the corresponding range of the arc may vary depending on the dimensions of the wafer303being polished.

In some embodiments, the force field applied to the wafer303in step709is static and does not change during the polishing process. In other embodiments, the force field applied to the wafer303may be dynamically adjusted one or more times during the polishing process. As the wafer303is polished and the thickness map of the bottommost layer307changes, the force field applied by the local pressure nodules3051to305Nmay be adjusted accordingly. In such embodiments, steps701,703,705and709may be repeated one or more times during preforming step711.

In some embodiments, the CMP process may be a one-step CMP process (e.g., where a single polishing pad103is used) or a multi-step CMP process. In a multi-step CMP process, the polishing pad103may be used during a bulk CMP process. In such embodiments, the wafer303may be removed from the polishing pad103and may be transferred to a second polishing pad (not illustrated). The second polishing pad may perform a similar CMP process as described above and the description is not repeated herein. In some embodiments, the second polishing pad may be a soft buffing pad which may polish the wafer303at a slower and more controlled rate than the first polishing pad206while also buffing and eliminating defects and scratches that may have been caused by the bulk CMP process. The buffing CMP process may be continued until desired materials have been removed from the bottommost layer307of the wafer303. In some embodiments, timed or optical end-point detection methods may be used to determine when to stop the polishing of the wafer303.

FIG. 8is a flow diagram of a method800of polishing a semiconductor wafer in accordance with some embodiments. In the illustrated embodiment, the thickness measurement apparatus is a part of the CMP apparatus100and the thickness map of the bottommost layer307is determined after loading the wafer330into the CMP apparatus100in step801. In some embodiments, steps803,805,807,809and811of the method800may be similar to steps701,703,705,709and711, respectively, of the method700described above with reference toFIG. 7and the description is not repeated herein.

Various embodiments presented herein may provide several advantages. Embodiments such as described herein allow for applying a non-uniform force field to the wafer such that local values of the non-uniform force field may be independently controlled. In various embodiments, local pressure nodules formed of a piezoelectric material may be employed to apply the non-uniform force field to a wafer. In various embodiments, the non-uniform force field may be determined based on a non-uniform thickness of a polished layer and allow for compensating for a thickness asymmetry or a thickness non-uniformity of the polished layer. Various embodiments further allow for reducing polishing time and increasing a wafer per hour (WPH) output of a CMP apparatus.

In accordance with an embodiment, a polishing apparatus includes a polisher head. The polisher head includes a membrane, and a first local pressure nodule and a second local pressure nodule physically contacting the membrane, the first local pressure nodule being configured to apply a first local force to the membrane, the second local pressure nodule being configured to apply a second local force to the membrane, the first local pressure nodule and the second local pressure nodule being independently controllable.

In accordance with another embodiment, a method includes attaching a wafer to a membrane of a polisher head. A first applied local force is applied to the membrane using a first local pressure nodule of the polisher head, the first local pressure nodule physically contacting the membrane. A second applied local force is applied to the membrane using a second local pressure nodule of the polisher head, the second local pressure nodule physically contacting the membrane, the first local pressure nodule and the second local pressure nodule being independently controllable. An exposed layer of the wafer is polished.

In accordance with yet another embodiment, a method includes determining a thickness map of a first side of a wafer. A desired force field to be applied to the wafer is determined based on the thickness map. A second side of the wafer is attached to a membrane of a polisher head, the second side being opposite the first side. An applied force field based upon the desired force field is applied to the membrane using a plurality of local pressure nodules of the polisher head, the plurality of local pressure nodules being configured to apply the applied force field to the membrane. The first side of the wafer is polished.