Patent Publication Number: US-7898183-B2

Title: Methods and apparatus for generating strongly-ionized plasmas with ionizational instabilities

Description:
RELATED APPLICATION SECTION 
     This application is a continuation application of U.S. patent application Ser. No. 11/738,491, filed on Apr. 22, 2007, which claims benefit of U.S. Provisional Application Ser. No. 60/745,398, filed Apr. 22, 2006 and is a continuation-in-part of U.S. patent application Ser. No. 11/376,036, filed on Mar. 15, 2006, now U.S. Pat. No. 7,345,429, which is a continuation application of U.S. patent application Ser. No. 10/708,281, filed on Feb. 22, 2004, which is now U.S. Pat. No. 7,095,179, the entire specifications of these patents and patent applications are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     A plasma can be created in a chamber by igniting a direct current (DC) electrical discharge between two electrodes in the presence of a feed gas. The electrical discharge generates electrons in the feed gas that ionize atoms thereby creating the plasma. The electrons in the plasma provide a path for an electric current to pass through the plasma. The energy supplied to the plasma must be relatively high for applications, such as magnetron plasma sputtering. Applying high electrical currents through a plasma can result in overheating the electrodes as well as overheating the work piece in the chamber. Complex cooling mechanisms can be used to cool the electrodes and the work piece. However, the cooling can cause temperature gradients in the chamber. These temperature gradients can cause non-uniformities in the plasma density which can cause non-uniform plasma process. 
     Temperature gradients can be reduced by pulsing DC power to the electrodes. Pulsing the DC power can allow the use of lower average power. This results in a lower temperature plasma process. However, pulsed DC power systems are prone to arcing at plasma ignition and plasma termination, especially when working with high-power pulses. Arcing can result in the release of undesirable particles in the chamber that can contaminate the work piece. 
     Plasma density in known plasma systems is typically increased by increasing the electrode voltage. The increased electrode voltage increases the discharge current and thus the plasma density. However, the electrode voltage is limited in many applications because high electrode voltages can effect the properties of films being deposited or etched. In addition, high electrode voltages can also cause arcing which can damage the electrode and contaminate the work piece. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       This invention is described with particularity in the detailed description and claims. The above and further advantages of this invention may be better understood by referring to the following description in conjunction with the accompanying drawings, in which like numerals indicate like structural elements and features in various figures. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. 
         FIG. 1  illustrates a cross-sectional view of a plasma sputtering apparatus having a pulsed direct current (DC) power supply according to one embodiment of the invention. 
         FIG. 2  is measured data of discharge voltage as a function of discharge current for a prior art low-current plasma and a high-current plasma according to the present invention. 
         FIG. 3  is measured data of a particular voltage pulse generated by the pulsed power supply of  FIG. 1  operating in a low-power voltage mode. 
         FIG. 4  is measured data of a multi-stage voltage pulse that is generated by the pulsed power supply of  FIG. 1  that creates a strongly-ionized plasma according to the present invention. 
         FIG. 5A-FIG .  5 C are measured data of other illustrative multi-stage voltage pulses generated by the pulsed power supply of  FIG. 1 . 
         FIG. 6A  and  FIG. 6B  are measured data of multi-stage voltage pulses generated by the pulsed power supply of  FIG. 1  that illustrate the effect of pulse duration in the transient stage of the pulse on the plasma discharge current. 
         FIG. 7A  and  FIG. 7B  are measured data of multi-stage voltage pulses generated by the pulsed power supply of  FIG. 1  that show the effect of the pulsed power supply operating mode on the plasma discharge current. 
         FIG. 8  is measured data for an exemplary single-stage voltage pulse generated by the pulsed power supply of  FIG. 1  that produces a high-density plasma according to the invention that is useful for high-deposition rate sputtering. 
         FIG. 9  illustrates a cross-sectional view of a plasma sputtering apparatus having a pulsed direct current (DC) power supply according to another embodiment of the invention. 
         FIG. 10A  illustrates a schematic diagram of a pulsed power supply that can generate multi-step voltage pulses according to the present invention. 
         FIG. 10B  shows a multi-step output voltage waveform and the corresponding micropulse voltage waveforms that are generated by switches and controlled by the drivers and the controller. 
         FIG. 11  illustrates a schematic diagram of a pulsed power supply having a magnetic compression network for supplying high-power pulses. 
         FIG. 12  illustrates a schematic diagram of a pulsed power supply having a Blumlein generator for supplying high-power pulses. 
         FIG. 13  illustrates a schematic diagram of a pulsed power supply having a pulse cascade generator for supplying high-power pulses. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a cross-sectional view of a plasma sputtering apparatus  100  having a pulsed direct current (DC) power supply  102  according to one embodiment of the invention. The plasma sputtering apparatus  100  includes a vacuum chamber  104  for containing a plasma. The vacuum chamber  104  can be coupled to ground  105 . The vacuum chamber  104  is positioned in fluid communication with a vacuum pump  106  that is used to evacuate the vacuum chamber  104  to high vacuum. The pressure inside the vacuum chamber  104  is generally less than 10 −1  Torr for most plasma operating conditions. A process or feed gas  108  is introduced into the vacuum chamber  104  through a gas inlet  112  from a feed gas source  110 , such as an argon gas source. The flow of the feed gas is controlled by a valve  114 . In some embodiments, the gas source is an excited atom or metastable atom source. 
     The plasma sputtering apparatus  100  also includes a cathode assembly  116 . The cathode assembly  116  shown in  FIG. 1  is formed in the shape of a circular disk, but can be formed in other shapes. In some embodiments, the cathode assembly  116  includes a target  118  for sputtering. The cathode assembly  116  is electrically connected to a first terminal  120  of the pulsed power supply  102  with an electrical transmission line  122 . 
     A ring-shaped anode  124  is positioned in the vacuum chamber  104  proximate to the cathode assembly  116 . The anode  124  is electrically connected to ground  105 . A second terminal  125  of the pulsed power supply  102  is also electrically connected to ground  105 . In other embodiments, the anode  124  is electrically connected to the second terminal  125  of the pulsed power supply  102  which is not at ground potential. 
     A housing  126  surrounds the cathode assembly  116 . The anode  124  can be integrated with or electrically connected to the housing  126 . The outer edge  127  of the cathode assembly  116  is electrically isolated from the housing  126  with insulators  128 . The gap  129  between the outer edge  127  of the cathode assembly  116  and the housing  126  can be an air gap or can include a dielectric material. 
     In some embodiments, the plasma sputtering apparatus  100  includes a magnet assembly  130  that generates a magnetic field  132  proximate to the target  118 . The magnetic field  132  is less parallel to the surface of the cathode assembly  116  at the poles of the magnets in the magnet assembly  130  and more parallel to the surface of the cathode assembly  116  in the region  134  between the poles of the magnets in the magnetic assembly  130 . The magnetic field  132  is shaped to trap and concentrate secondary electrons emitted from the target  118  that are proximate to the target surface  133 . The magnet assembly can consist of rotating magnets. 
     The magnetic field  132  increases the density of electrons and therefore, increases the plasma density in the region  134  that is proximate to the target surface  133 . The magnetic field  132  can also induce an electron Hall current  135  that is formed by the crossed electric and magnetic fields. The strength of the electron Hall current  135  depends, at least in part, on the density of the plasma and the strength of the crossed electric and magnetic fields. 
     The plasma sputtering apparatus  100  also includes a substrate support  136  that holds a substrate  138  or other work piece for plasma processing. In some embodiments, the substrate support  136  is biased with a RF field. In these embodiments, the substrate support  136  is electrically connected to an output  140  of a RF power supply  142  with an electrical transmission line  144 . A matching network (not shown) may be used to coupled the RF power supply  142  to the substrate support  136 . In some embodiments, a temperature controller  148  is thermally coupled to the substrate support  136 . The temperature controller  148  regulates the temperature of the substrate  138 . 
     In some embodiments, the plasma sputtering apparatus  100  includes an energy storage device  147  that provides a source of energy that can be controllably released into the plasma. The energy storage device  147  is electrically coupled to the cathode assembly  116 . In one embodiment, the energy storage device  147  includes a capacitor bank. 
     In some embodiments, the plasma sputtering apparatus  100  includes an arc control circuit  151  that is used to prevent undesirable arc discharges. The arc control circuit  151  includes a detection means that detects the onset of an arc discharge and then sends a signal to a control device that deactivates the output of the power supply  102  for some period of time. The probability that a magnetron discharge will transfer to an arc discharge is high under some processing conditions. For example, the probability that a magnetron discharge will transfer to an arc discharge is high for some reactive sputtering processes which use feed gases containing at least one a reactive gas. Arc discharges are generally undesirable because they can create particles that can damage the sputtered film. 
     In operation, the vacuum pump  106  evacuates the chamber  104  to the desired operating pressure. The feed gas source  110  injects feed gas  108  into the chamber  104  through the gas inlet  112 . The pulsed power supply  102  applies voltage pulses to the cathode assembly  116  that cause an electric field  149  to develop between the target  118  and the anode  124 . The magnitude, duration and rise time of the initial voltage pulse are chosen such that the resulting electric field  149  ionizes the feed gas  108 , thus igniting the plasma in the chamber  104 . 
     In one embodiment, ignition of the plasma is enhanced by one or more methods described in co-pending U.S. patent application Ser. No. 10/065,277, entitled High-Power Pulsed Magnetron Sputtering, and co-pending U.S. patent application Ser. No. 10/065,629, entitled Methods and Apparatus for Generating High-Density Plasma which are assigned to the present assignee. The entire disclosures of U.S. patent application Ser. No. 10/065,277 and U.S. patent application Ser. No. 10/065,629 are incorporated herein by reference. U.S. patent application Ser. No. 10/065,629 describes a method of accelerating the ignition of the plasma by increasing the feed gas pressure for a short period of time and/or flowing feed gas directly through a gap between an anode and a cathode assembly. In addition, U.S. patent application Ser. No. 10/065,277 describes a method of using pre-ionization electrodes to accelerate the ignition of the plasma. 
     The characteristics of the voltage pulses generated by the pulsed power supply  102  and the resulting plasmas are discussed in connection with the following figures. The pulsed power supply  102  can include circuitry that minimizes or eliminates the probability of arcing in the chamber  104 . Arcing is generally undesirable because it can damage the anode  124  and cathode assembly  116  and can contaminate the wafer or work piece being processed. In one embodiment, the circuitry of the pulse supply  102  limits the plasma discharge current up to a certain level, and if this limit is exceeded, the voltage generated by the power supply  102  drops for a certain period of time. 
     The plasma is maintained by electrons generated by the electric field  149  and also by secondary electron emission from the target  118 . In embodiments including the magnet assembly  130 , the magnetic field  132  is generated proximate to the target surface  133 . The magnetic field  132  confines the primary and secondary electrons in a region  134  thereby concentrating the plasma in the region  134 . The magnetic field  132  also induces the electron Hall current  135  proximate to the target surface  133  that further confines the plasma in the region  134 . 
     In one embodiment, the magnet assembly  130  includes an electromagnet in addition to a permanent magnet. A magnet power supply (not shown) is electrically connected to the magnetic assembly  130 . The magnet power supply can generate a constant current that generates a constant magnetic filed. Alternatively, the magnet power supply can generate a pulse that produces a pulsed magnetic field that creates an increase in electron Hall current  135  proximate to the target surface  133  that further confines the plasma in the region  134 . In one embodiment, the pulsing of the magnetic field is synchronized with the pulsing the electric field in the plasma discharge in order to increase the density of the plasma. The sudden increase in the electron Hall current  135  may create a transient non-steady state plasma. 
     Ions in the plasma bombard the target surface  133  because the target  118  is negatively biased. The impact caused by the ions bombarding the target surface  133  dislodges or sputters material from the target  118 . The sputtering rate generally increases as the density of the plasma increases. 
     The RF power supply  142  can apply a negative RF bias voltage to the substrate  138  that attracts positively ionized sputtered material to the substrate  138 . The sputtered material forms a film of target material on the substrate  138 . The magnitude of the RF bias voltage on the substrate  138  can be chosen to optimize parameters, such as sputtering rate and adhesion of the sputtered film to the substrate  138 . The magnitude of the RF bias voltage on the substrate  138  can also be chosen to minimize damage to the substrate  138 . In embodiments including the temperature controller  148 , the temperature of the substrate  138  can be regulated by the temperature controller  148  in order to avoid overheating the substrate  138 . 
     Although  FIG. 1  illustrates a cross-sectional view of a plasma sputtering apparatus  100 , it will be clear to skilled artisans that the principles of the present invention can be used in many other systems, such as plasma etching systems, hollow cathode magnetrons, ion beam generators, plasma-enhanced chemical vapor deposition (CVD) systems, plasma accelerators, plasma rocket thrusters, plasma traps, and any plasma system that uses crossed electric and magnetic fields. 
       FIG. 2  is measured data  150  of discharge voltage as a function of discharge current for a prior art low-current plasma and a high-current plasma according to the present invention. Current-voltage characteristic  152  represents measured data for discharge voltage as a function of discharge current for a plasma generated in a typical commercial magnetron plasma system with a commercially available DC power supply. The actual magnetron plasma system used to obtain the current-voltage characteristics  152  was a standard magnetron with a 10 cm diameter copper sputtering target. Similar results have been observed for a NiV sputtering target. Argon was used as the feed gas and the operating pressure was about 1 mTorr. The current-voltage characteristic  152  illustrates that discharge current increases with voltage. 
     The current-voltage characteristic  152  for the same magnetron plasma system generates a relatively low or moderate plasma density (less than 10 12 -10 13  cm −3 , measured close to the cathode/target surface) in a low-current regime. The plasma density in the low-current regime is relatively low because the plasma is mainly generated by direct ionization of ground state atoms in the feed gas. The term “low-current regime” is defined herein to mean the range of plasma discharge current densities that are less than about 0.5 A/cm 2  for typical sputtering voltages of between about −300V to −1000V. The power density is less than about 250 W/cm 2  for plasmas in the low-current regime. Sputtering with discharge voltages greater than −800V can be undesirable because such high voltages can increase the probability of arcing and can tend to create sputtered films having relatively poor film quality. 
     The current-voltage characteristic  154  represents actual data for a plasma generated by the pulsed power supply  102  in the plasma sputtering system  100  of  FIG. 1 . The current-voltage characteristic  154  illustrates that the discharge current is about 140 A (˜1.8 A/cm 2 ) at a voltage of about −500V. The discharge current is about 220 A (˜2.7 A/cm 2 ) when the voltage is about −575V. The data depends on various parameters, such as the magnitude and geometry of the magnetic field, chamber pressure, gas flow rate, pumping speed, and the design of the pulsed power supply  102 . For certain operating conditions, the discharge current can exceed 375 A with a discharge voltage of only −500V. 
     The voltage-current characteristic  154  is in a high-current regime. The current-voltage characteristic  154  generates a relatively high plasma density (greater than 10 12 -10 13  cm −3 ) in the high-current regime. The term “high-current regime” is defined herein to mean the range of plasma discharge currents that are greater than about 0.5 A/cm 2  for typical sputtering voltages of between about −300V to −1000V. The power density is greater than about 250 W/cm 2  for plasmas in the high-current regime. The voltage-current characteristic  154  generates high-density plasmas that can be used for high-deposition rate magnetron sputtering. 
     Some known magnetron systems operate within the high-current regime for very short periods of time. However, these known magnetron systems cannot sustain and control operation in the high-current regime for long enough periods of time to perform any useful plasma processing. The pulsed power supply  102  of the present invention is designed to generate waveforms that create and sustain the high-density plasma with current-voltage characteristics in the high-current regime. 
       FIG. 3  is measured data  200  of a particular voltage pulse  202  generated by the pulsed power supply  102  of  FIG. 1  operating in a low-power voltage mode. The pulsed power supply  102  produces a weakly-ionized plasma having a low or moderate plasma density (less than 10 12  10 13  cm −3 ) that is typical of known plasma processing systems. The pulsed power supply  102  is operating in a low-power mode throughout the duration of the voltage pulse  202 . The pulsed power supply  102  supplies energy to the plasma at a relatively slow rate in the low-power mode. The energy supplied by the pulsed power supply  102  in the low-power mode generates a weakly-ionized plasma by direct ionization of the ground state atoms in the feed gas. The weakly-ionized plasma corresponds to a plasma generated by a conventional DC magnetron. 
     The pulsed power supply  102  can be programmed to generate voltage pulses having various shapes. The desired voltage pulse of  FIG. 3  is a square wave voltage pulse as shown by the dotted line  203 . However, the actual voltage pulse  202  generated by the pulsed power supply  102  is not perfectly square, but instead includes low frequency oscillations that are inherent to the power supply  102 . Some of these low frequency oscillations can be on the order of 50V or more. In addition, the voltage pulse  202  has an initial value  204  of about −115V that is caused by the charge accumulation on the cathode assembly  116  for a particular repetition rate. 
     The voltage pulse  202  includes an ignition stage  205  that is characterized by a voltage  206  having a magnitude and a rise time that is sufficient to ignite a plasma from a feed gas. The magnitude of the voltage pulse  202  rises to about 550V in the ignition stage  205 . However, the voltage of the first pulse that initially ignites the plasma can be as high as −1500V. The ignition of the plasma is depicted as a rise in a discharge current  208  through the plasma. The duration of the ignition stage  205  is generally less than about 150 μsec. After the ignition stage  205 , the discharge current  208  continues to rise even as the voltage  210  decreases. 
     The rise in the discharge current  208  is caused at least in part by the interaction of the pulsed power supply  102  with the developing plasma. The impedance of the plasma decreases as the current density in the plasma increases. The pulsed power supply  102  attempts to maintain a constant voltage, but the voltage decreases due to the changing plasma resistive load. The peak discharge current  212  is less than about 50 A with a voltage  214  that is about −450V. The power  216  that is present at the peak discharge current  212 , which corresponds to a momentary peak density of the plasma, is about 23 kW. 
     As the voltage  218  continues to decrease, the discharge current  220  and the plasma density also decrease. As the density of the plasma decreases, the impedance of the plasma increases. The voltage level  222  corresponds to a quasi-static discharge current  224  that is substantially constant throughout the duration of the voltage pulse  202 . This region of quasi-static discharge current  224  is caused by the plasma having a substantially constant resistive load. The term “substantially constant” when applied to discharge current is defined herein to mean a discharge current with less than a 10% variation. 
     After about 200 μsec the oscillations dampen as the voltage  226  fluctuates between about −525V and −575V, the discharge current  228  remains constant with a value of about 25 A and the power  230  is between about 10-15 kW. These conditions correspond to a weakly-ionized or low-density plasma that is typical of most plasma processing systems, such as the conditions represented by the current-voltage characteristic  152  described in connection with  FIG. 2 . The plasma density is in the range of about 10 8 -10 13  cm −3 . 
     The total duration of the voltage pulse  202  is about 1.0 msec. The next voltage pulse (not shown) will typically include an ignition stage  205  in order to re-ignite the plasma. However, electrons generated from the first pulse can still be present so the required ignition voltage will typically be much less than the first pulse (on the order of about −600V) and the ignition will typically be much faster (on the order of less than about 200 μsec). 
       FIG. 4  is measured data  250  of a multi-stage voltage pulse  252  that is generated by the pulsed power supply of  FIG. 1  that creates a strongly-ionized plasma according to the present invention. The measured data  250  is from a magnetron sputtering system that includes a 10 cm diameter NiV target with an argon feed gas at a pressure of about 10 −3  Torr. The multi-stage voltage pulse  252  generates a weakly-ionized plasma in the low-current regime ( FIG. 2 ) initially, and then eventually generates a strongly-ionized or high-density plasma in the high-current regime according to the present invention. Weakly-ionized plasmas are generally plasmas having plasma densities that are less than about 10 12 -10 13  cm −3  and strongly-ionized plasmas are generally plasmas having plasma densities that are greater than about 10 12 -10 13  cm −3 . The multi-stage voltage pulse  252  is presented to illustrate the present invention. One skilled in the art will appreciate that there are numerous variations of the exact shape of the multi-stage pulse according to the present invention. 
     The multi-stage voltage pulse  252  is a single voltage pulse having multiple stages as illustrated by the dotted line  253 . An ignition stage  254  of the voltage pulse  252  corresponds to a voltage  256  having a magnitude (on the order of about −600V) and a rise time (on the order of about 4V/μsec) that is sufficient to ignite an initial plasma from a feed gas. The initial plasma is typically ignited in less than 200 μsec. 
     A first low-power stage  258  of the voltage pulse  252  has a peak voltage  260  that corresponds to a discharge current  261  in the developing initial plasma. In some embodiments, the ignition stage  254  is integrated into the first low-power stage  258  such that the plasma is ignited during the first low-power stage  258 . The peak voltage  260  is about −600V and can range from −300V to −1000V, the corresponding discharge current  261  is about 20 A, and the corresponding power is about 12 kW. In the first low-power stage  258 , the pulsed power supply  102  ( FIG. 1 ) is operating in the low-power mode. In the low power mode, the pulsed power supply  102  supplies energy to the initial plasma at a relatively slow rate. The slow rate of energy supplied to the initial plasma in the low-power mode maintains the plasma in a weakly-ionized condition. 
     The weakly-ionized or pre-ionized condition corresponds to an initial plasma having a relatively low (typically less than 10 12 -10 13  cm −3 ) plasma density. As the density of the initial plasma grows, the voltage  262  decreases by about 50V as the current  261  continues to rise to about 30 A before remaining substantially constant for about 200 μsec. The discharge current  261  rises as the voltage  262  decreases because of the changing impedance of the plasma. As the plasma density changes, the impedance of the plasma and thus the load seen by the pulsed power supply  102  also changes. In addition, the initial plasma can draw energy from the pulsed power supply  102  at a rate that is faster than the response time of the pulsed power supply  102  thereby causing the voltage  262  to decrease. 
     The impedance of the plasma decreases when the number of ions and electrons in the plasma increases as the current density in the initial plasma increases. The increase in the number of ions and electrons decreases the value of the plasma load. The pulsed power supply  102  attempts to maintain a constant voltage. However, the voltage  262  continues to decrease, at least in part, because of the changing plasma load. The substantially constant discharge current corresponds to a conventional DC magnetron discharge current as discussed in connection with current-voltage characteristic  152  of  FIG. 2 . The initial plasma can correspond to a plasma that is in a steady state or a quasi-steady state condition. 
     The peak plasma density can be controlled by controlling the slope of the rise time of the voltage pulse  252 . In a first transient stage  264  of the voltage pulse  252 , the voltage increase is characterized by a relatively slow rise time (on the order of about 2.8V/μsec) that is sufficient to only moderately increase the plasma density. The plasma density increases moderately because the magnitude and the rise time of the voltage  266  in the first transient stage  264  is not sufficient to energize the electrons in the plasma to significantly increase an electron energy distribution in the plasma. An increase in the electron energy distribution in the plasma can generate ionizational instabilities that rapidly increase the ionization rate of the plasma. The electron energy distribution and the ionizational instabilities are discussed in more detail with respect to generating a strongly-ionized plasma according to the invention. 
     The moderate increase in the plasma density will result in a current-voltage characteristic that is similar to the current-voltage characteristic  152  of a conventional DC magnetron that was described in connection with  FIG. 2 . The voltage  266  increases by about 50V to a voltage peak  268  of about −650V. The discharge current  270  increases by about 20 A to about 50 A and the power increases to about 30 kW. The pulsed power supply  102  is still operating in the low-power mode during the first transient stage  264 . 
     In a second low-power stage  272  of the voltage pulse  252 , the voltage  274  increases slowly by about 40V. The slow voltage increase is characterized by a discharge current  276  that remains substantially constant for about 350 μsec. The plasma can be substantially in a steady state or a quasi-steady state condition corresponding to the current-voltage characteristic  152  of  FIG. 2  during the second low-power stage  272 . The plasma density in the second low-power stage  272  is greater than the plasma density in the first low-power stage  258 , but is still only weakly-ionized. The pulsed power supply  102  is operating in the low-power mode. 
     In a second transient stage  278  of the voltage pulse  252 , the pulsed power supply  102  operates in the high-power mode. In this second transient stage  278 , the voltage  280  increases sharply compared with the first transient stage  264 . The rise time of the voltage  280  is greater than about 0.5V/μsec. The voltage increase is about 60V to the peak voltage. The relatively fast rise time (on the order of about 5V/μsec) of the voltage  280  and the corresponding energy supplied by the pulsed power supply  102  shifts the electron energy distribution in the weakly-ionized plasma to higher energies. The higher energy electrons rapidly ionize the atoms in the plasma and create ionizational instability in the plasma that drives the weakly-ionized plasma to a non-steady state condition or a transient state. In a non-steady state, the Boltzman, Maxwell, and Saha distributions can be modified. The rapid increase in ionization of the atoms in the plasma results in a rapid increase in electron density and a formation of the strongly-ionized plasma that is characterized by a significant rise in the discharge current  282 . The discharge current  282  rises to about 250 A at a non-linear rate for about 250 μsec. 
     One mechanism that contributes to a sharp increase in the electron energy distribution is known as diocotron instability. Diocotron instability is a wave phenomena that relates to the behavior of electron density gradients in the presence of electric and magnetic fields. Electron electrostatic waves can propagate along and across (parallel to and perpendicular to) field lines with different frequencies. These electron electrostatic waves can create electron drifts in the presence of a perpendicular electric field that are perpendicular to magnetic field lines. 
     Such electron drifts are inherently unstable, since any departure from charge neutrality in the form of charge bunching and separation (over distances on the order of the characteristic length scale in a plasma, the Debye length) create electric fields which cause second order ExB drifts that can exacerbate the perturbation. These instabilities are referred to as gradient-drift and neutral-drag instabilities. A charge perturbation associated with an electron Hall current developed by crossed magnetic and electric fields can produce radial electron drift waves. Drifts driven by the two density gradients (perpendicular and parallel) associated with a maximum in the radial electron density distribution can interact to cause the diocotron instability. Diocotron instability is described in “Magnetron Sputtering: Basic Physics and Application to Cylindrical Magnetrons” by John A. Thorton, J. Voc. Sci. Technol. 15(2), March/April p. 171-177, 1978. 
     A high-power stage  283  includes voltage oscillations  284  that have peak-to-peak amplitudes that are on the order of about 50V. These “saw tooth” voltage oscillations  284  may be caused by the electron density forming a soliton waveform or having another non-linear mechanism, such as diocotron instability discussed above, that increases the electron density as indicated by the increasing discharge current  286 . The soliton waveform or other non-linear mechanism may also help to sustain the high-density plasma throughout the duration of the voltage pulse  252 . Soliton waveforms, in particular, have relatively long lifetimes. 
     The discharge current  286  increases non-linearly through the high-power stage  283  until a condition corresponding to the voltage-current characteristic  154  of  FIG. 2  is reached. This condition corresponds to the point in which the pulsed power supply  102  is supplying an adequate amount of continuous power to sustain the strongly-ionized plasma at a constant rate as illustrated by a substantially constant discharge current  287 . The peak discharge current  288  in the high-power stage  283  is about 250 A at a voltage  290  of about −750V. The corresponding peak power  292  is about 190 kW. 
     The voltage pulse  252  is terminated at about 1.24 msec. The cathode assembly  116  remains negatively biased at about −300V after the termination of the voltage pulse  252 . The plasma then rapidly decays as indicated by the rapidly decreasing discharge current  294 . 
     The high-power stage  283  of the voltage pulse is sufficient to drive the plasma from a non-steady state in the second transient stage  278  to a strongly-ionized state corresponding to the voltage-current characteristic  154  of  FIG. 2 . The pulsed power supply  102  must supply a sufficient amount of uninterrupted power to continuously drive the initial plasma in the weakly-ionized state (in the second low-power stage  272 ) through the transient non-steady state (in the second transient stage  278 ) to the strongly-ionized state (in the high-power stage  283 ). The rise time of the voltage  280  in the second transient stage  278  is chosen to be sharp enough to shift the electron energy distribution of the initial plasma to higher energy levels to generate ionizational instabilities that creates many excited and ionized atoms. The rise time of the voltage  280  is greater than about 0.5V/μsec. 
     The magnitude of the voltage  280  in the second transient stage  278  is chosen to generate a strong enough electric field between the target  118  and the anode  124  ( FIG. 1 ) to shift the electron energy distribution to high energies. The higher electron energies create excitation, ionization, and recombination processes that transition the state of the weakly-ionized plasma to the strongly-ionized state. The transient non-steady state plasma state exists for a time period during the second transient stage  278 . The transient state results from plasma instabilities that occur because of mechanisms, such as increasing electron temperature caused by ExB Hall currents. Some of these plasma instabilities are discussed herein. 
     The strong electric field generated by the voltage  280  between the target  118  and the anode  124  ( FIG. 1 ) causes several ionization processes. The strong electric field causes some direct ionization of ground state atoms in the weakly-ionized plasma. There are many ground state atoms in the weakly-ionized plasma because of its relatively low level of ionization. In addition, the strong electric field heats electrons initiating several other different type of ionization process, such as electron impact, Penning ionization, and associative ionization. Plasma radiation can also assist in the formation and maintenance of the high current discharge. The direct and other ionization processes of the ground state atoms in the weakly-ionized plasma significantly increase the rate at which a strongly-ionized plasma is formed. 
     In one embodiment, the ionization process is a multi-stage ionization process. The multi-stage voltage pulse  252  initially raises the energy of the ground state atoms in the weakly-ionized plasma to a level where the atoms are excited. For example, argon atoms require an energy of about 11.55 eV to become excited. The magnitude and rise time of the voltage  280  is then chosen to create a strong electric field that ionizes the exited atoms. Excited atoms ionize at a much higher rate than neutral atoms. For example, Argon excited atoms only require about 4 eV of energy to ionize while neutral atoms require about 15.76 eV of energy to ionize. The multi-step ionization process is described in co-pending U.S. patent application Ser. No. 10/249,844, entitled High-Density Plasma Source using Excited Atoms which is assigned to the present assignee. The entire disclosure of U.S. patent application Ser. No. 10/249,844 is incorporated herein by reference. 
     The multi-step ionization process can be described as follows:
 
Ar+ e   − →Ar*+ e   − 
 
Ar*+ e   − →Ar + +2 e   − 
 
where Ar represents a neutral argon atom in the initial plasma, e −  represents an ionizing electron generated in response to an electric field, and Ar* represents an excited argon atom in the initial plasma. The collision between the excited argon atom and the ionizing electron results in the formation of an argon ion (Ar + ) and two electrons.
 
     In one embodiment, ions in the developing plasma strike the target  118  causing secondary electron emission. These secondary electrons interact with neutral or excited atoms in the developing plasma. The interaction of the secondary electrons with the neutral or excited atoms further increases the density of ions in the developing plasma as the feed gas  108  is replenished. Thus, the excited atoms tend to more rapidly ionize near the target surface  133  ( FIG. 1 ) than the neutral argon atoms. As the density of the excited atoms in the plasma increases, the efficiency of the ionization process rapidly increases. The increased efficiency can result in an avalanche-like increase in the density of the plasma thereby creating a strongly-ionized plasma. 
     In one embodiment, the magnet assembly  130  generates a magnetic field  132  proximate to the target  118  that is sufficient to generate an electron ExB Hall current  135  ( FIG. 1 ) which causes the electron density in the plasma to form a soliton or other non-linear waveform that increases at least one of the density and lifetime of the plasma as previously discussed. In some embodiments, the strength of the magnetic field  132  required to cause the electron density in the plasma to form such a soliton or non-linear waveform is in the range of fifty to ten thousand gauss. 
     An electron ExB Hall current  135  is generated when the voltage pulse  252  applied between the target  118  and the anode  124  generates primary electrons and secondary electrons that move in a substantially circular motion proximate to the target  118  according to crossed electric and magnetic fields. The magnitude of the electron ExB Hall current  135  is proportional to the magnitude of the discharge current in the plasma. In some embodiments, the electron ExB Hall current  135  is approximately in the range of three to ten times the magnitude of the discharge current. 
     The electron ExB Hall current  135  defines a substantially circular shape when the plasma density is relatively low. The substantially circular electron ExB Hall current  135  tends to form a more complex shape as the current density of the plasma increases. The shape is more complex because of the electron ExB Hall current  135  generates its own magnetic field that interacts with the magnetic field generated by the magnet assembly  130  and the electric field generated by the voltage pulse  252 . In some embodiments, the electron ExB Hall current  135  becomes cycloidal shape as the current density of the plasma increases. 
     The electron density in the plasma can form a soliton or other non-linear waveforms when the small voltage oscillations  284  create a pulsing electric field that interacts with the electron ExB Hall current  135 . The small voltage oscillations  284  tend to create oscillations in the plasma density that increase the density and lifetime of the plasma. The increase in plasma density shown in  FIG. 4  in the time period between about 900 μsec and 1.2 msec can be the result of the electron density forming a soliton or other non-linear waveform. In this time period, the voltage is only slightly increasing with time, but the discharge current  286  increases at a much more rapid rate. 
     In one embodiment, the electron density increases in an avalanche-like manner because of electron overheating instability. Electron overheating instabilities can occur when heat is exchanged between the electrons in the plasma, the feed gas, and the walls of the chamber. For example, electron overheating instabilities can be caused when electrons in a weakly-ionized plasma are heated by an external field and then lose energy in elastic collisions with atoms in the feed gas. The elastic collisions with the atoms in the feed gas raise the temperature and lower the density of the feed gas. The decrease in the density of the gas results in an increase in the electron temperature because the frequency of elastic collisions in the feed gas decreases. The increase in the electron temperature again enhances the heating of the gas. The electron heating effect develops in an avalanche-like manner and can drive the weakly-ionized plasma into the transient non-steady state. 
       FIG. 5A-FIG .  5 C are measured data  300 ,  300 ″, and  300 ′″ of other illustrative multi-stage voltage pulses  302 ,  302 ′, and  302 ″ generated by the pulsed power supply  102  of  FIG. 1 . The desired pulse shapes requested from the pulsed power supply  102  are superimposed in dotted lines  304 ,  304 ′, and  304 ″ onto each of the respective multi-stage voltage pulses  302 ,  302 ′, and  302 ″. The voltage pulses  302 ,  302 ′, and  302 ″ are generated for a magnetron sputtering source having a 10 cm diameter copper target and operating with argon feed gas at a chamber pressure of approximately 10 −6  Torr. The repetition rate of the voltage pulses is 40 Hz. 
     The voltage pulse  302  illustrated in  FIG. 5A  is a two-stage voltage pulse  302  having a transient region included in both the low-power stage and the high-power stage of the pulse. A low-power stage  306  of the voltage pulse  302  including the first transient region is sufficient to ignite an initial plasma and eventually sustain a weakly-ionized plasma. The duration of the low-power stage  306  of the voltage pulse  302  is about 1.0 msec. 
     The relatively fast rise time (on the order of about 6.25V/μsec) of the voltage during the first transient region in the low-power stage  306  is sufficient to shift the electron energy distribution of the initial plasma to higher energies to generate ionizational instability that drives the initial plasma into a transient non-steady state condition. The rise time of the voltage should be greater than about 0.5V/μsec as previously discussed. However, since the pulsed power supply  102  is operating in a low-power mode during the low-power stage  306  of the voltage pulse  302 , it does not supply a sufficient amount of uninterrupted power to continuously drive the initial plasma from the transient non-steady state to a strongly-ionized state corresponding to the current-voltage characteristic  154  of  FIG. 2 . Since there is insufficient energy stored in the pulsed power supply  102  in the low-power mode to create conditions that can sustain a strongly-ionized plasma, the plasma density oscillates and eventually the transient non-steady state of the plasma becomes weakly-ionized corresponding to the current-voltage characteristic  152  of  FIG. 2 . 
     The low-power stage  306  of the voltage pulse  302  includes relatively large voltage oscillations  308 . The voltage oscillations  308  dampen when the initial plasma reaches the weakly-ionized condition corresponding to the current-voltage characteristic  152  of  FIG. 2 . The weakly-ionized plasma is characterized by the substantially constant discharge current  312 . The voltage oscillations  308  occur because the pulsed power supply  102  does not supply enough energy in the low-power mode to drive the transient plasma into the strongly-ionized state that corresponds to the high-current regime illustrated by the current-voltage characteristic  154  of  FIG. 2 . Consequently, the discharge current  310  oscillates as the plasma rapidly expands and contracts. The rapidly expanding and contracting plasma causes the output voltage  308  to oscillate in response to the changing plasma load. The rapidly expanding and contracting plasma also prevents the electron density in the plasma from forming a soliton or other non-linear waveform that can increase the plasma density. 
     The average power  314  during the generation of the initial plasma is less than about 50 kW. The voltage  316  and the discharge current  318  are substantially constant after about 500 μsec, which corresponds to a plasma in a weakly-ionized condition. 
     A high-power stage  320  of the voltage pulse  302  includes a second transient region  321 . The voltage increases by about 30V in the second transient region  321 . The pulsed power supply  102  generates the high-power stage  320  of the voltage pulse  304  at about 1.1 msec. The voltage in the second transient region  321  has a magnitude and a rise time (on the order of about 5V/μsec) that is sufficient to drive the weakly-ionized plasma into a transient non-steady state. The rise time of the voltage is greater than about 0.5V/μsec. In the high-power stage  320 , the pulsed power supply  102  is operating in the high-power mode and supplies a sufficient amount of uninterrupted power to drive the weakly-ionized plasma from the transient non-steady state to a strongly-ionized state corresponding to the current-voltage characteristic  154  of  FIG. 2 . 
     Voltage oscillations  322  occur for about 300 μsec. The voltage oscillations  322  create current oscillations  324  in the transient plasma. The voltage oscillations  322  are caused, at least in part, by the changing resistive load in the plasma. The pulsed power supply  102  attempts to maintain a constant voltage and a constant discharge current, but the transient plasma exhibits a rapidly changing resistive load. 
     The voltage oscillations  322  can also be caused by ionizational instabilities in the plasma as previously discussed. Ionizational instabilities can occur when the degree of ionization in the plasma changes because of varying magnitudes of the crossed electric and magnetic fields. The degree of ionization can grow exponentially as the ionizational instability develops. The exponential growth in ionization may be a consequence of electron gas overheating as a result of developing electron Hall currents. The exponential growth in ionization dramatically increases the discharge current. 
     The voltage oscillations  322  are minimized after about 1.5 msec. The minimum voltage oscillations  323  can create a pulsing electric field that interacts with the electron ExB Hall current  135  ( FIG. 1 ) to generate oscillations in the plasma density that increase the density and lifetime of the plasma. The plasma is in the high-current regime corresponding to the current-voltage characteristic  154  of  FIG. 2  in which the pulsed power supply  102  supplies an adequate amount of energy to increase the density of the plasma non-linearly to the strongly-ionized state. The average voltage  326  is substantially constant while the current  328  increases nonlinearly with insignificant oscillations. 
     After the voltage oscillations  322 , the average voltage  326  remains lower than the voltage  316  present during the low-power stage  306  of the voltage pulse  304 . The discharge current  324  rises to a peak current  330 . After about 2.0 msec the average voltage  326  is about −500V, the discharge current  330  is almost 300 A and the power  332  is about 150 kW. These conditions correspond to a strongly-ionized plasma in the high-current regime. 
     The pulsed power supply  102  supplies power to the transient plasma during the high-power stage  320  at a relatively slow rate. This relatively slow rate corresponds to a relatively slow rate of increase in the discharge current  328  over a time period of about 1.0 msec. In one embodiment of the invention, the pulsed power supply  102  supplies high-power to the plasma relatively quickly thereby increasing the density of the plasma more rapidly. The density of the plasma can also be increased by increasing the pressure inside the plasma chamber. 
       FIG. 5A  illustrates that in order to sustain a strongly-ionized plasma in the high-current regime corresponding to the current-voltage characteristic  154  of  FIG. 2  at least two conditions must be satisfied. The first condition is that the rise time of a voltage in a transient region must be sufficient to shift the electron energy distribution of the initial plasma to higher energies to generate ionizational instability that drives the plasma into a transient non-steady state condition. The second condition is that the pulsed power supply must supply a sufficient amount of uninterrupted power to drive the plasma from the transient non-steady state to a strongly-ionized state corresponding to the current-voltage characteristic  154  of  FIG. 2 . 
     In the low-power stage  306 , the voltage in the first transient region has a sufficient rise time to shift the electron energy distribution of the initial plasma to higher energies as shown by current oscillations  310 . However, the pulsed power supply  102  is in the low-power mode and does not supply a sufficient amount of uninterrupted power to drive the initial plasma from the transient non-steady state to a strongly-ionized state. In the high-power stage  320 , the voltage in the second transient region  321  has a sufficient rise time to shift the electron energy distribution of the initial plasma to higher energies as shown by current oscillations  324 . Also, the pulsed power supply  102  (in the high-power mode) supplies a sufficient amount of uninterrupted power to drive the weakly-ionized plasma from the transient non-steady state to a strongly-ionized state. 
       FIG. 5B  is measured data  300 ′ of another illustrative multi-stage voltage pulse  302 ′ generated by the pulsed power supply  102  of  FIG. 1 . The voltage pulse  302 ′ is a three-stage voltage pulse  302 ′. The low-power stage  306 ′ of the voltage pulse  302 ′ including a first transient region has a rise time and magnitude that ignites an initial plasma. The low-power stage  306 ′ corresponds to a low-power mode of the pulsed power supply  102  and is similar to the low-power stage  306  of the voltage pulse  302  that was described in connection with  FIG. 5A . 
     A transient stage  340  of the three-stage voltage pulse  302 ′ is a transition stage where the pulsed power supply  102  transitions from the low-power mode to the high-power mode. The duration of the transient stage  340  is about 40 μsec, but can have a duration that is in the range of about 10 μsec to 5,000 μsec. The discharge voltage  342  and discharge current  344  both increase sharply in the transient stage  340  as previously discussed. 
     The transient stage  340  of the voltage pulse  302 ′ has a rise time that shifts the electron energy distribution in the weakly-ionized plasma to higher energies thereby causing a rapid increase in the ionization rate by driving the weakly-ionized plasma into a transient non-steady state. Plasmas can be driven into transient non-steady states by creating plasma instabilities from the application of a strong electric field. 
     A high-power stage  350  of the three-stage voltage pulse  302 ′ is similar to the high-power stage  320  of the two-stage voltage pulse  302  that was described in connection with  FIG. 5A . However, the discharge current  352  increases at a much faster rate than the discharge current  328  that was described in connection with  FIG. 5A . The discharge current  328  increases more rapidly because the transient stage  340  of the voltage pulse  302 ′ supplies high power to the weakly-ionized initial plasma at a rate and duration that is sufficient to more rapidly create a strongly-ionized plasma having a discharge current  352  that increases non-linearly. 
     Voltage oscillations  354  in the high-power stage  350  are sustained for about 100 μsec. The voltage oscillations can are caused by the ionizational instabilities in the plasma as described herein, such as diocotron oscillations. The voltage oscillations  354  cause current oscillations  356 . The maximum power  358  in the third stage  350  is approaching 200 kW, which corresponds to a maximum discharge current  360  that is almost 350 A. The third stage  350  of the voltage pulse  302 ′ is terminated after about 1.0 msec. 
       FIG. 5C  is measured data  300 ″ of another illustrative multi-stage voltage pulse  302 ″ generated by the pulsed power supply  102  of  FIG. 1 . The voltage pulse  302 ″ is a three-stage voltage pulse  302 ″. The low-power stage  306 ″ of the voltage pulse  302 ″ including a first transient region has a rise time and magnitude that ignites an initial plasma. The low-power stage  306 ″ corresponds to a low-power mode of the pulsed power supply  102  and is similar to the low-power stage  306  of the voltage pulse  302  that was described in connection with  FIG. 5A  and the low-power stage  306 ′ of the voltage pulse  302 ′ that was described in connection with  FIG. 5B . 
     A transient stage  370  of the three-stage voltage pulse  302 ″ is a transition stage where the pulsed power supply  102  transitions from the low-power mode to the high-power mode. The duration of the transient stage  370  is about 60 μsec, which is about 1.5 times longer than the duration of the transient stage  340  of the voltage pulse  302 ′ that was described in connection with  FIG. 5B . The peak-to-peak magnitude of the voltage  376  (˜100V) is greater than the peak-to-peak magnitude of the voltage  346  (˜70V) of  FIG. 5B . The discharge voltage  372  and discharge current  374  both increase sharply in the transient stage  370  because of the high value of the peak-to-peak magnitude of the voltage  376 . 
     The magnitude and rise time of the transient stage  370  is sufficient to drive the initial plasma into a non-steady state condition. The discharge voltage  372  and the discharge current  374  increase sharply. The peak discharge voltage  376  is about −650V, which corresponds to a discharge current  377  that is greater than about 200 A. The discharge voltage  378  then decreases as the discharge current  374  continues to increase. 
     The discharge current  374  in the transient stage  370  increases at a much faster rate than the discharge current  352  that was described in connection with  FIG. 5B  because the peak-to-peak magnitude of the voltage  376  is higher and the duration of the transient stage  370  is longer than in the transient stage  340  of  FIG. 5B . The duration of the transient stage  370  is long enough to supply enough uninterrupted energy to the weakly-ionized plasma to rapidly increase the rate of ionization of the transient plasma. 
     A high-power stage  380  of the three-stage voltage pulse  302 ″ is similar to the high-power stage  350  of the three-stage voltage pulse  302 ′ that was described in connection with  FIG. 5B . However, the voltage pulse  302 ″ does not include the large voltage oscillations that were described in connection with  FIGS. 5A and 5B . The large voltage oscillations are not present in the voltage pulse  302 ″ because the transient plasma is already substantially strongly-ionized as a result of the energy supplied in the transient stage  370 . Consequently, the initial plasma transitions in a relatively short period of time from a weakly-ionized condition to a strongly-ionized condition. 
     Small voltage oscillations  384  in the voltage pulse  302 ″ may be caused by the electron density forming a soliton waveform or having another non-linear mechanism that increases the electron density as indicated by the increasing discharge current  286 . The soliton waveform or other non-linear mechanism may also help to sustain the high-density plasma throughout the duration of the voltage pulse  302 ′. 
     The discharge current  382  in the third stage  380  is greater than about 300 A. The maximum power  386  in the third stage  380  approaches 200 kW. The third stage  380  of the voltage pulse  304 ″ is terminated after about 1.0 msec. 
       FIG. 6A  and  FIG. 6B  are measured data of multi-stage voltage pulses  400 ,  400 ′ generated by the pulsed power supply  102  of  FIG. 1  that illustrate the effect of pulse duration in the transient stage of the pulse on the plasma discharge current. The multi-stage voltage pulses  400 ,  400 ′ were applied to a standard magnetron with a 15 cm diameter copper target. The feed gas was argon and the chamber pressure was about 3 mTorr. 
     The multi-stage voltage pulse  400  shown in  FIG. 6A  is a three-stage voltage pulse  402  as indicated by the dotted line  404 . A low-power stage  406  of the voltage pulse  402  has a magnitude and a rise time that is sufficient to ignite a feed gas and generate an initial plasma. The pulsed power supply  102  is operating in the low-power mode during the low-power stage  406 . The maximum voltage in the low-power stage  406  is about −550V. The initial plasma develops into a weakly-ionized plasma having a relatively low-level of ionization corresponding to the current-voltage characteristic  152  of  FIG. 2 . The weakly-ionized plasma can be in a steady state corresponding to a substantially constant discharge current  408  that is less than about 50 A. 
     The pulsed power supply  102  is in the high-power mode during a transient stage  410 . In the transient stage  410 , the voltage increases by about 100V. The rise time of the voltage increase is sufficient to create a strong electric field through the weakly-ionized plasma that promotes excitation, ionization, and recombination processes. The excitation, ionization, and recombination processes create plasma instabilities, such as ionizational instabilities, that result in voltage oscillations  412 . The duration of the transient stage  410  of the voltage pulse  402  is, however, insufficient to shift the electron energy distribution in the plasma to higher energies because the energy supplied by the pulsed power supply  102  in the transient stage  410  is terminated abruptly as illustrated by the dampening discharge current  414 . Consequently, the transient plasma exhibits ionizational relaxation and eventually decays to a weakly-ionized plasma state corresponding to a substantially constant discharge current  416 . 
     A high-power stage  418  of the voltage pulse  402  has a lower magnitude than the transient stage  410  of the voltage pulse, but a higher magnitude than the low-power stage  406 . The high-power stage  418  is sufficient to maintain the weakly-ionized plasma, but cannot drive the plasma from the weakly-ionized condition to the strongly-ionized condition corresponding to the current-voltage characteristic  154  of  FIG. 2 . This is because the transient stage  410  did not provide the conditions necessary to sufficiently shift the electron energy distribution in the weakly-ionized plasma to high enough energies to create ionizational instabilities in the plasma. The voltage pulse  402  is terminated after about 2.25 msec. 
     The multi-stage voltage pulse  400 ′ illustrated in  FIG. 6B  is a three-stage voltage pulse  402 ′ as indicated by the dotted line  404 ′. A low-power stage  406 ′ of the voltage pulse  402 ′ is similar to the low-power stage  406  of the voltage pulse  402  that was described in connection with  FIG. 6A . The low-power stage  406 ′ has a magnitude and a rise time that is sufficient to ignite a feed gas and to generate an initial plasma. The pulsed power supply  102  is operating in the low-power mode as described herein during the low-power stage  406 ′. In one embodiment, the maximum voltage in the low-power stage  406 ′ is also about −550V. The initial plasma develops into a weakly-ionized plasma having a relatively low-level of ionization corresponding to the current-voltage characteristic  152  of  FIG. 2 . The weakly-ionized plasma can be in a steady state corresponding to a substantially constant discharge current  408 ′ that is less than about 50 A. 
     The transient stage  410 ′ of the voltage pulse  402 ′ creates a strong electric field through the weakly-ionized plasma that promotes excitation, ionization, and recombination processes. The excitation, ionization, and recombination processes create plasma instabilities, such as ionizational instabilities, that result in voltage oscillations  412 ′. The rise time of the peaks in the oscillating voltage  412 ′ create instabilities in the weakly-ionized plasma that rapidly increase the ionization rate of the weakly-ionized plasma as illustrated by the rapidly increasing discharge current  414 ′. 
     The duration of the transient stage  410 ′ of the voltage pulse  402 ′ is sufficient to shift the electron energy distribution in the plasma to higher energies that rapidly increase the ionization rate. The duration of the transient stage  410 ′ of  FIG. 6B  is five times more than the duration of the transient stage  410  of  FIG. 6A . The discharge current  420  increases nonlinearly as the average discharge voltage  422  decreases. The magnitude of the discharge current can be controlled by varying the magnitude and the duration of the transient stage  410 ′ of the voltage pulse  402 ′. 
     The high-power stage  418 ′ of the voltage pulse  402 ′ has a lower magnitude than the transient stage  410 ′. The pulsed power supply  102  provides a sufficient amount of energy during the high-power stage  418 ′ to maintain the plasma in a strongly-ionized condition corresponding to the current-voltage characteristic  154  of  FIG. 2 . The maximum discharge current  416 ′ for the plasma in the strongly-ionized state is about 350 A. The voltage pulse  402 ′ is terminated after about 2.25 msec. 
       FIG. 7A  and  FIG. 7B  are measured data of multi-stage voltage pulses  430 ,  430 ′ generated by the pulsed power supply  102  of  FIG. 1  that show the effect of the pulsed power supply operating mode on the plasma discharge current. The multi-stage voltage pulses  430 ,  430 ′ were applied to a standard magnetron with a 15 cm diameter copper target. The feed gas was argon and the chamber pressure was about 3 mTorr. 
     The multi-stage voltage pulse  430  shown in  FIG. 7A  is a three-stage voltage pulse  432  as indicated by the dotted line  434 . The pulsed power supply  102  generates a low-power stage  436  of the voltage pulse  432  that has a magnitude and a rise time that is sufficient to ignite a feed gas to generate an initial plasma. The maximum voltage in the ignition stage is about −550V. The pulsed power supply  102  is operating in the low-power mode. The initial plasma develops into a weakly-ionized plasma having a relatively low-level of ionization corresponding to the current-voltage characteristic  152  of  FIG. 2 . The weakly-ionized plasma can be in a steady state corresponding to a substantially constant discharge current  408 ′ that is less than about 50 A. 
     The pulsed power supply  102  generates a transient stage  440  of the voltage pulse  432  that increases the voltage by about 150V. The rise time, amplitude and duration of the voltage in the transient stage  440  of the voltage pulse  432  is sufficient to promote enough excitation, ionization, and recombination processes for the weakly-ionized plasma to experience a high rate of ionization as illustrated by the rapidly increasing discharge current  442 . The pulsed power supply  102  is operating in a high-power mode during the transient stage  440 . 
     The high-power stage  444  of the voltage pulse  432  has a lower magnitude than the transient stage  440  but has a sufficient magnitude to maintain the strongly-ionized plasma in the high-current regime corresponding to the current-voltage characteristic  154  of  FIG. 2 . The discharge current  446  for the strongly-ionized plasma is about 350 A. The pulsed power supply  102  operates in the high-power mode during the high-power stage  444  and generates enough uninterrupted energy to sustain the strongly-ionized plasma. The voltage pulse  432  is terminated after about 2.25 msec. 
     The multi-stage voltage pulse  430 ′ of  FIG. 7B  is a three-stage voltage pulse  432 ′ as indicated by the dotted line  434 ′. The pulsed power supply generates a low-power stage  436 ′ of the voltage pulse  432 ′ that is similar to the low-power stage  436  of the voltage pulse  432  of  FIG. 7A . The low-power stage  436 ′ of the voltage pulse  432 ′ has a magnitude and a rise time that is sufficient to ignite a feed gas to generate an initial plasma. The pulsed power supply  102  is operating in the low-power mode. The maximum voltage in the ignition stage is about −550V. The initial plasma develops into a weakly-ionized plasma having a relatively low-level of ionization. The weakly-ionized plasma can be in a steady state that corresponds to a substantially constant discharge current  438 ′ that is less than about 50 A. 
     The pulsed power supply  102  generates a transient stage  440 ′ of the voltage pulse  432 ′ that increases the voltage by about 150V. The transient stage  440 ′ is similar to the transient stage  440  of  FIG. 7A . The amplitude and duration of the transient stage  440 ′ of the voltage pulse  432 ′ is sufficient to promote enough excitation, ionization, and recombination processes to rapidly increase the ionization rate of the weakly-ionized plasma as illustrated by the rapidly increasing discharge current  442 ′. The pulsed power supply  102  is operating in a high-power mode during the transient stage  440 ′. 
     The pulsed power supply  102  generates a high-power stage  444 ′ that includes a voltage having a lower magnitude than the voltage in the second stage  440 ′. The voltage in the high-power stage  444 ′ decreases to below −500V which is insufficient to sustain a strongly-ionized plasma. Thus, the strongly-ionized plasma exhibits ionizational relaxation and eventually decays to a weakly-ionized plasma state corresponding to a quasi-stationary discharge current  449 . The voltage pulse  432 ′ is terminated after about 2.25 msec. 
       FIG. 8  is measured data  450  for an exemplary single-stage voltage pulse  452  generated by the pulsed power supply  102  of  FIG. 1  that produces a high-density plasma according to the invention that is useful for high-deposition rate sputtering. The voltage pulse  452  is a single-stage voltage pulse as indicated by the dotted line  453 . The pulsed power supply  102  operates in a high-power mode throughout the duration of the voltage pulse  452 . 
     The voltage pulse  452  includes an ignition region  454  that has a magnitude and a rise time that is sufficient to ignite a feed gas to generate an initial plasma. The discharge current  458  increases after the initial plasma is ignited. The initial plasma is ignited in about 100 μsec. 
     After ignition, the discharge current  460  and the voltage  456  both increase. The initial peak voltage  462  is about −900V. The voltage then begins to decrease. The discharge current  460  reaches an initial peak current  464  corresponding to a voltage  466 . The initial peak discharge current  464  is about 150 A at a discharge voltage  466  of about The peak discharge current  464  and corresponding discharge voltage  466  corresponds to a power  468  that is about 120 kW. The time period from the ignition of the plasma to the initial peak discharge current  464  is about 50 μsec. The initial plasma does not reach a steady state condition but instead remains in a transient state. 
     The voltage pulse  452  also includes a transient region  454 ′ having voltage oscillations  467  that include rise times which are sufficient to shift the electron energy distribution in the initial plasma to higher energies that create ionizational instabilities that cause a rapid increase in the ionization rate as described herein. The initial plasma remains in a transient state. 
     The voltage pulse  452  also includes a high-power region  454 ″. The voltage in the high-power region  454 ″ has a magnitude that is sufficient to sustain a strongly-ionized plasma. Small voltage oscillations  469  in the voltage pulse  452  may be caused by the electron density forming a soliton waveform or having another non-linear mechanism that increases the electron density as indicated by the increasing discharge current  470 . The soliton waveform or other non-linear mechanism may also help to sustain the strongly-ionized plasma throughout the duration of the voltage pulse  452 . 
     The single-stage voltage pulse  452  includes a voltage  456  that is sufficient to ignite an initial plasma, voltage oscillations  467  that are sufficient to create ionizational instabilities in the initial plasma, and a voltage  472  that is sufficient to sustain the strongly-ionized plasma. The pulsed power supply  102  operates in the high-power mode throughout the duration of the single-stage voltage pulse  452 . The peak discharge current  470  in the high-density plasma is greater than about 250 A for a discharge voltage  472  of about −500V. The power  474  is about 125 kW. The pulse width of the voltage pulse  452  is about 1.0 msec. 
       FIG. 9  illustrates a cross-sectional view of a plasma sputtering apparatus  500  having a pulsed direct current (DC) power supply  501  according to another embodiment of the invention. The plasma sputtering apparatus  500  includes a vacuum chamber  104  for containing a plasma. The vacuum chamber  104  can be coupled to ground  105 . The vacuum chamber  104  is positioned in fluid communication with a vacuum pump  106  that is used to evacuate the vacuum chamber  104  to high vacuum. The pressure inside the vacuum chamber  104  is generally less than 10 −1  Torr for most plasma operating conditions. 
     The plasma sputtering apparatus  500  also includes a cathode assembly  502 . The cathode assembly  502  is generally in the shape of a circular ring. The cathode assembly  502  includes a target  504 . The target  504  is generally in the shape of a disk and is secured to the cathode assembly  502  through a locking mechanism, such as a clamp  506 . The cathode assembly  502  is electrically connected to a first terminal  508  of the pulsed power supply  501  with an electrical transmission line  510 . 
     In some embodiments, the plasma sputtering apparatus  500  includes an energy storage device  503  that provides a source of energy that can be controllably released into the plasma. The energy storage device  503  is electrically coupled to the cathode assembly  502 . In one embodiment, the energy storage device  503  includes a capacitor bank. 
     A ring-shaped anode  512  is positioned in the vacuum chamber  104  proximate to the cathode assembly  502  so as to form a gap  514  between the anode  512  and the cathode assembly  502 . The gap  514  can be between about 1.0 cm and 12.0 cm wide. The gap  514  can reduce the probability that an electrical breakdown condition (i.e., arcing) will develop in the chamber  104 . The gap  514  can also promote increased homogeneity of the plasma by controlling a gas flow through the gap. The anode  512  can include a plurality of feed gas injectors  516  that inject feed gas into the gap  514 . In the embodiment shown, the feed gas injectors  516  are positioned within the anode  512 . The feed gas injectors  516  are coupled to one or more feed gas sources  518 . The feed gas sources can include atomic feed gases, reactive gases, or a mixture of atomic and reactive gases. Additionally, excited atom sources (not shown) or metastable atom sources (not shown) can be coupled to the feed gas injectors  516  to supply excited atoms or metastable atoms to the chamber  104 . 
     The anode  512  is electrically connected to ground  105 . A second terminal  520  of the pulsed power supply  501  is also electrically connected to ground  105 . In other embodiments, the anode  512  is electrically connected to the second terminal  520  of the pulsed power supply  501 . 
     The anode  512  can be integrated with or connected to a housing  521  that surrounds the cathode assembly  502 . An outer edge  522  of the cathode  502  is isolated from the housing  521  with insulators  523 . The space  524  between the outer edge  522  of the cathode assembly  502  and the housing  521  can be filled with a dielectric. 
     The plasma sputtering apparatus  500  can include a magnet assembly  525  that generates a magnetic field  526  proximate to the target  504 . The magnetic field  526  is less parallel to the surface of the cathode assembly  502  at the poles of the magnets in the magnet assembly  525  and more parallel to the surface of the cathode assembly  502  in the region  527  between the poles of the magnets in the magnetic assembly  525 . 
     The magnetic field  526  is shaped to trap and concentrate secondary electrons emitted from the target  504  that are proximate to the target surface  528 . The magnetic field  526  increases the density of electrons and therefore, increases the plasma density in the region  527 . The magnetic field  526  can also induce an electron Hall current that is generated by the crossed electric and magnetic fields. The strength of the electron Hall current depends, at least in part, on the density of the plasma and the strength of the crossed electric and magnetic fields. Crossed electric and magnetic fields generated in the gap  514  can enhance the ionizational instability effect on the plasma as discussed herein. 
     The plasma sputtering apparatus  500  also includes a substrate support  530  that holds a substrate  532  or other work piece. The substrate support  530  can be electrically connected to a first terminal  534  of a RF power supply  536  with an electrical transmission line  538 . A second terminal  540  of the RF power supply  536  is coupled to ground  105 . The RF power supply  536  can be connected to the substrate support  530  through a matching unit (not shown). In one embodiment a temperature controller  542  is thermally coupled to the substrate support  530 . The temperature controller  542  regulates the temperature of the substrate  532 . 
     The plasma sputtering apparatus  500  can also include a cooling system  544  to cool the target  504  and the cathode assembly  502 . The cooling system  544  can be any one of numerous types of liquid or gas cooling system that are known in the art. 
     In operation, the vacuum pump  106  evacuates the chamber  104  to the desired operating pressure. The feed gas is injected into the chamber  104  from the feed gas source  518  through the gas inlet  516 . The pulsed power supply  501  applies negative voltage pulses to the cathode  502  (or positive voltage pulses to the anode  512 ) that generate an electric field  546  in the gap  514  between the cathode assembly  502  and the anode  512 . The magnitude and rise time of the voltage pulse are chosen such that the resulting electric field  546  ionizes the feed gas in the gap  514 , thereby igniting an initial plasma in the gap  514 . 
     The geometry of the gap  514  can be chosen to minimize the probability of arcing and to facilitate the generation of a very strong electric field  546  with electric field lines that are perpendicular to the surface  528  of the target  504  and the cathode  502 . This strong electric field  546  can enhance the ionizational instability in the plasma by increasing the volume of excited atoms including metastable atoms that are generated from ground state atoms in the initial plasma. The increased volume of exited atoms can increase the density of the plasma in a non-linear manner as previously discussed. 
     The plasma is maintained, in part, by secondary electron emission from the target  504 . In embodiments including the magnet assembly  525 , the magnetic field  526  confines the secondary electrons proximate to the region  527  and, therefore, concentrates the plasma proximate to the target surface  528 . The magnetic field  526  also induces an electron Hall current proximate to the target surface  528 , which further confines the plasma and can cause the electron density to form a soliton waveform or other non-linear waveform. 
     Ions in the plasma bombard the target surface  528  since the target  504  is negatively biased. The impact caused by the ions bombarding the target  504  dislodges or sputters material from the target  504 . The sputtering rate generally increases as the density of the plasma increases. 
     The RF power supply  536  generates a negative RF bias voltage on the substrate  532  that attracts positively ionized sputtered material to the substrate  532 . The sputtered material forms a thin film of target material on the substrate  532 . The magnitude of the RF bias voltage on the substrate  532  can be chosen to optimize parameters, such as sputtering rate and adhesion of the sputtered firm to the substrate  532 , and to minimize damage to the substrate  532 . The temperature controller  542  can regulate the temperature of the substrate  532  to avoid overheating the substrate  532 . 
     Although  FIG. 9  illustrates a magnetron sputtering system, skilled artisans will appreciate that many other plasma systems can utilize methods for generating high-density plasmas using ionizational instability according to the invention. For example, the methods for generating high-density plasmas using ionizational instability according to the invention can be used to construct a plasma thruster. The method of generating a high-density plasma for a thruster is substantially the same as the method described in connection with  FIG. 9  except that the plasma is accelerated through an exhaust by external fields. 
       FIG. 10A  illustrates a schematic diagram  550  of a pulsed power supply  552  that can generate multi-step voltage pulses according to the present invention. The pulsed power supply  552  includes an input voltage  554  that charges a bank of capacitors  556 . In one embodiment, the input voltage  554  is in the range of 100V to 5000V. A parallel bank of high-power solid state switches  558 , such as insulated gate bipolar transistors (IGBTs), are coupled to a primary coil  560  of a pulse transformer  562 . The solid state switches  558  are controlled by driver  557  that send signals to the solid state switches  558  that activate or deactivate the switches  558 . When the solid state switches  558  are activated by the drivers  557  they release energy stored in the capacitors  556  to the primary coil  560  of the pulse transformer  562  in the form of voltage micropulses. In some embodiments, the duration of the voltage micropulses is in the range of two microseconds to one hundred microseconds. we already mentioned about the micropulses duration) 
     The pulse transformer  562  also includes a secondary coil  564 . The voltage gain from the pulse transformer  562  is proportional to the number of secondary turns in the secondary coil  564 . A first end  566  and a second end  570  of the secondary coil  564  are coupled to an output driving circuit  568 . In many embodiments, the output driving circuit  568  includes diodes, inductors, and capacitors. The output driving circuit  568  provides voltage pulses across a first output  574  and a second output  576 . The first output  574  can be coupled to a cathode and the second output  576  can be coupled to an anode, for example. The pulsed power supply  552  can provide pulse power up to about 10 MW with a relatively fast rise time and duration up to 100 milliseconds. 
     The pulsed power supply  552  can include a controller or processor  578  which determines the output waveform generated by the pulsed power supply  552 . In some embodiments, a separate controller or processor, such as a computer, is electrically connected to the drivers  557  of the solid state switches  558  so as to control the operation of the solid state switches  558 . In other embodiments, the processor  578  is integrated directly into the pulsed power supply  552  as shown in  FIG. 10A . The processor  578  and drivers  557  can be used to determine parameters, such as the pulse width of the micropulses, and the repetition rate and/or duty cycle of the micropulses that is generated by solid state switches  558  in order to control of output pulse trains generated by the pulsed power supply  552 . 
     In some embodiments, the pulsed power supply  552  is used in conjunction with the arc control circuit  151  that was described in connection with  FIG. 1 . The arc control circuit  151  includes a detection means that detects the onset of an arc discharge and then sends a signal to a control device in the pulsed power supply  552  that deactivates the drivers  557  for the high-power solid state switches  558  for some period of time. The deactivation of the drivers  557  for the high-power solid state switches  558  reduces the voltage between the anode and the cathode assembly to levels that can not support an arc discharge. 
     Energy stored in cables that connect the pulse power supply  552 , magnetron, and the output driving circuit  568  still can be released after the drivers  557  for the solid state switches  558  are deactivated and, under some circumstances, can sustain an arc discharge for a short period of time. In order to minimize these undesirable arc discharges, the control circuit  151  should be positioned close to the magnetron and the length of cables connecting the control circuit  151  and the magnetron should also be minimized. For example, the length of cables connecting the control circuit  151  and the magnetron should be less than about 100 cm. 
     In some embodiments, the power supply  552  generates a single step voltage pulse. For example, the processor  578  can instruct the drivers  557  for the high-power solid state switches  558  to generate micropulses with a ten microseconds pulse width and a fifty microsecond period (i.e. a forty microseconds off time). These micropulses generate output voltage pulses having a duration that is one millisecond with an amplitude that is equal to −400 V. The resulting voltage waveform has a 20% duty cycle. In this example, the power supply  552  generates twenty pulses. Thus, the total duration of the voltage waveform generated by the power supply  552  is one millisecond (50 microsecond pulse width×20 periods). The resulting magnetron discharge had a current of 10 A with a −400V voltage. 
     In other embodiments, the power supply  552  generates multi-step voltage pulses by varying the duty cycle of the signals generated by the drivers  557  for the high-power solid state switches  558  for predetermined times. In various embodiments, a two stage voltage pulse is used to generate plasmas having particular properties, such as plasmas that are formed initially with a weakly ionized plasma and then with a strongly ionized plasma as described herein. For example, a two stage voltage pulse with a first stage having an amplitude that is −500 V and a second stage having an amplitude that is −600V with a total pulse width of two milliseconds can be generated by pulsed power supply  552 . 
     During the first stage, the processor  578  instructs the drivers  557  for the high-power solid state switches  558  to generate −500V pulses with a fifteen microseconds pulse width and a fifty microsecond period (i.e. a thirty-five microseconds off time). The resulting voltage waveform had a 30% duty cycle. Twenty pulses were generated. The total duration of the first stage waveform was one millisecond. During the first stage, the magnetron discharge voltage was −500V and the magnetron discharge current was 15 A. The first stage waveform generated a weakly ionized plasma as described herein. The voltage rise time between the first stage waveform and the second stage waveform was 20 V/microsecond. 
     During the second stage, the processor  578  instructs the drivers  557  for the high-power solid state switches  558  to generate −600V pulses with a 16 microseconds duration and a forty microsecond period (i.e. a twenty-four microseconds off time). This resulting voltage waveform had a 40% duty cycle. Twenty five pulses were generated. The total duration of the second stage waveform was one millisecond. The total duration of the two-step waveform was two milliseconds. During the second stage voltage waveform, the magnetron discharge voltage was −600V and magnetron discharge current was −300 A. The second stage waveform generated a strongly ionized plasma as described herein. 
     In various embodiments, the voltage rise time between the first stage waveform and the second stage waveform of the two stage voltage pulse waveform is selected to generate plasmas with particular properties as described herein. The rise time between the first stage waveform and the second stage waveform can be varied by changing the width of the micropulses or the duty cycle of the micropulses at the end of the first stage waveform and the width of the micropulse or the duty cycle of the micropulses in the beginning of second stage waveform. It should be understood that multi-stage pulses with any number of stages can be generated with the methods and apparatus of the present invention. 
       FIG. 10B  shows a multi-step output voltage waveform  590  and the corresponding micropulse voltage waveforms  592  that are generated by switches  558  and controlled by the drivers  557  and the controller  578 . The micropulse voltage waveforms  592  that generate the multi-step output voltage waveform  590  illustrates how a multi-step voltage waveform can be formed by varying the pulse widths and the duty cycle of the micropulses generated by the switches  558 . In addition, the micropulse voltage waveforms  592  that generate the multi-step output voltage waveform  590  illustrates how the rise times of the multi-step voltage waveform can be varied by varying the pulse widths and the duty cycle of the micropulses generated by the drivers  557 . 
       FIG. 11  illustrates a schematic diagram  600  of a pulsed power supply  602  having a magnetic compression network  604  for supplying high-power pulses. The pulsed power supply  602  generates a long pulse with a switch and applies the pulse to an input stage of a multi-stage magnetic compression network  604 . Each stage of magnetic compression reduces the time duration of the pulse, thereby increasing the power of the pulse. 
     The pulsed power supply  602  includes a DC supply  606 , a capacitor  608 , and a power-MOS solid switch  610  for providing power to the magnetic compression network  604 . The magnetic compression network  604  includes four non-linear magnetic inductors  612 ,  614 ,  616 ,  618  and four capacitors  620 ,  622 ,  624 ,  626 . The non-linear magnetic inductors  612 ,  614 ,  616 ,  618  behave as switches that are off when they are unsaturated and on when they are saturated. The magnetic compression network  604  also includes a transformer  628 . 
     When the solid switch  610  is activated, the capacitor  620  begins to charge and the voltage V 1  increases. At a predetermined value of the voltage V 1 , the magnetic core of the non-linear magnetic inductor  612  saturates and the inductance of the non-linear magnetic inductor  612  becomes low causing the non-linear magnetic inductor  612  to turn on. This results in charge transferring from the capacitor  608  to the capacitor  620 . The electric charge stored in the capacitor  620  is then transferred through the transformer  628  to the capacitor  622  and so on. The charge that is transferred to the capacitor  626  is eventually discharged through a load  630 . The magnetic compression network  604  can generate high-power pulses up to a terawatt in tens of nanoseconds with a relatively high repetition rate. 
       FIG. 12  illustrates a schematic diagram  650  of a pulsed power supply  652  having a Blumlein generator  654  for supplying high-power pulses. The pulsed power supply  652  having the Blumlein generator  654  can deliver short duration high voltage pulses with a fast rise time and a relatively flat top. The pulsed power supply  652  includes a high voltage DC supply  656 . A first terminal  658  of the high voltage DC supply  656  is coupled through a current-limiting inductor  660  to a dielectric material  662  that is located between an inner conductor  664  and an outer conductor  666  of a coaxial cable  668 . The inner conductor  664  is coupled to ground  670  through an inductance  672 . The outer conductor  666  is also coupled to ground  670 . The Blumlein generator  654  operates as follows. The high voltage power supply  656  slowly charges the Blumlein generator  654 . A very fast high-power switch  674  discharges the charge through a load  676 , such as a plasma load. 
       FIG. 13  illustrates a schematic diagram  700  of a pulsed power supply  702  having a pulse cascade generator  704  for supplying high-power pulses. A high frequency power supply  706  is coupled to a transformer  708 . The transformer  708  is coupled to a cascade of “low voltage” (1 kV to 3 kV) pulse generators  710  that are connected in series. The pulse cascade generator  704  operates as follows. The high frequency power supply  706  charges capacitors  712  in each of the pulse generators  710 . Switches  714  in each of the pulse generators  710  close at predetermined times thereby discharging energy in the capacitors  712 . When the required output voltage appears between the terminal  716  and ground  718 , the stored energy discharges through a load  720 , such as a plasma load. 
     EQUIVALENTS 
     While the invention has been particularly shown and described with reference to specific preferred embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined herein.