Abstract:
A method and system for measuring at least one of a plasma density and an electron density (e.g., in a range of 10 10  to 10 12  electrons/cm −3 ) using plasma induced changes in the frequency of a microwave oscillator. Measurement of at least one of the plasma density and the electron density enables plasma-assisted processes, such as depositions or etches, to be controlled using a feedback control. Both the measurement method and system generate a control voltage that in turn controls a plasma generator to maintain at least one of the plasma density and the electron density at a pre-selected value.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is related to provisional applications Ser. No. 60/144,880 filed on Jul. 20, 1999 entitled “ELECTRON DENSITY MEASUREMENT AND PLASMA PROCESS CONTROL SYSTEM USING A MICROWAVE OSCILLATOR LOCKED TO AN OPEN RESONATOR CONTAINING THE PLASMA,” and Ser. No. 60/144,833, filed on Jul. 21, 1999, “ELECTRON DENSITY MEASUREMENT AND PLASMA PROCESS CONTROL SYSTEM USING CHANGES IN TE RESONANT FREQUENCY OF AN OPEN RESONATOR CONTAINING THE PLASMA”. Both of those applications are herein incorporated by reference in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the invention 
     The present invention provides a method and system for measuring electron densities in a plasma processing system, such as is used in semiconductor processing systems. 
     2. Description of the Background 
     There are at least three known microwave-based techniques for determining plasma electron densities: (1) microwave interferometry, (2) measurement of reflection and absorption, and (3) perturbation of cavity resonant frequencies. Each of the concepts is described in simplified terms below. 
     Microwave interferometry involves the determination of the phase difference between two microwave beams. The first bears provides a reference signal, and the second beam passes through a reactive environment and undergoes a phase shift relative to the first beam. The index of refraction is calculated from the measured change in the phase difference between the two beams. This interferometric technique has been documented by Professor L. Goldstein of the University of Illinois at Urbana. Interferometry is described in the following U.S. Pat. Nos. 2,971,153; 3,265,967; 3,388,327; 3,416,077; 3,439,266; 3,474,336; 3,490,037; 3,509,452; and 3,956,695, each of which is incorporated herein by reference. Some plasma properties may be indirectly determined from measurements of the absorption of a microwave beam as it traverses a region in which a plasma is present. Signal reflections in plasmas are described in U.S. Pat. No. 3,599,089 and 3,383,509. 
     Plasma electron densities have also been measured using a technique which measures the perturbations of cavity resonant frequencies. The presence of a plasma within a resonator affects the frequency of each resonant mode because the plasma has an effective dielectric constant that depends on plasma electron density. This technique has been documented by Professor S. C. Brown of the Massachusetts Institute of Technology. Portions of this technique are described in U.S. Pat. No. 3,952,246 and in the following non-patent articles: Haverlag, M., et al., J Appl Phys 70 (7) 3472-80 (1991): Measurements of negative ion densities in 13.56 MHZ RF plasma of CF 4 , C 2 F 6 , CHF 3 , and C 3 F 8  using microwave resonance and the photodetachment effect and Haverlag, M., et al., Materials Science Forum, vol. 140-142, 235-54 (1993): Negatively charged particles in fluorocarbon RF etch plasma: Density measurements using microwave resonance and the photodetachment effect. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a more accurate plasma measuring system than the prior art. 
     It is a further object of the present invention to provide an improved plasma measuring system using plasma induced changes in the frequency of a microwave oscillator. 
     These and other objects of the present invention are achieved through the use of a feedback loop that measures and controls a signal passing through a plasma chamber. Using a computer or digital signal processor (DSP), the present invention measures a frequency of a signal passing through the plasma and compares the measured frequency to a desired frequency. Based on a difference between the measured and desired frequencies, the computer/DSP controls the plasma generator to increase or decrease power to the plasma chamber, thereby affecting plasma electron density. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete appreciation of the invention and many of the attendant advantages thereof will become readily apparent with reference to the following detailed description, particularly when considered in conjunction with the accompanying draings, in which: 
     FIG. 1A is a block diagram of a plasma electron density measurement system according to the present invention; 
     FIG. 1B is a block diagram of a plasma electron density measurement system according to the present invention using multiple receivers; 
     FIG. 2 is a schematic illustration of a computer system for implementing a portion of the measurement system of FIG. 1A; and 
     FIG. 3 is a graph showing system response vresus frequency. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to the drawings, in which like reference numerals designate identical or corresponding parts throughout the several views, FIG. 1A is a block diagram of a plasma electron density measurement system according to the present invention for measuring a plasma generated in a plasma chamber  200 . One embodiment of the present invention uses a plasma generator  205  and a self-excited microwave oscillator  210  that comprises, in a closed loop, an oscillation circuit  201   a  (including an attenuator  213   a , a narrow-band microwave amplifier  215 , an isolator  220 , a phase shifter  225 , and a directional coupler  230 ) and the plasma chamber  200  including an open radiation path that further includes at least one transmitter antenna  235 , at least one receiver antenna  240 , and may include one or more reflectors.  245 . The transmitter antennas  235  and receiver antennas  240  may be horns, dielectric lenses, or other forms of radiators; and the reflectors  245  may have planar or curved surfaces or may be diffraction gratings. 
     As shown in the embodiment in FIG. 1A, the transmitter  235 , the reflectors  245 , and the receiver  240  may be oriented in such a way that the open radiation path lies essentially in a plane that is parallel to the surface of a wafer being processed in the plasma chamber  200 . However, alternate embodiments include other configurations for which the plane of the open radiation path is not parallel to the surface of a wafer being processed, or for which the open radiation path does not even lie in a plane. Moreover, alternate embodiments also include using plural microwave beam paths, either of the same length or of different lengths, in a variety of configurations (see, for example, FIG. 1B utilizing plural receivers  235  and their corresponding oscillator circuits  201   b  and  201   c ). Examples of configurations include, but are not limited to, star- and triangular-shapes. Likewise, when using multiple systems whose microwave beams intersect at several locations within the interior of the plasma, it may be possible to extract spatial information (similar to tomography) rather than the plasma electron density integrated along a beam length. 
     If the gain of the amplifier is sufficiently high, self excited oscillators at distinct frequencies will occur. These frequencies satisfy two criteria: 
     1. The net round-trip gain, which is a product of the numerical power gain of the amplifier, G, the transmission coefficients of all junctions, and the reflection coefficients of all mirrors, must exceed 1.                G   ·     {       ∑     i   =   1     n            T   i     ·       ∑     j   =   1     m          R   j           }       ≥   1           (   1   )                                
     where it is assumed that there are “n” junctions whose transmission coefficients are less than 1 and the path includes “m” reflectors whose reflection coefficients are less than 1. While this is a necessary condition for oscillation, it is not sufficient; sufficiency is provided by the second criterion. 
     2. The round-trip shift of the electromagnetic waves in the loop due to all causes must add to an integer multiple of 2π radians. This insures the build-up of coherent oscillation from noise. The phase shifts associated with the majority of the passive junctions and mirrors in the loop are virtually independent of frequency and thus do not play an important role in the measurement method described herein, as described below. The phase shifts of the electromagnetic waves traversing the round-thp are predominantly due to three sources: the propagation in the region in which the plasma is formed; the propagation in the waveguides and components in the waveguides; and the propagation (and amplification) by the amplifier. Thus the sufficiency condition can be written as:                  [         ∑     i   =   1     n          φ   i       +       ∑     j   =   1     m          φ   j         ]     +       φ   amp          (     ω   ′     )       +       β        (     ω   ′     )            d   ckt       +         ω   ′     c            ∫   0     d   p                n   p          (       ω   ′     ,   z     )               z             =       q   ·   2        π             (   2   )                                
     where the first bracket represents the phase shifts from any junctions (i) or mirrors (m); φ amp (ω′) is the phase shift of the amplifier; β(ω′)d ckt  is the phase shift of the wave propagating through the connecting waveguides, attenuators, phase shifters and other passive components comprising the circuit; and the last term on the left-hand-side of the equation is the phase shift of the wave traversing the region containing the plasma. The term n p (ω′,Z) is the index of refraction of the plasma, ω′ is the radian frequency of the wave in the presence of a plasma filling the arm from Z=0 to Z=d p , and the electromagnetic length is assumed to be d p  inside the processing chamber and d ckt  for the rest of the connecting circuit. It is also assumed that the unguided waves in the plasma region can be approximated by uniform plane waves with a phase constant given by ω′n/c. 
     A graphical display of the consequences of (1) and (2) (plotted as a function of ω) is shown in FIG. 3 in which G 0 (ω) is the small signal gain of the amplifier and S is the fraction of the electromagnetic power that survives a round-trip and is an abbreviation for the brace in (1); and the bracket and phase shift of the amplifier in (2) is ignored for graphical clarity; and β(ω) is approximated by ω/c, the phase constant for a uniform plane wave. The left-hand side of (2) becomes a straight line with a slope vs. radian frequency of [d ckt +n p d p ]/c if the frequency dependence of the plasma refractive index is ignored for the purpose of the figure. It is noted that the requirement of (1) merely restricts oscillation to be a fraction of the amplifier bandwidth in which G 0 ≧1, and that fraction can be decreased by adding attenuation in the feedback loop, decreasing the value of S and increasing the value of 1/S. 
     The intersection of the straight line representing (2) with the dashed horizontal lines separated vertically by 2π are the radian frequencies that satisfy (2) and if they also satisfy (1) become the frequencies of oscillation. Those that do so are shown as a solid arrow pointing up. Each amplitude is proportional to the excess gain (i.e., G 0 (ω)S−1) at the frequency. If the free spectral range (i.e., the separation between adjacent solutions to (2)), is small compared to the bandwidth of possible oscillation, then oscillation at multiple frequencies is possible and/or probable. 
     Returning to the description of FIG. 1A, FIG. 1A also shows a frequency meter  250   a  connected between the output of the directional coupler  230  and one input of a mixer  255 . A frequency stable local oscillator  260  is connected through an attenuator  213   b  to the second input of the mixer  255 . The frequency of the frequency stable local oscillator  260  is chosen to be either slightly below or slightly above the pass-band of the narrow-band amplifier  215 . (The attenuator  213   b  is also connected to a second frequency meter  250   b  which verifies the frequency of the stable local oscillator  260 .) To simplify subsequent discussions, it is assumed that the frequency of the frequency stable local oscillator  260  is set slightly below the pass-band of the narrow-band amplifier  215 . The frequency of the IF signal that emerges from the mixer  255  is the difference between the frequency of the frequency stable local oscillator  260  and the frequency of the self-excited oscillator  210 . The frequency of the IF signal is typically in the range from 0 to approximately 2 GHz, according to the described embodiment. Other frequency ranges are, of course, possible for other amplifier parameters. 
     FIG. 2 is a schematic illustration of a computer system  100  for measuring and controlling the plasma generated in the plasma chamber  200  by the plasma generator  205 . A computer  100  implements the method of the present invention, wherein the computer housing  102  houses a motherboard  104  which contains a CPU  106 , memory  108  (e.g., DRAM, ROM, EPROM, EEPROM, SRAM and Flash RAM), and other optional special purpose logic devices (e.g., ASICs) or configurable logic devices (e.g., GAL and reprogrammable FPGA). The computer  100  also includes plural input devices, (e.g., a keyboard  122  and mouse  124 ), and a display card  110  for controlling monitor  120 . In addition, the computer system  100  further includes a floppy disk drive  114 ; other removable media devices (e.g., compact disc  119 , tape, and removable magneto-optical media (not shown)); and a hard disk  112 , or other fixed, high density media drives, connected using an appropriate device bus (e.g., a SCSI bus, an Enhanced IDE bus, or an Ultra DMA bus). Also connected to the same device bus or another device bus, the computer  100  may additionally include a compact disc reader  118 , a compact disc reader/writer unit (not shown) or a compact disc jukebox (not shown). Although compact disc  119  is shown in a CD caddy, the compact disc  119  can be inserted directly into CD-ROM drives which do not require caddies. In addition, a printer (not shown) also provides printed listings of plasma electron densities for different times and conditions. 
     As stated above, the system includes at least one computer readable medium. Examples of computer readable media are compact discs  119 , hard disks  112 , floppy disks, tape, magneto-optical disks, PROMs (EPROM, EEPROM, Flash EPROM), DRAM, SRAM, etc. Stored on any one or on a combination of computer readable media, the present invention includes software for controlling both the hardware of the computer  100  and for enabling the computer  100  to interact with a human user. Such software may include, but is not limited to, device drivers, operating systems and user applications, such as development tools. Such computer readable media further include the computer program product of the present invention for monitoring and controlling a plasma in a plasma chamber. The computer code devices of the present invention can be any interpreted or executable code mechanism, including but not limited to scripts, interpreters, dynamic link libraries, Java classes, and complete executable programs. 
     As shown in FIG. 1A, the IF signal frequency is received by a frequency-to-voltage convertor  152  in the computer  100  and converted into a digital signal by analog-to-digital (A/D) convertor  150   b . (In an alternate embodiment, the frequency-to-voltage convertor  152  and the A/D convertor  150   b  are replaced by a digital counter which counts the number of IF cycles.) The computer  100  also received input data  275  provided by the equipment operator which is converted by a second A/D convertor  150   a . In an alternate embodiment, the input data  275  is received directly in digital form (e.g., through the keyboard  122 ), and in that embodiment the second AID convertor  150 A is not necessary. The DSP or CPU  106  receives and compares the digital IF signal to the input data  275  and transmits a digital output signal to a digital-to-analog (D/A) converter  160  which, in turn, transmits an analog signal to the plasma generator  205  to modify, if necessary, the output power of the plasma generator  205 . In an alternate embodiment, the D/A convertor  160  is incorporated in a modified plasma generator  205 ′, and the digital output from the DSP/CPU  106  is applied directly to the modified plasma generator  205 ′. 
     The frequency of the self-excited oscillator shown in FIG. 1A is dependent upon the electron density of the plasma along the path of the circuit within the processing chamber, and thus the shift in its operating frequency can be used to control the plasma generator. The relationship between the shift in frequency and the spatially averaged electron density of the plasma is derived below. 
     If the plasma electron density is zero, n p (ω, Z)=1, so then equation (2) becomes:                  [         ∑     i   =   1     n          φ   i       +       ∑     j   =   1     m          φ   j         ]     +       φ   amp          (   ω   )       +       β        (   ω   )            d   ckt       +       ω   c            ∫   0     d   p            1           z             =       q   ·   2        π             (   3   )                                
     where it is recognized that the index of refraction in the processing chamber reverts back to its vacuum value (n=1) along the path from z=0 to Z=d p . As a consequence, the frequency reverts to ω rather than ω′, where ω′=ω+Δω=ω+0 because there is no frequency shift. The same quantity appears on the right hand side of equations (2) and (3), thus the left-hand sides of (2) and (3) can be equated. Thus the first bracket in equations (2) and (3) cancel, and the remaining terms can be grouped as follows:                      ω                   d   p       c     ·     1     d   p                ∫   0     d   p              [     1   -       n   p          (     ω   ,   z     )         ]             z           =            [         φ   amp          (     ω   ′     )       -       φ   amp          (   ω   )         ]     +     [         β        (     ω   ′     )            d   ckt       -       β        (   ω   )            d   ckt         ]                 (   4   )                                
     where the distinction between ω′ andω is ignored for the terms multiplying the integral and in the expression for the plasma refractive index.                  n   p          (   ω   )       ≈       1   -       ω   p   2       ω   2           ≈     1   -         1   2     ·       ω   p   2       ω   2                       for                     ω   p   2       ω   2                1                 and             (   5   )                   ω   p   2     =           N   e             2         m                   ɛ   0         =     plasma                 frequency         ,           (   6   )                                
     with N e =electron density (in m −3 ). 
     A Taylor series expansion is used to evaluate the quantities φ amp  and β at ω′ in terms of the values at ω and the shift in frequency Δω.                  φ   amp          (     ω   ′     )       =         φ   amp          (   ω   )       +           ∂       φ   amp          (   ω   )           ∂   ω       ·   Δ                   ω               (7a)                 β                   (     ω   ′     )       =       β        (   ω   )       +           ∂     β        (   ω   )           ∂   ω       ·   Δ                   ω               (7b)                                
     The term involving the partial derivative of φ amp  is the group delay T g  inserted by the amplifier and is usually quite small; the term involving the partial derivative of β is the inverse of the group velocity v g  (where v g  is less than c). Thus equation (4) can be approximated by:                       2       m                   ɛ   0         ·     [       1     d   p              ∫   0     d   p                N   e          (   z   )               z           ]       =           〈     N   e     〉             2         m                   ɛ   0         =       2   ·   Δ                     ω   ·   ω   ·     {         c     v   g       ·       d   ckt       d   p         +       cT   g       d   p         }                   (   8   )                                
     Equation (8) states the spatially averaged electron density is related to the frequency shift Δω, the nominal frequency of oscillation ω, the fundamental constants c, m, and ε 0 , and the quantities in the brace of (8) which need to be determined only once. 
     The frequency of oscillation ω can be measured with a common wavemeter to better than 1% accuracy; the fundamental constants are known very precisely; and the brace can be determined experimentally by filling the path d p  with a heavy gas such as SF 6 , Argon, or Xenon at various pressures and evaluating the frequency shift Δω. (For such a calibration procedure, the local oscillator (LO) should be higher in frequency than the controlled oscillator.) The latter can be measured to great accuracy using the heterodyne technique in which the frequency ω′ is mixed with a stable local oscillator at ω LO  and so that the difference ω′−ω LO  can be measured with a frequency counter or other well known frequency determining techniques. 
     The average electron density of equation (8) is then used as a feedback control for controlling the voltage applied to the plasma generator  205  connected to the plasma chamber  200 . 
     According to the present invention, one example of a method for obtaining an approximate value for the average electron density between the transmitter  235  and the receiver  245  comprises the following steps: 
     1. Turn on the measurement apparatus and allow it to come to a stable condition after plasma initiation. 
     2. Enter the value of the term in the braces of equation (8). Note that this value depends on the settings of the adjustable elements in the feedback loop (e.g., the attenuator  213   a  and the phase shifter  225 ); so the settings should not be changed after the determination has been made. In an alternate embodiment, plural values are constructed for the term in braces in equation (8) (with one for each possible combination of environmental settings), and the proper value is chosen during operation based on the environmental settings. 
     3. Verify the frequency of the frequency stable local oscillator  260  and adjust if necessary. 
     4. Enter the desired plasma electron density at the keyboard  122  or at another data entry port. 
     5. Initiate the process from the data entry port. 
     Based on the difference between the desired IF signal and the measured IF signal, the output of the plasma generator  205  is adjusted to make the desired and measured IF signals more closely matching. For example, if the measured IF signal is greater than the desired IF signal, the output RF power is reduced by one increment. Likewise, if the measured IF signal is less than the desired IF signal, the output RF power is increased by one increment. Moreover, for coarse adjustments, a predetermined relationship between the plasma electron density and the RF power can be used to approximate an RF power to be applied. Then, finer tuning is applied to more accurately control the plasma system. 
     In one embodiment of a fine tuning method, the RF power applied is adjusted (i.e., increased or decreased by a given increment) until the difference between the measured and desired signals cannot be more closely matched based on the size of the given increment. The given increment is then decreased (e.g., by half), and the fine tuning is continued until the new given increment is also too coarse. However, if the difference between the measured and desired signals becomes greater than that which can be matched by the current interval, the current interval is increased. 
     In yet another embodiment of the tuning method, additional information is used to fine tune the feedback/control process. Such information may include, but is not limited to, the change of the signal per change in RF power (i.e., the first derivative), the second derivative, and the integral. The present invention is a general control mechanism and is not limited by the type of information or the feedback mechanism chosen. 
     The accuracy of the present method as compared with the prior art is described hereinafter. It is assumed that the feedback loop can be divided into two parts of equal physical length L. The first part represents the open radiation path, and the second part represents the rest of the feedback loop. In the absence of a plasma the frequency is f, and the wavelength in the open radiation path is λ 2 . The wavelength in the rest of the feedback loop is λ 1 , and the length of the feedback loop in wavelengths is q. For simplicity, it is assumed also that the phase velocity of the signal in the entire feedback loop is c. (Clearly the phase velocity in the waveguide is greater than c, but that complicating factor is neglected here.) From these assumptions, it follows that 
     
       
           L/λ   1   +L/λ   2   ≈Lf   1   /c+Lf   1   /c≈q.   (9) 
       
     
     In the presence of a plasma, the frequency becomes f 2 , the mean index of refraction in the open radiation path becomes &lt;n&gt; and the total length of the feedback path in wavelengths remains q. Consequently, 
     
       
           Lf   2   /c+&lt;n&gt;Lf   2   /c≈q.   (10) 
       
     
     Equations (9) and (10) are combined to yield:                  1   -     〈   n   〉         1   +     〈   n   〉         ≈           f   2     -     f   1         f   1       .             (   11   )                                
     The frequency difference f 2 −f 1  corresponds to the IF frequency described above. By evaluating the differentials of the natural logarithm, equation (15) is obtained as follows:                δ                   ln        (       1   -     〈   n   〉         1   +     〈   n   〉         )         =     δ                   ln        (         f   2     -     f   1         f   1       )                 (   12   )                   δ        (       1   -     〈   n   〉         1   +     〈   n   〉         )         (       1   -     〈   n   〉         1   +     〈   n   〉         )       ≈       δ        (         f   2     -     f   1         f   1       )         (         f   2     -     f   1         f   1       )       ≈         δ        (     IF     f   1       )         (     IF     f   1       )       .             (   13   )                                
     Here IF=f 2 −f 1  is the IF signal frequency. For a fixed f 1  and with the approximation that 
     
       
         1 +&lt;n &gt;≈2  (14) 
       
     
     which is quite good for the situations of interest here, one can show that:                       δ        (     1   -     〈   n   〉       )         1   -     〈   n   〉                            δ                 IF     IF          +            δ                   f   1         f   1                      (   15   )                                
     Reasonable expectations for measurement accuracies lead to estimations of about 0.0025 for each of the terms on the right side of equation (15) above. Consequently,                       δ        (     1   -     〈   n   〉       )         1   -     〈   n   〉              ≈     0.005   .             (   16   )                                
     Given that:                n   ≈     1   -            2       8                   π   2          ɛ   0          mf   2            N         ,           (   17   )                                
     it follows that:                  δ        (     1   -     〈   n   〉       )         1   -     〈   n   〉         ≈   0.005   ≈       δ        〈   N   〉         〈   N   〉               (   18   )                                
     and the expected accuracy is on the order of 0.5% 
     Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.