Precise, Sub-Nanosecond, and High-Voltage Switching of Complex Loads Enabled by Gallium Nitride Electronics
John W. Simonaitis, Benjamin Slayton, Yugu Yang-Keathley, Phillip D. Keathley, Karl K. Berggren
PPrecise, Subnanosecond, and High-Voltage Switching of Complex Loads Enabledby Gallium Nitride Electronics
John W. Simonaitis, a) Benjamin Slayton, Yugu Yang-Keathley, Phillip D. Keathley, and Karl K. Berggren Research Laboratory of Electronics, Massachusetts Institute of Technology Wentworth Institute of Technology (Dated: 8 February 2021)
In this work, we report the use of commercial Gallium Nitride (GaN) power electronics toprecisely switch complex distributed loads, such as electron lenses and deflectors, withoutimpedance matching. Depending on the chosen GaN field effect transistor (GaNFET) anddriver, these GaN pulsers are capable of generating pulses ranging from 100 - 650 V and 5- 60 A in 0.25 - 8 ns using simple designs with easy control, few-nanosecond propagationdelays, and MHz repetition rates. We experimentally demonstrate a simple 250 ps, 100V pulser measured by a directly coupled 2 GHz oscilloscope. By introducing resistivedampening, we can eliminate ringing to allow for precise 100 V transitions that complete a-10 V to -90 V transition in 1.5 ns, limited primarily by the inductance of the oscilloscopemeasurement path. The performance of the pulser attached to various load structures issimulated, demonstrating the possibility of even faster switching of internal fields in theseloads. These circuits also have 0 .
25 cm active regions and under 1 W power dissipation,enabling their integration into a wide variety of environments and apparatus. The proximityof the GaNFETs to the load due to this integration minimizes parasitic quantities that slowswitching as well as remove the need to match from 50 Ω lines by allowing for a lumpedelement approximation small loads. We expect these GaN pulsers to have broad applicationin fields such as optics, nuclear sciences, charged particle optics, and atomic physics thatrequire nanosecond, high-voltage transitions. a) Electronic mail: [email protected] a r X i v : . [ phy s i c s . i n s - d e t ] F e b . INTRODUCTION Nanosecond, high-voltage pulses have broad application in in the physical sciences, rangingfrom their use in optics for driving Pockels cells and piezoelectric actuators , to their use in de-flecting and gating electrons or ions in nuclear science, spectroscopy , charged particle optics ,and quantum measurement schemes . In the past, these fast pulses have been generated by a widevariety of technologies such as silicon power FETs , avalanche transistor circuits , step re-covery diodes , non-linear transmission lines , spark gaps , and laser-triggered semiconductorgaps . Various reviews and studies exist comparing some of these techniques , and most re-cently the use of nanoplasmas has given record switching performance. While some techniquesdeliver pulses greater than 100 kV in < 100 ps, these approaches have varied trade-offs and short-comings. Among the most important are the cost and complexity of pulser designs, their large sizeand high power dissipation that force us place pulsers far away from the loads they drive, the lackof simple, single-shot driving schemes, and slow repetition rates. All of these techniques also haveproblems with ringing due to resonances in the pulse generating circuits and loads, and impedancemismatch problems developed over the length scales of the transmission line and loads. For struc-tures that requires precise switching, removing ringing requires either slowing of the pulse edgewith low pass filtering to avoid load resonances, the use of resonant filters to selectively removethose worst resonances, or predistortion calibration techniques that require high bandwidth arbi-trary waveform generators to create messy pulses that result in clean output switching .In this work, we demonstrate the potential of simple and low-cost GaN power electronics forfast and precise high-voltage switching. While such electronics have been used extensively forhigh-efficiency power converters , amplifiers , and pulsed lasers , we believe that these cir-cuits have the potential for wide application in physics and engineering for high power nanosecondswitching. These circuits are fast and simple to control, with single-shot pulsing triggered by a5 V logic inputs up to a repetition rate of 60 MHz and propagation delays of a few nanoseconds.The high power efficiency and low thermal dissipation of these circuits also offer advantages inoperation, leading to small form factors that are compatible with vacuum environments common inphysics applications. They are also inexpensive, costing two orders-of-magnitude less than equiv-alent commercial pulsers. Through careful selection of parts and layout optimization, the reportedpulser achieves both undamped 250 ps and damped 1.5 ns, 100 V transitions (as measured by thetime to go from -10 V to -90 V, or 10% to 90%) into a 2 GHz oscilloscope. These measurements2re limited primarily by the path inductance into the oscilloscope. We then simulate the responseof various predominantly inductive, capacitive, and mixed loads to the GaNFET pulser, demon-strating precise nanosecond transitions even faster than those we measured experimentally, withringing controlled to within 1% the transition amplitude by resistive damping. We discuss alter-native topologies allowing for symmetric pulse edges and higher voltage operation. Finally wediscuss how our GaNFET-based switching performance in real loads compares to that of low-passfiltered pulses on 50 Ω lines. II. EXPERIMENTAL VALIDATION
Wide bandgap semiconductors have long been considered excellent candidates for power elec-tronics due to their ability to withstand voltage and currents far beyond that of silicon, low channelresistances, and high temperature compatibility . In recent years, GaN on silicon technology hasemerged as a low cost and robust option with commercial products that have small gate and outputcapacitances, optimized packages with minimal parasitic inductances, and a wide variety of cur-rent and voltage ratings . Along with these advances, commercial drivers with subnanosecondrise times, 7 A of peak drive current, 60 MHz repetition rates, and 2.5 ns propagation delays haveemerged . Together, these offer the possibility of subnanosecond switching of hundreds of voltsand tens of amperes.In order to validate these switching speeds, we built a testing circuit from the LMG1020 driverfrom Texas Instruments along with the 200 V EPC2012C enhancement mode GaNFET from theEfficient Power Corporation. The basic circuit design is shown in Figure 1a. The load is held topotential V bias until the gate driver is triggered by V trig . When the driver is triggered, the gate driveroutputs a high current signal through R gate to turn on the GaNFET by charging its gate. Chargeis then shunted out from both the GaNFET’s parasitic output capacitance and the arbitrary loadthrough R damp into ground, bringing the load bias to zero . When the GaNFET is shut back off, V bias pulls the voltage back up through R bias , though this transition is significantly slower due tothe larger value of R bias set to limit power dissipation in this element. The resistors R gate and R damp are also used to set the turn on time and damp and ringing for the FET and the load, respectively.A tunable trimming circuit, as shown in red in Figure 1a, was incorporated to ensure that thetransition was critically damped, since the RF damping resistors used had values too coarse toprecisely damp the circuit. 3 IG. 1. Test-bed for GaN pulsing. (a) The circuit schematic, where the gate driver is the LMG1020, andGaNFET the EPC2012C. R gate damps the gate turn on loop, R damp damps the load loop, and R bias sets thepower usage and load recovery time. The optional trimming circuit in red allows for fine tuning of the loaddamping that the course-valued resistors used could not achieve, though this was not used in the the resultsshown. (b) The physical layout of the circuit mounted on a Kapton on copper substrate. The highlightedwhite region shows the active portion of the circuit which is less than 0 .
25 cm . The circuit is directlycoupled into a LeCroy 6200A oscilloscope with ∼
20 pF of input capacitance through a 2.2 pF capacitor.(c) The undamped response, showing significant long-term ringing. The inset shows a zoomed in version ofthis ringing. The full transition is approximately 540 ps, while the 10% to 90% transition is in 230 ps. (d)The same pulse edge, but damped through a 200 Ω resistor. It achieves a 10% to 90% transition in 1.5 ns,0% to 90% accuracy in 1.9 ns, and 0% to 99% accuracy in 5.1 ns. Note that all traces are multiplied by afactor of ∼
10 to account for the voltage division caused by the 2.2 pF coupling capacitor, in order to matchthe final voltage to the biasing applied.
Figure 1b shows the realization of this circuit on a 100 µm thick Kapton dielectric and coppersubstrate, directly coupled through an SMA and SMA-to-BNC adapter to the oscilloscope. Thewhite shaded region shows the active area of the GaNFET, driver, bypass capacitors and damping,taking up less than 0 .
25 cm , while the power supply makes up the rest of the circuit and can4e placed off-board. Detailed optimization of the components and layout to minimize parasiticquantities and maximize switching speed is discussed in the supplement.The undamped and damped response of the circuit coupled through a 2.2 pF capacitor to a2 GHz LeCroy 6200A oscilloscope is shown in Figure 1c and d respectively. Initially we tookmeasurements with a passive, 500 MHz, 10 M Ω probe (LeCroy PP007-WR), but we found thatthe distributed nature of the probe complicated our attempts to reduce the circuit to a simplelumped element model. This is discussed further in the supplement. The undamped response at R damp = 0 Ω shows a full, 0% to 100% transition in 540 ps, but suffers from massive overshootand significant ringing. To ensure we did not damage the oscilloscope with this overshoot, we keptthis measurement to 50 V, though when measured by the probe we easily pushed this to 100 V asseen in Figure S4b in the supplement. The damped response obtained at R damp = 200 Ω shows atransition from -10 V to -90 V (10% to 90% of the amplitude) in less than 1.5 ns with no residualringing, as shown in Figure 1c. More significantly, the damped circuit is capable of reaching 10%of the final voltage in under 1.9 ns, and 1% accuracy in ∼ ∼
20 pF oscilloscope capacitance in parallelwith the 2.2 pF capacitor, and is validated by the 1:10 attenuated voltage transition we measure onthe oscilloscope.We then measure the ringing frequency of the undamped load. This is approximately 1.1 GHz.Assuming that this measurement is relatively undamped, we can then use Eqn. 1 below to estimatethe loop inductance. Here L osc is the oscilloscope inductance, f ring the ringing frequency, and C osc the oscilloscope capacitance see through the 2.2 pF coupling capacitor. This leads us to estimatethe inductance to be ∼
10 nH, which is roughly consistent with the 200 Ω damping we requiredto prevent ringing. This is also validated by the fact that commonly used RG-58/U coaxial cablehas an inductance of 3.66 nH/cm, and the measured connector to oscilloscope length is ∼ ∼
11 nH of inductance.5 osc = ( π f ring ) C osc . (1)The response times of both of these transitions are limited by the inductance of the oscilloscopepath, which results in a ∼ III. SIMULATION OF RESPONSE TO REALISTIC LOADS
In order to validate the performance of the GaNFET pulser for switching realistic loads, wesimulated the GaNFET pulser’s switching performance in various systems, including a primarilycapacitive load, a primarily inductive load, and a load with characteristics of both, as shown inFigure 2a, Figure 3d, and Figure 3a respectively.The basic approach and results of these simulations are outlined in Figure 2a-d. First, wedefined a geometric structure in COMSOL Multiphysics to be excited. In the case of the primarilycapacitive load, we defined three 304 stainless steel plates from Kimball Physics stacked withalumina spacers, with the central electrode (red) receiving the GaNFET excitation as shown inFigure 2a. This kind of structure is widely used in electron optics for the fast gating (if the beamenters vertically) and deflection (if the beam enters horizontally) of charged particles. We definedthe source and drain of the GaNFET to be our input ports for the simulations.Using the RF Module in COMSOL, we ran a full wave simulation of the structure in the fre-quency domain, extracting both the field distributions in the load and the port impedance seen bythe GaNFET, as shown in Figure 2b and 2c respectively. The rational fit and the circuit model ofthe port impedance was generated in MATLAB and imported into LTSpice to simulate the voltageat the port. This is shown in the supplement. Then in MATLAB, we took the Fourier transformof this output voltage and multiplied it with the voltage-to-field transfer function at the point indi-6
IG. 2. Simulated models of a parallel plate load. (a) The geometry of the load where the length of theplate is 3 cm, with the red x denoting the point at which we are probing the electric field. (b) The fieldstructure of the load at various frequencies. At 10 MHz, the load all is driven in unison. Until ∼ damp , which slows the response as it removes ringing. Notethat higher-frequency ringing does still exist in the load fields due to the higher-order resonances, but theyare less than 1% the transition magnitude Ω to 50 Ω .At a damping of 25 Ω we see the fastest ringing-free transition, which corresponds to a 200 Vtransition in less than 1 ns. The underlying switching performance and its dependence on R damp isconsistent with the measurement on a similarly resonant load, the oscilloscope-GaNFET systemresonant at ∼ . Explicitly, we require λ = v eff / f >> ‘, (2)where λ is the wavelength, v eff the propagation velocity in the medium (in this case just c for vacuum), and f the frequency of interest. This approximation is generally held valid if thestructure length-scale λ is ’ ‘ .We can see this lumped element behavior emerge explicitly in the impedance plotted in Figure2c. At frequencies below 500 MHz, the parallel plates exhibit the characteristic of a 7.38 pFcapacitor. As the frequency increases beyond 500 MHz and approaches the first resonance at 1.4GHz, the load is no longer purely capacitive, but is well-modeled using an RLC resonant circuitwith an inductance of 1.70 nH as shown in the Figure 2c. However, above 2 GHz, the system canno longer be treated as an 2nd-order LC lumped circuit due to the many resonant modes developedby the length scale of the load, some examples of which are shown in Figure 2b.This simplified RLC lumped element treatment offers significant advantage in the ability to es-timate and remove ringing in our system. By treating the load as a lumped RLC model, it becomessignificantly easier to understand the effects of the parasitic output capacitance and inductanceof the driving FET. This treatment also allows “critical dampening” of the circuit with an appro-priately selected series resistance, dramatically simplifying the filter design that would normallybe needed for such a precise transition. This is demonstrated in Figure 2d, where a damping re-sistance is selected to cause a highly smooth transition that resembles a critical damping in RLC8 IG. 3. Other simulated loads. (a) A high voltage electron lens structure, with the red x showing the fieldsampling point near the center of the mirror. (b) The response of the lens at various frequencies, withresonances fitting the geometry of the structure. (c) The temporal field response with increasing damping.(d) An inductive load with the vertical magnetic field sampled in the center of the structure. (e) The magneticfield distribution, which is complicated even at low frequencies, and concentrates the field via capacitivecoupling near the edge of the coils at higher frequencies. (f) The result of damping the inductor, with a hugeringing period due to the large DC inductance of the structure. circuits. Ringing-like behavior at ∼ . This load has varied capacitance from the outside of the structureto the inside, as well as a much more significant inductive component due to the large ground return9oop. Various resonances of this structure are shown in Figure 3b, and we can clearly see strongerelectric fields near the center due to the closer plate spacing. Unlike the first capacitor model,this load cannot be easily simplified into a transmission line segment and thus matched to 50 Ω systems. However, the load can still be simplified into 5.50 pF capacitive model at low frequenciesand a series RLC circuit with 2.35 nH inductance at higher frequencies. This fit is shown in FigureS9a of the supplement. This higher inductance and lower capacitance is consistent with the largerground return path of this structure compared to the primarily capacitive load. As before, usingGaNFET driving and dampening of the first RLC resonance, it was possible to generate a ringing-free field transitions in the load at the field probe point, this time in 1.2 ns, slightly slower. Thegenerated field strength is equivalent to that that would be generated from a 200 V potential appliedto the center electrode. It is interesting to note that nominally the first resonance of this lens andthe first deflector are roughly the same, but this lens has a slightly slower response. This is due tothe output capacitance of the GaNFET in the LTSpice model, which results in a response that ismuch more sensitive to the inductance of the load. This is discussed in the supplement in greaterdetail.Another load we drove is the inductive coil shown in Figure 3a, which primarily generates amagnetic field rather than an electric field and is used commonly for applying strong magneticfields to samples and for electron beam deflection systems . The driving topology for this circuitis different from that of the previous cases due to the low DC impedance of the load. This is shownin the supplement. At low frequencies, this element behaves as a near perfect 313 nH inductor,with an impedance that increases linearly as a function of frequency. As the frequency increases,the capacitance between the wires begin to shunt current, resulting in a reduced impedance andmore concentrated fields near the edges as shown in Figure 3e. When the first resonance is reachedaround 260 MHz, we can model the circuit as a parallel RLC circuit with a capacitance of 1.15pF. Similar to the previously discussed loads, we were able to tune R coil to achieve a ringing-free magnetic field response driven by a 20 A current as shown in Figure 3f. However, due to thelarge inductive component coupled to the GaNFET’s output capacitance, this load requires a largerresistance of 110 Ω to damp, slowing the response substantially. Although the current transitiontime of roughly 20 ns can be shortened by reducing the loop size or number, inductive loads willalmost always be slower that capacitive loads due to the fixed output capacitance of the GaNFETcircuit and layout. 10 V. DISCUSSION
Besides providing fast, ringing-free switching of hundreds of volts and tens of amperes, theGaNFET switches described above also offer the following useful features. (1) Affordability.The circuit shown in Figure 1b is simple to assemble using standard soldering tools, and coststwo-orders-of magnitude less than commercial pulsers. This enables wide use in a range of exper-imental apparatus. (2) Compatibility with computer and FPGA driving. These circuits also offersimple and arbitrary control by 3.3 V pulses on 50 Ω lines; (3) repetition rates up to 60 MHz (ifa high side P-Channel transistor is used rather than the resistor), in comparison to several KHzfor spark gap technologies and 25 MHz for custom state-of-the-art avalanche circuits ; (4) 2.5ns propagation delays which open the possibility of real-time control based on triggering of othersingle-shot measurements in an apparatus; (5) a <0 .
25 cm active form factor that allows for theintegration of these circuits extremely close to the loads they drive, minimizing parasitic energystorage that slow transitions; (6) <1 W power dissipation at 10 MHz, which scales approximatelylinearly with the circuit repetition rate. The low power dissipation means that it is possible to op-erate these circuits under vacuum, a requirement for driving loads such as charged particle opticsin this manner.The pulsers discussed so far have been optimized for single-sided driving, where one transition(the negative sloped one) is on the order of nanoseconds, while the reset transition is on the order oftens of nanoseconds. This maximizes the speed of the faster edge and simplifies the circuit designsignificantly, though limits the technique in terms of repetition rates and for some applications.In order to drive both positive and negative edges, alternative topologies such as a half-bridgeconfiguration with bootstrapping is required. Commercial drivers, such as the LMG1210 fromTexas Instruments, do exist for this, though the increased size and complexity of the circuitryslows their transition times. Also note that fully integrated GaNFET circuits do exist, such as theLMG3410 from Texas Instruments, though have slower switching transitions than demonstratedhere.By varying the FET technology and topology, this approach can be extended to switching evenhigher voltages and currents. The simplest way of doing this is to vary the GaNFET technology,using for example the GS61004B from GaN Systems or the TP65H070LSG from Transphorm,both of which are capable of 650 V operation, though their increased gate capacitance, outputcapacitance, and parasitic inductance lead to slowed output transitions. Another approach would11 IG. 4. Step response of the load in Figure 2a. (a) The response of the load to a 50 ps step (dotted line), setby the bandwidth of the simulation. This shows ringing at not just the lowest resonant frequency, but alsoat the higher order frequencies shown by the roughness on the trace. (b) The same response, but with theedge slowed by a Gaussian filter to reduce the ringing to 1% the transition magnitude. The orange trace istaken from Figure 2d for comparison, showing an even faster RLC-based response. be to use SiC technology, allowing for transitions of several thousand volts though at the cost ofeven slower transitions. Alternate topologies used historically to improve silicon performance,such as parallel and stacked FETs or cascode configurations could also be used to improve bothvoltage ratings and transition performance in these GaN systems.Several routes also could be used to increase the speed of these switches to achieve subnanosec-ond transitions. Smaller, lower voltage FETs such as the 100 V EPC2037 from the Efficient PowerCorporation would have significantly faster switching due to its smaller gate and output capaci-tance, as well as its lower form factor. For low voltages and medium currents of ∼ ∼
400 pstransition times. If state-of-the-art rise times are desired, non-linear pulse sharpening techniquessuch as step recovery diodes and nanoplasmas could be used together with these FETs, whichwould allow for transitions on the order ∼
100 ps or less, and would not increase layout size sig-nificantly.A natural question that arises as we increase the speed of the transitions is how fast the loads12undamentally can be driven, especially when trying to ensure no ringing. Even if we drovethe load with an ideal 100 ps step, the high-frequency resonances of the load would drown outthe signal in ringing and drag out the transition. This is demonstrated in Figure 4a for the realload in Figure 2a. If we then put this transition through an ideal Gaussian filter to reduce thepulse bandwidth and reduce the ringing to ∼
1% the transition, we get the result in Figure 4bwhich is significantly slower, taking roughly 2 ns to get within 1% accuracy. This transition issignificantly slower than the RLC response also shown in Figure 4b, which took only 1.2 ns toachieve equivalent accuracy. Different filtering schemes, such as Chebyshev or Butterworth filtersmight improve this further, but these were not explored.Two general approaches come to mind for driving these loads faster: optimizing the load struc-ture to minimize resonances, and shaping the incident signal to avoid these resonances. The firstrelies on pushing the load resonances up or reducing their magnitude. Increasing the resonancescan be achieved by reducing the physical size of the load and avoiding the use high permeabil-ity and permittivity materials. Reducing their quality factor can be done by introducing surfaceroughness to the load, increasing the structures resistivity with different materials or coatings, orintroducing a lossy propagating media. However, we have not explored any of these routes indepth.The input engineering approach can be realized with various schemes of increasing complexity.The simplest approach would be to use a low-pass filter to generate a transition with a sharpercutoff that excites the first resonance less than the Gaussian filter we simulated. Exactly howmuch faster you could drive this circuit with that is unclear and depends strongly on the load andspecific filter used. A second approach that would give a faster response would be to design aresonant filter that selectively removes the strongest resonant peaks in the output. Exactly howaccurately one could find and remove these resonances and to what bandwidth is unclear. A thirdapproach similar to the resonant one would be to use an arbitrary waveform generator (AWG) todigitally generate create an input signal with the resonant modes removed. This would removeringing to the bandwidth and gain to the limits of the AWG and amplifier used, though againprobing to precisely remove the ringing would be a challenge. This approach has been explored inrecent work . 13 . CONCLUSION In this work, we demonstrated the potential of inexpensive GaN power electronics to switchreal loads commonly found in physics and engineering with high power and few-nanosecond,ringing-free transitions. We first validated this concept by constructing a test-bed circuit capableof switching 100 V in 250 ps with ringing, and 1.5 ns without ringing. This was done with adesign using raw parts costing two orders of magnitude less than comparable commercial pulsegenerators. Switching up to 200 V was tested to ensure the switch did not fail, but was nevermeasured in operation due to concerns of damaging the oscilloscope used. Due to our inability toreduce measurement parasitics at such high voltages, and in order to see the field distribution witha real load, we simulated the output of the circuit for various structures ranging from capacitive toinductive. We then extracted the temporal response of the electric and magnetic fields in the load atvarious points, demonstrating ∼ ∼ ACKNOWLEDGMENTS
This work was supported by the Gordon and Betty Moore Foundation. This material is basedupon work supported by the National Science Foundation Graduate Research Fellowship under14rant No. 1745302. Yugu Yang-Keathley and Ben Slayton acknowledge support from the DouglasD. Schumann Professorship. The authors thank Marco Turchetti and Navid Abedzadeh for helpwith designing the original structures simulated, Texas Instruments for providing internal SPICEmodels of the LMG1020 used in the simulations, and the QEM-II collaboration for insightfuldiscussions. In particular, we would like to thank the Kasevich group at Stanford, especially AdamBowman, Brannon Klopfer, and Stewart Koppell, for many discussions of fast pulsing technology,alternative techniques to drive such loads, and applications of these pulsers. The authors also thankIlya Charaev and Owen Medeiros for helpful feedback on the manuscript.
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Microwave Engineering (Wiley, New York, 2009). Handbook of Charged Particle Optics (2017). H. Rahaman, J. W. Nam, S. H. Nam, and K. Frank, “A miniaturized spark gap switch in theregime of high repetition rate,” Proceedings of the 2010 IEEE International Power Modulatorand High Voltage Conference, IPMHVC 2010 , 385–387 (2010). N. Beev, J. Keller, and T. E. Mehlstäubler, “Note: An avalanche transistor-based nanosec-ond pulse generator with 25 MHz repetition rate,” Review of Scientific Instruments (2017),10.1063/1.5000417. G. Wong Choi, J. Joo Choi, and S. Hoon Han, “Note: Picosecond impulse generator driven bycascaded step recovery diode pulse shaping circuit,” Review of Scientific Instruments (2011),10.1063/1.3523342. 17 recise, Subnanosecond, and High-Voltage Switching of Complex Loads Enabledby Gallium Nitride Electronics: Supplementary Information John W. Simonaitis, a) Benjamin Slayton, Yugu Yang-Keathley, Phillip D. Keathley, and Karl K. Berggren Research Laboratory of Electronics, Massachusetts Institute of Technology Wentworth Institute of Technology (Dated: 8 February 2021) a) Electronic mail: [email protected] a r X i v : . [ phy s i c s . i n s - d e t ] F e b . CIRCUIT DESIGN The full circuit used is shown in Figure S1a, with part numbers labeled. The power supply isbased on the TPS7A4700RGWT from Texas Instruments, though any low-noise DC supply willsuffice. In order to minimize switching times and ringing, significant care was taken to choosedriver capacitors with high self resonant frequencies (SRFs) and low equivalent series resistances(ESRs). We placed the capacitors as close to the LMG1020 driver as possible, as shown in Figure1b. We used the combination of a 0 . Label(s) Value Manufacturer Part NumberC6 0 . Ω Vishay Dale CRCW02012R00FXEDR3 1 k Ω Bourns Inc. CR0603-JW-102ELFR4, R5 10 Ω Vishay Thin Film FC0402E10R0BTT0R6, R7 25 Ω Vishay Thin Film FC0402E25R0BTT0J2, J5 12 GHz Murata Electronics MM5829-2700RJ4TABLE S1. List of components from schematic shown in Figure S1 IG. S1. Test-bed circuit schematics and layout. (a) The main part of the circuit design, excluding the powersupply which is represented by VCC. (b) The layout. The active region is to the right. Note the proximityof the input capacitors to the LMG1020 and the minimized ground return path directly under the drive loop.
Damping was implemented using high-frequency thin film resistors ranging from 10 Ω to 200 Ω (Vishay Thin Film FC Series). Though the 0.125 W power rating would indicate they can onlyoperate to 1.25 MHz (assuming 100 V switching of 10 pF), we found the resistor continued work-ing to 5 MHz. Using better heat-sinking and multiple damping resistors in parallel to spread outthe dissipation, we found this circuit could operate up to 20 MHz, the maximum repetition rate3e tested. However, in this condition, the load never fully recharged due to the large bias pathimpedance. This exercise was primarily aimed at measuring power dissipation limits. If a fasterresetting rate is needed a high-side P-channel FET would need to be put in place of the dampingresistor, or a bootstrapping circuit based on the LMG1210 used.We were also able to make these circuits vacuum compatible. This was done by using silver-based solder (SMD291SNL-ND from Chip Quik Inc.) and low-outgassing Kapton substrates(PCBWay). After assembly, the circuits were mounted on Oxygen-free high conductivity (OFHC)copper, sonicated in PCB cleaning solution (PELCO Kleensonic™ APC) rinsed by water and IPA,and finally encased in thermally conductive and electrically insulating ceramic epoxy (EPO-TEK®H70E Thermally Conductive Epoxy). II. ASSEMBLY PROCEDURE
The following details the construction of this high-speed GaN circuit.1. First, we prepare our work space. Electrostatic discharge (ESD) safe mats and groundingbracelets are a necessity to get high circuit yields. We first preheat a hot plate to 190°C. Wethen preheat a soldering iron to 300°C. Tape the circuit using an easy release masking tapeto whatever work surface you hope to assemble it on, as shown in Figure S2a.2. Next, we use a soldering stencil from the layout given (also from PCBway) and align itusing a magnifying glass or microscope to the pattern. Tape one side of the mask as shownwith the flipped stencil in Figure S2a. We found aligning to the smallest component padswas the easiest way to do this.3. Apply a small amount of solder paste to the edge of the mask. Holding the stencil firmlyand evenly down, use a straight edge (such as a plastic card) to gently spread the paste overall of the holes, ensuring each hole is covered. Then, pressing more strongly on the card,scrape away any excess material.4. Remove the stencil, being careful to pop it directly up. Inspect the layout, ensuring thereare no solder paste connections between different pads. If there are only a few, it is possibleto correct by breaking the bridges with a fine tip such as some tweezers. If there are toomany bridges or the paste is too spread out, wipe the surface clean and repeat. An exampleof good looking paste application is shown in Figure S2b.4. Now assemble components. If not already done, make sure to wear an ESD bracelet, or atleast ground your tweezers with an alligator clip or something similar. Even the slightestdischarge will destroy the GaNFET, causing your FET to be measured as approximate 1 Ω to 10 Ω across the source to drain even when off. Other various tips are below.• When assembling, we generally we start with the largest components and work downin size, finishing with the EPC2012c and LMG1020 as their pads are the most delicateand they are the most expensive. The only exception to this size rule is placing R1 andR2, which we generally do fairly early since they are inexpensive and easy to messup, and it is nice to have space to place them without worrying about knocking theGaNFETs or driver out of place. FIG. S2. Overview of circuit assembly for thermal management and vacuum compatibility. (a) Taping ofthe circuit to the board, and the stencil attached to the left with tape (flipped upside-down). (b) Solder pasteclearly on pads, resulting from a well-aligned stencil. (c) Heating of the circuit on a hot plate to solder eachconnection. Also shown is the solder spread on the copper mount, which we place the circuit on for heat-sinking. (d) the final circuit without wires, showing successful soldering of the components and bonding tothe copper heat sink.
II. CIRCUIT SAFETY AND TESTING
Next, we test the circuit. We first connect the circuit to ground. Next, we attach the high voltagebiasing port to a high voltage port. In our case, we used a 150 V piezo supply (Thorlabs modelMDT693B) with a 1 M Ω resistor tied to ground (for safety and ESD protection) coupled througha BNC cable (rated to 300 V). This high voltage supply is left off until testing. We then turn on thepower supply supply. In early tests we used a 6 V power supply (XP Power VEL05US060-US-JA) with the designed regulator circuit. For later tests, to reduce power dissipation in the circuitand it more vacuum compatible, we used a 5 V direct connection from a low noise power supply(Keithley Model 2220). We saw no difference in results using either source.We then hook up the RF ports. We used an SMA-to-JSC adapter (GradConn CABLE 366RF-200-A) and BNC-to-SMA adapter to get the input signal from the signal generator (Keysight33250A) to the driving board. For traces shown, we input a 3 V, 100 ns wide pulse with 5 nsrising edges at a repetition rate of 100 KHz. This low rate was chosen to reduce the voltage offset FIG. S3. Testing setup used, showing shielding, ground insulation, and probing. IG. S4. Passive probing. (a) Close up on the grounding connection used. (b) Damped and undampedtraces, showing recurring ringing we hypothesize are due to probe reflections. caused by AC-coupling, reduce thermal effects, and ensure we did not put too much power intothe oscilloscope. Using the probe, which protects the oscilloscope, we tested to 20 MHz, withoutfailure, though this limited by the recharge time of the biasing resistor which reduced the fullvoltage swing of the circuit. The second input was grounded.We then turned on the high voltage supply, starting at 5 V to ensure the circuit functionedproperly. Once this was verified we slowly increased to voltage to the set point. For initial testswe used a LeCroy PP007-WR 500 MHz 10 M Ω probe, tested up to 100 V with a blade groundconnector, as shown in Figure S3. The probe was compensated using a 1 MHz square wave signalfrom the signal generator.A zoom in of this testing, as well as the resulting traces is shown in Figure S4a and b respec-tively. Both traces were acquired with 100 V biasing. The undamped trace in Figure S4b showssignificant ringing, and a recurring ringing at 12 ns. We hypothesis that the recurring ringingaround 12 ns is due to reflections in the probe line, as their occurrence matches the round trip timeof the line (knowing the cable length is 1.2 m, and assuming the wave propagates at 66% thespeed of light, a common value for many coaxial cables). The damped trace shows a well-dampedtransition. However, as the probe reflection indicates, this system can not be easily modelled as anRLC-lumped element circuit since the cable length scale is similar to the transition time.For the final testing, we directly hooked up our circuit through an SMA connector which weadapted to a BNC connector and inserted into the oscilloscope. This is described in the main text.In Figure S5a, we show models of each measurement. Figure S5a shows our model for the passiveprobe. This consists of a capacitance C probe in series with a lossy transmission line (TL) with a8 IG. S5. Comparison of measurement types. (a) Passive probe model. (b) Direct connection model. length of 1.2 m. This length scale results in a roughly 100 MHz resonance in the load we drive.Though this resonance is designed to be weak by making the cable highly lossy, this length scalestill breaks down our analysis of this system as an RLC-type load. The observed reflection in S4bis evidence of this. For simplicity, compensating circuitry in the probe is not shown.Figure S5b shows the resulting model from directly hooking up our circuit to the oscilloscope.This simply results in C decouple being placed in series with R damp and L parasitic , creating a simpleRLC-type resonator that we can damp. By carefully selecting the value of C decouple , we can thenattenuate our voltage signal, allowing us to safely probe voltages up to 100 V. If this capacitoris not used, changing the range of the oscilloscope changes the measured ringing of the circuit.This is demonstrated in Figure S6. We hypothesize that this is due to the oscilloscope amplifierchanging impedance as the gain changes. By decoupling the impedance with a much smallercapacitor, we then stabilize the impedance seen by the GaNFET, and thus the measurement. IV. SIMULATION DETAILS
The first modeling step of this work was to represent the printed circuit board (PCB) layout andthe load in COMSOL. This was done by extracting the dimensions of the PCB and drain pad of9
IG. S6. Effect of changing gain on the measurement. (a) A trace with a gain of 1.02 V/division. (b) Thesame trace with a gain of 1.00 V/division. Switching this range causes an audible click in the oscilloscope,likely due to some sort of switched amplifier configuration on the input, which visibly changes the responseof the circuit. the GaNFET from the layout to Autodesk Fusion 360 and attaching this to various structures wedesigned. This PCB port model is shown in Figure S7a. The models of these structures were thenimported into COMSOL.The simulation consisted of a frequency-domain calculation of the loads using the RF Elec-tromagnetics Module of COMSOL Multiphyics, exporting of the S-Parameters to MATLAB andusing MATLAB’s RF Toolbox rationalfit function to generate a rational fit to the model. Thesimulation was run from 10 MHz to 10 GHz at 10 MHz steps. Then using the MATLAB gener-ateSPICE function we exported a SPICE circuit fitting this resonant behavior up to 10 GHz. Acomparison of this fit is shown in Figure S7e.The LTSpice circuit model used is shown in Figure S7d. Note that the circuit is AC-coupledby a 1 µF capacitor. This capacitor was used because the rational fit model is unable to correctlyrepresent the capacitor’s infinite impedance at DC. Figure S7e shows the impedance response ofthis combined system, which has a plateau around 1 MHz. The 1 µF decoupling capacitor allows10
IG. S7. Representation of the simulation. (a) A close up of the PCB, with the area treated in the simulationhighlighted in green. (b) The simplified PCB model that was used to launch the RF signals in all of thesimulations. (c) The RF port attached to the load of interest, in this case the deflector. (d) The SPICE sim-ulation, which interacts the EPC2012C and LMG1020 with the RF port, denoted as JWS_TestNetwork_v0.(e) A comparison of the full impedance response from COMSOL to the circuit model fit generated in MAT-LAB from the rationalfit and generateSPICE functions, and output as JWS_TestNetwork_v0. Note that therational fit model smooths some features of the COMSOL simulation, shown by the deviations of the blueand orange curves around 3.5 GHz and the three blips from 7 - 9 GHz shown. These individual points arelikely not physical and due to glitches in the simulation. IG. S8. Fourier calculations of field ringing in the loads. In this example we show that multiplying (a) thefrequency spectrum of the pulse by (b) the port voltage to field in load transfer function (the top right, takenat the red x in Figure 2a) results in the spectrum in (c). Note that (b) is basically flat until 500 MHz, thenbegins to rise until a peak at 1.44 GHz. This occurs because a quarter-wave mode that forms in the mirrorwith the minimum at the port, and maximum at the edge of the deflector as shown in Figure 2b at 1.44 GHz.This means that if we force a small set field (normalized to 1 V) at the input port near this resonance, a largefield will result at the edge, and thus a large field at the sampling point as well. Depending on the distance ofthe sampling point away from the port, the frequency at which this peaks changes. The closer the samplingis to the port, the higher frequency this resonance. Taking the inverse Fourier transform results in the timedomain response shown (d). the circuit model to treat the infinite DC impedance properly, and as long as this capacitance ismuch larger than the system under test, has virtually no effect on the results. The existence ofthis plateau should not effect the performance of this simulation, as the impedance here is alreadysignificantly higher than that of the rest of the circuit.Next, we took the time domain output from LTSpice, interpolated it to match the COMSOL12requency stepping, and took the Fourier transform of this. This resulted in the plot shown inFigure S8a. We then multiplied it with the voltage to field transfer function of the load (FigureS8b) resulting in the output seen in Figure S8c. Taking the inverse Fourier transform of this led toFigure 2d in the main text.
V. ANALYSIS OF OTHER LOADS
The impedance response and transfer functions of the Einzel lens and coil are shown in FigureS9a-d. From the RLC fits shown we extract the lumped parameters of the loads given in the maintext. Note that for the inductor model we only simulated up to 5 GHz due to the lower resonancesof the structure which lead to increasing complex and likely non-physical resonances in the 5-10 GHz range.The inductive load was unable to be driven effectively by the circuit topology in Figure 1aof the main text due to the significant impedance differences of inductive and capacitive loads.The SPICE model used is shown in Figure S10. The damping approach for the inductive load isnot very efficient for real driving, but still demonstrates the fundamental switching capabilities ofthe GaNFET. Alternative damping techniques such as the use of a series resistor and capacitor inparallel would probably be more feasible, though was not explored.Order-of magnitude estimates can be made for these loads without the need for full simulations.For inductive loads, we can estimate the load inductance using equation S1, where A is the looparea, µ the core permeability, N the number of loops, and ‘ the length of the coil. The outputcapacitance of the GaNFET circuit will generally dominate the capacitive portion of the response,and so the resonator can be treated as a combination of the circuit capacitance of 1 pF directly toan ideal inductor. L coil = µ N A ‘ . (S1)For capacitors, we can roughly estimate the capacitance of the structure with a parallel plateapproximation using equation S2, where ε is the permittivity of the medium, ‘ the length of theplates, w the width, and d the separation. If the spacing varies over the structure, a very roughestimate of the capacitance can be made by using the "average" spacing of the plates over the fullstructure. The inductance can be over-estimated by forming a loop from the GaNFET to the endof the structure at the average spacing, and using equation S3 below, where µ is the permeability13 IG. S9. Example impedance plots and transfer functions of the other loads shown. (a) The port impedanceof the Einzel lens, with the fit to a series capacitive-inductive load. (b) The transfer function relating thefield in center of the lens to the voltage at the input port. (c) The port impedance of the inductive coil load.The resonance is much lower than in the other cases due to the large inductance of the coil. (d) The transferfunction of the magnetic field in the center of the coil to the current input into the load. of the medium and the other quantities the same as for S2. C plates = ε w ‘ d , (S2) L plates = µ d ‘ w . (S3)Using these lumped element quantities, we can estimate the "critical" damping ( R damp ) neededof any structure using equation S4. This takes into account the total capacitance ( C total ), induc-14 IG. S10. Simulated inductor topology. Notice the replaced ground symbol attached to nGnd. This wasused because the circuit model of the inductor was internally referenced to ground, so in order to drive theinductor as if it was attached to a voltage source to the drain, we had to drop the potential of the rest of thecircuit to this so-called "new" ground. tance ( L total ), and resistance ( R internal ) ) of the system. In our circuit, the layout capacitance isapproximately 1 pF, the inductance approximately 0.5 nH, and the resistance (from the GaNFETchannel and PCB roughness at such high frequencies) approximately 20 Ω , which we add to thequantities calculated for the load above. However, none of these quantities were experimentallyverified. Better estimates of the inductive and capacitive quantities can be found from ? . Doublingthe damping estimated from the rough estimation of these quantities ensured over-damped results. R damp = R internal + r L total C total . (S4)If we would like to go a step further than damping the port voltage and ensure there is no fieldringing, we would have to estimate the frequency spectrum of the pulse as well as the locationsand magnitudes of the resonances in the load, and then multiply these together in the frequencydomain. Calculating the frequency spectrum of the pulse is the most straightforward part of thisto estimate, and thus we do it to start.We first need to estimate what the port voltage would look like. This can be done in threeways. The first, more accurate approach is to simulate the circuit in LTSpice, using an RLC circuitwith the estimated parameters as the load, and inserting the GaNFET of choice. Selecting thesimulation time as the repetition rate, interpolating the output to a chosen sample rate, and thentaking the Fourier transform of this gives the frequency spectrum. This approach accurately takes15nto account the GaNFET turn-on time and any coupling from the gate drive circuit. A simpler butless accurate approach for estimating edge shape can be taken by an ideal RLC circuit respondingto a step. In this case, it is possible to solve for the response analytically, then take the Fouriertransform of this at the resolution and repetition rate that is desired, which we do in the attachedcode. Third, it should also be possible to analytically solve for the RLC transfer function, thenmultiply this by an ideal step in the frequency domain to get a fully analytic solution, though wedid not do this.We then must estimate the position of the resonances. We do this only for the capacitive case.We do this by taking the distance from the GaNFET to the point of interest in our system, weightedby the average velocity of propagation in the system. In the simplified case of pure dielectrics( µ r = ‘ i is the length of each segment, ‘ tot the total length to the point of interest, and ε i thepermittivity of each segment. Next, we use this effective impedance to derive the position of thefirst resonance, assuming that this is a quarter-wave resonance (caused by the low impedance atthe input port set by the damping resistance and high impedance at the sampling point). This isshown in equation S5. We estimate the first resonance to be roughly 10 times larger than the DCresponse, which is consistent with our simulations. ε eff ≈ ‘ ‘ tot ε + ‘ ‘ tot ε + ... (S5) f res ≈ c ‘ tot √ ε eff (S6)We now multiply the frequency response of the driving edge with this resonant point to estimatethe total ringing in the field quantities. By tuning the resistance used in our circuit we can filter towhatever ringing accuracy we hope to achieve. If, for example, the first resonance is at 1.4 GHzand we want 1% ringing, we then would need the amplitude of the driving edge’s frequencyresponse at 1.4 GHz to be 10 − times that of the DC response. This comes from the need toachieve 10 − accuracy in the resonance relative to the ideal step, divided by the enhancement ofthat frequency component due to the resonance, which we estimate it to be 10 . Resonator qualityfactors vary drastically depending on the metal chosen, surface roughness, dielectric losses, anddetailed geometry, and so an improved estimate of this is deeply dependent on the exact structure.16 I. DATA AVAILABILITY
All data, COMSOL simulations, circuit schematics, and MATLAB scripts for this work areavailable at https://github.com/qnngroup/GaN_Pulsers.githttps://github.com/qnngroup/GaN_Pulsers.git