Patent Publication Number: US-11646176-B2

Title: Efficient nanosecond pulser with source and sink capability for plasma control applications

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Patent Application No. 62/789,526 filed Jan. 8, 2019, titled “EFFICIENT ENERGY RECOVERY IN A NANOSECOND PULSER CIRCUIT,” which is incorporated by reference in its entirety. 
     This application claims priority to U.S. Provisional Patent Application No. 62/789,523 filed Jan. 8, 2019, titled “EFFICIENT NANOSECOND PULSER WITH SOURCE AND SINK CAPABILITY FOR PLASMA CONTROL APPLICATIONS,” which is incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Producing high voltage pulses with fast rise times and/or fast fall times is challenging. For instance, to achieve a fast rise time and/or a fast fall time (e.g., less than about 50 ns) for a high voltage pulse (e.g., greater than about 5 kV), the slope of the pulse rise and/or fall must be incredibly steep (e.g., greater than 10 −11  V/s). Such steep rise times and/or fall times are very difficult to produce especially in circuits driving a load with low capacitance. Such pulse may be especially difficult to produce using standard electrical components in a compact manner; and/or with pulses having variable pulse widths, voltages, and repetition rates; and/or within applications having capacitive loads such as, for example, a plasma. 
     SUMMARY 
     Some embodiments include a high voltage, high frequency switching circuit. In some embodiments, the high voltage, high frequency switching circuit includes a high voltage switching power supply that produces pulses having a voltage greater than 1 kV and with frequencies greater than 10 kHz (or any frequency); a transformer having a primary side and secondary side; an output electrically coupled with the secondary side of the transformer; and a primary sink electrically coupled with the primary side of the transformer and in parallel with the high voltage switching power supply, the primary sink comprising at least one resistor that discharges a load coupled with the output. 
     In some embodiments, the primary sink is configured to dissipate over about 1 kilowatt of average power. In some embodiments, the primary sink is configured to dissipate 30 W-30 kW of average power. 
     In some embodiments, the primary sink comprises at least on inductor in series with the at least one resistor. 
     In some embodiments, the primary sink comprises a switch in series with the at least one resistor. 
     In some embodiments, the output is coupled with a plasma load that is largely capacitive. 
     In some embodiments, the output is coupled with a plasma load that includes a dielectric barrier discharge. 
     In some embodiments, the resistance of the resistor in the primary sink has a value less than about 400 ohms. 
     In some embodiments, the high voltage high frequency switching power supply delivers peak powers greater than 100 kW. 
     In some embodiments, the resistor in the primary sink includes a resistance R and the output is coupled with a load having a capacitance C such that 
             R   ≈       t   f         a   2     ⁢   C             
where t f  is the pulse fall time and
 
     
       
         
           
             
               a 
               = 
               
                 
                   N 
                   p 
                 
                 
                   N 
                   s 
                 
               
             
             . 
           
         
       
     
     In some embodiments, the load is capacitive in nature with a capacitance less than 50 nF, wherein the load capacitance does not hold charges for times greater than 1 μs. 
     In some embodiments, the load is capacitive in nature and the high voltage, high frequency switching circuit rapidly charges the load capacitance and discharges the load capacitance. 
     In some embodiments, the output produces a negative bias voltage on an electrode, substrate, or wafer with respect to the plasma and ground that is greater than −2 kV when the high voltage switching power supply is not providing a high voltage pulse. In some embodiments, the bias voltage may be positive. 
     In some embodiments, the output can produce a high voltage pulse having a voltage greater than 1 kV and with frequencies greater than 10 kHz with pulse fall times less than about 400 ns, 40 ns, 4 ns, etc. 
     Some embodiments include a high voltage, high frequency switching circuit. In some embodiments, the high voltage, high frequency switching circuit includes a high voltage switching power supply that produces pulses having a voltage greater than 1 kV and with frequencies greater than 10 kHz; a transformer having a primary side and secondary side; an output electrically coupled with the secondary side of the transformer; and a primary sink electrically coupled to the primary side of the transformer and in parallel with the output of the high voltage switching power supply, the primary sink comprising at least one resistor that discharges a load coupled with the output coupled with the secondary of the transformer and at least one inductor in series with the at least one resistor. 
     In some embodiments, the primary sink comprises a switch in series with the at least one resistor and/or the at least one inductor. 
     In some embodiments, the output can produce a high voltage pulse having a voltage greater than 1 kV and with frequencies greater than 10 kHz and with a pulse fall time less than about 400 ns. 
     In some embodiments, the primary sink is configured to dissipate over about 1 kilowatt of power. 
     In some embodiments, the high voltage switching power supply comprises a power supply, at least one switch, and a step-up transformer. 
     In some embodiments, the primary sink handles a peak power greater than 10 kW. 
     In some embodiments, the resistance of the resistor in the primary sink is less than about 400 ohms. 
     In some embodiments, the primary sink includes an inductor and a resistor, and wherein the inductance L of the inductor and the resistance R of the resistor are set to satisfy L/R≈tp, where tp is the pulse width of the pulse. 
     In some embodiments, the resistor in the primary sink includes a resistance R and the output is coupled with a load having a capacitance C such that 
             R   ≈       t   f         a   2     ⁢   C             
where t f  is the pulse fall time and
 
     
       
         
           
             
               a 
               = 
               
                 
                   N 
                   p 
                 
                 
                   N 
                   s 
                 
               
             
             . 
           
         
       
     
     In some embodiments, the high voltage switching power supply establishes a potential within a plasma that is used to accelerate ions into a surface. 
     In some embodiments, the output produces a negative potential difference from the electrode or substrate (or wafer and plasma) with respect to ground that is greater than −2 kV when the high voltage switching power supply is not providing a high voltage pulse. 
     Some embodiments include a high voltage, high frequency switching circuit. In some embodiments, the high voltage, high frequency switching circuit includes a high voltage switching power supply that produces pulses having a voltage greater than 1 kV and with frequencies greater than 10 kHz; a transformer having a primary side and secondary side; an output electrically coupled with the secondary side of the transformer; and a primary sink electrically coupled with the primary side of the transformer and in parallel with the output of the high voltage switching power supply, the primary sink comprising at least one resistor, at least one inductor, and a switch arranged in series. In some embodiments, the output can produce a high voltage pulse having a voltage greater than 1 kV with frequencies greater than 10 kHz and with pulse fall times less than about 400 ns, and wherein the output is electrically coupled to a plasma type load. 
     In some embodiments, the plasma type load can be modeled as having capacitive elements less than 20 nF, 10 nF, 100 pF, 10 pF, 1 pF, 0.5 pF, etc. 
     In some embodiments, the plasma type load is designed to accelerate ions into a surface. 
     In some embodiments, a potential is established to accelerate ions into a surface through the action of the high voltage high frequency switching power supply. 
     In some embodiments, the plasma type is largely capacitive in nature. 
     In some embodiments, the plasma type load includes a dielectric barrier discharge. 
     In some embodiments, the high voltage high frequency switching power supply delivers peak powers greater than 100 kW. 
     In some embodiments, the high voltage switching power supply comprises a power supply, at least one switch, and a step-up transformer. 
     These illustrative embodiments are mentioned not to limit or define the disclosure, but to provide examples to aid understanding thereof. Additional embodiments are discussed in the Detailed Description, and further description is provided there. Advantages offered by one or more of the various embodiments may be further understood by examining this specification or by practicing one or more embodiments presented. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       These and other features, aspects, and advantages of the present disclosure are better understood when the following Detailed Description is read with reference to the accompanying drawings. 
         FIG.  1    is a circuit diagram of a nanosecond pulser system with a primary sink according to some embodiments. 
         FIG.  2    is a circuit diagram of a nanosecond pulser system with a primary sink according to some embodiments. 
         FIG.  3    is a circuit diagram of a nanosecond pulser system with a primary sink according to some embodiments. 
         FIG.  4    is a circuit diagram of a nanosecond pulser system with a primary sink according to some embodiments. 
         FIG.  5    are waveforms produced by a nanosecond pulser system. 
         FIG.  6    is a circuit diagram of a nanosecond pulser system with a primary sink, a bias compensation circuit, and a plasma load according to some embodiments. 
         FIG.  7    is a circuit diagram of a nanosecond pulser system with a primary sink, a bias compensation circuit, and a plasma load according to some embodiments. 
         FIG.  8    is a circuit diagram of a nanosecond pulser system with a primary sink, a bias compensation circuit, and a plasma load according to some embodiments. 
         FIG.  9    is a circuit diagram of a nanosecond pulser system with a primary sink, a bias compensation circuit, and a plasma load according to some embodiments. 
         FIG.  10    are waveforms produced by a nanosecond pulser system. 
         FIG.  11    is a block diagram of a high voltage switch with isolated power according to some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Systems and methods are disclosed for a nanosecond pulser system (e.g., a high voltage, high frequency switching circuit) having a primary sink. In some embodiments, a nanosecond pulser system may be used to drive a plasma deposition system, plasma etch system, plasma sputtering system, e-beam system, ion beam system, etc. 
       FIG.  1    is a circuit diagram of a nanosecond pulser system  100  according to some embodiments. The nanosecond pulser system  100  includes a nanosecond pulser  105 , a primary sink  106 , a transformer T 1 , and a load stage  115 . 
     In some embodiments, the nanosecond pulser  105  may produce pulses with high pulse voltage (e.g., voltages greater than 1 kV, 10 kV, 20 kV, 50 kV, 100 kV, etc.), high frequencies (e.g., frequencies greater than 1 kHz, 10 kHz, 100 kHz, 200 kHz, 500 kHz, 1 MHz, etc.), fast rise times (e.g., rise times less than about 1 ns, 10 ns, 50 ns, 100 ns, 250 ns, 500 ns, 1,000 ns, etc.), fast fall times (e.g., fall times less than about 1 ns, 10 ns, 50 ns, 100 ns, 250 ns, 500 ns, 1,000 ns, etc.) and/or short pulse widths (e.g., pulse widths less than about 1,000 ns, 500 ns, 250 ns, 100 ns, 20 ns, etc.). 
     For example, the nanosecond pulser  105  may include all or any portion of any device described in U.S. patent application Ser. No. 14/542,487, titled “High Voltage Nanosecond Pulser,” which is incorporated into this disclosure for all purposes, or all or any portion of any device described in U.S. patent application Ser. No. 14/635,991, titled “Galvanically Isolated Output Variable Pulse Generator Disclosure,” which is incorporated into this disclosure for all purposes, or all or any portion of any device described in U.S. patent application Ser. No. 14/798,154, titled “High Voltage Nanosecond Pulser With Variable Pulse Width and Pulse Repetition Frequency,” which is incorporated into this disclosure for all purposes. 
     In some embodiments, the nanosecond pulser  105  includes a switch S 1  coupled with a power supply C 7  (e.g., energy storage capacitor that may be coupled with a power supply), that may provide a consistent DC voltage that is switched by the switch S 1  and provides the switched power to the transformer T 1 . The switch S 1 , for example, may include one or more solid state switches such as, for example, an IGBT, a MOSFET, a SiC MOSFET, SiC junction transistor, FETs, SiC switches, GaN switches, photoconductive switch, etc. In some embodiments, a gate resistor coupled with the switch S 1  may be set with short turn on pulses. 
     In some embodiments, the resistor R 8  and/or the resistor R 5  may represent the stray resistance within the nanosecond pulser  105 . In some embodiments, the inductor L 3  and/or the inductor L 1  may represent the stray inductance within the nanosecond pulser  105 . 
     In some embodiments, the nanosecond pulser  105  may include snubber circuit that may include snubber resistor R 1  and snubber inductor L 3  both of which may be arranged in parallel with snubber diode D 2 . The snubber circuit may also include a snubber capacitor C 5 . In some embodiments, the snubber resistor R 1  and snubber inductor L 3  and/or the snubber diode D 2  may be placed between the collector of switch S 1  and the primary winding of the transformer T 1 . The snubber diode D 2  may be used to snub out any over voltages in the switching. A large and/or fast capacitor C 5  may be coupled on the emitter side of the switch S 1 . The freewheeling diode D 1  may also be coupled with the emitter side of the switch S 1 . Various other components may be included that are not shown in the figures. 
     In some embodiments, the freewheeling diode D 1  may be used in combination with inductive loads to ensure that energy which is stored in the inductor is allowed to dissipate after the switch S 1  is opened by allowing current to keep flowing in the same direction through the inductor and energy is dissipated in the resistive elements of the circuit. If they are not used then this can, for example, lead to a large reverse voltage on the switch S 1 . 
     In some embodiments, the primary sink  106  may be disposed in parallel with the switch S 1  (and snubber circuit). The primary sink  106 , for example, may include a sink diode D 6 , a resistor R 2 , and sink inductor L 6  arranged in series. In some embodiments, the resistor R 2  may include one or more resistors with a resistance of about 100 ohms. In some embodiments, the sink inductor L 6  may include one or more inductors with an inductance of about 100 μH. In some embodiments, the resistor R 2  may comprise a plurality of resistors arranged in parallel and/or series. In some embodiments, the sink inductor L 6  may comprise a plurality of inductors arranged in parallel and/or series. 
     In some embodiments, the sink diode D 6  may be arranged to allow current to flow from the transformer T 1  to ground. 
     In some embodiments, the sink diode D 6 , the resistor R 2  and the sink inductor L 6  are arranged in parallel with the transformer T 1 . 
     In some embodiments, the resistor R 2  and the sink inductor L 6  are disposed on the primary side of the transformer T 1 . 
     The use of a primary sink to achieve high voltage pulses at high frequencies that have fast rise/fall times, and/or short pulse widths may constrain the selection of the circuit elements in the resistive output stage (e.g., R 2  and L 6 ). The primary sink may be selected to handle high average power, high peak power, fast rise times and/or fast fall times. For example, the average power rating might be greater than about 10 W, 50 W, 100 W, 0.5 kW, 1.0 kW, 10 kW, 25 kW, etc., the peak power rating might be greater than about 1 kW, 10 kW, 100 kW, 1 MW, etc., and/or the rise and fall times might be less than 1000 ns, 100 ns, 10 ns, or 1 ns. 
     The high average power and/or peak power requirement may arise both from the need to dissipate stored energy in the load stage  115  rapidly, and/or the need to do so at high frequency. For example, if the load stage  115  is capacitive in nature (as shown in  FIG.  1   , with capacitance C 12 ), with a 1 nF capacitance that needs discharging in 20 ns, and if the primary sink may be purely resistive (e.g., minimal value of L 6 ), the primary sink may have a resistance value of about 12.5 mOhms. If the high voltage pulse applied to the load is 100 ns long at 20 kV, then each pulse will dissipate about 2 J during the 100 ns pulse width (e.g., E=t p V p   2 /R) and an additional 0.2 J draining the stored energy from the 1 nF capacitive load (e.g., E=½t p CV s   2 ), where t p  is the pulse width, V is the pulse voltage, R 2  is the resistance of the primary sink, C is the capacitance of the load, V p  is the voltage on the primary side of the transformer, V s  is the voltage on the secondary side of the transformer, and E is the energy. If operated at 10 kHz, the total per pulse energy dissipation of 2.2 J may result in an average power dissipation of 22 kW into the primary sink. The peak power dissipation in the primary sink during the pulse may be about 20 MW, and may be calculated from Power=V 2 /R. 
     The high frequency and high voltage operation, combined with the need for the resistance in the primary sink to be small, for example, may lead to examples with either or both high peak power and high average power dissipation within the primary sink. Standard pulldown resistors that are used in TTL type electrical circuits and/or data acquisition type circuits (e.g., around 5 volts) usually operate far below 1 W for both average and peak power dissipation. 
     In some embodiments, the ratio of the power the primary sink  106  dissipates compared to the total power dissipated by the load stage  115  may be 10%, 20% 30% or greater, for example. In standard low voltage electronic circuits, pull down resistors dissipate less than 1% of the power consumed, and typically much less. 
     The fast rise time and/or fast fall time requirements may constrain both the allowable stray inductance and/or stray capacitance within the primary sink. In the above example, for the 1 nF capacitive load to be discharged in around 20 ns, the series stray inductance in the primary sink may be less than about 1,000 nH, 500 nH, 300 nH, 100 nH, 30 nH, etc. In some embodiments, L 6 /R 2 &lt;t f . In some embodiments, the L/R time for the For the primary sink to not waste significant additional energy due to its stray capacitance, for example, less than 10% of the capacitive energy stored in the load capacitance, then the stray capacitance of the primary sink may be less than 100 pF. Since the primary sink may tend to be physically large due to its high power dissipation requirements, realizing both this low stray inductance and stray capacitance can be challenging. The design generally requires significant parallel and series operation using numerous discrete components (e.g., resistors), with the components tightly grouped together, and/or spaced far from any grounded surfaces that could significantly increase the stray capacitance. 
     In some embodiments, the load stage  115  may include a dielectric barrier discharge device. The load stage  115  in a dielectric barrier discharge can be dominantly capacitive. In some embodiments, the load may be modeled as a purely capacitive load CL, for example, like a dielectric barrier discharge. For example, when the power supply P is switched on, capacitive load CL may be charged, when power supply P is not switched on, the charge on capacitive load CL may be drained through resistor R. In addition, due to high voltages and/or high frequencies and/or fast fall time requirements a primary sink may need to discharge a significant amount of charge from the capacitive load CL quickly, which may not be the case with low voltage applications (e.g., standard 5 V logic levels and or low voltage data pulsers). 
     For example, a typical dielectric barrier discharge device might have a capacitance of about 10 pF and/or may be driven to about 20 kV with about a 20 ns rise time and/or about a 20 ns fall time. In some embodiments, the desired pulse width might be 80 ns long. For the fall time to match the rise time, resistor R 2  may be about 12.5 Ohms can be used to create the desired fall time. Various other values for the circuit element resistor R 2  may be used depending on the load and/or the other circuit elements and/or the requirements rise time, fall time, and/or pulse width, etc. 
     In some embodiments, for a capacitive like load, or a load that has an effective capacitance C (e.g., the capacitance C 12 ), the characteristic pulse fall time can be designated as t f  and the pulse rise time can be designated by t r . In some embodiments, the rise time t r  can be set by the specifics of the driving power supply. In some embodiments, the pulse fall time t f  can be approximately matched to the pulse rise time t r  by selecting resistor R 2 , where 
                 R   ⁢   2     ≈       t   f         a   2     ⁢   C         .         
In some embodiments, R 2  can be specifically selected to provide a specific relation between the pulse rise time t r  and the pulse fall time t f . This is different from the concept of a pull down resistor, where in general, a pull down resistor is selected to carry/dissipate voltage/charge on some longer time scale, and at much lower power levels. Resistor R 2 , in some embodiments, can be specifically used as an alternative to a pull down switch, to establish a specific relation between the pulse rise time t r  and the pulse fall time t f .
 
     In some embodiments, the power dissipated in resistor R 2  during a pulse having a pulse width t p  and a drive voltage V can be found from P=V 2 /R. Because fall time t f  is directly proportional to resistance R 
               (       e   .   g   .     ,           ⁢       R   ⁢           ⁢   2     ≈       t   f         a   2     ⁢   C           )     ,         
as the requirement for fall time t f  decreases then the requirement for the resistance R also decreases, and the power P dissipated in resistor R 2  increases according to P=V 2 C/t f . Thus, resistor R 2  may be designed to ensure the proper fall time t f  yet be capable of handling high power such as, for example, power greater than about 1.0 kW, or 100 kW. In some embodiments the resistor may handle the average power requirements as well as peak power requirements. The need for fast fall time t f  resulting in low resistance values and the resulting high power dissipation are challenges that can make primary sinks undesirable as a way to quickly remove charge from a capacitive load C 2 . In some embodiments, a resistor R can include a resistor with low resistance and yet have a high average power rating and peak power rating.
 
     In some embodiments, the resistor R 2  may include a series and/or parallel stack of resistors that collectively have the required resistance and power rating. In some embodiments, the resistor R 2  may include a resistor have a resistance less than about 2,000 ohms, 500 ohms, 250 ohms, 100 ohms, 50 ohms, 25 ohms, 10 ohms, 1 ohm, 0.5 ohms, 0.25 ohms, etc., and have an average power rating greater than about 0.5 kW, 1.0 kW, 10 kW, 25 kW, etc., and have a peak power rating greater than about 1 kW, 10 kW, 100 kW, 1 MW, etc. 
     Using the example above, with tp=80 ns, V=500 kV, and resistor R 2  12.5 kOhms, each pulse applied to the load may dissipate 16 mJ once the capacitance in the load is fully charged. Once the pulse is turned off, charge from the load is dissipated by resistor R 2 . If operated at 100 kHz, then resistor R 2  may dissipate 1.6 kW. If resistor R 2  had been selected to create a 10 ns t f , then the power dissipated in resistor R 2  would be 3.2 kW. In some embodiments, a high voltage pulse width may extend to 500 ns. At 500 ns with t f =20 ns, resistor R 2  would dissipate 10 kW. 
     In some embodiments, the power dissipated in the resistor R 2  can be considered large if it exceeds 10% or 20% of the power consumed by the load stage  115 . 
     When fast fall times t f  are needed, then the power dissipation can be large such as, for example, about one third the total power consumed. If resistor R 2 , for example, includes a resistor R 2  in series with an sink inductor L 6 , then sink inductor L 6  can, for example, reduce the power flow into the resistor R while the voltage V is present and/or hasten the fall time beyond that set by an RC decay. 
     For example, the time constant L 6 /R 2  can be set to approximately the pulse width t p , for example, L 6 /R 2 ≈t p . This, for example, may reduce energy dissipation and/or shorten the fall time t f , (e.g., decreases t f ). In some embodiments, R 2 ≈C/t f ≈C/t r , assuming one wanted to match t f  to t r . In this application, disclosure, and/or claims, the symbol “≈” means within a factor of ten. 
     In some embodiments, the transformer T 1  may be part of the nanosecond pulser  105 . 
       FIG.  2    is a circuit diagram of a nanosecond pulser system  200  according to some embodiments. The nanosecond pulser system  200  includes the nanosecond pulser  105 , a primary sink  206 , the transformer T 1 , and the load stage  115 . 
     In some embodiments, the primary sink  206  may include a sink switch S 2  in place of or in addition to the sink diode D 6 . In some embodiments, the sink switch S 2  may be arranged in series with the sink inductor L 6  and/or the sink resistor R 2 . 
     In some embodiments, the sink switch S 2 , for example, can be closed when the load capacitance C 2  is to be dumped through the sink resistor R 2  and/or the sink inductor L 6 . For example, the sink switch S 2  may switch on and/or off to dump charge from the load capacitor C 2  after each pulse. During each pulse, for example, sink switch S 2  may be open. At the end of each pulse, the sink switch S 2  may be closed to dump the load capacitance into the resistor R 2 . For example, the sink switch S 2  may closed when the switch S 1  is open and/or the sink switch S 2  may be open when the switch S 1  is closed. 
     In some embodiments, the sink switch S 2  may include the high voltage switch  1100  described in  FIG.  11   . 
       FIG.  3    is a circuit diagram of a nanosecond pulser system  300  according to some embodiments. The nanosecond pulser system  300  includes a nanosecond pulser  305 , a primary sink  306 , the transformer T 1 , and the load stage  115 . 
     In some embodiments, the nanosecond pulser  305  may include a diode D 4  disposed between the sink switch S 2  and the primary sink  306 . The diode D 4  may be arranged to allow current to flow through the switch S 1  toward the transformer T 1  and restrict current from flowing from the transformer T 1  toward the switch S 1 . 
     The primary sink  306  may include the components of primary sink  106  except the sink diode D 6 . In some embodiments, primary sink  306  may include the sink diode D 6  and/or the sink switch S 2 . 
       FIG.  4    is a circuit diagram of a nanosecond pulser system  400  according to some embodiments. The nanosecond pulser system  400  includes the nanosecond pulser  105 , a primary sink  406 , the transformer T 1 , and the load stage  115 . 
     In some embodiments, the primary sink  406  may include the sink switch S 2  and the sink diode D 6 . In some embodiments, the sink switch S 2  may be arranged in series with the sink inductor L 6  and/or the sink resistor R 2 . In some embodiments, a crowbar diode D 8  may be included across the sink switch S 2 . 
     In some embodiments, the sink switch S 2 , for example, can be closed when the load capacitance C 2  is to be dumped through the sink resistor R 2  and/or the sink inductor L 6 . For example, the sink switch S 2  may switch on and/or off to dump charge from the load capacitor C 2  after each pulse. During each pulse, for example, sink switch S 2  may be open. At the end of each pulse, the sink switch S 2  may be closed to dump the load capacitance into the resistor R 2 . For example, the sink switch S 2  may closed when the switch S 1  is open and/or the sink switch S 2  may be open when the switch S 1  is closed. 
       FIG.  5    illustrates waveform  505  showing the voltage at the input to the transformer T 1  and waveform C 8  showing the voltage at the load stage  115  using the nanosecond pulser system  300  shown in  FIG.  3   . 
       FIG.  6    illustrates a nanosecond pulser system  600  according to some embodiments. The nanosecond pulser system  600  includes the nanosecond pulser  105 , the primary sink  106 , the transformer T 1 , a bias compensation circuit  610 , and a load stage  615 . 
     In some embodiments, the bias compensation circuit  610 , may include a high voltage switch S 3  coupled across the bias compensation diode D 8  and arranged in series with offset power supply V 1  and bias compensation resistor R 9 . In some embodiments, the high voltage switch S 3  may include a plurality of switches arranged in series to collectively open and close high voltages. For example, the high voltage switch S 3  may include the high voltage switch  1100  described in  FIG.  11   . In some embodiments, the high voltage switch S 3  may be opened and closed based on signals Sig 3 + and Sig 3 −. 
     The high voltage switch S 3  may be coupled in series with either or both an inductor L 9  and a resistor R 11 . The inductor L 9  may limit peak current through high voltage switch S 3 . The inductor L 9 , for example, may have an inductance less than about 100 μH such as, for example, about 250 μH, 100 μH, 50 μH, 25 μH, 10 μH, 5 μH, 1 μH, etc. The resistor R 11 , for example, may shift power dissipation to the primary sink. The resistance of resistor R 11 , for example, may have a resistance of less than about 1,000 ohms, 500 ohms, 250 ohms, 100 ohms, 50 ohms, 10 ohms, etc. 
     In some embodiments, the high voltage switch S 3  may include a snubber circuit. The snubber circuit may include resistor R 9 , snubber diode D 8 , snubber capacitor C 15 , and snubber resistor R 10 . 
     In some embodiments, the resistor R 8  can represent the stray resistance of the offset supply voltage V 1 . The resistor R 8 , for example, may have a high resistance such as, for example, a resistance of about 10 kOhm, 100 kOhm, 1 MOhm, 10 MOhm, 100 MOhm, 1 GOhm, etc. 
     In some embodiments, the bias compensation capacitor C 8  may have a capacitance less than 100 nF to 100 μF such as, for example, about 100 μF, 50 μF, 25 μF, 10 μF, 2 μF, 500 nF, 200 nF, etc. 
     In some embodiments, the bias compensation capacitor C 8  and the bias compensation diode D 8  may allow for the voltage offset between the output of the nanosecond pulser  105  (e.g., at the position labeled  125 ) and the voltage on the electrode (e.g., at the position labeled  124 ) to be established at the beginning of each burst, reaching the needed equilibrium state. For example, charge is transferred from capacitor C 12  into capacitor C 8  at the beginning of each burst, over the course of a plurality of pulses (e.g., maybe about 5-100), establishing the correct voltages in the circuit. 
     In some embodiments, the bias capacitor C 12  may allow for a voltage offset between the output of the nanosecond pulser  105  (e.g., at the position labeled  125 ) and the voltage on the electrode (e.g., at the position labeled  124 ). In operation, the electrode may, for example, be at a DC voltage of −2 kV during a burst, while the output of the nanosecond pulser alternates between +6 kV during pulses and 0 kV between pulses. 
     The bias capacitor C 12 , for example, may have a capacitance of about 100 nF, 10 nF, 1 nF, 100 μF, 10 μF, 1 μF, etc. The resistor R 9 , for example, may have a high resistance such as, for example, a resistance of about 1 kOhm, 10 kOhm, 100 kOhm, 1 MOhm, 10 MOhm, 100 MOhm, etc. 
     The bias compensation circuit  610  may include any number of other elements or be arranged in any number of ways. 
     In some embodiments, the high voltage switch S 3  may be open while the nanosecond pulser  105  is pulsing and closed when the nanosecond pulser  105  is not pulsing. When the high voltage switch S 3  is closed, for example, current can short across the bias compensation diode D 8 . Shorting this current may allow the bias between the wafer and the chuck to be less than 2 kV (or another voltage value), which may be within acceptable tolerances. In some embodiments, the bias compensation diode D 8  may conduct currents of between 10 A and 1 kA at a frequency of between 10 Hz and 10 kHz. 
     In some embodiments, the high voltage switch S 3  may include the high voltage switch  1100  described in  FIG.  11   . 
     In some embodiments, the load stage  615  may represent an idealized or effective circuit for semiconductor processing chamber such as, for example, a plasma deposition system, semiconductor fabrication system, plasma sputtering system, etc. The capacitance C 2 , for example, may represent the capacitance of the chuck upon which the wafer may sit. The chuck, for example, may comprise a dielectric material. For example, the capacitor C 1  may have small capacitance (e.g., about 10 pF, 100 pF, 500 pF, 1 nF, 10 nF, 100 nF, etc.). 
     The capacitor C 3 , for example, may represent the sheath capacitance between the plasma and the wafer. The resistor R 6 , for example, may represent the sheath resistance between the plasma and the wafer. The inductor L 2 , for example, may represent the sheath inductance between the plasma and the wafer. The current source  12 , for example, may be represent the ion current through the sheath. For example, the capacitor C 1  or the capacitor C 3  may have small capacitance (e.g., about 10 pF, 100 pF, 500 pF, 1 nF, 10 nF, 100 nF, etc.). 
     The capacitor C 9 , for example, may represent capacitance within the plasma between a chamber wall and the top surface of the wafer. The resistor R 7 , for example, may represent resistance within the plasma between a chamber wall and the top surface of the wafer. The current source I 1 , for example, may be representative of the ion current in the plasma. For example, the capacitor C 1  or the capacitor C 9  may have small capacitance (e.g., about 10 pF, 100 pF, 500 pF, 1 nF, 10 nF, 100 nF, etc.). 
     As used in this document the plasma voltage is the voltage measured from ground to circuit point  123 ; the wafer voltage is the voltage measured from ground to circuit point  122  and may represent the voltage at the surface of the wafer; the chucking voltage is the voltage measured from ground to circuit point  121 ; the electrode voltage is the voltage measure from ground to circuit point  124 ; and the input voltage is the voltage measured from ground to circuit point  125 . 
       FIG.  7    illustrates a nanosecond pulser system  700  according to some embodiments. The nanosecond pulser system  700  includes the nanosecond pulser  105 , the primary sink  206 , the transformer T 1 , the bias compensation circuit  610 , and the load stage  615 . 
       FIG.  8    illustrates a nanosecond pulser system  800  according to some embodiments. The nanosecond pulser system  800  includes the nanosecond pulser  305 , the primary sink  106 , the transformer T 1 , the bias compensation circuit  610 , and the load stage  615 . 
       FIG.  9    illustrates a nanosecond pulser system  900  according to some embodiments. The nanosecond pulser system  900  includes the nanosecond pulser  105 , the primary sink  406 , the transformer T 1 , the bias compensation circuit  610 , and the load stage  615 . 
       FIG.  10    illustrates a waveform  1005  of the voltage at the input to the transformer T 1 , a waveform  1010  of the voltage at the chuck (the point labeled  121 ), and a waveform of the voltage at the wafer (the point labeled  122 ) using the nanosecond pulser system  900 . 
     In some embodiments, the chucking potential is shown as negative, however, the chucking potential could also be positive. 
       FIG.  11    is a block diagram of a high voltage switch  1100  with isolated power according to some embodiments. The high voltage switch  1100  may include a plurality of switch modules  1105  (collectively or individually  1105 , and individually  1105 A,  1105 B,  1105 C, and  1105 D) that may switch voltage from a high voltage source  1160  with fast rise times and/or high frequencies and/or with variable pulse widths. Each switch module  1105  may include a switch  1110  such as, for example, a solid state switch. 
     In some embodiments, the switch  1110  may be electrically coupled with a gate driver circuit  1130  that may include a power supply  1140  and/or an isolated fiber trigger  1145  (also referred to as a gate trigger or a switch trigger). For example, the switch  1110  may include a collector, an emitter, and a gate (or a drain, a source, and a gate) and the power supply  1140  may drive the gate of the switch  1110  via the gate driver circuit  1130 . The gate driver circuit  1130  may, for example, be isolated from the other components of the high voltage switch  1100 . 
     In some embodiments, the power supply  1140  may be isolated, for example, using an isolation transformer. The isolation transformer may include a low capacitance transformer. The low capacitance of the isolation transformer may, for example, allow the power supply  1140  to charge on fast time scales without requiring significant current. The isolation transformer may have a capacitance less than, for example, about 100 pF. As another example, the isolation transformer may have a capacitance less than about 30-100 pF. In some embodiments, the isolation transformer may provide voltage isolation up to 1 kV, 5 kV, 10 kV, 25 kV, 50 kV, etc. 
     In some embodiments, the isolation transformer may have a low stray capacitance. For example, the isolation transformer may have a stray capacitance less than about 1,000 pF, 100 pF, 10 pF, etc. In some embodiments, low capacitance may minimize electrical coupling to low voltage components (e.g., the source of the input control power) and/or may reduce EMI generation (e.g., electrical noise generation). In some embodiments, the transformer stray capacitance of the isolation transformer may include the capacitance measured between the primary winding and secondary winding. 
     In some embodiments, the isolation transformer may be a DC to DC converter or an AC to DC transformer. In some embodiments, the transformer, for example, may include a 110 V AC transformer. Regardless, the isolation transformer can provide isolated power from other components in the high voltage switch  1100 . In some embodiments, the isolation may be galvanic, such that no conductor on the primary side of the isolation transformer passes through or makes contact with any conductor on the secondary side of the isolation transformer. 
     In some embodiments, the transformer may include a primary winding that may be wound or wrapped tightly around the transformer core. In some embodiments, the primary winding may include a conductive sheet that is wrapped around the transformer core. In some embodiments, the primary winding may include one or more windings. 
     In some embodiments, a secondary winding may be wound around the core as far from the core as possible. For example, the bundle of windings comprising the secondary winding may be wound through the center of the aperture in the transformer core. In some embodiments, the secondary winding may include one or more windings. In some embodiments, the bundle of wires comprising the secondary winding may include a cross section that is circular or square, for example, to minimize stray capacitance. In some embodiments, an insulator (e.g., oil or air) may be disposed between the primary winding, the secondary winding, or the transformer core. 
     In some embodiments, keeping the secondary winding far from the transformer core may have some benefits. For example, it may reduce the stray capacitance between the primary side of the isolation transformer and secondary side of the isolation transformer. As another example, it may allow for high voltage standoff between the primary side of the isolation transformer and the secondary side of the isolation transformer, such that corona and/or breakdown is not formed during operation. 
     In some embodiments, spacings between the primary side (e.g., the primary windings) of the isolation transformer and the secondary side of the isolation transformer (e.g., the secondary windings) can be about 0.1″, 0.5″, 1″, 5″, or 10″. In some embodiments, typical spacings between the core of the isolation transformer and the secondary side of the isolation transformer (e.g., the secondary windings) can be about 0.1″, 0.5″, 1″, 5″, or 10″. In some embodiments, the gap between the windings may be filled with the lowest dielectric material possible such as, for example, vacuum, air, any insulating gas or liquid, or solid materials with a relative dielectric constant less than 3. 
     In some embodiments, the power supply  1140  may include any type of power supply that can provide high voltage standoff (isolation) or have low capacitance (e.g., less than about 1,000 pF, 100 pF, 10 pF, etc.). In some embodiments, the control voltage power source may supply 1120 VAC or 240 VAC at 60 Hz. 
     In some embodiments, each power supply  1140  may be inductively electrically coupled with a single control voltage power source. For example, the power supply  1140 A may be electrically coupled with the power source via a first transformer; the power supply  1140 B may be electrically coupled with the power source via a second transformer; the power supply  1140 C may be electrically coupled with the power source via a third transformer; and the power supply  1140 D may be electrically coupled with the power source via a fourth transformer. Any type of transformer, for example, may be used that can provide voltage isolation between the various power supplies. 
     In some embodiments, the first transformer, the second transformer, the third transformer, and the fourth transformer may comprise different secondary winding around a core of a single transformer. For example, the first transformer may comprise a first secondary winding, the second transformer may comprise a second secondary winding, the third transformer may comprise a third secondary winding, and the fourth transformer may comprise a fourth secondary winding. Each of these secondary winding may be wound around the core of a single transformer. In some embodiments, the first secondary winding, the second secondary winding, the third secondary winding, the fourth secondary winding, or the primary winding may comprise a single winding or a plurality of windings wound around the transformer core. 
     In some embodiments, the power supply  1140 A, the power supply  1140 B, the power supply  1140 C, and/or the power supply  1140 D may not share a return reference ground or a local ground. 
     The isolated fiber trigger  1145 , for example, may also be isolated from other components of the high voltage switch  1100 . The isolated fiber trigger  1145  may include a fiber optic receiver that allows each switch module  1105  to float relative to other switch modules  1105  and/or the other components of the high voltage switch  1100 , and/or, for example, while allowing for active control of the gates of each switch module  1105 . 
     In some embodiments, return reference grounds or local grounds or common grounds for each switch module  1105 , for example, may be isolated from one another, for example, using an isolation transformer. 
     Electrical isolation of each switch module  1105  from common ground, for example, can allow multiple switches to be arranged in a series configuration for cumulative high voltage switching. In some embodiments, some lag in switch module timing may be allowed or designed. For example, each switch module  1105  may be configured or rated to switch 1 kV, each switch module may be electrically isolated from each other, and/or the timing of closing each switch module  1105  may not need to be perfectly aligned for a period of time defined by the capacitance of the snubber capacitor and/or the voltage rating of the switch. 
     In some embodiments, electrical isolation may provide many advantages. One possible advantage, for example, may include minimizing switch to switch jitter and/or allowing for arbitrary switch timing. For example, each switch  1110  may have switch transition jitters less than about 500 ns, 50 ns, 20 ns, 5 ns, etc. 
     In some embodiments, electrical isolation between two components (or circuits) may imply extremely high resistance between two components and/or may imply a small capacitance between the two components. 
     Each switch  1110  may include any type of solid state switching device such as, for example, an IGBT, a MOSFET, a SiC MOSFET, SiC junction transistor, FETs, SiC switches, GaN switches, photoconductive switch, etc. The switch  1110 , for example, may be able to switch high voltages (e.g., voltages greater than about 1 kV), with high frequency (e.g., greater than 1 kHz), at high speeds (e.g., a repetition rate greater than about 500 kHz) and/or with fast rise times (e.g., a rise time less than about 25 ns) and/or with long pulse lengths (e.g., greater than about 10 ms). In some embodiments, each switch may be individually rated for switching 1,200 V-1,700 V, yet in combination can switch greater than 4,800 V-6,800 V (for four switches). Switches with various other voltage ratings may be used. 
     There may be some advantages to using a large number of lower voltage switches rather than a few higher voltage switches. For example, lower voltage switches typically have better performance: lower voltage switches may switch faster, may have faster transition times, and/or may switch more efficiently than high voltage switches. However, the greater the number of switches the greater the timing issues that may be required. 
     The high voltage switch  1100  shown in  FIG.  11    includes four switch modules  1105 . While four are shown in this figure, any number of switch modules  1105  may be used such as, for example, two, eight, twelve, sixteen, twenty, twenty-four, etc. For example, if each switch in each switch module  1105  is rated at 1100 V, and sixteen switches are used, then the high voltage switch can switch up to 19.2 kV. As another example, if each switch in each switch module  1105  is rated at 1700 V, and sixteen switches are used, then the high voltage switch can switch up to 27.2 kV. 
     In some embodiments, the high voltage switch  1100  may switch voltages greater than 5 kV, 10 kV, 11 kV, 20 kV, 25 kV, etc. 
     In some embodiments, the high voltage switch  1100  may include a fast capacitor  1155 . The fast capacitor  1155 , for example, may include one or more capacitors arranged in series and/or in parallel. These capacitors may, for example, include one or more polypropylene capacitors. The fast capacitor  1155  may store energy from the high voltage source  1160 . 
     In some embodiments, the fast capacitor  1155  may have low capacitance. In some embodiments, the fast capacitor  1155  may have a capacitance value of about 1 μF, about 5 μF, between about 1 μF and about 5 μF, between about 100 nF and about 1,000 nF etc. 
     In some embodiments, the high voltage switch  1100  may or may not include a crowbar diode  1150 . The crowbar diode  1150  may include a plurality of diodes arranged in series or in parallel that may, for example, be beneficial for driving inductive loads. In some embodiments, the crowbar diode  1150  may include one or more Schottky diodes such as, for example, a silicon carbide Schottky diode. The crowbar diode  1150  may, for example, sense whether the voltage from the switches of the high voltage switch is above a certain threshold. If it is, then the crowbar diode  1150  may short the power from switch modules to ground. The crowbar diode, for example, may allow an alternating current path to dissipate energy stored in the inductive load after switching. This may, for example, prevent large inductive voltage spikes. In some embodiments, the crowbar diode  1150  may have low inductance such as, for example, 1 nH, 10 nH, 100 nH, etc. In some embodiments, the crowbar diode  1150  may have low capacitance such as, for example, 100 pF, 1 nF, 10 nF, 100 nF, etc. 
     In some embodiments, the crowbar diode  1150  may not be used such as, for example, when the load  1165  is primarily resistive. 
     In some embodiments, each gate driver circuit  1130  may produce less than about 1000 ns, 100 ns, 10.0 ns, 5.0 ns, 3.0 ns, 1.0 ns, etc. of jitter. In some embodiments, each switch  1110  may have a minimum switch on time (e.g., less than about 10 μs, 1 μs, 500 ns, 100 ns, 50 ns, 10, 5 ns, etc.) and a maximum switch on time (e.g., greater than 25 s, 10 s, 5 s, 1 s, 500 ms, etc.). 
     In some embodiments, during operation each of the high voltage switches may be switched on and/or off within 1 ns of each other. 
     In some embodiments, each switch module  1105  may have the same or substantially the same (±5%) stray inductance. Stray inductance may include any inductance within the switch module  1105  that is not associated with an inductor such as, for example, inductance in leads, diodes, resistors, switch  1110 , and/or circuit board traces, etc. The stray inductance within each switch module  1105  may include low inductance such as, for example, an inductance less than about 300 nH, 100 nH, 10 nH, 1 nH, etc. The stray inductance between each switch module  1105  may include low inductance such as, for example, an inductance less than about 300 nH, 100 nH, 10 nH, 1 nH, etc. 
     In some embodiments, each switch module  1105  may have the same or substantially the same (±5%) stray capacitance. Stray capacitance may include any capacitance within the switch module  1105  that is not associated with a capacitor such as, for example, capacitance in leads, diodes, resistors, switch  1110  and/or circuit board traces, etc. The stray capacitance within each switch module  1105  may include low capacitance such as, for example, less than about 1,000 pF, 100 pF, 10 pF, etc. The stray capacitance between each switch module  1105  may include low capacitance such as, for example, less than about 1,000 pF, 100 pF, 10 pF, etc. 
     Imperfections in voltage sharing can be addressed, for example, with a passive snubber circuit (e.g., the snubber diode  1115 , the snubber capacitor  1120 , and/or the freewheeling diode  1125 ). For example, small differences in the timing between when each of the switches  1110  turn on or turn off or differences in the inductance or capacitances may lead to voltage spikes. These spikes can be mitigated by the various snubber circuits (e.g., the snubber diode  1115 , the snubber capacitor  1120 , and/or the freewheeling diode  1125 ). 
     A snubber circuit, for example, may include a snubber diode  1115 , a snubber capacitor  1120 , a snubber resistor  1116 , and/or a freewheeling diode  1125 . In some embodiments, the snubber circuit may be arranged together in parallel with the switch  1110 . In some embodiments, the snubber capacitor  1120  may have low capacitance such as, for example, a capacitance less than about 100 pF. 
     In some embodiments, the high voltage switch  1100  may be electrically coupled with or include a load  1165  (e.g., a resistive or capacitive or inductive load). The load  1165 , for example, may have a resistance from 50 ohms to 500 ohms. Alternatively or additionally, the load  1165  may be an inductive load or a capacitive load. 
     In some embodiments, the primary sink  106 , the primary sink  206 , or the primary sink  406  can decrease the energy consumption of a high voltage nanosecond pulser system and/or the voltage required to drive a given load. For example, the energy consumption can be reduced as much as 10%, 15% 20%, 25%, 30%, 40%, 45%, 50%, etc. or more. 
     In some embodiments, the diode D 4 , the diode  110 , and/or the diode D 6  may comprise a high voltage diode. 
     Unless otherwise specified, the term “substantially” means within 5% or 10% of the value referred to or within manufacturing tolerances. Unless otherwise specified, the term “about” means within 5% or 10% of the value referred to or within manufacturing tolerances. 
     The term “or” is inclusive. 
     Numerous specific details are set forth herein to provide a thorough understanding of the claimed subject matter. However, those skilled in the art will understand that the claimed subject matter may be practiced without these specific details. In other instances, methods, apparatuses or systems that would be known by one of ordinary skill have not been described in detail so as not to obscure claimed subject matter. 
     Some portions are presented in terms of algorithms or symbolic representations of operations on data bits or binary digital signals stored within a computing system memory, such as a computer memory. These algorithmic descriptions or representations are examples of techniques used by those of ordinary skill in the data processing arts to convey the substance of their work to others skilled in the art. An algorithm is a self-consistent sequence of operations or similar processing leading to a desired result. In this context, operations or processing involves physical manipulation of physical quantities. Typically, although not necessarily, such quantities may take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared or otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to such signals as bits, data, values, elements, symbols, characters, terms, numbers, numerals or the like. It should be understood, however, that all of these and similar terms are to be associated with appropriate physical quantities and are merely convenient labels. Unless specifically stated otherwise, it is appreciated that throughout this specification discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining,” and “identifying” or the like refer to actions or processes of a computing device, such as one or more computers or a similar electronic computing device or devices, that manipulate or transform data represented as physical electronic or magnetic quantities within memories, registers, or other information storage devices, transmission devices, or display devices of the computing platform. 
     The system or systems discussed herein are not limited to any particular hardware architecture or configuration. A computing device can include any suitable arrangement of components that provides a result conditioned on one or more inputs. Suitable computing devices include multipurpose microprocessor-based computer systems accessing stored software that programs or configures the computing system from a general-purpose computing apparatus to a specialized computing apparatus implementing one or more embodiments of the present subject matter. Any suitable programming, scripting, or other type of language or combinations of languages may be used to implement the teachings contained herein in software to be used in programming or configuring a computing device. 
     Embodiments of the methods disclosed herein may be performed in the operation of such computing devices. The order of the blocks presented in the examples above can be varied—for example, blocks can be re-ordered, combined, and/or broken into sub-blocks. Certain blocks or processes can be performed in parallel. 
     The use of “adapted to” or “configured to” herein is meant as open and inclusive language that does not foreclose devices adapted to or configured to perform additional tasks or steps. Additionally, the use of “based on” is meant to be open and inclusive, in that a process, step, calculation, or other action “based on” one or more recited conditions or values may, in practice, be based on additional conditions or values beyond those recited. Headings, lists, and numbering included herein are for ease of explanation only and are not meant to be limiting. 
     While the present subject matter has been described in detail with respect to specific embodiments thereof, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing, may readily produce alterations to, variations of, and equivalents to such embodiments. Accordingly, it should be understood that the present disclosure has been presented for purposes of example rather than limitation, and does not preclude inclusion of such modifications, variations and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art.