Abstract:
A method for processing a workpiece in a plasma reactor having a set of n coils includes constructing, for each one of the n coils, a set of plasma distributions for discrete values of coil current in a predetermined current range. The distributions are grouped, each group having one distribution for each of the n coils, and being a unique set of n distributions. A combined plasma distribution is computed from each group of distributions. The variance of each combined distribution is computed. The method further includes finding an optimum one of the combined distributions having an at least nearly minimum variance, and identifying the n coil currents associated with the optimum distribution. During plasma processing of the workpiece, currents through the coils are maintained at levels corresponding to the n coil currents associated with the one combined distribution.

Description:
BACKGROUND 
       [0001]    Plasma processing of workpieces such as semiconductor wafers to form nanometer-sized thin film features requires precise control over plasma uniformity. Improving device performance requires decreasing feature sizes, which increases requirements for plasma ion density distribution uniformity across the surface of a workpiece or wafer. Using two axially displaced solenoidal coils over a plasma reactor chamber, plasma distribution can be changed by changing the D.C. currents applied to the coils. 
         [0002]    Plasma ion density distribution non-uniformity has been reduced to as low as 5% (the measured variance or standard deviation) by choosing the D.C. currents in the overhead solenoidal coils. The problem is that nonuniformity must be reduced even further, and it has not seemed possible to reduce the uniformity below 5%. 
       SUMMARY 
       [0003]    A method is provided for processing a workpiece in a chamber of a plasma reactor having a set of n solenoidal electromagnet coils. The method includes constructing, for each one of the n coils, a set of plasma distributions for discrete values of coil current in a predetermined current range. The method further includes defining different groups of the distributions, each group having one distribution for each of the n coils, each group being a unique set of n distributions. A combined plasma distribution is computed from each group of distributions. The variance of each combined distribution is computed. The method further includes finding an optimum one of the combined distributions having an at least nearly minimum variance, and identifying the n coil currents associated with the optimum distribution. During plasma processing of the workpiece, currents through the coils are maintained at levels corresponding to the n coil currents associated with the one combined distribution. 
         [0004]    In one embodiment, constructing the set of plasma distributions for discrete values of coil current is carried out by measuring, for each of the n coils, a plasma distribution at each one of a small set of widely spaced values of coil current spanning the range, determining the change in plasma distribution for a predetermined incremental change ΔI in coil current, and then synthesizing plasma distributions at finely spaced values of coil current lying between the widely spaced values by interpolating between the measured distributions at intervals of ΔI. In one implementation, the plural predetermined plasma density distributions are two-dimensional. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0005]    So that the manner in which the exemplary embodiments of the present invention are attained and can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof which are illustrated in the appended drawings. It is to be appreciated that certain well known processes are not discussed herein in order to not obscure the invention. 
           [0006]      FIG. 1A  is a simplified block diagram of a plasma reactor system in accordance with one embodiment. 
           [0007]      FIG. 1B  depicts a simplified implementation of a process controller of the reactor of  FIG. 1A . 
           [0008]      FIG. 2  is a graph depicting the behavior of plasma distribution non-uniformity as a function of overhead coil current. 
           [0009]      FIG. 3  is a graph depicting the radial components of center-high and center-low plasma distributions and a composite distribution obtained by their superposition. 
           [0010]      FIG. 4  is a graph depicting the azimuthal components of different plasma distributions and a composite distribution obtained by their superposition. 
           [0011]      FIG. 5A  is a graph representing a two-dimensional plasma distribution obtained by a first set of D.C. currents applied to the overhead coils. 
           [0012]      FIG. 5B  is a graph representing a two-dimensional plasma distribution obtained by a second set of D.C. currents applied to the overhead coils. 
           [0013]      FIG. 5C  is a graph representing a net plasma distribution corresponding to a measured etch rate distribution obtained by switching the coil currents between the two sets of currents corresponding to the distributions of  FIGS. 5A and 5B  for a predetermined duty cycle. 
           [0014]      FIG. 5D  is a graph depicting the separate radial components of the plasma distributions of  FIGS. 5A ,  5 B and  5 C. 
           [0015]      FIG. 6  is a block flow diagram of a simplified process implemented by the process controller of the reactor of  FIG. 1A . 
           [0016]      FIG. 7  is a block flow diagram of a comprehensive process including an optimization search method which the process controller of  FIG. 1A  may be programmed to execute. 
           [0017]      FIGS. 8A and 8B  constitute a block diagram depicting a method in accordance with another embodiment. 
           [0018]      FIGS. 9A ,  9 B,  9 C and  9 D are graphs depicting interpolations employed in carrying out certain portions of the method of  FIGS. 8A and 8B . 
       
    
    
       [0019]    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. It is to be noted, however, that the appended drawings illustrate only exemplary embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. 
       DETAILED DESCRIPTION 
       [0020]    Referring to  FIG. 1A , a plasma reactor includes a chamber  100  defined by side walls  102 , a ceiling  104  and a workpiece support  106  within the chamber for supporting a workpiece or wafer  108  to face the ceiling  104 . A plasma source power applicator, which may be adapted to couple power such as RF plasma source power into the chamber is provided. The plasma source power applicator may be any suitable form, such as a coil antenna (not shown) overlying the ceiling  104 , an electrode formed by the ceiling  104  as shown in  FIG. 1A , a toroidal plasma source or other sources such as a microwave source, a Helicon source, etc. In  FIG. 1A , the ceiling  104  is formed of metal to provide an electrode as the RF plasma source power applicator, and an insulating ring  110  separates the ceiling electrode  104  from the side wall  102 . An RF source power generator  112  provides RF plasma source power through an impedance match element  114  to the ceiling electrode  104 . An RF bias power generator  116  provides RF plasma bias power through another impedance match element  118  to an electrode  120  within the workpiece support  106 . A pair of inner and outer solenoidal electromagnet coils  122 ,  124  overlie the reactor chamber  100 , the coils  122 ,  124  being of different diameters and at different axial locations, as shown in  FIG. 1A . In the embodiment of  FIG. 1A , the inner coil  122  is disposed at a higher axial location than the outer coil  124 , although an opposite arrangement may be employed. Also, the number of solenoidal coils may exceed two. Furthermore, while the solenoidal coils  122 ,  124  are depicted as being mutually coaxial and coaxial with the axis of symmetry of the reactor chamber  100 , other arrangements not involving such symmetries may be employed. 
         [0021]      FIG. 2  depicts the behavior of the non-uniformity or variance, a, in plasma ion distribution (vertical axis) as a function of D.C. currents I inner , I outer  (x and y horizontal axes) in the two coils  122 ,  124 . At a low current level in each coil, the plasma ion distribution tends to be highly non-uniform, the non-uniformity corresponding to a center high distribution, such as the center-high radial distribution  300  in the graph of  FIG. 3 . At a high current, the plasma ion distribution tends to be high non-uniform, the non-uniformity corresponding to a center-low distribution, such as the center-low distribution in  305  in the graph of  FIG. 3 . At some intermediate current in each coil, the non-uniformity is minimum. The location of the trough or ideal operating point of minimum non-uniformity in  FIG. 2  is typically difficult or impractical to locate. Therefore, in one embodiment, the ideal behavior at the minimum uniformity or trough in the graph of  FIG. 2  is obtained by switching the coil currents between two sets of values corresponding to two distributions A 1  and A 2  fairly near but on opposite sides of the trough. The net effect over time corresponds to a superposition of the center-high and center-low distributions  300 ,  305  of  FIG. 3 , resulting in an intermediate distribution  310  that is neither center-high nor center-low and therefore more uniform. 
         [0022]    The switching of the coil currents I inner , I outer  to switch the plasma between the distributions A 1  and A 2  is performed by a programmed process controller  130  of the reactor of  FIG. 1A . In one embodiment, the process controller  130  includes a microprocessor programmed to perform the methods described below in this specification. A simplified representation of the controller  130  is depicted in  FIG. 1B , in which the controller  130  governs current flow from two sources  132 ,  134  of respective current pairs that produce the plasma ion distributions A 1  and A 2 . The distributions A 1  and A 2  are depicted in  FIG. 3  as radial distributions (functions of radius r). The controller  130  further has a switching element  136  that switches the respective coils  122 ,  124  between the corresponding output pairs of the two sources. The switching element  136  may be programmable to spend a duty cycle, a 1 , connected to the A 1  current source  132  and a duty cycle, a 2 , connected to the A 2  current source  134 , where 
         [0000]        a   1   +a   2 =1 
         [0000]      and 
         [0000]        a   2 =|1− a   1 |. 
         [0023]    The controller  130  generates a time-weighted superposition of the two plasma distributions A 1  and A 2  (the distributions  300 ,  305  of  FIG. 3 ) to produce the intermediate distribution  310 , which may be defined as the time-weighted superposition or combination 
         [0000]    
       
      
       A 
       comb 
       =a 
       1  
       A 
       1 
       +a 
       2  
       A 
       2  
      
     
         [0024]    The time-weights or coefficients a 1  and a 2  can be chosen to minimize the non-uniformity or variance in A comb . 
         [0025]    The distributions A 1  and A 2  may be two-dimensional, so that what is depicted in  FIG. 3  are their radial components. For the two-dimensional case, the azimuthal components of the distributions A 1  and A 2  are depicted in  FIG. 4  as functions of angle θ. 
         [0026]    More than two solenoidal coils may be employed. More than two different plasma distributions may be included in the time-weighted superposition or combination A comb . 
         [0027]      FIGS. 5A-5D  depict a working example. In  FIG. 5A , the D.C. coil currents I inner , I outer  are set to produce a center-low two-dimensional plasma ion density distribution A 1  depicted in  FIG. 5A . Specifically, I inner =−8 amps and I outer =+10 amps. In  FIG. 5B , the D.C. coil currents I inner , I outer  are set to produce a center-high two-dimensional plasma ion density distribution A 2  depicted in  FIG. 5B . Specifically, I inner =0 amps and I outer =0 amps. The distribution A 1  had a deviation between maximum and minimum density values of 7.7% and a variance σ=4.7%. The distribution A 2  had a deviation between maximum and minimum density values of 5.9% and a variance σ=2.5%. The time duration or weighting coefficient a 1  was 38.8% while the time duration or weighting coefficient a 2  was 61.2%. The resulting effective combined distribution A comb  depicted in  FIG. 5C  had a maximum-to-minimum deviation of only 3.9% and a very low variance σ=1.8%.  FIG. 5D  compares the radial components of the two-dimensional distributions A 1  (solid line), A 2  (dashed line) and A comb  (thick line). The plasma distributions A 1 , A 2 , and A comb  were obtained by measuring etch rate distributions across the surfaces of test wafers. 
         [0028]    A method for carrying out an embodiment is depicted in  FIG. 6 . The programmable process controller  130  of  FIG. 1A  may be programmed to carry out the method of  FIG. 6 . In this case, the controller  130  may include machine-readable media storing instructions for carrying out the steps of  FIG. 6 . In the method of  FIG. 6 , the reactor is provided with plural solenoidal coils capable of generating different plasma ion density distributions by changing the D.C. currents through the coils to different values (block  600  of  FIG. 6 ). Two different plasmas distributions (A 1  and A 2 ) are chosen, tending to have different shapes that may compensate for non-uniformities inherent in each other (block  605 ). Unknown time weighting coefficients a 1 , a 1  are defined and a combined time weighted plasma distribution A comb =a 1  A 1 +a 2  A 2  is defined (block  610 ). A search is made to find the set of time weighting coefficients a 1 , a 2  that minimizes plasma distribution variance or maximizes uniformity (block  615 ). How this search process is performed is discussed below in this specification. During plasma processing, the processor  130  changes the coil currents between the coil current pairs that generate the different distributions or states A 1  and A 2  so that each state lasts for a time period corresponding to the respective coefficient a 1 , a 2  (block  620 ). 
         [0029]      FIG. 7  depicts a method employing any number (two or more) of different plasma distributions that are two dimensional. The programmable process controller  130  of  FIG. 1A  may be programmed to carry out the method of  FIG. 7 . In this case, the controller  130  may include machine-readable media storing instructions for carrying out the steps of  FIG. 7 . The method of  FIG. 7  includes a method for optimizing the time weighting coefficients a 1  and a 2 . First, two (or more) different two-dimensional (2-D) plasma distributions are chosen (block  700  of  FIG. 7 ). Each of these distributions may be designated as A j (r,θ) in cylindrical coordinates relative to the surface of the workpiece or wafer. The index or subscript “j” identifies a particular one of the chosen distributions. Preferably, the different distributions have mutually complementary behaviors. Each distribution A j (r,θ) is produced by a different pair of known coil currents I inner   j , I outer   j  which are stored in a memory of the controller  130 . Unknown time weighting coefficients a j  are defined and a combined time weighted plasma distribution A comb =a 1  A 1 +a 2  A 2 + . . . is defined (block  710 ). An average plasma density value A ave  is defined as a function of all the chosen A j  (block  715 ), which in one embodiment may be in accordance with the following equation: 
         [0000]    
       
         
           
             
               
                 A 
                 ave 
               
               = 
               
                 
                   ∑ 
                   
                     j 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                     
                 
                  
                 
                   
                     ∫ 
                     0 
                     R 
                   
                    
                   
                     
                       ∫ 
                       0 
                       
                         2 
                          
                         π 
                       
                     
                      
                     
                       
                         a 
                         j 
                       
                       · 
                       
                         A 
                         j 
                       
                       · 
                       
                          
                         r 
                       
                       · 
                       
                          
                         θ 
                       
                     
                   
                 
               
             
              
             
                 
             
           
         
       
     
         [0000]    where a j  is the time duration of plasma distribution A j  and R is the radius of the wafer to be plasma processed. 
         [0030]    A variance function is defined as the standard deviation of A comb  from A ave  which is a function of the chosen distributions A j &#39;s, their unknown time weighting coefficients a j &#39;s and A ave  (block  720 ). This variance function in one embodiment may be defined in accordance with the following equation: 
         [0000]    
       
         
           
             σ 
             = 
             
               
                 [ 
                 
                   
                     1 
                     
                       A 
                       ave 
                     
                   
                    
                   
                     
                       ∫ 
                       0 
                       R 
                     
                      
                     
                       
                         ∫ 
                         0 
                         
                           2 
                            
                           π 
                         
                       
                        
                       
                         
                           1 
                           R 
                         
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     1 
                                   
                                   n 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     a 
                                     j 
                                   
                                    
                                   
                                     A 
                                     j 
                                   
                                 
                               
                               - 
                               
                                 A 
                                 ave 
                               
                             
                             ) 
                           
                           2 
                         
                          
                         
                           
                              
                             r 
                           
                           · 
                           
                               
                           
                            
                           
                              
                             θ 
                           
                         
                       
                     
                   
                 
                 ] 
               
               
                 1 
                 / 
                 2 
               
             
           
         
       
     
         [0031]    This formula is used by the controller  130  to search for an optimum set of time weighting coefficients a j  that minimizes the variance function a (block  725  of  FIG. 7 ). Such as search may be constructed by the skilled worker in view of the foregoing teachings using standard mathematical programming practices. A number of mathematical programs are readily available that the skilled worker can employ to find the optimum values of the time weighting coefficients, the a j &#39;s. 
         [0032]    After the optimum time weighting coefficients have been found, the solenoidal coil currents are switched between the sets of currents corresponding to the chosen distributions A j  such that the time spent in a particular plasma distribution A j  is proportional to its time weighting coefficient a j  (block  730 ). This switching operation may be performed in any one of the following modes. 
         [0033]    In a first mode, the coil currents are switched between sets of currents defining successive chosen distributions A j  (block  732 ). That is, the currents are switched between states in mutually exclusive duty cycles. 
         [0034]    In a second mode, one of the coil currents is maintained at a constant level another coil current is switched between different values (block  734 ). 
         [0035]    In a third mode, the plasma is switched to between two chosen distributions by reversing the polarities of the coil currents (block  736 ). 
         [0036]      FIGS. 8A and 8B  constitute a flow diagram illustrating a method in which the coil currents I inner , I outer  are held constant rather than being switched, and a search is made for the optimum pair of constant coil currents I inner ′, I outer ,′ that produces an ideal plasma distribution A′ having the least variance or non-uniformity. The programmable process controller  130  of  FIG. 1A  may be programmed to carry out the method of  FIGS. 8A and 8B . In this case, the controller  130  may include machine-readable media storing instructions for carrying out the steps of  FIGS. 8A and 8B . 
         [0037]    Referring to  FIGS. 8A and 8B , in block  800 , a set of plasma distributions A 1  is constructed for all discrete values of I inner  in a predetermined range. (The subscript “1” refers to the inner coil.) This is carried out as follows. First, in block  802 , a reduced number of plasma distributions A 1  are measured at a small set of widely spaced values of I inner  spanning the chosen range. One example of this step is depicted in  FIG. 9A , in which the chosen range is −24 to +24 amps, and the values of I inner  occur in steps of ΔI inner =4 amps, so that only twelve measurements are taken. Each of the twelve measurements is carried out by etching a test wafer while holding the current on the inner coil at one of the twelve values of I inner  and then deducing the two-dimensional plasma distribution Al from the etch depth distribution on the test wafer, and storing the corresponding two-dimensional distribution A 1 . The result is a set of twelve measured inner coil plasma distributions A 1 . Then, in block  804 , a measurement is made to determine the change ΔA 1 in plasma distribution A 1  for a predetermined incremental change ΔI inner =4 amps in the coil current I inner . This determination may be made while I inner =0. In one embodiment, it is assumed that the distribution change ΔA 1  is the same regardless of location within the range −24 amps to +24 amps. The distribution change ΔA 1  may be found by subtracting any two measured plasma distributions A 1  generated by inner coil currents that differ by 4 amps. For example, ΔA 1 =A 8 amps −A 16 amps . In the example depicted in  FIG. 9A , ΔA 1 =A 0 amps −A 2 amps . This measurement requires the etching of two test wafers at constant inner coil currents of 0 amps and 2 amps respectively. 
         [0038]    The twelve measured distributions at the twelve inner coil current values of  FIG. 9A  and the plasma distribution change ΔA 1  are used to construct all the remaining A 1 &#39;s at the eighteen remaining current values depicted in  FIG. 9B  (block  806  of  FIGS. 8A-8B ). This construction is performed by interpolating between the twelve measured A 1 &#39;s of  FIG. 9A  at intervals of ΔI inner  by adding (or subtracting) the appropriate multiple of ΔA 1  from each distribution A 1 . 
         [0039]    Next, in block  820  of  FIGS. 8A-8B , a set of plasma distributions A 2  are measured for all discrete values of I outer  in a predetermined range (e.g., −24 amps to +24 amps). (The subscript “2” refers to the outer coil current). This is carried out as follows. First, in block  822 , a reduced number of outer coil current plasma distributions A 2  are measured at a small number (e.g., twelve) of widely spaced values of I outer  spanning the chosen range. One example of this step is depicted in  FIG. 9C , in which the chosen range is −24 amps to +24 amps, and the values of I outer  occur in steps of ΔI outer =4 amps, so that only twelve measurements are taken. Each of the twelve measurements is carried out by etching a test wafer while holding the current on the inner coil at one of the six values of I outer  and then deducing the two-dimensional plasma distribution A 2  from the etch depth distribution on the test wafer, and storing the corresponding two-dimensional distribution A 2 . Then, in block  824 , a measurement is made to determine the change ΔA 2  in A 2  for a predetermined incremental change ΔI outer =4 amps in the coil current I outer . In one embodiment, it is assumed that the change ΔA 2  is the same regardless of location within the range −24 amps to +24 amps. The change ΔA 2  may be found by subtracting any two measured distributions A 2  generated by coil currents that differ by 4 amps. For example, ΔA 2 =B 8 amps −B 16 amps . In the example depicted in  FIG. 9C , ΔA 2 =B 0 amps −B 2 amps . This measurement requires the etching of two test wafers at constant outer coil currents of 0 amps and 2 amps respectively. 
         [0040]    The twelve measured distributions A 2  at the twelve outer coil current values of  FIG. 9C  and the distribution change ΔA 2  are used to construct all the remaining A 2 &#39;s at the eighteen remaining current values depicted in  FIG. 9D  (block  826  of  FIGS. 8A-8B ). This construction is performed by interpolating between the measured twelve A 2 &#39;s of  FIG. 9C  at intervals of ΔI outer  by adding (or subtracting) ΔA 2  from each distribution. 
         [0041]    In block  830  of  FIGS. 8A-8B , a set of combined plasma distributions C are constructed as sums of all possible pairings of A 1 &#39;s with A 2 &#39;s, where each C is defined as C=A 1 +A 2 . For each C, an average distribution A ave  is computed as the average plasma density of C (block  835 ). This computation may be carried out in one embodiment in accordance with the following equation: 
         [0000]    
       
         
           
             
               A 
               ave 
             
             = 
             
               
                 ∑ 
                 
                   j 
                   = 
                   1 
                 
                 n 
               
                
               
                   
               
                
               
                 
                   ∫ 
                   0 
                   R 
                 
                  
                 
                   
                     ∫ 
                     0 
                     
                       2 
                        
                       π 
                     
                   
                    
                   
                     · 
                     
                       A 
                       j 
                     
                     · 
                     
                        
                       r 
                     
                     · 
                     
                        
                       θ 
                     
                   
                 
               
             
           
         
       
     
         [0000]    where dr is an incremental radius, dθ is an incremental angle in cylindrical coordinates and R is the radius of the workpiece, and j runs from 1 (inner coil) to 2 (outer coil). 
         [0042]    In block  840 , a variance function is defined as the standard deviation of C from A ave . The variance function may be defined in one embodiment in accordance with the following equation: 
         [0000]    
       
         
           
             σ 
             = 
             
               
                 [ 
                 
                   
                     1 
                     
                       A 
                       ave 
                     
                   
                    
                   
                     
                       ∫ 
                       0 
                       R 
                     
                      
                     
                       
                         ∫ 
                         0 
                         
                           2 
                            
                           π 
                         
                       
                        
                       
                         
                           1 
                           R 
                         
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     1 
                                   
                                   n 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   A 
                                   j 
                                 
                               
                               - 
                               
                                 A 
                                 ave 
                               
                             
                             ) 
                           
                           2 
                         
                          
                         
                           
                              
                             r 
                           
                           · 
                           
                               
                           
                            
                           
                              
                             θ 
                           
                         
                       
                     
                   
                 
                 ] 
               
               
                 1 
                 / 
                 2 
               
             
           
         
       
     
         [0043]    The foregoing equations use the more general notation in which j is the index of each coil running from 1 to n. In the foregoing example, there are only two coils, an inner coil and an outer coil, so that n=2. However, in the more general case, the number of coils, n, may be any integer greater than 1. 
         [0044]    In block  845 , the processor  130  computes the variances a for all possible combinations of n plasma distributions A j  and stores the results in memory, and then searches the memory for the particular “optimum” combination of n Aj&#39;s for which the variance function σ is minimum. In block  850 , the processor  130  looks up in memory for the n coil currents corresponding to the optimum combination of n Aj&#39;s, and chooses those currents as the optimum coil currents. In the present example employing only and inner coil and outer coil, n=2, and each combination of distribution is a sum of a pair of distributions A 1 +A 2  produced by corresponding coil currents I inner , I outer . The processor  130  searches the results of the foregoing search for the coil current pair I inner ′, I outer ′ corresponding to the particular combination distribution A 1 +A 2  having the minimum variance σ. In block  855 , a wafer or workpiece is processed in the plasma reactor by constantly maintaining the coil currents at the designated optimum values I inner ′, I outer ′. 
         [0045]    While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.