Patent Publication Number: US-2021183618-A1

Title: Antennas, circuits for generating plasma, plasma processing apparatus, and methods of manufacturing semiconductor devices using the same

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation application of, and claims priority to, U.S. application Ser. No. 15/723,837, filed Oct. 3, 2017, which claims priority under 35 U.S.C. § 119 to Korean Patent Application No. 10-2016-0138589, filed on Oct. 24, 2016, and to Korean Patent Application No. 10-2017-0098634, filed on Aug. 3, 2017, in the Korean Intellectual Property Office, the entire contents of which are hereby incorporated herein by reference in their entireties. 
    
    
     BACKGROUND 
     Embodiments of the inventive concepts relate to apparatus and methods for manufacturing semiconductor devices and, more particularly, to antennas for inducing plasma, circuits for generating plasma, plasma processing apparatus, and methods of manufacturing semiconductor devices using the same. 
     In general, a semiconductor device may be manufactured by a plurality of unit processes. The unit processes may include a deposition process, a diffusion process, a thermal treatment process, a photolithography process, a polishing process, an etching process, an ion implantation process, and/or a cleaning process. The etching process of these unit processes may include a dry etching process and/or a wet etching process. The dry etching process may be performed using plasma. A substrate may be treated or processed at a high temperature by the plasma. 
     SUMMARY 
     Embodiments of the inventive concepts may provide plasma generating circuits and plasma processing apparatus, which are capable of stably matching impedance. 
     Embodiments of the inventive concepts may also provide antennas capable of inducing uniform plasma. 
     In an aspect of the inventive concepts, a plasma generating circuit may include first and second radio-frequency power sources configured to generate first and second radio-frequency powers, first and second antennas configured receive the first and second radio-frequency powers to generate plasma and having a first mutual inductance, and first and second inductors electrically connecting the first and second antennas to the first and second radio-frequency power sources, respectively. The first and second inductors may have a second mutual inductance to cancel the first mutual inductance. 
     In an aspect of the inventive concepts, a plasma processing apparatus may include a chamber, a gas supply part configured to provide a reaction gas into the chamber, and a plasma generating circuit on the chamber and configured to induce plasma of the reaction gas in the chamber. The plasma generating circuit may include first and second radio-frequency power sources configured to generate first and second radio-frequency powers, first and second antennas configured to generate the plasma by using the first and second radio-frequency powers, the first and second antennas having a first mutual inductance, and first and second inductors configured to couple the first and second antennas to the first and second radio-frequency power sources, respectively. The first and second inductors may have a second mutual inductance to cancel the first mutual inductance. 
     In an aspect of the inventive concepts, a plasma generating circuit may include radio- frequency power sources configured to generate radio-frequency powers, matching circuits connected to the radio-frequency power sources, respectively, the matching circuits configured to match impedances of the radio-frequency powers, respectively, antennas connected to the matching circuits, respectively, the antennas configured to generate plasma by using the radio-frequency powers, and the antennas having a first mutual inductance, capacitors configured to ground the antennas, respectively, the capacitors configured to control impedances of the radio-frequency powers, and inductors connected between the antennas and the matching circuits, respectively. The inductors may have a second mutual inductance to cancel the first mutual inductance. 
     In an aspect of the inventive concepts, an antenna may include an input electrode, branch electrodes connected to the input electrode, coil electrodes connected to the branch electrodes, respectively, the coil electrodes extending along an imaginary circle connecting ends of the branch electrodes, and output electrodes connected to the coil electrodes, respectively. The output electrodes may be disposed in parallel to the input electrode. 
     In an aspect of the inventive concepts, a method for manufacturing a semiconductor device may include providing a substrate, and generating plasma on the substrate. The generating of the plasma may include supplying first and second radio-frequency powers to first and second antennas disposed on a central portion and an edge portion of the substrate to etch the substrate without interference of the first and second radio-frequency powers by a second mutual inductance to cancel a first mutual inductance between the first and second antennas. 
     In an aspect of the inventive concepts, a plasma generating circuit for a plasma processing apparatus may include a first radio-frequency power source configured to generate a first radio-frequency power, a second radio-frequency power source configured to generate a second radio-frequency power, a first inductor configured to receive the first radio-frequency power, a first antenna coupled to the first inductor and configured to transmit the first radio-frequency power to a gas of the plasma processing apparatus, a second inductor configured to receive the second radio-frequency power, and a second antenna coupled to the second inductor and configured to transmit the second radio-frequency power to the gas of the plasma processing apparatus. The first antenna and the second antenna may be inductively coupled to one another by a first mutual inductance, and the first inductor and the second inductor may be inductively coupled to one another by a second mutual inductance configured to offset the first mutual inductance of the first antenna and the second antenna. 
     In an aspect of the inventive concepts, a method for manufacturing a semiconductor device may include providing first and second radio-frequency powers into first and second antennas, respectively, sweeping a current phase difference of the first and second radio-frequency powers, measuring first and second currents flowing through the first and second antennas to calculate current ratios, each of which corresponds to a ratio of the first current to the second current, determining whether a standard value exists among the current ratios, and calculating a first current phase difference of the first and second currents at the current ratio corresponding to the standard value when the standard value exists. 
     In an aspect of the inventive concepts, a plasma processing apparatus may include a chamber, a gas supply part providing a gas into the chamber, a plasma generating circuit including first and second antennas disposed on the chamber and first and second radio-frequency power sources providing first and second radio-frequency powers into the first and second antennas, and first and second current measuring instruments disposed between the first and second antennas and the first and second radio-frequency power sources, respectively, to measure first and second currents of the first and second radio-frequency powers, respectively. When a current ratio corresponding to a ratio of the first current to the second current is a standard value, the first and second radio-frequency power sources may provide the first and second radio-frequency powers having a first current phase difference calculated at the current ratio corresponding to the standard value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The inventive concepts will become more apparent in view of the attached drawings and accompanying detailed description. 
         FIG. 1  is a view illustrating a plasma processing apparatus according to some embodiments of the inventive concepts. 
         FIG. 2  is a circuit diagram illustrating an example of a plasma generating circuit of  FIG. 1 . 
         FIGS. 3A to 3F  are graphs illustrating waveforms of first and second radio-frequency powers of first and second radio-frequency power sources of  FIG. 2 . 
         FIG. 4  is a perspective view illustrating first and second antennas of  FIG. 2 . 
         FIG. 5  is a perspective view illustrating the first antenna of  FIG. 4 . 
         FIG. 6  is a plan view illustrating a first input electrode, first branch electrodes, and first coil electrodes of  FIG. 5 . 
         FIG. 7  is a perspective view illustrating the second antenna of  FIG. 4 . 
         FIG. 8  is a plan view illustrating a second input electrode, second branch electrodes, and second coil electrodes of  FIG. 7 . 
         FIG. 9  is a graph illustrating a coupling efficiency according to a distance between first and second inductors of  FIG. 2 . 
         FIG. 10  is a graph illustrating an output current according to the first radio-frequency power of  FIG. 2  and an output current according to the second radio-frequency power of  FIG. 2 . 
         FIG. 11  is a graph illustrating a variation of an etch rate according to a position on a substrate of  FIG. 1 . 
         FIG. 12  is a circuit diagram illustrating an example of a plasma generating circuit of  FIG. 1 . 
         FIGS. 13 to 16  are views illustrating examples of arrangements of first to third inductors of  FIG. 11 . 
         FIG. 17  is a flow chart illustrating methods for manufacturing semiconductor devices using the plasma processing apparatus of  FIG. 1 . 
         FIG. 18  is a view illustrating a plasma processing apparatus according to some embodiments of the inventive concepts. 
         FIG. 19  is a circuit diagram illustrating an example of a plasma generating circuit of  FIG. 18 . 
         FIG. 20  is a flowchart illustrating a method for manufacturing a semiconductor device using a plasma processing apparatus according to some embodiments of the inventive concepts. 
         FIG. 21  is a graph illustrating a current phase difference between first and second radio-frequency powers. 
         FIG. 22  is a graph illustrating an intensity of an electromagnetic field according to a position on a substrate of  FIG. 18 . 
         FIG. 23  is a graph illustrating a center etch rate and an edge etch rate of a substrate according to a current phase difference of  FIG. 22 . 
         FIG. 24  is a graph illustrating first and second currents in first and second antennas according to the current phase difference of  FIG. 22  and a current ratio of the first and second currents. 
         FIG. 25  is a graph illustrating an M-shaped etch rate uniformity and a flat etch rate uniformity of a substrate. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a plasma processing apparatus  10  according to some embodiments of the inventive concepts. 
     Referring to  FIG. 1 , the plasma processing apparatus  10  according to some embodiments of the inventive concepts may include an inductively coupled plasma (ICP) apparatus. In some embodiments, the plasma processing apparatus  10  may include a capacitively coupled plasma (CCP) apparatus. In some embodiments, the plasma processing apparatus  10  may include a microwave plasma apparatus. In some embodiments, the plasma processing apparatus  10  may include a chamber  100 , a gas supply part  200 , and a circuit  300  for generating plasma (hereinafter, referred to as “a plasma generating circuit  300 ”). 
     The chamber  100  may provide an inner space into which a substrate W is loaded. The inner space of the chamber  100  may be isolated from the outside of the chamber  100  when a process is performed. In some embodiments, the chamber  100  may include a lower housing  110 , an upper housing  120 , a window  130 , and an electrostatic chuck  140 . The lower housing  110  and the upper housing  120  may surround the window  130 , the electrostatic chuck  140 , and a substrate W. The upper housing  120  may be disposed on the lower housing  110  and the window  130 . The window  130  may be disposed between the lower housing  110  and the upper housing  120 . For example, the window  130  may include a ceramic disk. The electrostatic chuck  140  may be disposed in the lower housing  110 . The electrostatic chuck  140  may receive a substrate W. 
     The gas supply part  200  may supply a gas (not shown) into the chamber  100  between the lower housing  110  and the window  130 . In some embodiments, the gas supply part  200  may include a storage tank  210  and a mass flow controller  220 . The storage tank  210  may store a gas. The gas may include, for example, a purge gas, an etching gas, a deposition gas, or a reaction gas. For example, the gas may include at least one of a nitrogen (N 2 ) gas, a hydrogen (H 2 ) gas, an oxygen (O 2 ) gas, a hydrofluoric acid (HF) gas, a chlorine (Cl 2 ) gas, a sulfur hexafluoride (SF 6 ), a methylene (CH 3 ) gas, or a silane (SiH 4 ) gas. The mass flow controller  220  may be connected between the storage tank  210  and the chamber  100 . The mass flow controller  220  may control a supply flow rate of the gas. 
     The plasma generating circuit  300  may generate or induce plasma  301  of the supplied gas in the chamber  100 . For example, the plasma generating circuit  300  may be disposed on the window  130 . In some embodiments, the plasma generating circuit  300  may be disposed on the upper housing  120  outside the chamber  100 . The plasma  301  may be remotely induced between the lower housing  110  and the window  130 . The plasma  301  may be generated on the substrate W. 
       FIG. 2  is a circuit diagram illustrating an example of the plasma generating circuit  300  of  FIG. 1 . 
     Referring to  FIGS. 1 and 2 , the plasma generating circuit  300  may provide a first radio-frequency (RF) power  311  and a second radio-frequency (RF) power  313  to the gas disposed on a central portion of the substrate W and the gas disposed on an edge portion of the substrate W, respectively. The first and second radio-frequency powers  311  and  313  may generate the plasma  301  on the central portion and the edge portion of the substrate W. In some embodiments, the plasma generating circuit  300  may include first and second radio-frequency power sources  312  and  314 , first and second matchers  322  and  324 , first and second antennas  332  and  334 , first and second inductors  342  and  344 , and first and second capacitors  352  and  354 . 
     The first and second radio-frequency power sources  312  and  314  may generate the first and second radio-frequency powers  311  and  313 , respectively. The first and second radio-frequency powers  311  and  313  may be provided to the first and second antennas  332  and  334 , respectively. The first and second radio-frequency powers  311  and  313  may be controlled independently of each other. 
       FIGS. 3A to 3F  illustrate waveforms of the first and second radio-frequency powers  311  and  313  of the first and second radio-frequency power sources  312  and  314 . 
     Referring to  FIGS. 3A to 3F , the first and second radio-frequency powers  311  and  313  may be provided in a combination of a continuous wave and a pulse wave or in a combination of pulse waves. 
     Referring to  FIG. 3A , when the first radio-frequency power  311  is a pulse wave, the second radio-frequency power  313  may be a continuous wave. In some embodiments, the second radio-frequency power  313  may be considered a continuous wave when the second radio-frequency power  313  is a substantially constant power. In some embodiments, the first radio-frequency power  311  may be a continuous wave, and the second radio-frequency power  313  may be a pulse wave. 
     Referring to  FIG. 3B , the first and second radio-frequency powers  311  and  313  may be synchronized pulses. For example, frequencies and/or phases of the first and second radio-frequency powers  311  and  313  may be equal to each other. A voltage and/or current of the first radio-frequency power  311  may be greater than a voltage and/or current of the second radio-frequency power  313 . The first and second radio-frequency powers  311  and  313  may be reverse pulses. 
     Referring to  FIG. 3C , phases of the first and second radio-frequency powers  311  and  313  may be opposite to each other. For example, frequencies of the first and second radio-frequency powers  311  and  313  may be equal to each other. In some embodiments, a phase of the first and second radio-frequency powers  311  and  313  may be shifted by  180  degrees with respect to one another. 
     Referring to  FIG. 3D , a duty cycle of each of the first and second radio-frequency powers  311  and  313  may be controlled. For example, the duty cycles of the first and second radio-frequency powers  311  and  313  may be different from each other. 
     Referring to  FIG. 3E , shapes of pulse waves of the first and second radio-frequency powers  311  and  313  may be changed. For example, each of the first and second radio-frequency powers  311  and  313  may be a triangular wave or a quadrilateral wave. In some embodiments, the shape of the pulse wave of the first radio-frequency power  311  and the second radio-frequency power  313  may be different from one another. 
     Referring to  FIG. 3F , base voltage levels of pulse waves of the first and second radio-frequency powers  311  and  313  may be different from each other. For example, the first radio-frequency power  311  may have a base voltage that is equal to a ground voltage. On the other hand, the second radio-frequency power  313  may have a base voltage that is higher than the ground voltage. 
     It will be understood that  FIGS. 3A to 3F  illustrate the waveforms of the first and second radio-frequency powers  311  and  313  at respective comparative periods and are not intended to represent the waveforms of the first and second radio-frequency powers  311  and  313  in their entirety. In some embodiments, either or both of the waveforms of the first and second radio-frequency powers  311  and  313  may change to any of the respective waveforms illustrated in  FIGS. 3A to 3F , or to other waveforms. 
     Referring again to  FIG. 2 , the first and second matchers  322  and  324  may be connected to the first and second radio-frequency power sources  312  and  314 , respectively. The first and second matchers  322  and  324  may match impedances of the first and second radio-frequency powers  311  and  313 , respectively. In some embodiments, the first matcher  322  and/or the second matchers  324  may be matching circuits. 
     Referring to  FIGS. 1 and 2 , the first and second antennas  332  and  334  may be disposed between the window  130  and the upper housing  120 . In some embodiments, the first antenna  332  may be disposed over the central portion of the substrate W. The second antenna  334  may be disposed over the edge portion of the substrate W. As used herein, the central portion of the substrate W may extend beyond the exact center of the substrate W, and may be a portion of the substrate W that is closer to the exact center of the substrate W than the edge portion of the substrate W. In some embodiments, the central portion of the substrate W may include fifty percent of the surface area of the substrate W that surrounds the center of the substrate W. In some embodiments, the edge portion of the substrate W may include fifty percent of the surface area of the substrate W that surrounds the central portion. The first antenna  332  may transmit the first radio-frequency power  311 , and second antenna  334  may transmit the second radio-frequency power  313 , to the gas on the substrate W. 
     Energy and/or intensity of the plasma  301  may be proportional to the first and second radio-frequency powers  311  and  313  transmitted to the gas. In some embodiments, the energy and/or the intensity of the plasma  301  may be proportional to an etch rate of the substrate W. For example, the first antenna  332  may control an etch rate of the central portion of the substrate W by using the first radio-frequency power  311 . The second antenna  334  may control an etch rate of the edge portion of the substrate W by using the second radio-frequency power  313 . In some embodiments, the energy and/or the intensity of the plasma  301  may be proportional to a deposition rate of a thin film on the substrate W. 
     Referring to  FIG. 2 , the first and second antennas  332  and  334  may be disposed to be adjacent to each other. In some embodiments, the first and second antennas  332  and  334  may be coupled to each other within an adjacent distance. For example, the first and second antennas  332  and  334  may have a first mutual inductance M 1 . Coiled directions of the first and second antennas  332  and  334  may be indicated by the dots of  FIG. 2 . In some embodiments, the first and second antennas  332  and  334  may be coiled and/or wound in the same direction. 
       FIG. 4  illustrates the first and second antennas  332  and  334  of  FIG. 2 . 
     Referring to  FIG. 4 , the first antenna  332  may be disposed within an interior space of the second antenna  334 . The first and second antennas  332  and  334  may have shapes similar to each other. For example, the first and second antennas  332  and  334  may have ring shapes. In some embodiments, the first and second antennas  332  and  334  may have shapes different from each other. 
       FIG. 5  illustrates the first antenna  332  of  FIG. 4 .  FIG. 6  is a plan view illustrating a first input electrode  410 , first branch electrodes  420 , and first coil electrodes  430  of  FIG. 5 . 
     Referring to  FIG. 5 , the first antenna  332  may include a first input electrode  410 , first branch electrodes  420 , first coil electrodes  430 , first output electrodes  440 , and a first ring electrode  450 . 
     The first input electrode  410  may be disposed on a center at which the first branch electrodes  420  meet each other. The first input electrode  410  may be parallel to a direction vertical to the first branch electrodes  420  and the first coil electrodes  430 . 
     Referring to  FIGS. 5 and 6 , the first branch electrodes  420  may be connected to the first input electrode  410 . For example, the number of the first branch electrodes  420  may be two. The first branch electrodes  420  may extend from the first input electrode  410  in directions opposite to each other. The first branch electrodes  420  may divide the first coil electrodes  43 Q at a rotation angle of 180 degrees. 
     The first coil electrodes  430  may be connected to end portions of the first branch electrodes  420 , respectively. In some embodiments, end portions of the first branch electrodes  420  may be portions of the first branch electrodes  420  that are disposed at ends of the first branch electrodes  420  that are opposite from the first input electrode  410 . In some embodiments, the first coil electrodes  430  may be wound from the first branch electrodes  420  in a counterclockwise direction. In some embodiments, the first coil electrodes  430  may be wound in a clockwise direction. In some embodiments, the number of turns of the first coil electrodes  430  may be about four. In some embodiments, the first coil electrodes  430  may include a first eccentric coil electrode  431  and a second eccentric coil electrode  432 . Centers of the first eccentric coil electrode  431  and the second eccentric coil electrode  432  may be different from the center on which the first input electrode  410  is disposed. In some embodiments, the first eccentric coil electrode  431  and the second eccentric coil electrode  432  may include turns which have different centers from other turns. 
     In some embodiments, the first and second eccentric coil electrodes  431  and  432  may be turned two times. In some embodiments, each of the first and second eccentric coil electrodes  431  and  432  may include an inner top coil  433 , an inner connection electrode  434 , and an inner bottom coil  435 . 
     The inner top coil  433  may be connected to the first branch electrode  420 . In some embodiments, the inner top coil  433  may be turned one time. The inner top coil  433  may be disposed on the inner bottom coil  435 . The inner top coil  433  may have a large top-half-turn  433   a  and a small top-half-turn  433   b.  The large top-half-turn  433   a  may be connected to the first branch electrode  420 . The small top-half-turn  433   b  may have a radius smaller than a radius of the large top-half-turn  433   a.  For example, the large top-half-turn  433   a  of the first eccentric coil electrode  431  may be disposed outside the small top-half-turn  433   b  of the second eccentric coil electrode  432 . The small top-half-turn  433   b  of the first eccentric coil electrode  431  may be disposed inside the large top-half-turn  433   a  of the second eccentric coil electrode  432 . The small top-half-turns  433   b  of the first and second eccentric coil electrodes  431  and  432  may be rotated one time in an area on the central portion of the substrate W. The large top-half-turns  433   a  of the first and second eccentric coil electrodes  431  and  432  may be rotated one time outside the small top-half-turns  433   b.    
     The inner connection electrode  434  may be connected between the inner top coil  433  and the inner bottom coil  435 . For example, the inner connection electrode  434  may be connected between the small top-half-turn  433   b  and the inner bottom coil  435 . The inner connection electrode  434  may be parallel to the first input electrode  410 . 
     The inner bottom coil  435  may be connected to the first output electrode  440 . The inner bottom coil  435  may be turned one time. The inner bottom coil  435  may have a small bottom-half-turn  435   a  and a large bottom-half-turn  435   b.  The small bottom-half-turn  435   a  may be connected to the inner connection electrode  434 . The large bottom-half-turn  435   b  may connect the small bottom-half-turn  435   a  to the first output electrode  440 . The small bottom-half-turn  435   a  may have a radius smaller than a radius of the large bottom-half-turn  435   b.  For example, the large bottom-half-turn  435   b  of the first eccentric coil electrode  431  may be disposed outside the small bottom-half-turn  435   a  of the second eccentric coil electrode  432 . The small bottom-half-turn  435   a  of the first eccentric coil electrode  431  may be disposed inside the large bottom-half-turn  435   b  of the second eccentric coil electrode  432 . The small bottom-half-turns  435   a  of the first and second eccentric coil electrodes  431  and  432  may be rotated one time in an area on the central portion of the substrate W. The large bottom-half-turns  435   b  of the first and second eccentric coil electrodes  431  and  432  may be rotated one time outside the small bottom-half-turns  435   a.    
     Thus, the first and second eccentric coil electrodes  431  and  432  may induce the plasma  301  on the central portion of the substrate W by using the first radio-frequency power  311 . 
     The first output electrodes  440  may connect the large bottom-half-turns  435   b  of the first and second eccentric coil electrodes  431  and  432  to the first ring electrode  450 . For example, the first output electrodes  440  may be parallel to the first input electrode  410  and the inner connection electrode  434 . The number of the first output electrodes  440  may be equal to the number of first coil electrodes  430  (e.g., first and second eccentric coil electrodes  431  and  432 ). In some embodiments, the number of the first output electrodes  440  may be two. 
     The first ring electrode  450  may connect the first output electrodes  440  to each other. The first ring electrode  450  may connect the first output electrodes  440  to the first capacitors  352 . The first ring electrode  450  may be disposed above the first and second eccentric coil electrodes  431  and  432 . The first ring electrode  450  may have a width greater than widths of the first and second eccentric coil electrodes  431  and  432 . The first ring electrode  450  may isotropically and uniformly induce the plasma  301  on the central portion of the substrate W by using the first radio-frequency power  311 . 
     Referring again to  FIG. 4 , the second antenna  334  may surround the first antenna  332 . The second antenna  334  may be coplanar with the first antenna  332  on the window  130 . 
       FIG. 7  illustrates the second antenna  334  of  FIG. 4 .  FIG. 8  is a plan view illustrating a second input electrode  510 , second branch electrodes  520 , and second coil electrodes  530  of  FIG. 7 . 
     Referring to  FIG. 7 , the second antenna  334  may include a second input electrode  510 , second branch electrodes  520 , second coil electrodes  530 , second output electrodes  540 , and a second ring electrode  550 . 
     The second input electrode  510  may be disposed at centers of the second branch electrodes  520 , the second coil electrodes  530 , and the second ring electrode  550 . The second input electrode  510  may be disposed around the first input electrode  410  (see  FIGS. 4 and 5 ). 
     Referring to  FIGS. 7 and 8 , the second branch electrodes  520  may be connected to the second input electrode  510 . For example, the number of the second branch electrodes  520  may be four. In some embodiments, the second branch electrodes  520  may divide the second coil electrodes  530  at a rotation angle of 90 degrees. In some embodiments, respective pairs of the second branch electrodes  520  may extend from the second input electrode  510  in directions opposite to each other. 
     The second coil electrodes  530  may be connected to the second branch electrodes  520 , respectively. The second coil electrodes  530  may extend from outer ends of the second branch electrodes  520  along the second ring electrode  550 . The second coil electrodes  530  may surround the first coil electrodes  430 . In some embodiments, the number of turns of the second coil electrodes  530  may be equal to the number of the turns of the first coil electrodes  430 , though the inventive concepts are not limited thereto. For example, the second coil electrodes  530  may be turned about four times. In some embodiments, the number of turns of the second coil electrodes  530  may be different than the number of the turns of the first coil electrodes  430 . In some embodiments, the second coil electrodes  530  may include third to sixth eccentric coil electrodes  531  to  534 . 
     Each of the third to sixth eccentric coil electrodes  531  to  534  may be turned one time. In some embodiments, each of the third to sixth eccentric coil electrodes  531  to  534  may include an outer top coil  535 , an outer connection electrode  536 , and an outer bottom coil  537 . 
     The outer top coil  535  may be connected to the second branch electrode  520 . For example, the outer top coil  535  may be turned a half turn. In some embodiments, the outer top coil  535  may include a large top-quarter-turn  535   a  and a small top-quarter-turn  535   b.  The large top-quarter-turn  535   a  may be connected to the second branch electrode  520 . The small top-quarter-turn  535   b  may connect the large top-quarter-turn  535   a  to the outer connection electrode  536 . The small top-quarter-turn  535   b  may have a radius smaller than a radius of the large top-quarter-turn  535   a.  For example, the large top-quarter-turns  535   a  of the third to sixth eccentric coil electrodes  531  to  534  may be rotated one time along an imaginary circle connecting the outer ends of the second branch electrodes  520 . In other words, the large top-quarter-turns  535   a  of the third to sixth eccentric coil electrodes  531  to  534  may be rotated one time in an area on the edge portion of the substrate W. The small top-quarter-turns  535   b  of the third to sixth eccentric coil electrodes  531  to  534  may be rotated one time inside the large top-quarter-turns  535   a.    
     The outer connection electrode  536  may connect the outer top coil  535  to the outer bottom coil  537 . For example, the outer connection electrode  536  may connect the small top-quarter-turn  535   b  to the outer bottom coil  537 . The outer connection electrode  536  may be parallel to the second input electrode  510 . 
     The outer bottom coil  537  may connect the outer top coil  535  and the outer connection electrode  536  to the second output electrodes  540 . The outer bottom coil  537  may be disposed under the outer top coil  535 . For example, the outer bottom coil  537  may be turned a half turn. In some embodiments, the outer bottom coil  537  may include a small bottom-quarter-turn  537   a  and a large bottom-quarter-turn  537   b.  The small bottom-quarter-turn  537   a  may connect the outer connection electrode  536  to the large bottom-quarter-turn  537   b.  The large bottom-quarter-turn  537   b  may connect the small bottom-quarter-turn  537   a  to the second output electrode  440 . The large bottom-quarter-turn  537   b  may have a radius larger than a radius of the small bottom-quarter-turn  537   a.  The small bottom-quarter-turns  537   a  of the third to sixth eccentric coil electrodes  531  to  534  may be rotated one time in an area on the edge portion of the substrate W. The large bottom-quarter-turns  537   b  of the third to sixth eccentric coil electrodes  531  to  534  may be rotated one time outside the small bottom-quarter-turns  537   a.    
     Thus, the third to sixth eccentric coil electrodes  531  to  534  may induce the plasma  301  on the edge portion of the substrate W by using the second radio-frequency power  313 . 
     The second output electrodes  540  may connect the large bottom-quarter-turns  537   b  of the third to sixth eccentric coil electrodes  531  to  534  to the second ring electrode  550 . For example, the second output electrodes  540  may be parallel to the second input electrode  510  and the outer connection electrode  536 . The number of the second output electrodes  540  may be equal to the number of second coil electrodes  530  (e.g., third to sixth eccentric coil electrodes  531  to  534 ). In some embodiments, the number of the second output electrodes  540  may be four. 
     The second ring electrode  550  may connect the second output electrodes  540  to each other. The second ring electrode  550  may connect the second output electrodes  540  to the second capacitors  354 . The second ring electrode  550  may be disposed above the third to sixth eccentric coil electrodes  531  to  534 . The second ring electrode  550  may have a width greater than widths of the third to sixth eccentric coil electrodes  531  to  534 . The second ring electrode  550  may isotropically and uniformly induce the plasma  301  on the edge portion of the substrate W by using the second radio-frequency power  313 . 
     Referring again to  FIG. 2 , the first and second inductors  342  and  344  may connect the first and second antennas  332  and  334  to the first and second matchers  322  and  324 , respectively. The first and second inductors  342  and  344  may be adjacent to each other and may be coupled to each other. The first and second inductors  342  and  344  may have a second mutual inductance M 2 . In some embodiments, the second mutual inductance M 2  may cancel the first mutual inductance M 1  between the first and second antennas  332  and  334 . In some embodiments, the second mutual inductance M 2  may partially or fully offset the first mutual inductance M 1 . For example, the second mutual inductance M 2  may have substantially the same absolute value as the first mutual inductance M 1 . When the second mutual inductance M 2  has a negative value, the first mutual inductance M 1  may have a positive value. Alternatively, when the second mutual inductance M 2  has a positive value, the first mutual inductance M 1  may have a negative value. The first mutual inductance M 1  may cause interference between the first and second radio-frequency powers  311  and  313 . When the first mutual inductance M 1  is reduced and/or canceled by the second mutual inductance M 2 , the interference between the first and second radio-frequency powers  311  and  313  may be removed and/or reduced. Thus, the first and second matchers  322  and  324  may stably match the impedances of the first and second radio-frequency powers  311  and  313 . 
     In some embodiments, coiled directions and/or a coupled direction of the first and second inductors  342  and  344  may be different from coiled directions and/or a coupled direction of the first and second antennas  332  and  334 . The coiled directions of the first and second inductors  342  and  344  may be indicated by the dots of  FIGS. 1 and 2 . For example, the first and second inductors  342  and  344  may be coiled and/or wound in directions different from each other. In some embodiments, the number of turns of the first inductor  342  may be equal to the number of turns of the second inductor  344 . The numbers of the turns of the first and second inductors  342  and  344  may be equal to the numbers of the turns of the first and second antennas  332  and  334 . For example, the number of the turns of each of the first and second inductors  342  and  344  may be four. 
       FIG. 9  is a graph illustrating a coupling efficiency according to a distance between the first and second inductors  342  and  344  of  FIG. 2 . 
     Referring to  FIG. 9 , a coupling efficiency between the first and second inductors  342  and  344  may be changed when a distance between the first and second inductors  342  and  344  is changed. For example, when the distance between the first and second inductors  342  and  344  is zero (0), the first and second inductors  342  and  344  may have a coupling efficiency of about 0.05%. When the distance between the first and second inductors  342  and  344  is −7 mm or −14 mm in a certain direction (e.g., an x-direction), the first and second inductors  342  and  344  may have a coupling efficiency of about 6% or about 10%. When the distance between the first and second inductors  342  and  344  is 7 mm or 14 mm in a certain direction (e.g., the x-direction), the first and second inductors  342  and  344  may have a coupling efficiency of about 33% or about 52%. 
     Referring again to  FIG. 2 , the first capacitor  352  may be connected between the first antenna  332  and ground, and the second capacitor  354  may be connected between the second antenna  334  and ground. The first and second capacitors  352  and  354  may adjust the impedances of the first and second radio-frequency powers  311  and  313  of the first and second antennas  332  and  334 . In some embodiments, the first and second capacitors  352  and  354  may remove noise of the first and second radio-frequency powers  311  and  313 . For example, each of the first and second capacitors  352  and  354  may have a capacitance of about 50 pF to about 2000 pF. In some embodiments, the first and second capacitors  352  and  354  may control the ignition of the plasma  301 . 
       FIG. 10  is a graph illustrating an output current  311   a  according to the first radio-frequency power  311  of  FIG. 2  and an output current  313   a  according to the second radio-frequency power  313  of  FIG. 2 . 
     Referring to  FIG. 10 , an output current  313   a  of the second radio-frequency power  313  may be substantially constant even though the first radio-frequency power  311  increases. For example, an output current  311   a  of the first radio-frequency power  311  may increase from about 17 A to about 50 A as the first radio-frequency power  311  gradually increases from about 100 W to about 800 W. However, the output current  313   a  of the second radio-frequency power  313  may be substantially constant in a range of about 27 A to about 30 A even though the first radio-frequency power  311  gradually increases from about 100 W to about 800 W. As used herein, substantially constant with respect to the output current  313   a  means that the output current  313   a  may vary within a range of 10 percent or less. The second radio-frequency power  313  may not interfere with the first radio-frequency power  311 . In other words, since the first mutual inductance M 1  of the first and second antennas  332  and  334  is reduced and/or canceled by the second mutual inductance M 2  of the first and second inductors  342  and  344 , the second radio-frequency power  313  may be controlled independently of the first radio-frequency power  311 . 
       FIG. 11  is a graph illustrating a variation of an etch rate according to a position on the substrate W of  FIG. 1 . 
     Referring to  FIGS. 1, 2, and 11 , an etch rate of an edge of the substrate W may be adjusted according to the second radio-frequency power  313 . The etch rate of the edge of the substrate W may be normalized by an etch rate of a center of the substrate W. The first radio-frequency power  311  may be about 600 W. In some embodiments, the first radio-frequency power  311  may be lower than about 600 W. In a case  370  in which the second radio-frequency power  313  is 300 W, the etch rate of the edge of the substrate W may be about 70% of the etch rate of the center of the substrate W. In a case  380  in which the second radio-frequency power  313  is 600 W, the etch rate of the edge of the substrate W may be substantially equal to the etch rate of the center of the substrate W. As used herein, substantially equal with respect to the etch rate means that the etch rate may vary within a range of 5 percent or less. In other words, the second radio-frequency power  313  may be adjusted in such a way that the etch rate of the edge of the substrate W is substantially equal to the etch rate of the center of the substrate W. In a case  390  in which the second radio-frequency power  313  is 900 W, the etch rate of the edge of the substrate W may be about 110% of the etch rate of the center of the substrate W. 
       FIG. 12  is a circuit diagram illustrating an example of a plasma generating circuit  300  of  FIG. 1 . 
     Referring to  FIG. 12 , a plasma generating circuit  300  may further include a third radio-frequency power source  316 , a third matcher  326 , a third antenna  336 , a third inductor  346 , and a third capacitor  356 . First and second radio-frequency power sources  312  and  314 , first and second matchers  322  and  324 , first and second antennas  332  and  334 , first and second inductors  342  and  344 , and first and second capacitors  352  and  354  may be the same as described with reference to  FIG. 2 . 
     The third radio-frequency power source  316  may generate a third radio-frequency power  315 . 
     The third matcher  326  may be connected to the third radio-frequency power source  316 . The third matcher  326  may match impedance of the third radio-frequency power  315 . 
     The third antenna  336  may generate plasma  301  by using the third radio-frequency power  315 . The third antenna  336  may be coupled to the first and second antennas  332  and  334 . For example, the third antenna  336  may be disposed between the first and second antennas  332  and  334 . Alternatively, the third antenna  336  may be disposed inside the first antenna  332 . In certain embodiments, the third antenna  336  may be disposed outside the second antenna  334 . The first to third antennas  332 ,  334 , and  336  may have a first mutual inductance M 1 , a third mutual inductance M 3 , or a fourth mutual inductance M 4 . For example, the first and third antennas  332  and  336  may have the third mutual inductance M 3 . The second and third antennas  334  and  336  may have the fourth mutual inductance M 4 . 
     The third inductor  346  may connect the third antenna  336  to the third matcher  326 . The third inductor  346  may be turned and/or wound in the same direction as the first inductor  342  or the second inductor  344 . For example, the third inductor  346  may be turned and/or wound in the same direction as the first inductor  342 . The first and third inductors  342  and  346  may have a fifth mutual inductance M 5 . The fifth mutual inductance M 5  may reduce and/or cancel the third mutual inductance M 3 . The second and third inductors  344  and  346  may have a sixth mutual inductance M 6 . The sixth mutual inductance M 6  may reduce and/or cancel the fourth mutual inductance M 4 . 
       FIGS. 13 to 16  illustrate examples of arrangements of the first to third inductors  342 ,  344 , and  346  of  FIG. 11 . 
     Referring to  FIG. 13 , the first to third inductors  342 ,  344 , and  346  may be arranged in a triangular shape. For example, the first to third inductors  342 ,  344 , and  346  may be disposed at positions corresponding to sides of a regular triangle, respectively. 
     Referring to  FIG. 14 , the first to third inductors  342 ,  344 , and  346  may be arranged in branch shapes. A divergence angle between respective ones of the first to third inductors  342 ,  344 , and  346  may be about 120 degrees. 
     Referring to  FIG. 15 , the first to third inductors  342 ,  344 , and  346  may be arranged substantially in parallel to each other. In some embodiments, the first to third inductors  342 ,  344 , and  346  may have the same length. Distances between the first to third inductors  342 ,  344 , and  346  may be adjusted. 
     Referring to  FIG. 16 , the third inductor  346  may be longer than the first and second inductors  342  and  344 . When the first and second inductors  342  and  344  are arranged in a line, the third inductor  346  may be disposed side by side with the first and second inductors  342  and  344 . 
     Referring again to  FIG. 12 , the third capacitor  356  may connect the third inductor  346  to ground. In some embodiments, the third capacitor  356  may connect the third inductor  346  to the third radio-frequency power source  316 . In some embodiments, the third capacitor  356  may adjust the impedance of the third radio-frequency power  315 . In some embodiments, the third capacitor  356  may remove noise of the third radio-frequency power  315 . The third capacitor  356  may have a capacitance of about 50 pF to about 2000 pF. In some embodiments, the third capacitor  356  may control the ignition of the plasma  301 . 
       FIG. 17  is a flow chart illustrating methods for manufacturing semiconductor devices using the plasma processing apparatus of  FIG. 1 . 
     Referring to  FIGS. 1, 2, and 17 , a method for manufacturing a semiconductor device may include providing a substrate W (S 10 ) and generating plasma  301  (S 20 ). 
     A robot arm (not shown) may provide the substrate W on the electrostatic chuck  140  in the chamber  100  (S 10 ). The substrate W may be provided on the electrostatic chuck  140  after the lower housing  110  and the window  130  are separated from each other. Thereafter, the window  130  and the upper housing  120  may be provided on the lower housing  110 . 
     Next, the plasma generating circuit  300  may generate the plasma  301  on the substrate W (S 20 ). The plasma  301  may be used in an etching process or a thin film deposition process of the substrate W. In some embodiments, generating the plasma  301  (S 20 ) may include supplying first and second radio-frequency powers  311  and  313  (S 22 ) and supplying the second radio-frequency power  313  (S 24 ). 
     The first and second radio-frequency power sources  312  and  314  may provide the first and second radio-frequency powers  311  and  313  to the first and second antennas  332  and  334  (S 22 ). The first and second radio-frequency powers  311  and  313  may control etch rates or thin film deposition rates of the central portion and the edge portion of the substrate W with little and/or no interference caused by the first mutual inductance M 1  of the first and second antennas  332  and  334 . The first mutual inductance M 1  may be reduced and/or canceled by the second mutual inductance M 2  of the first and second inductors  342  and  344 . For example, the first radio-frequency power  311  may be proportional to the etch rate of the central portion of the substrate W. The second radio-frequency power  313  may be proportional to the etch rate of the edge portion of the substrate W. Thus, the etching process and/or the thin film deposition process may be stably performed by controlling the first and second radio-frequency powers  311  and  313 . 
     The second radio-frequency power source  314  may supply the second radio-frequency power  313  (S 24 ). The second radio-frequency power  313  may generate plasma  301  on the edge portion of the substrate W. The generated plasma  301  may treat the edge portion and/or a bevel of the substrate W. Polymers may be formed on the edge portion and/or the bevel of the substrate W in the etching process and/or the thin film deposition process. For example, the plasma  301  may etch the polymers on the edge portion and/or the bevel of the substrate W. 
       FIG. 18  illustrates a plasma processing apparatus  10   a  according to some embodiments of the inventive concepts.  FIG. 19  is a circuit diagram illustrating an example of a plasma generating circuit  300  of  FIG. 18 . 
     Referring to  FIGS. 18 and 19 , the plasma processing apparatus  10   a  according to the inventive concepts may include first and second current measuring instruments  410  and  420 . A chamber  100 , a gas supply part  200 , and a plasma generating circuit  300  of the plasma processing apparatus  10   a  may be substantially the same as described with reference to  FIG. 1 . 
     The first and second current measuring instruments  410  and  420  may be disposed between the first and second antennas  332  and  334  and the first and second inductors  342  and  344 , respectively. The first current measuring instrument  410  may measure a first current of the first radio-frequency power  311  in the first antenna  332 . The second current measuring instrument  420  may measure a second current of the second radio-frequency power  313  in the second antenna  334 . 
     A controller (not shown) may calculate a current ratio of the first and second currents and a current phase difference at the current ratio. For example, when the current ratio is a standard value and/or the minimum value, the first and second radio-frequency powers  311  and  313  may etch the substrate W without a difference in etch rate between the central portion and the edge portion of the substrate W. A method of eliminating the etch rate difference will be described in more detail through the following method for manufacturing a semiconductor device. 
       FIG. 20  illustrates a method (S 100 ) for manufacturing a semiconductor device using the plasma processing apparatus  10   a  according to some embodiments of the inventive concepts. The method for manufacturing a semiconductor device according to the inventive concepts may include an etching method and a deposition method. 
     Referring to  FIGS. 19 and 20 , the method (S 100 ) for manufacturing a semiconductor device according to the inventive concepts may include providing a gas (S 110 ), providing first and second radio-frequency powers  311  and  313  (S 120 ), sweeping a current phase difference of the first and second radio-frequency powers (S 130 ), measuring first and second currents (S 140 ), determining whether a standard value exists among current ratios (S 150 ), calculating a first current phase difference (S 160 ), etching a substrate W (S 170 ), obtaining an etch rate uniformity (S 180 ), determining whether the etch rate uniformity is a threshold value or more (S 190 ), and sampling a second current phase difference (S 200 ). 
     First, the gas supply part  200  provides the gas into the chamber  100  (S 110 ). Before the gas is provided, the substrate W may be provided onto the electrostatic chuck  140  in the chamber  100 . The substrate W may include, for example, poly-silicon or a silicon oxide layer. The gas may include at least one of, for example, a nitrogen (N 2 ) gas, a hydrogen (H 2 ) gas, an oxygen (O 2 ) gas, a hydrofluoric acid (HF) gas, a chlorine (Cl 2 ) gas, a sulfur hexafluoride (SF 6 ) gas, a methylene (CH 3 ) gas, or a carbon tetrafluoride (CF 4 ) gas. 
     Next, the first and second radio-frequency power sources  312  and  314  provide the first and second radio-frequency powers  311  and  313  into the first and second antennas  332  and  334  (S 120 ). The first and second radio-frequency powers  311  and  313  may have the same intensity, the same energy, and/or the same frequency. For example, each of the first and second radio-frequency powers  311  and  313  may have the energy of about 100 W to about 100 KW and the frequency of about 100 KHz to about 100 MHz. When the first and second radio-frequency powers  311  and  313  have the first and second currents of which frequencies are equal to each other and/or of which periods are equal to each other, phases of the first and second currents may be equal to each other. Alternatively, when the first and second radio-frequency powers  311  and  313  have the first and second currents of which frequencies are equal to each other and/or of which periods are equal to each other, the phases of the first and second currents may be different from each other. The first and second radio-frequency powers  311  and  313  having the first and second currents of which the phases are different from each other will be described hereinafter. 
       FIG. 21  illustrates a current phase difference ΔΦ of the first and second radio-frequency powers  311  and  313 . 
     Referring to  FIGS. 18 to 21 , the first and second radio-frequency power sources  312  and  314  sweep a current phase difference ΔΦ of the first and second radio-frequency powers  311  and  313  (S 130 ). The current phase difference ΔΦ may be swept in a range from 0 degree to 360 degrees (2π). The first radio-frequency power  311  may have a first current phase  311   a,  and the second radio-frequency power  313  may have a second current phase  313   a.  In addition, the first and second radio-frequency powers  311  and  313  may have the current phase difference ΔΦ. In some embodiments, the current phase difference ΔΦ may be defined as an angle difference between a positive peak of the first current phase  311   a  and a positive peak of the second current phase  313   a.  Alternatively, the current phase difference ΔΦ may be defined as an angle difference between a node of the first current phase  311   a  and a node of the second current phase  313   a.    
       FIG. 22  illustrates an intensity |Htotal|2 of an electromagnetic field according to a position on the substrate W of  FIG. 18 . 
     Referring to  FIG. 22 , an intensity |H total | 2  of a total electromagnetic field of the substrate W may be calculated as a sum of an intensity ((H in ) 2 ) of a center electromagnetic field of the substrate W, an intensity (2H in H out  cos(ΔΦ)) of a mid-zone electromagnetic field of the substrate W, and an intensity ((H out ) 2 ) of an edge electromagnetic field of the substrate W (|H total | 2 =(H in ) 2  +2H in H out  cos(ΔΦ)+(H out ) 2 ). The intensity |H total | 2  of the total electromagnetic field may be calculated as the square of the absolute value of the total electromagnetic field (H total ) of the substrate W, and the intensity ((H in ) 2 ) of the center electromagnetic field may be calculated as the square of the center electromagnetic field (H in ). The intensity ((H out ) 2 ) of the edge electromagnetic field may be calculated as the square of the edge electromagnetic field (H out ), and the intensity (2H in H out  cos(ΔΦ)) of the mid-electromagnetic field may be calculated as the product of a constant (e.g., 2), the center electromagnetic field (H in ), the edge electromagnetic field (H out ) and a cosine value of the current phase difference ΔΦ. 
     If the intensity ((H in ) 2 ) of the center electromagnetic field is equal to the intensity ((H out ) 2 ) of the edge electric field, an increase rate (or an decrease rate) of the intensity (2H in H out  cos(ΔΦ)) of the mid-zone electromagnetic field may be twice an increase rate (or an decrease rate) of the intensity ((H in ) 2 ) of the center electromagnetic field or the intensity ((H out ) 2 ) of the edge electromagnetic field on the basis of the current phase difference ΔΦ. In addition, the intensity (2H in H out  cos(ΔΦ)) of the mid-zone electromagnetic field may be changed more rapidly than the intensity ((H in ) 2 ) of the center electromagnetic field or the intensity ((H out ) 2 ) of the edge electromagnetic field on the basis of the current phase difference ΔΦ. In some embodiments, when the current phase difference ΔΦ is properly adjusted, the intensity (2H in H out  cos(ΔΦ)) of the mid-zone electromagnetic field may be equal to the intensity (H in ) 2 ) of the center electromagnetic field of the substrate W or the intensity ((H out ) 2 ) of the edge electromagnetic field of the substrate W. The intensity |H total | 2  of the total electromagnetic field of the substrate W may be substantially uniform. When the intensity |H total | 2  of the total electromagnetic field of the substrate W is substantially uniform, an etch rate difference according to a position on the substrate W may be eliminated. When the substrate W has a radius of about 15 cm, the mid-zone of the substrate W may correspond to a zone between about 5 cm from a center of the substrate W and about 10 cm from the center of the substrate W in a radial direction of the substrate W. 
       FIG. 23  illustrates a center etch rate  510  and an edge etch rate  520  of the substrate W according to the current phase difference ΔΦ of  FIG. 22 . 
     Referring to  FIG. 23 , when the current phase difference ΔΦ ranges from about 100 degrees to about 170 degrees, the center etch rate  510  of the substrate W may be approximately equal to the edge etch rate  520  of the substrate W. Even though not shown in the drawings, when the center etch rate  510  is equal to the edge etch rate  520 , a mid-zone etch rate of the substrate W may be approximately equal to the center etch rate  510  or the edge etch rate  520 . The mid-zone etch rate of the substrate W may correspond to an etch rate on the mid-zone between the center and the edge of the substrate W. 
       FIG. 24  illustrates first and second currents  530  and  540  in the first and second antennas  332  and  334  according to the current phase difference ΔΦ of  FIG. 22  and a current ratio  550  of the first and second currents  530  and  540 . 
     Referring to  FIGS. 20 and 24 , the first and second current measuring instruments  410  and  420  measure the first and second currents  530  and  540 , respectively (S 140 ), and the controller (not shown) calculates the current ratio  550 . Each of the first and second currents  530  and  540  may be changed in a range of about  20 A to about  40 A. The current ratio  550  may be defined as a value obtained by dividing the first current  530  by the second current  540 . 
     Next, the controller determines whether the standard value and/or the minimum value exist among the current ratios  550  (S 150 ). When the current phase difference ΔΦ ranges from about 100 degrees to about 170 degrees, the current ratio  550  may be about 0.8. 0.8 may be the standard value. Alternatively, the current ratio  550  may be the minimum value. In other words, when the current ratio  550  is the standard value and/or the minimum value, the current phase difference ΔΦ may range from about 100 degrees to about 170 degrees to reduce or eliminate the etch rate difference of  FIG. 6 . 
     When the standard value and/or the minimum value does not exist among the current ratios  550  (or in the graph of the current ratio  550 ), the step S 130  of sweeping the current phase difference of the first and second radio-frequency powers  311  and  313 , the step S 140  of measuring the first and second currents  530  and  540  and the step S 150  of determining whether the standard value exists among the current ratios  550  may be performed again. 
     When the standard value and/or the minimum value exists among the current ratios  550  (or in the graph of the current ratio  550 ), the controller calculates the first current phase difference of the first and second currents  530  and  540  at the current ratio  550  corresponding to the standard value (S 160 ). The first current phase difference calculated by the controller may range from about 100 degrees to about 170 degrees. The first and second radio-frequency powers  311  and  313  of the first current phase difference may reduce or eliminate the etch rate difference of the substrate W. 
     Thereafter, the first and second antennas  332  and  334  may etch the substrate W by using the first and second radio-frequency powers  311  and  313  of the first current phase difference calculated (S 170 ). Thus, the first and second radio-frequency powers  311  and  313  having the first current phase difference of the standard value may reduce or eliminate the etch rate difference according to a position on the substrate W. 
     Subsequently, a measuring apparatus (not shown) may measure an etch rate according to a position on the substrate W, and the controller may obtain the etch rate uniformity of the substrate W (S 180 ). The etch rate uniformity may be obtained as a shape or a percent according to a position on the substrate W. 
       FIG. 25  illustrates an M-shaped etch rate uniformity  560  and a flat etch rate uniformity  570  of the substrate W. 
     Referring to  FIGS. 19, 20, and 25 , the first and second radio-frequency powers  311  and  313  controlled to the first current phase difference may etch the substrate W at the substantially flat etch rate uniformity  570  in a diameter direction of the substrate W. The first and second radio-frequency powers  311  and  313  not controlled to the first current phase difference may etch the substrate W at the M-shaped etch rate uniformity  560  in the diameter direction. 
     Next, the controller determines whether the etch rate uniformity is the threshold value or more (S 190 ). The threshold value may be about 99.5%. When the etch rate uniformity is the threshold value or more, a method of adjusting the etch rate uniformity may be finished. Thereafter, the plasma processing apparatus  10   a  may etch the substrate W using the first and second radio-frequency powers  311  and  313  having the first current phase difference without the etch rate difference. The substrate W may include a plurality of substrates to be etched. 
     When the etch rate uniformity is less than the threshold value, the controller may simple a second current phase difference different from the first current phase difference (S 200 ). The second current phase difference may be selected from approximate values of the first current phase difference. For example, the second current phase difference may be selected in the range of about 100 degrees to about 170 degrees. Alternatively, the second current phase difference may be selected in a range of about 0 degree to about 360 degrees. 
     Thereafter, the first and second antennas  332  and  334  may etch the substrate W by using the first and second radio-frequency powers  311  and  313  having the second current phase difference (S 170 ). The step S 170  of etching the substrate W, the step S 180  of obtaining the etch rate uniformity, the step S 190  of determining whether the etch rate uniformity is the threshold value or more and the step S 200  of sampling the second current phase difference may be repeatedly performed until the etch rate uniformity is the threshold value or more. As a result, the method S 100  for manufacturing a semiconductor device according to the inventive concepts can reduce or eliminate the etch rate difference of the substrate W. 
     The plasma generating circuit according to some embodiments of the inventive concepts may include the inductors having the second mutual inductance reducing and/or canceling the first mutual inductance of the antennas. The matchers may stably match the impedances of the first and second radio-frequency powers with little and/or no interference of the first and second radio-frequency powers caused by the first mutual inductance between the antennas. Thus, the antennas may uniformly induce the plasma. 
     It will be understood that although the terms “first,” “second,” etc. are used herein to describe members, regions, layers, portions, sections, components, and/or elements in example embodiments of the inventive concepts, the members, regions, layers, portions, sections, components, and/or elements should not be limited by these terms. These terms are only used to distinguish one member, region, portion, section, component, or element from another member, region, portion, section, component, or element. Thus, a first member, region, portion, section, component, or element described below may also be referred to as a second member, region, portion, section, component, or element without departing from the scope of the inventive concepts. For example, a first element may also be referred to as a second element, and similarly, a second element may also be referred to as a first element, without departing from the scope of the inventive concepts. 
     Spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “upper” and the like, may be used herein for ease of description to describe the relationship of one element or feature to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including,” if used herein, specify the presence of stated features, integers, steps, operations, elements and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and/or groups thereof. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those of ordinary skill in the art to which the inventive concepts pertain. It will also be understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     When a certain example embodiment may be implemented differently, a specific process order may be performed differently from the described order. For example, two consecutively described processes may be performed substantially at the same time or performed in an order opposite to the described order. 
     In the accompanying drawings, variations from the illustrated shapes as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, the example embodiments of the inventive concepts should not be construed as being limited to the particular shapes of regions illustrated herein but may be construed to include deviations in shapes that result, for example, from a manufacturing process. Thus, the regions illustrated in the figures are schematic in nature, and the shapes of the regions illustrated in the figures are intended to illustrate particular shapes of regions of devices and not intended to limit the scope of the inventive concepts. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. Expressions such as “at least one of,” when preceding a list of elements, modify the entire list of elements and do not modify the individual elements of the list. 
     It will be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present. As used herein the term “and/or” includes any and all combinations of one or more of the associated listed items. Other words used to describe the relationship between elements or layers should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” “on” versus “directly on”). 
     Like numbers refer to like elements throughout. Thus, the same or similar numbers may be described with reference to other drawings even if they are neither mentioned nor described in the corresponding drawing. Also, elements that are not denoted by reference numbers may be described with reference to other drawings. 
     While the inventive concepts have been described with reference to example embodiments, it will be apparent to those skilled in the art that various changes and modifications may be made without departing from the spirits and scopes of the inventive concepts. Therefore, it should be understood that the above embodiments are not limiting, but illustrative. Thus, the scopes of the inventive concepts are to be determined by the broadest permissible interpretation of the following claims and their equivalents, and shall not be restricted or limited by the foregoing description.