Abstract:
Novel structures and methods for evaluating lines in semiconductor integrated circuits. A first plurality of lines can be formed on a wafer each of which comprises multiple line sections. All the line sections are of the same length. The electrical resistances of the line sections are measured. Then, a first line geometry adjustment is determined based on the electrical resistances of all the sections of all the lines. The first line geometry adjustment represents an effective reduction of cross-section size of the lines due to grain boundary electrical resistance. A second plurality of lines of same length and thickness can be formed on the same wafer. Then, second and third line geometry adjustments can be determined based on the electrical resistances of these lines measured at different temperatures. The second and third line geometry adjustments represent an effective reduction of cross-section size of the lines due to grain boundary electrical resistance and line surface roughness.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Technical Field  
         [0002]     The present invention relates to semiconductor integrated circuits, and more particularly, to the non-destructive evaluation of electrically conducting lines in semiconductor integrated circuits.  
         [0003]     2. Related Art  
         [0004]     As dimensions reach the deep-submicron level on the order of the mean-free path of electrons of Cu interconnect wires, the size effect on the resistivity of Cu interconnects corresponding to reductions of wire dimensions becomes more significant. While advances in development of integrated circuits continue to lead to higher conductivity Cu and lower effective dielectric constant (k) insulation layer, the size effect in reduced geometries can degrade the benefit of small RC delay provided by Cu and low-k insulation layers. Three types of extra electron scattering mechanisms due to the size effect in addition to the isotropic background scattering were verified. These three scattering mechanisms including scattering at the grain boundaries, diffuse scattering at the external surfaces, and the surface roughness induced scattering deviations, were simultaneously operative in interconnect thin films. For interconnect lines in deep sub-micron regime, electron scattering from the surface and aggravated by line surface roughness and grain boundary is the dominant reason for significantly increasing of wire resistance. Therefore, it is important to control and monitor line surface roughness and line grain boundary resistance to minimize such additional electron scatterings. Besides resistivity increase due to line surface roughness and grain boundary resistance, line long-term reliability such as electromigration (EM) and stress migration (SM) is also dependent on surface roughness and grain distributions. EM mass transport and SM void diffusion usually are very sensitive to surface/interface conditions and grain size. Presently, there is no any simple, non-destructive methodology available to monitor integrated line surface quality and grain size/boundary configuration for manufacture process monitoring, in-line characterization, or reliability pre-screening.  
         [0005]     Therefore, there is a need for novel structures and methods for evaluating the impacts of grain boundary electrical resistance and line surface roughness on interconnect line electrical resistance and reliability.  
       SUMMARY OF THE INVENTION  
       [0006]     The present invention provides a method for grain size determination, the method comprising the steps of (a) providing an electrically conducting line including N sections of equal length, wherein N is an integer greater than 1; (b) measuring N electrical resistances respectively corresponding to the N sections; (c) determining a number of grains in the line based on the N measured electrical resistances of the N sections; and (d) determining an average grain size of the line based on a length of the line and the number of grains in the line.  
         [0007]     The present invention also provides a method of line evaluation, comprising the steps of (a) providing a line evaluation structure comprising N electrically conducting lines, wherein N is a positive integer, wherein, for i=1, 2, . . . , N, the i th  line of the N electrically conducting lines comprises M i  line sections, M i  being a positive integer, such that the N electrically conducting lines comprise in total S line sections, wherein S=ΣM i  (i=1,2, . . . , N), wherein each line section of the S line sections is of the same length, and (b) measuring electrical resistance of each line section of the S line sections; and (c) determining a line geometry adjustment for the line evaluation structure based on the electrical resistances of the S line sections obtained in step (b), wherein the line geometry adjustment represents an effective reduction of cross-section size of the N electrically conducting lines as a result of grain boundary electrical resistance.  
         [0008]     The present invention also provides a method of line evaluation, comprising the steps of (a) providing a line evaluation structure comprising N electrically conducting lines of a same length and a same thickness, wherein N is a positive integer, wherein the N electrically conducting lines have M different line widths, wherein M is a positive integer and M≦N, and wherein each line of the N electrically conducting lines is configured to be measured for electrical resistance; (b) for each temperature of P different temperatures and for each line width of the M line widths, measuring an electrical resistance for the line width at the temperature, wherein P is an integer greater than 1; (c) for each line width of the M line widths, determining a temperature coefficient of electrical resistance (TCR) based on the P electrical resistances at P temperatures for the line width; (d) determining first and second line geometry adjustments for the N electrically conducting lines based on the M TCRs of the M line widths determined in step (c), wherein the first line geometry adjustment represents an effective reduction of line width of the N electrically conducting lines as a result of grain boundary electrical resistance and sidewall surface roughness of the N electrically conducting lines, and wherein the second line geometry adjustment represents an effective reduction of thickness of the N electrically conducting lines as a result of grain boundary electrical resistance and top/bottom surface roughness of the N electrically conducting lines.  
         [0009]     The present invention provides novel structures and methods for evaluating the impacts of grain boundary electrical resistance and line surface roughness on interconnect line electrical resistance. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]      FIGS. 1A-1C  show a structure and a method for determining (a) line grain boundary electrical resistance R b , (b) line geometry adjustment ε due to grain boundary electrical resistance for a line fabrication process and (c) the average grain size for a line width for the line fabrication process, in accordance with embodiments of the present invention.  
         [0011]      FIGS. 2A-2B  show a structure and a method for determining line geometry adjustments δ and θ due to both grain boundary electrical resistance and line surface roughness for a line fabrication process, in accordance with embodiments of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0012]      FIG. 1A  shows a top view of a macro  100  comprising a conducting line  110  used for (a) determining line geometry adjustment ε for the macro  100  due to grain boundary electrical resistance and (b) estimating the average grain size of the grains of the line  110 , in accordance with embodiments of the present invention. More specifically, the line geometry adjustment ε represents an effective reduction of cross-section size (thickness and line width) of a line as a result of grain boundary electrical resistance.  
         [0013]     In one embodiment, for illustration, the macro  100  can comprise the conducting line  110 , eleven pads  120 . 0 - 120 . 10  (collectively referred to as pads  120 ) and eleven coupling lines  130 . 0 - 130 . 10  (collectively referred to as coupling lines  130 ) that electrically couple the pads  120  to the line  110 . More specifically, the coupling line  130 . i  electrically couples the pad  120 . i  to the line  110 , wherein i=0-10. In one embodiment, the points at which the 11 coupling lines  130  contact the line  110  divide the line  110  into 10 line sections  1 ,  2 , . . . , and  10  of equal length. In one embodiment, the macro  100  can be formed in a wafer (not shown) during the fabrication of other devices (not shown) on the same wafer.  
         [0014]     In one embodiment, the pads  120  can be formed at the same interconnect level as the conducting line  110 . Alternatively, the pads  120  can be formed at interconnect levels higher than the level of the conducting line  110 .  
         [0015]     Assume that the conducting line  110  comprises, illustratively, 6 grains  140   a , . . . , and  140   f  (collectively referred to as the grains  140 ) and 5 grain boundaries  150   a , . . . , and  150   e . Assume further that the conducting line  110  has a line width  160  that is smaller than the average grain size of the grains  140 .  
         [0016]      FIG. 1B  shows a flow chart of a method  180  for determining the line grain boundary resistance R b  and geometry adjustment ε due to grain boundary electrical resistance for the macro  100  (and therefore, also for the line fabrication process that forms the macro  100  and other devices on the same wafer as the macro  100 ). In one embodiment, the method  180  starts with a step  182  of measuring the electrical resistances of the sections  1 ,  2 , . . . , and  10  of the line  110  using any known method (e.g., the 4-point Kelvin measurement method). The pads  120  can be used as contact points by the measuring device. As a result, ten electrical resistance values are obtained for the ten sections  1 ,  2 , . . . , and  10  of the line  110 .  
         [0017]     Next, in one embodiment, in step  184 , the line geometry adjustment ε can be determined by analyzing the ten electrical resistance values obtained in step  182 . More specifically, ε can be extracted from the following equation: 
 
 R (no  GB )/ R   b (one  GB )=( w− ε)*( h −ε)/( w*h )   (1) 
 
         [0018]     wherein:  
         [0019]     R(no GB) is the average section electrical resistance of the sections containing no GB (grain boundary).  
         [0020]     R b  (one GB) is the average section electrical resistance of the sections containing only one GB.  
         [0021]     w and h are line width  160  and line thickness  162  ( FIG. 1A ′, which shows a cross-section view along a line  1 A′- 1 A′ of the line  110  of  FIG. 1A ) of the line  110 , respectively, which are both known.  
         [0022]     In one embodiment, the sections of the line  110  that contain no grain boundary and the sections of the line  110  that contain only one grain boundary can be identified by depicting the ten section electrical resistances of the ten sections  1 , . . . , and  10  on a same graph with each section electrical resistance represented by a vertical bar ( FIG. 1C ). It should be clear from  FIG. 1C  that the ten section electrical resistances can be divided into groups of similar section electrical resistances.  
         [0023]     For instance, the electrical resistances of the sections  1 ,  3 ,  5 ,  6 ,  8 , and  10  are similar and are the lowest. Therefore, it can be inferred that the respective sections  1 ,  3 ,  5 ,  6 ,  8 , and  10  contain no grain boundary. As a result, the average section electrical resistance of the sections  1 ,  3 ,  5 ,  6 ,  8 , and  10  can be used as R(no GB) in equation (1) above.  
         [0024]     Similarly, the electrical resistances of the sections  2 ,  4 , and  7  are similar and are the next-higher. Therefore, it can be inferred that the respective sections  2 ,  4 , and  7  contain only one grain boundary. As a result, the average section electrical resistance of the sections  2 ,  4 , and  7  can be used as R b  (one GB) in equation (1) above.  
         [0025]     In practice, not all grain boundaries are expected to have the same resistance, but will instead have a range of resistances. Nevertheless, the values of resistance obtained are expected to fall with definable groups or distributions which have mean values that can be treated in the same manner indicated above.  
         [0026]     With w and h known and R(no GB) and R b  (one GB) obtained as described supra, line geometry adjustment ε can be extracted from equation (1) above. The resulting line geometry adjustment ε gives the process engineer an idea about the quality of the line  110  of the macro  100 , and therefore gives the process engineer a general idea about the quality of the process that forms the line  110 . More specifically, the line geometry adjustment ε indicates that if a line section contains one grain boundary and has thickness h and line width w, then the line section is equivalent to (i.e., has the same electrical resistance as) another line section that contains no grain boundary and has thickness h-ε and line width w-ε. In other words, line geometry adjustment ε represents an effective reduction of cross-section size of the line  110  as a result of grain boundary electrical resistance.  
         [0027]     In an alternative embodiment, instead of comprising only one line  110  as described above, the macro  100  can comprise multiple lines (not shown) similar to the line  110  (i.e., having the same thickness and section length), but having different line widths. In one embodiment, the lengths of these lines may be different. The inventors of the present invention have found that although grain size may change with line width and fabrication process conditions, the average grain size is known to be in the range of 0.3-0.7 μm for a normal Cu metallurgy process. As a result, in one embodiment, the line  110  can comprise conducting lines (not shown) some of which have line widths smaller than the average grain size (i.e., bamboo structures) and some of which have line widths larger than the average grain size. For instance, for illustration, the macro  100  can comprise  111  conducting lines (not shown) having the following 11 different line widths: 0.1 μm, 0.3 μm, 0.5 μm, 0.7 μm, 1 μm, 1.5 μm, 2 μm, 3 μm, 5 μm, 7 μm, and 10 μm.  
         [0028]     Then, the step  182  of the method  180  ( FIG. 1B ) can be performed for each of the 11 lines of the macro  100  (i.e., measuring electrical resistances of the sections of each of the 11 lines of the macro  110 ). Although the lines having line widths above 0.7 μm are not useful to effectively detect grain boundary electrical resistance under normal process condition, this multiple line width macro  100  will guarantee to cover all different grain sizes and even abnormal grain size cases due to abnormal process.  
         [0029]     Then, in one embodiment, the step  184  ( FIG. 1B ) can be performed as if all the section electrical resistances obtained in step  182  came from one conducting line. More specifically, in equation (1), R(no GB) can be obtained by averaging the similar, lowest section electrical resistances of the section electrical resistances. R b  (one GB) can be obtained by averaging the similar, next-higher section electrical resistances of the section electrical resistances. w can be the line width closest to but lower than the average grain size (i.e., w=0.5 micron). h can be the common thickness of the 11 conducting lines, which is known. As a result, the resulting line geometry adjustment ε extracted from equation (1) is applicable to the entire macro  100  comprising 11 lines of same thickness h but different line widths.  
         [0030]     In one embodiment, the macro  100  comprising 11 lines can be used to electrically estimate an average grain size for each of the 11 lines. More specifically, by examining the section electrical resistances of each line, the average grain size for that line can be roughly estimated. In one embodiment, the average grain size for a line can be estimated by dividing the length of the line (which can be represented by the number of sections of the line) by the number of detected grains in the line.  
         [0031]     For example, assume that the line  110  ( FIG. 1A ) is one of the 11 lines of the macro  100 . The number of sections of line  110  is known (i.e., 10 sections). The six grains  140  can be detected by using the graph of  FIG. 1C . It could be inferred from  FIG. 1C  that there are no grain boundary in sections  1 ,  3 ,  5 ,  6 ,  8 , and  10 ; one grain boundary in each of sections  2 ,  4 , and  7 ; and two grain boundaries in section  9  of the line  110 . In other words, there are 5 grain boundaries and, therefore, 6 grains in the line  110 . As a result, the average grain size for line  110  can be determined by dividing the length of the line (i.e., 10 sections, if measured in terms of number of sections) by the number of detected grains in the line  110  (i.e., 6 grains).  
         [0032]     In one embodiment, the above steps can be repeated for the other 10 different lines. The 11 lines have 11 different line widths. As a result, the average grain size of each particular line also represents the average grain size for the associated line width. Average grain size is one of the key parameters that need to be closely monitored during manufacturing process, interconnect research, and material development.  
         [0033]     In one embodiment, the macro  100  can be formed in a chip. As a result, ε can represent line quality of the chip. If ε of the chip exceeds a pre-specified value ε 0 , the process engineer can determine that the conducting lines in the chip have too high electrical resistance due to excessive grain boundary electrical resistance and therefore the chip should be marked as defective. Similarly, in one embodiment, if an average grain size of a line of the macro  100  does not fall in a pre-specified range (either too small or too large), the process engineer can determine that the conducting lines in the chip are possibly mis-processed and therefore the chip should be marked as defective.  
         [0034]      FIG. 2A  shows a top view of a macro  200  used for determining line geometry adjustments δ and θ due to both grain boundary electrical resistance and line surface roughness for the lines of the macro  200 , in accordance with embodiments of the present invention. In one embodiment, the line geometry adjustment δ represents an effective reduction of line width of the lines of the macro  200  as a result of grain boundary electrical resistance and sidewall surface roughness of the lines of the macro  200 . The line geometry adjustments θ represents an effective reduction of thickness of the lines of the macro  200  as a result of grain boundary electrical resistance and top/bottom surface roughness of the lines of the macro  200 .  
         [0035]     In one embodiment, for illustration, the macro  200  can comprise five conducting lines  210   a , . . . ,  210   e  having the same length L and same thickness H (not shown) but having five different line widths Wa, Wb, Wc, Wd, and We, respectively.  
         [0036]     In one embodiment, the macro  200  can be formed in a wafer (not shown) during the fabrication of other devices (not shown) in the same wafer.  
         [0037]      FIG. 2B  shows a flow chart of a method  280  for determining the line geometry adjustments δ and θ for the conducting lines  210   a , . . . ,  210   e  of the macro  200 . In one embodiment, the method  280  starts with a step  282  of measuring the electrical resistances of the conducting lines  210   a , . . . ,  210   e  at different temperatures using any known electrical resistance measuring method. Illustratively, the electrical resistances of the conducting lines  210   a , . . . ,  210   e  can be measured at three different temperatures such as 30° C., 45° C., and 60° C. As a result, 15 electrical resistance values are obtained for the five conducting lines  210   a , . . . ,  210   e . In step  282 , assume that the conducting lines  210   a , . . . ,  210   e  have measured electrical resistances Ra 1 , Rb 1 , Rc 1 , Rd 1 , and Re 1  at temperature T 1 =30° C., respectively; have measured electrical resistances Ra 2 , Rb 2 , Rc 2 , Rd 2 , and Re 2  at temperature T 2 =45° C., respectively; and have measured electrical resistances Ra 3 , Rb 3 , Rc 3 , Rd 3 , and Re 3  at temperature T 3 =60° C., respectively.  
         [0038]     Next, in step  284 , in one embodiment, for each of the five different line widths Wa, Wb, Wc, Wd, and We, a TCR (temperature coefficient of electrical resistance) is determined. More specifically, in one embodiment, the TCR of line width Wa (hereafter referred to as TCRa) can be obtained by curve-fitting a straight line having the following equation 
 
 R=Ro*[ 1 +TCRa *( T−To )]  (2) 
 
         [0039]     to three points (T 1 , Ra 1 ); (T 2 , Ra 2 ); and (T 3 , Ra 3 ) on an orthogonal x-y axis system having horizontal T-axis and vertical Ra-axis, wherein T is temperature variable, R is electrical resistance variable for the line width, TCRa is the temperature coefficient of electrical resistance of the line width, (To,Ro) is a point on the straight line, and Ra is electrical resistance of line  210   a . In one embodiment, the least-square curve fit method can be used.  
         [0040]     From the resulting curve-fit straight line, TCRa can be determined. More specifically, in one embodiment, assume the curve-fit straight line cuts the three vertical lines T=T 1 , T=T 2 , and T=T 3  at three points (T 1 , Ra 1 ′); (T 2 , Ra 2 ′); and (T 3 , Ra 3 ′), respectively. Then (T 1 , Ra 1 ′) can be used as the reference point (To,Ro) and (T 2 , Ra 2 ′) can be plugged into the equation (2). As a result, 
 
 TCRa =(1 /Ra   1 ′)*[( Ra   2 ′− Ra   1 ′)/( T   2 − T   1 )]=(1 /Ra   1 ′)* k,    (2a), 
 
         [0041]     wherein k is the slope of the resulting curve-fit straight line.  
         [0042]     Depending on which pair of three points (T 1 , Ra 1 ′); (T 2 , Ra 2 ′); and (T 3 ,Ra 3 ′) is used in equation (2), the formula for TCRa can change. There are two other formulas for TCRa: 
 
TCRa(1/Ra 2 ′)*k   (2b), and 
 
TCRa(1/Ra 3 ′)*k   (2c). 
 
         [0043]     Either (2a), (2b), or (2c) can be used to determine TCRa because Ra 1 ′, Ra 2 ′, and Ra 3 ′ are approximately equal. In one embodiment, the average value of Ra 1 ′, Ra 2 ′, and Ra 3 ′ can be used in place of Ra 1 ′, Ra 2 ′, and Ra 3 ′ in equations (2a), (2b), or (2c), respectively.  
         [0044]     In one embodiment, TCRb, TCRc, TCRd, and TCRe can be obtained in a similar manner for the line widths Wb, Wc, Wd, and We, respectively.  
         [0045]     Next, in step  286 , in one embodiment, the line geometry adjustments δ and θ for the lines  210   a , . . . ,  210   e  can be obtained by first depicting five points (Wa, TCRa); (Wb, TCRb); (Wc, TCRc); (Wd, TCRd); and (We, TCRe) on an orthogonal x-y axis plane having horizontal line width W-axis and vertical TCR-axis. Then, a curve 
 
 TCR=TCRo *( W −δ)*( H −θ)/( W*H ),   (3) 
 
         [0046]     is curve-fitted to the five points (Wa, TCRa); (Wb, TCRb); (Wc, TCRc); (Wd, TCRd); and (We, TCRe),  
         [0047]     wherein:  
         [0048]     TCRo is the bulk TCR of the material of the conducting lines  210   a , . . . ,  210   e , which is known.  
         [0049]     H is the common thickness of the conducting lines  210   a , . . . ,  210   e , which is known.  
         [0050]     δ and θ are two constant parameters to be obtained.  
         [0051]     TCR and W are temperature coefficient of electrical resistance and line width, respectively, which are variables.  
         [0052]     In one embodiment, the least-square curve fit method can be used. As a result of this curve-fitting step, δ and θ can be determined for the macro  200 .  
         [0053]     In one embodiment, line geometry adjustment pw due to sidewall surface roughness can be defined as pw=δ−ε. Similarly, line geometry adjustment ph due to top/bottom surface roughness can be defined as ph=0−ε.  
         [0054]     In one embodiment, multiple macros (not shown) like the macro  200  ( FIG. 2A ) can be formed (i.e., embedded) in different chips (not shown) across a wafer (not shown). For each of such macros, a pair of δ and θ can be obtained using the method  280  ( FIG. 2B ) described above, and then a pair of pw and ph are obtained using the formulas pw=δ−ε and ph=θ−ε, wherein ε can be obtained for the entire wafer using method  180  ( FIG. 1B ) described above. Then, pw, ph, and ε can be plotted across the wafer to help a process engineer evaluate the quality of the conducting lines in different chips across the wafer.  
         [0055]     In one embodiment, if pw of a chip exceeds a pre-specified value pw o , the process engineer can determine that the conducting lines in the chip are too small due to excessive sidewall surface roughness and therefore the chip should be marked as defective. Similarly, if ph of a chip exceeds a pre-specified value ph o , the process engineer can determine that the conducting lines in the chip are too small due to excessive top/bottom surface roughness and therefore the chip should be marked as defective.  
         [0056]     In the embodiments described above, the macro  100  ( FIG. 1A ) has one line for each line width. In general, there can be more than one line for each line width in the macros  100  and  200 .  
         [0057]     In the embodiments described above with respect to  FIG. 2A , there is only one conducting line corresponding to a line width. In general, there can be more than one conducting line for each line width. If so, the electrical resistance for the line width at a temperature can be determined by averaging the electrical resistances of the lines of that line width at that temperature.  
         [0058]     While particular embodiments of the present invention have been described herein for purposes of illustration, many modifications and changes will become apparent to those skilled in the art. Accordingly, the appended claims are intended to encompass all such modifications and changes as fall within the true spirit and scope of this invention.