Patent Publication Number: US-2022223386-A1

Title: Circuits for edge ring control in shaped dc pulsed plasma process device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims benefit of U.S. Pat. No. 11,289,310, filed Nov. 21, 2018 (Attorney Docket No. APPM/44015905US01), of which is incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Field 
     Examples of the present disclosure generally relate to a substrate support for a plasma processing chamber, and more particularly, to an apparatus and methods for varying voltages applied to an edge ring portion of the substrate support relative to a substrate support portion of the substrate support to control the plasma sheath in the plasma processing chamber. 
     Description of the Related Art 
     As semiconductor technology nodes advanced with reduced size device geometries, substrate edge critical dimension uniformity requirements become more stringent and affect die yields. Commercial plasma reactors include multiple tunable knobs for controlling process uniformity across a substrate, such as, for example, temperature, gas flow, RF power, and the like. 
     During processing, a substrate disposed on a substrate support may undergo a process that deposits material on the substrate and to remove, or etch, portions of the material from the substrate, often in succession or in alternating processes. It is typically beneficial to have uniform deposition and etching rates across the surface of the substrate. However, process non-uniformities often exist across the surface of the substrate and may be significant at the perimeter or edge of the substrate. The etch profile at an extreme edge of the substrate may deviate from that at the center of the substrate due to different ion density, RF uniformity, or previous processing. These non-uniformities at the perimeter may be attributable to electric field termination affects and are sometimes referred to as edge effects. These edge effects reduce usable die yield near the edge of the substrate. 
     One technique in the art for obtaining better uniformity is to tune the voltage applied to an edge ring disposed on the substrate support to change the ion density at the substrate edge. This provides a control knob to control the extreme edge process profile and feature tilting. This may be accomplished by applying a first RF voltage to an edge ring electrode embedded in the edge ring and a second RF voltage to a substrate support electrode embedded in the substrate support. However, employing multiple RF source voltages is expensive. Other methods and apparatus for controlling a plasma sheath exist, such as edge rings which are movable relative to the substrate support. However, certain electronic device manufacturing processes are subject to stringent particle requirements which make moving parts undesirable. Movable edge rings are also subjectable to arcing. 
     Therefore, there is a need for apparatus and methods that improve process uniformity on a substrate. 
     SUMMARY 
     The present disclosure provides apparatus and methods for manipulating the voltage at the edge ring relative to a substrate located on a substrate support, which functions as an effective tuning knob to control the process profile near a substrate edge. Manipulating the edge ring&#39;s voltage can improve the process uniformity on the substrate. Also, controlling the edge ring&#39;s voltage can assist in controlling the verticality (i.e., tilting) of features formed near the substrate edge. 
     In one example, the apparatus includes a substrate support assembly that has a body having a substrate support portion having a substrate electrode embedded therein for applying a substrate voltage to a substrate. The body of the substrate support assembly further has an edge ring portion disposed adjacent to the substrate support portion. The edge ring portion has an edge ring electrode embedded therein for applying an edge ring voltage to an edge ring. The apparatus further includes an edge ring voltage control circuit coupled to the edge ring electrode. A substrate voltage control circuit is coupled to the substrate electrode. The edge ring voltage control circuit and the substrate voltage control circuit are independently tunable to generate a difference in voltage between the edge ring voltage and the substrate voltage. 
     In another example, the apparatus includes a process chamber that includes a chamber body, a lid disposed on the chamber body, an inductively coupled plasma apparatus positioned above the lid, and a substrate support assembly positioned within the chamber body. The substrate support assembly has a body having a substrate support portion having a substrate electrode embedded therein for applying a substrate voltage to a substrate. The body of the substrate support assembly further has an edge ring portion disposed adjacent to the substrate support portion. The edge ring portion has an edge ring electrode embedded therein for applying an edge ring voltage to an edge ring. The apparatus further includes an edge ring voltage control circuit coupled to the edge ring electrode. A substrate voltage control circuit is coupled to the substrate electrode. The edge ring voltage control circuit and the substrate voltage control circuit are independently tunable to generate a difference in voltage between the edge ring voltage and the substrate voltage. 
     In another example, a method of operating a process chamber is disclosed. The process chamber comprises a chamber body and a substrate support assembly positioned within the chamber body, the substrate support assembly having a body, the body having a substrate support portion having a substrate electrode embedded therein and an edge ring portion disposed adjacent to the substrate support portion, the edge ring portion having an edge ring electrode embedded therein. The method comprises applying a substrate voltage to the substrate electrode by a substrate voltage control circuit. The method further comprises applying an edge ring voltage to the edge ring electrode by an edge ring voltage control circuit. The method further comprises independently tuning the edge ring voltage control circuit and the substrate voltage control circuit to change a ratio between the edge ring voltage and the substrate voltage. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only exemplary embodiments and are therefore not to be considered limiting of its scope, and may admit to other equally effective embodiments. 
         FIG. 1  is a schematic sectional view of a process chamber according to one embodiment of the disclosure. 
         FIGS. 2A-2C  are schematic views of a plasma sheath relative to the edge of a substrate, according to examples of the disclosure. 
         FIGS. 3A and 3B  illustrate enlarged schematic views of the substrate support shown in  FIG. 1 . 
         FIG. 4  is schematic circuit diagram illustrating one embodiment of the edge ring voltage control circuit/substrate voltage control circuit for driving the electrodes of the substrate support assembly. 
         FIG. 5  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit for driving the electrodes of the substrate support assembly. 
         FIG. 6  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit for driving the electrodes of the substrate support assembly. 
         FIG. 7  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit for driving the electrodes of the substrate support assembly. 
         FIG. 8  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit for driving the electrodes of the substrate support assembly. 
         FIG. 9  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit for driving the electrodes of the substrate support assembly. 
         FIG. 10  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit for driving the electrodes of the substrate support assembly. 
         FIG. 11  is a flow diagram illustrating an operation process for the support circuits described above according to one aspect of the disclosure. 
         FIGS. 12A and 12B  depict example simulation results of modulated an edge ring or wafer voltage waveform created by varying the variable capacitors and/or inductors of  FIGS. 4-10  given a shaped DC pulse voltage source. 
     
    
    
     To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements and features of one embodiment may be beneficially incorporated in other embodiments without further recitation. 
     DETAILED DESCRIPTION 
     The present disclosure generally relates to apparatus and methods that apply a voltage difference between a substrate support portion and an edge ring support portion of a substrate support assembly. The substrate support assembly has a body having the substrate support portion having a substrate electrode embedded therein for applying a substrate voltage to a center portion of a substrate. The body of the substrate support assembly further has the edge ring portion disposed adjacent to the substrate support portion. The edge ring portion has an edge ring electrode embedded therein for applying an edge ring voltage to the edge portion of the substrate. 
     The apparatus and methods further include an edge ring voltage control circuit coupled to the edge ring electrode. A substrate voltage control circuit coupled to the substrate electrode. At least one shaped DC pulse voltage source is coupled to one or both of the edge ring voltage control circuit and the substrate voltage control circuit. The edge ring voltage control circuit and the substrate voltage control circuit are independently tunable to generate a difference in voltage between the edge ring voltage and the substrate voltage. 
     As the plasma sheath becomes non-uniform adjacent the edge ring due to different ion density, RF uniformity, or previous processing, one or both of the edge ring voltage control circuit and the substrate voltage control circuit is adjusted in order to affect the voltage amplitude difference between the substrate and the edge ring. Adjustment of the voltage amplitude difference via tuning one or both of the edge ring voltage control circuit and the substrate voltage control circuit results in an adjustment of the plasma sheath near the substrate perimeter. Bending of the sheath at the perimeter of the substrate will either focus ions (increase etch rate) or de-focus ions (decrease etch rate) in the region of approximately 0 mm-10 mm (depending on the process condition) from the edge of the substrate. 
     The present disclosure also addresses the need to compensate for extreme edge non-uniformities left by previous process steps. In all of these applications, when the process is very sensitive to particles, for example in logic circuit applications, it is considered a high risk to have moving parts in the vicinity of the substrate. The present disclosure addresses the need for extreme edge voltage tunability with no moving parts. 
       FIG. 1  is a schematic sectional view of a process chamber  100 , according to one example of the disclosure. The process chamber  100  includes a chamber body  101  and a lid  102  disposed thereon that together define an internal volume  124 . The chamber body  101  is typically coupled to an electrical ground  103 . A substrate support assembly  104  is disposed within the inner volume to support a substrate  105  thereon during processing. An edge ring  106  is positioned on the substrate support assembly  104  and surrounds the periphery of the substrate  105 . The process chamber  100  also includes an inductively coupled plasma apparatus  107  for generating a plasma of reactive species within the process chamber  100 , and a controller  108  adapted to control systems and subsystems of the process chamber  100 . 
     The substrate support assembly  104  is disposed in the internal volume  124 . The substrate support assembly  104  generally includes at least a substrate support  152 . The substrate support  152  includes an electrostatic chuck  150  comprising a substrate support portion  154  configured to underlay and support the substrate  105  to be processed and an edge ring portion  156  configured to support an edge ring  106 . The substrate support assembly  104  may additionally include a heater assembly  169 . The substrate support assembly  104  may also include a cooling base  131 . The cooling base  131  may alternately be separate from the substrate support assembly  104 . The substrate support assembly  104  may be removably coupled to a support pedestal  125 . The support pedestal  125  is mounted to the chamber body  101 . The support pedestal  125  may optionally include a facility plate  180 . The substrate support assembly  104  may be periodically removed from the support pedestal  125  to allow for refurbishment of one or more components of the substrate support assembly  104 . Lifting pins  146  are disposed through the substrate support assembly  104  as conventionally known to facilitate substrate transfer. 
     The facility plate  180  is configured to accommodate a plurality of fluid connections from the electrostatic chuck  150  and the cooling base  131 . The facility plate  180  is also configured to accommodate the plurality of electrical connections from the electrostatic chuck  150  and the heater assembly  169 . The myriad of connections may run externally or internally of the substrate support assembly  104 , while the facility plate  180  provides an interface for the connections to a respective terminus. 
     A substrate electrode  109  is embedded within the substrate support portion  154  of the electrostatic chuck  150  for applying a substrate voltage to a substrate  105  disposed on an upper surface  160  of the substrate support assembly  104 . The edge ring portion  156  has an edge ring electrode  111  embedded therein for applying an edge ring voltage to the edge ring  106 . An edge ring voltage control circuit  155  is coupled to the edge ring electrode  111 . A substrate voltage control circuit  158  is coupled to the substrate electrode  109 . In one embodiment, a first shaped DC pulse voltage source  159  is coupled to one or both of the edge ring voltage control circuit  155  and the substrate voltage control circuit  158 . In another embodiment, the first shaped DC pulse voltage source  159  is coupled to the edge ring voltage control circuit  155  and a second shaped DC pulse voltage source  161  is coupled to the substrate voltage control circuit  158 . The edge ring voltage control circuit  155  and the substrate voltage control circuit  158  are independently tunable to generate a difference in voltage between the edge ring voltage and the substrate voltage. The substrate voltage control circuit  158  and the edge ring voltage control circuit  155  each include variable and/or fixed capacitors and/or inductors to provide the independent tunability of the edge ring voltage and the substrate voltage. The substrate electrode  109  is further coupled to a chucking power source  115  to facilitate chucking of the substrate  105  to the upper surface  160  with the electrostatic chuck  150  during processing. 
     The inductively coupled plasma apparatus  107  is disposed above the lid  102  and is configured to inductively couple RF power to gasses within the process chamber  100  to generate a plasma  116 . The inductively coupled plasma apparatus  107  includes first and second coils  118 ,  120 , disposed above the lid  102 . The relative position, ratio of diameters of each coil  118 ,  120 , and/or the number of turns in each coil  118 ,  120  can each be adjusted as desired to control the profile or density of the plasma  116  being formed. Each of the first and second coils  118 ,  120  is coupled to an RF power supply  121  through a matching network  122  via an RF feed structure  123 . The RF power supply  121  may illustratively be capable of producing up to about 4000 W (but not limited to about 4000 W) at a tunable frequency in a range from 50 kHz to 13.56 MHz, although other frequencies and powers may be utilized as desired for particular applications. 
     In some examples, a power divider  126 , such as a dividing capacitor, may be provided between the RF feed structure  123  and the RF power supply  121  to control the relative quantity of RF power provided to the respective first and second coils  118 ,  120 . 
     In other embodiments, a capacitively coupled plasma apparatus (not shown) can be used above the lid  102 . 
     A heater element  128  may be disposed on the lid  102  to facilitate heating the interior of the process chamber  100 . The heater element  128  may be disposed between the lid  102  and the first and second coils  118 ,  120 . In some examples, the heater element  128  may include a resistive heating element and may be coupled to a power supply  130 , such as an AC power supply, configured to provide sufficient energy to control the temperature of the heater element  128  within a desired range. 
     During operation, the substrate  105 , such as a semiconductor substrate or other substrate suitable for plasma processing, is placed on the substrate support assembly  104 . Substrate lift pins  146  are movably disposed in the substrate support assembly  104  to assist in transfer of the substrate  105  onto the substrate support assembly  104 . After positioning of the substrate  105 , process gases are supplied from a gas panel  132  through entry ports  134  into the internal volume  124  of the chamber body  101 . The process gases are ignited into a plasma  116  in the process chamber  100  by applying power from the RF power supply  121  to the first and second coils  118 ,  120 . The pressure within the internal volume  124  of the process chamber  100  may be controlled using a valve  136  and a vacuum pump  138 . 
     The process chamber  100  includes the controller  108  to control the operation of the process chamber  100  during processing. The controller  108  comprises a central processing unit (CPU)  140 , a memory  142 , and support circuits  144  for the CPU  140  and facilitates control of the components of the process chamber  100 . The controller  108  may be one of any form of general-purpose computer processor that can be used in an industrial setting for controlling various chambers and sub-processors. The memory  142  stores software (source or object code) that may be executed or invoked to control the operation of the process chamber  100  in the manner described herein. The controller  108  is configured to control the first shaped DC pulse voltage source  159 , the second shaped DC pulse voltage source  161 , the edge ring voltage control circuit  155 , and the substrate voltage control circuit  158 . 
       FIGS. 2A-2C  are schematic views of a plasma sheath  176  underlying a plasma  116  generated within the process chamber  100  relative to the edge of a substrate  105 , according to examples of the disclosure.  FIG. 2A  illustrates a baseline plasma sheath  176  relative to an edge ring  106  and a substrate  105  overlying the electrostatic chuck  150 . When the same voltage is applied to the substrate electrode  109  and edge ring electrode  111 , the upper surface of the edge ring  106  and the substrate  105  are generally coplanar and the boundary of the plasma sheath  176  is generally linear and parallel to the substrate  105  as the sheath  176  crosses on an edge portion  166  of the substrate  105 . The plasma sheath  176  is substantially parallel with and equally spaced from the upper surfaces of the edge ring  106  and the substrate  105 . The profile of the plasma sheath  176  illustrated in  FIG. 2A  results in uniform center to edge ion density and ion energy towards to the substrate  105 , given uniform plasma generated above the substrate  105  and the edge ring  106 . In an example, there is no difference in voltage between the substrate  105  and the edge ring  106 . This may be referred to as a baseline voltage. 
     After processing a predetermined number of substrates, the height of the edge ring  106  may be lower, not coplanar with the substrate top any more, resulting in undesired edge effects forming on the edge portion  166  of the substrate  105 . In other applications, the nonuniformity of the plasma density, gas concentration, etc. can cause nonuniformity of the processing profile near the edge portion  166  of the substrate  105 . In still other applications, previous processes may result in a non-uniform center-to-edge feature profile and it is desired to compensate such uniformity with an edge tuning knob. To combat edge effects, a positive voltage difference or a negative voltage difference is formed between the edge ring  106  and the substrate  105 . 
     As illustrated in  FIG. 2B , where a higher voltage is applied to the edge ring electrode  111  compared to that of the substrate electrode  109 , the boundary plasma sheath  176  is no longer flat at the interface of the substrate  105  and the edge ring  106  and has different spacings from the surface of the edge ring  106  versus the substrate  105 . The profile of the plasma sheath  176  is wider at the edge portion  166  of the substrate  105  relative to the center  168  of the substrate  105 . This is indicative of a defocused ion concentration at the edge portion  166  of the substrate  105  relative to the center of the substrate  105 . Accordingly, this reduces etch rate at the edge portion  166  of the substrate  105  relative to the center  168  of the substrate  105 , and also changes the angle of incidence of ions striking the edge portion  166  of the substrate  105 . 
       FIG. 2C  shows how the sheath boundary/height may be controllably changed at the edge of the substrate  105  when a lower voltage is applied to the edge ring electrode  111  compared to the substrate electrode  109 . The profile of the plasma sheath  176  is narrower at the edge portion  166  of the substrate  105  relative to the center  168  of the substrate  105 . Accordingly, ions are focused to the edge portion  166  of the substrate  105 . Accordingly, this increases the etch rate at the edge portion  166  of the substrate  105  and also changes the angle of incidence of ions striking the edge portion  166  of the substrate  105 . 
       FIGS. 3A and 3B  illustrate enlarged schematic views of the substrate support  152  shown in  FIG. 1 . The substrate support  152  has a body  174 . The body  174  includes a substrate support portion  154  and an edge ring portion  156 . The substrate support portion  154  includes a first isolation layer  182 , an optional second isolation layer  184 , and a first cathode  188 . The first isolation layer  182  of the substrate support portion  154  may be made of a ceramic. The first isolation layer  182  of the substrate support portion  154  may have the substrate electrode  109  embedded therein for applying a substrate voltage a substrate  105 . The optional second isolation layer  184  underlays the first isolation layer  182  and be made of a ceramic to improve the thermal and electrical isolation of the substrate electrode  109  from other conductive components in the substrate support  152 . The first cathode  188  may underlay one or both of the first isolation layer  182  and the second isolation layer  184  of the substrate support portion  154 . 
     The edge ring portion  156  is disposed adjacent to the substrate support portion  154 . The edge ring portion  156  may support the edge ring  106 . The edge ring portion  156  may include a first isolation layer  183 , an optional second isolation layer  185 , and a second cathode  191 . The first isolation layer has an edge ring electrode  111  embedded therein for applying an edge ring voltage to the edge ring  106 . The first isolation layer  183  may be made of a ceramic. The optional second isolation layer  185  underlays the first isolation layer  183  made of a ceramic to improve the thermal and electrical isolation of the edge ring electrode  111  from other conductive components in the substrate support  152 . The second cathode  191  may underlay one or both of the first isolation layer  183  and the second isolation layer  185  of the edge ring portion  156 . A low-k dielectric cylindrical layer  195  may laterally separate the edge ring portion  156  from the substrate support portion  154  completely or partially. In the embodiments of partial separation of the edge ring portion  156  from the substrate support portion  154 , the first cathode  188  and the second cathode  191  may be one piece, and/or the second isolation layer  184  under the substrate  105  and that under the edge ring  106  may be one piece. 
     A first contact of an edge ring voltage control circuit  155  is electrically coupled to the edge ring electrode  111 . A first contact of a substrate voltage control circuit  158  is electrically coupled to the substrate electrode  109 . The edge ring voltage control circuit  155  may be either incorporated into the substrate support assembly  104 , be external to the substrate support assembly  104  but internal to the process chamber  100  or may be entirely external to the process chamber  100 . 
     In one embodiment, a second contact of both the edge ring voltage control circuit  155  and the substrate voltage control circuit  158  may be coupled together to a first shaped DC pulse voltage source  159 . In another embodiment, the second contact of the edge ring voltage control circuit  155  is not tied to the second contact of the substrate voltage control circuit  158 , but the second contact of the edge ring voltage control circuit  155  is individually coupled to the first shaped DC pulse voltage source  159  while the second contact of the substrate voltage control circuit  158  is coupled to the second shaped DC pulse voltage source  161 . In either configuration of one or two shaped DC pulse voltage sources, the edge ring voltage control circuit  155  and the substrate voltage control circuit  158  are independently tunable to generate a difference in voltage between the edge ring voltage and the substrate voltage. 
     In one embodiment, the edge ring voltage control circuit  155  and the substrate voltage control circuit  158  are identical circuits. In another embodiment, the edge ring voltage control circuit  155  and the substrate voltage control circuit  158  differ from each other. In an embodiment, at least one of the edge ring voltage control circuit  155  and the substrate voltage control circuit  158  comprises at least one variable passive component to provide tunability of the voltage applied to either the edge ring electrode  111  and/or the substrate electrode  109 . 
       FIG. 4  is schematic circuit diagram illustrating one embodiment of the edge ring voltage control circuit/substrate voltage control circuit  400  for driving the electrodes  109 ,  111  of the substrate support assembly  104 . The first or second shaped DC pulse voltage source  159 ,  161  is coupled between ground and a forward biasing diode  194 . The forward-biased diode  194  is connected to a current returning path  163  comprising a resistor  196  coupled in series with an inductor  197  to ground. A capacitance  199  may exist between the stray capacitance  198  and the plasma sheath  176 . A variable capacitor  202  is coupled to the forward biasing diode  194  and to either the edge ring electrode  111  or the substrate electrode  109 . The variable capacitor  202  is also coupled to stray capacitance  198 . The plasma sheath  176  may be modeled (plasma model  176 ) as a circuit comprising a capacitor  204  coupled in parallel with a diode  206  and a current source  208  coupled to ground and the variable capacitor  202 . 
     Voltage can be measured at the edge ring electrode  111  and the substrate electrode  109 . Using the measured voltage, the controller  108  determines a voltage ratio of edge ring electrode  111  to the substrate electrode  109 . Based on the measured results, the variable capacitor  202  in either or both of the edge ring voltage control circuit  155  or the substrate voltage control circuit  158  can be adjusted to manipulate voltage applied to the edge ring electrode  111 , which affects the voltage developed at the edge ring  106  and/or the substrate electrode  109  at the substrate  105 . Consequently, the height of the plasma sheath  176  above the edge ring  106  and the substrate  105  can be shaped. The edge ring  106  or substrate voltage waveform amplitude can vary between almost zero to full shaped DC pulse input voltage by varying the variable capacitor  202 . 
       FIG. 5  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit  500  that can be used to drive the electrodes  109 ,  111  of the substrate support assembly  104 . The first or second shaped DC pulse voltage source  159 ,  161  is coupled between ground and the forward biasing diode  194 , which is coupled to the to a current returning path  163  comprising of a resistor  196  coupled in series with an inductor  197  to ground. In an embodiment, a variable inductor  210  is coupled to the forward biasing diode  194  and to either the edge ring electrode  111  or the substrate electrode  109 . The variable inductor  210  is also coupled to stray capacitance  198 . 
     As stated above, voltage can be measured at the edge ring electrode  111  and the substrate electrode  109 . Using the measured voltage, the controller  108  determines a voltage ratio of edge ring electrode  111  to the substrate electrode  109 . Based on the measured results, the variable inductor  210  in either or both of the edge ring voltage control circuit  155  or the substrate voltage control circuit  158  can be adjusted to manipulate voltage applied to the edge ring electrode  111 , which affects the voltage developed at the edge ring  106  and/or the substrate electrode  109  at the substrate  105 . Consequently, the height of the plasma sheath  176  above the edge ring  106  and the substrate  105  can be changed. The edge ring or substrate voltage waveform amplitude can vary between almost zero to full shaped DC pulse input voltage by varying the variable inductor  210 . 
       FIG. 6  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit  600  for driving the electrodes  109 ,  111  of the substrate support assembly  104 . The first or second shaped DC pulse voltage source  159 ,  161  is coupled between ground and the forward biasing diode  194 , which is coupled to the to a current returning path  163  comprising a resistor  196  coupled in series with an inductor  197  to ground. One terminal of a variable inductor  212  is coupled in series with a fixed capacitor  214 , which is coupled to the forward biasing diode  194 . The other terminal of the variable inductor  212  is coupled to either the edge ring electrode  111  or the substrate electrode  109 . The variable inductor  212  is also coupled to stray capacitance  198 . 
     As stated above, voltage can be measured at the edge ring electrode  111  and the substrate electrode  109 . Using the measured voltage, the controller  108  determines a voltage ratio of edge ring electrode  111  to the substrate electrode  109 . Based on the measured results, the variable inductor  212  in either or both of the edge ring voltage control circuit  155  or the substrate voltage control circuit  158  can be adjusted to manipulate voltage applied to the edge ring electrode  111 , which affects the voltage developed at the edge ring  106  and/or the substrate electrode  109  at the substrate  105 . Consequently, the height of the plasma sheath  176  above the edge ring  106  and the substrate  105  can be shaped. The edge ring or substrate voltage waveform amplitude can vary between almost zero to full shaped DC pulse input voltage by varying the variable inductor  212 . 
       FIG. 7  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit  700  for driving the electrodes  109 ,  111  of the substrate support assembly  104 . The first or second shaped DC pulse voltage source  159 ,  161  is coupled between ground and the forward biasing diode  194 , which is coupled to the to a current returning path  163  comprising a resistor  196  coupled in series with an inductor  197  to ground. A variable capacitor  216  is coupled in series with a variable inductor  218 . The variable capacitor  216  is also coupled to the forward biasing diode  194 . The variable inductor  218  is also coupled in series with to either the edge ring electrode  111  or the substrate electrode  109 . The variable inductor  218  is also coupled to stray capacitance  198 . 
     As stated above, voltage can be measured at the edge ring electrode  111  and the substrate electrode  109 . Using the measured voltage, the controller  108  determines a voltage ratio of edge ring electrode  111  to the substrate electrode  109 . Based on the measured results, the variable capacitor  216  and/or the variable inductor  218  in either or both of the edge ring voltage control circuit  155  or the substrate voltage control circuit  158  can be adjusted to manipulate voltage applied to the edge ring electrode  111 , which affects the voltage developed at the edge ring  106  and/or the substrate electrode  109  at the substrate  105 . Consequently, the height of the plasma sheath  176  above the edge ring  106  and the substrate  105  can be shaped. The edge ring or substrate voltage waveform amplitude can vary between almost zero to full shaped DC pulse input voltage by varying the variable capacitor  216  and/or the variable inductor  218 . 
       FIG. 8  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit  800  for driving the electrodes  109 ,  111  of the substrate support assembly  104 . The first or second shaped DC pulse voltage source  159 ,  161  is coupled between ground and the forward biasing diode  194 , which is coupled to the to a current returning path  163  comprising of a resistor  196  coupled in series with an inductor  197  to ground. A first terminal of a variable capacitor  220  is coupled to the forward biasing diode  194 . The first terminal of the variable capacitor  220  is further coupled to a fixed resistor  224 , which is coupled to the current returning path  163  and to one terminal of a fixed capacitor  222  the second terminal of the fixed capacitor  222  is coupled to a second terminal of the variable capacitor  220 , and to either the edge ring electrode  111  or the substrate electrode  109 . The variable capacitor  220  is also coupled to stray capacitance  198 . 
     As stated above, voltage can be measured at the edge ring electrode  111  and the substrate electrode  109 . Using the measured voltage, the controller  108  determines a voltage ratio of edge ring electrode  111  to the substrate electrode  109 . Based on the measured results, the variable capacitor  220  in either or both of the edge ring voltage control circuit  155  or the substrate voltage control circuit  158  can be adjusted to manipulate voltage applied to the edge ring electrode  111 , which affects the voltage developed at the edge ring  106  and/or the substrate electrode  109  at the substrate  105 . Consequently, the height of the plasma sheath  176  above the edge ring  106  and the substrate  105  can be shaped. The edge ring or substrate voltage waveform amplitude can vary between almost zero to full shaped DC pulse input voltage by varying the variable capacitor  220 . 
       FIG. 9  is schematic circuit diagram illustrating another embodiment of the edge ring voltage control circuit/substrate voltage control circuit  900  for driving the electrodes  109 ,  111  of the substrate support assembly  104 . The first or second shaped DC pulse voltage source  159 ,  161  is coupled between ground and the forward biasing diode  194 . A first terminal of a variable capacitor  225  is coupled to the forward biasing diode  194 . The first terminal of the variable capacitor  225  is further coupled to a first fixed resistor  226 , which is coupled to the current returning path  163 and to one terminal of a second fixed resistor  228 . The second fixed resistor  228  is coupled in series with a first terminal of a fixed capacitor  230 . The second terminal of the fixed capacitor  230  is coupled to a second terminal of the variable capacitor  225 , and to either the edge ring electrode  111  or the substrate electrode  109 . The variable capacitor  225  is also coupled to stray capacitance  198 . 
     As stated above, voltage can be measured at the edge ring electrode  111  and the substrate electrode  109 . Using the measured voltage, the controller  108  determines a voltage ratio of edge ring electrode  111  to the substrate electrode  109 . Based on the measured results, the variable capacitor  225  in either or both of the edge ring voltage control circuit  155  or the substrate voltage control circuit  158  can be adjusted to manipulate voltage applied to the edge ring electrode  111 , which affects the voltage developed at the edge ring  106  and/or the substrate electrode  109  at the substrate  105 . Consequently, the height of the plasma sheath  176  above the edge ring  106  and the substrate  105  can be shaped. The edge ring or substrate voltage waveform amplitude can vary between almost zero to full shaped DC pulse input voltage by varying the variable capacitor  225 . 
       FIG. 10  is schematic circuit diagram illustrating another embodiment of the edge ring control circuit/substrate voltage control circuit  1000  for driving the electrodes  109 ,  111  of the substrate support assembly  104 . The first or second shaped DC pulse voltage source  159 ,  161  is coupled between ground and the forward biasing diode  194 . A first terminal of a variable capacitor  231  is coupled to the forward biasing diode  194 . The first terminal of the variable capacitor  231  is further coupled to a first fixed resistor  232  in series with one terminal of a fixed inductor  234 . The fixed inductor  234  is coupled to the current returning path  163 . The second terminal of the fixed inductor  234  is further coupled to a first terminal of a second fixed resistor  236 . The second terminal of the second fixed resistor  236  is coupled to a first terminal of a fixed capacitor  238 . The second terminal of the fixed capacitor  238  is coupled to the second terminal of the variable capacitor  231  and to either the edge ring electrode  111  or the substrate electrode  109 . The variable capacitor  231  is also coupled to stray capacitance  198 . 
     As stated above, voltage can be measured at the edge ring electrode  111  and the substrate electrode  109 . Using the measured voltage, the controller  108  determines a voltage ratio of edge ring electrode  111  to the substrate electrode  109 . Based on the measured results, the variable capacitor  231  in either or both of the edge ring voltage control circuit  155  or the substrate voltage control circuit  158  can be adjusted to manipulate voltage applied to the edge ring electrode  111 , which affects the voltage developed at the edge ring  106  and/or the substrate electrode  109  at the substrate  105 . Consequently, the height of the plasma sheath  176  above the edge ring  106  and the substrate  105  can be shaped. The edge ring or substrate voltage waveform amplitude can vary between almost zero to full shaped DC pulse input voltage by varying the variable capacitor  231 . 
       FIG. 11  is a flow diagram illustrating an operation process  1100  for the support circuits  155 ,  158  described above. The operation process  1100  can be implemented using the circuit configurations of  FIGS. 4-10  provided in this disclosure. The operation process  1100  also provides a method of operating the process chamber  100 . 
     At operation  1105 , the controller  108  applies a substrate voltage to the substrate electrode  109  by the substrate voltage control circuit  158 . At operation  1110 , the controller  108  applies an edge ring voltage to the edge ring electrode  111  by the edge ring voltage control circuit  155 . At operation  1115 , the controller  108  measures voltage at the edge ring electrode  111  and the substrate electrode  109 . Based on the measured results, the controller  108  determines an amplitude ratio between the voltages of the edge ring  106  and the substrate  105 . At operation  1120 , the controller  108  updates a prediction for a variable capacitor or variable inductor value in the edge ring voltage control circuit  155  and/or the substrate voltage control circuit  158  and values for the output voltage(s) of the shaped DC pulse voltage source(s)  159 ,  161 . At operation  1125 , the controller  108  tunes the edge ring voltage control circuit  155 , the substrate voltage control circuit  158 , and the output voltage(s) of the shaped DC pulse voltage source(s)  159 ,  161 , in order to achieve the target edge ring voltage and the substrate voltage with specified difference in amplitude (ratio) through feedback control loop  1115 ,  1120 , and  1125 . 
       FIGS. 12A and 12B  depict example simulation results of modulated edge ring or wafer voltage waveform created by varying the variable capacitors and/or inductors of  FIGS. 4-10  given a shaped DC pulse voltage input. For a fixed input voltage amplitude, the variable capacitors and inductors can tune the amplitude of the output voltage of the tuning circuit between almost zero to full input voltage while maintaining the shape of the output voltage to keep a constant voltage difference between the substrate voltage and the edge ring voltage throughout the pulse on-time. 
     Benefits of the disclosure include the ability to adjust plasma sheaths at the substrate edge in lieu of replacing chamber components, thereby improving device yield while mitigating downtime and reducing expenditures on consumables. Additionally, aspects described herein allow for the plasma sheath to be adjusted at the substrate edge without affecting the plasma parameters at substrate center, thereby providing a tuning knob for extreme edge process profile control and feature tilting correction.