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A coupled-circuit representation of IGBT module geometry for high di/dt switching applications Rablah, Blake Kenton 2007

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A Coupled-Circuit Representation of IGBT Module Geometry for High di/dt Switching Applications by Blake Kenton Rablah B.Eng., The University of Victoria, 2004 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F Master of Applied Science i n The Faculty of Graduate Studies (Electrical & Computer Engineering) The University Of British Columbia January 5th, 2007 © Blake Kenton Rablah, 2007 A b s t r a c t A coupled-circuit element representation of an IGBT module from Westcode Semiconductors Inc. has been developed, simulated, and experimentally confirmed at TRJUMF in Vancouver, BC. This model can be simulated in PSpice to predict the distribution of current within the IGBT module under high di/dt switching conditions. The goal of the simulations is to determine if the module is an acceptable candidate for implementation in a thyratron replacement switch for high-power pulse-power applications. The model developed has been shown to agree well with frequency do-main measurements, and also with finite element method (FEM) simulations and boundary element method (BEM) simulations of the device. ii Table of Contents Abstract ii Table of Contents iii List of Tables v List of Figures vi Acknowledgements viii 1 Background 1 1.1 Intended Application 1 1.2 Available Technology 2 1.2.1 Thyratrons 2 1.2.2 Solid State Thyratron Replacements 3 1.3 Switch Selection 6 1.3.1 Electrical Criteria 6 1.3.2 Form Factor 6 1.3.3 Prior Work 8 1.3.4 Westcode Module Specifics 9 1.4 Focus of this Thesis 13 2 Simulation of Current Distribution 15 2.1 Simulation Methods 15 2.1.1 Software Tools 16 2.1.2 Simulation Geometries 18 2.2 Simulation Workflow 19 2.2.1 Workflow 1: Opera 2D Field Solution 20 2.2.2 Workflow 2: IES OERSTED Field Solver 23 2.2.3 Workflow 3: OERSTED Extraction with PSpice Sim-ulation 25 iii Table of Contents 2.2.4 Workf low 4: Fasthenry Ex t rac t ion w i th PSpice S imu-lat ion 30 2.3 S imulat ion Results 34 2.3.1 A C Steady State Results 34 2.3.2 Resistive Modu le Results 41 2.3.3 A C Steady State Results 42 2.3.4 Pulsed T i m e Doma in Results 45 3 E x p e r i m e n t a l V e r i f i c a t i o n 51 3.1 Me thod of Analys is 51 3.1.1 Frequency Domain 51 3.1.2 Resistive Elements ( I G B T Replacements) 52 3.1.3 Current Sensing 53 3.2 Test J ig 58 3.2.1 Requirements 58 3.2.2 Design 59 3.3 A C Measurement Results 63 3.3.1 Pure ly Copper Modu le 63 3.3.2 Resistive Modu le 65 4 C o n c l u s i o n s a n d R e c o m m e n d a t i o n s fo r F u t u r e W o r k . . . 68 B i b l i o g r a p h y 70 A p p e n d i x A : I G B T O n - s t a t e R e s i s t a n c e 74 A p p e n d i x B : F r e q u e n c y D e p e n d a n c e o f P a r a m e t e r s 77 A p p e n d i x C : C o u p l e d I n d u c t o r s F r o m I m p e d a n c e M a t r i x e s 81 List of Tables 1.1 Anticipated requirements for a thyratron replacement . . . . 2 2.1 Modelling and simulation software 17 v V List of Figures 1.1 Silicon wafer comparisons - A = SCR Thyristor, B = IGCT, C = IGBT chip wafer 5 1.2 Comparison of IGBT module packaging options 7 1.3 Rendering of a Westcode press pack IGBT module intended for pulsed power applications 10 1.4 Photos of a dismantled Westcode module 11 1.5 Rendering of the internals of a Westcode press pack IGBT module with numbered current paths 12 1.6 Westcode provided equivalent circuit of press pack module . . 13 2.1 Opera2D Field Solver workflow 20 2.2 Modelled geometry - Opera 2D 21 2.3 External circuit for Opera2D AC analysis 22 2.4 Workflow 2 - IES OERSTED Field Solver 23 2.5 Modelled geometry - IES OERSTED, IGBT die are shown in red, return paths in blue 24 2.6 Workflow 3 - OERSTED extraction and PSpice simulation . . 25 2.7 OERSTED geometry for circuit parameter extraction . . . . 26 2.8 PSpice AC Analysis with OERSTED Circuit Parameters . . . 28 2.9 Workflow 4 - Fasthenry extraction and PSpice simulation . . 30 2.10 Fasthenry 3D geometry for circuit parameter extraction . . . 31 2.11 Field solver predictions of steady state current distribution for an "all copper" module 35 2.12 PSpice simulated predictions of steady state current distribu-tion for an "all copper" module 38 2.13 Comparison of workflow predicted distributions at low fre-quency and high frequency AC drives 40 2.14 Effect of introducing resistive Si region to model current dis-tribution 43 2.15 Simulation tool comparison with 2.5mf} Si region resistance . 44 List of Figures 2.16 Pulse forming circuit used for time domain pulsed distribution analyses 46 2.17 Current distribution for simulated module with 12.5mfJ on-state resistance and a 10% to 90% rise-time of 300ns 47 2.18 Effect of varying rise-time and on-state resistance on current distribution for a 8kA pulse 48 2.19 Predicted current distribution for simulated 12.5mf2 module with scaled post-heights 50 3.1 Resistive elements to replace IGBT die, in place within the Westcode module . . . . 53 3.2 Rogowski coil construction 55 3.3 Rogowski coils in-place within Westcode module . 56 3.4 Instrumentation amplifier circuit diagram 57 3.5 Photograph of the instrumentation amplifier used for AC measurements 58 3.6 CERN Prevessin test jig for presspack IGBTs (Note: "Muli-Contact" (sic) should read "MultiContact")[l] 60 3.7 TRIUMF test jig assembly photos 61 3.8 Current path through TRIUMF test jig 62 3.9 Test setup electrical layout 62 3.10 Experimental results for high-frequency (2MHz) distribution with copper-only module . 64 3.11 Comparison of simulated and measured current distribution within the IGBT module with 2.5mf2 of series resistance . . . 66 A . l V-I relationship for Westcode IGBT die to determine on-state resistance (Vg a ^ e = 15V) 75 A. 2 Measurement set up for IGBT die on-state resistance mea-surements 75 B. l Extracted resistance, inductance and mutual coupling terms for a "copper only" model of the Westcode IGBT module as a function of frequency 78 B.2 Different extraction frequencies and their effect on module current distribution 80 Acknowledgements I would like to thank TRIUMF, and in particular Ewart Blackmore, for their continued support, funding and lab-space, dating back to my original co-op placement at the facility. I would also like to thank Mike Barnes and Gary Wait for their mentorship and guidance, without which this work would not have possible. viii C h a p t e r 1 Background In the field of high-power pulsed-power, high speed switching is the founda-tion upon which all else is built. Switches in this field are often required to withstand blocking voltages in the tens of kilovolts and switch several kilo-amps in less than a microsecond. One application in which these switches are in frequent deployment is in high energy physics labs around the world. These switches drive kicker magnets that deflect charged beams of particles, or drive klystrons that accelerate these particles. New developments in semiconductor research are leading to faster solid state switches that are encroaching on other established pulsed-power tech-nologies. However, many of these switches have been designed for larger commercial markets such as traction applications, and have not been de-signed explicitly with pulsed-power in mind [2]. Pulsed power places an ex-tra burden on the designers of semiconductor switches. Specifically, the high-frequency content of the pulses and the large di/dt and dv/dt that re-sult make the geometry and resulting parasitic components of the devices a particular concern. This puts designers of pulsed semiconductor devices and modules in territory that has historically been the concern of VLSI packaging designers. 1.1 Intended Applicat ion The work described in this document was begun in response to the need for a semiconductor based switch for high pulsed currents with very short risetimes. One potential application of such a switch was for the yet-to-be-funded International Linear Collider to drive klystron modulators. It is envisioned that this semiconductor-switch would be able to turn-on approx-1 Chapter 1. Background imately 3kA in approximately 300ns, for a peak di/dt >10kA//_is, and would be able to be connected in series configurations to permit blocking voltages of at least 75kV [3]. Other thyratron replacement designs cite similar requirements [4], so these figures can be considered general design goals. However, in order to be considered sufficient for application to kicker magnet applications, the re-quirements become somewhat more demanding. Table 1.1 details the design objectives for which the Westcode module is being considered. Table 1.1: Anticipated requirements for a thyratron replacement Criteria Requirement Blocking voltage Stackable to >65kV Peak current (Ipk) >8kA Risetime (to Ipk) <l;us (min. 10kA//is) Pulsewidth {Tpuise) 1/xs -» DC 1.2 Available Technology 1.2.1 Thyratrons At the present time, the main devices used for high-power high-speed switch-ing are hydrogen gas filled thyratrons. Similar in design to the more common vacuum tube, a thyratron is a gas-filled device, with an anode and a cath-ode separated by one or more grids. Switching is achieved when the gas inside the thyratron ionizes and goes from being strongly insulating, to con-ducting in a very short time. Some thyratrons are capable of blocking over lOOkV, and are able to switch tens of kiloamps in just tens of nanoseconds[5]. Typical kicker magnet applications require current rise-times in the neigh-bourhood of 30ns to peak currents above 3kA. This results in a di/dt in excess of 100kA///s. As an example of one such application: a TRIUMF-designed kicker-magnet for the LHC at CERN featured a thyratron driver that switched a 54kV PFN into a 5J7 load: the current rises to a maximum 2 Chapter 1. Background of 5.4kA with a 10% to 90% rise-time of 30ns, corresponding to a di/dt of 180kA/fis[6]. As impressive as these numbers are, thyratrons exhibit some very signif-icant drawbacks when compared to semiconductor devices: Spontaneous Turn-on Thyratrons are known to have a finite probability of spontaneous turn-on. Furthermore, this probability goes up consid-erably as the voltage across a thyratron rises, and also with the length of time this voltage is held. Designers of thyratron circuits sometimes employ fast resonant power supplies to quickly ramp up the voltage on the thyratron shortly before switching, minimizing the thyratron's exposure to high voltage and reducing the chance of spontaneous turn on. [7] Switching Control The second disadvantage of thyratrons is the lack of control while switching. Thyratrons latch into the on-state, and will remain latched until they reach zero-current, and the plasma inside the tube is exhausted [5]. Lifetime Thyratrons also have a limited life span that is dependent both on the number of pulses and the total charge transferred. For any remotely high-frequency high-current application, this can make them expensive to deploy. One such application: as klystron modulators for the International Linear Collider (ILC), would require a team of individuals dedicated to thyratron replacement and adjustment (see below) [8]. Maintenance In addition to lifetime concerns, thyratrons require frequent adjustment over their lifespan to maintain their switching character-istics. This adds both to the complexity and cost of a thyratron de-ployment. 1.2.2 Solid State Thyratron Replacements Even the most advanced solid state devices still have limited voltage and current ratings in comparison to high power thyratrons. Nonetheless, since 3 Chapter 1. Background approximately 1990, considerable effort has been made to produce a solid state replacement for hydrogen gas filled thyratrons. Companies like ABB and Dynex Semiconductor now manufacture thyratron replacement modules constructed from series connected SCR or IGBT devices[4] [9]. However, these devices fall far behind gas thyratrons in terms of switching speed, and as such are not yet suitable "replacements". S C R Based Solutions Both ABB and Dynex, as well as some other manufacturers have devel-oped thyratron replacement stacks from SCR modules. These stacks are capable of di/dt values in excess of 20kA//US, and are capable of very high peak currents, with 90kA advertised for one Dynex device (Dynex part #: PT85QWx45). However, while SCRs fix the lifetime and spontaneous turn-on issues of Thyratrons, they still exhibit some significant drawbacks. SCRs also latch in the on-state and exhibit a similar lack of control during switching as thyratrons. Also, thyristor SCRs require considerable gate currents to switch on. This is especially true when fast switching is desired, where gate currents can exceed 200A [3]. The necessity of a large gate current places strong demands on the gate drive circuit; this can be problematic to implement when each gate drive circuit is floating several kilovolts apart from the next. IGBT Based Solutions IGBTs are bipolar power switching devices that feature a MOSFET-like insulated gate. IGBTs have begun to take over in industry sectors previously dominated by SCRs, especially for medium power applications. The ability to turn-off, even under load, and the simplicity of the gate drive circuit are the two main selling points for IGBT based switches. Additionally, IGBTs can self-limit their current when short circuited[11], which is of interest to a designer looking for some degree of fault tolerance in their design. 4 Chapter 1. Background A B C Figure 1.1: Silicon wafer comparisons - A = SCR Thyristor, B = IGCT, C = IGBT chip wafer Controlled switching is also possible with IGBT modules, and active control of series connected modules has been achieved [12]. There are some significant shortcomings associated with current IGBT technologies that limit their applications in the high-power pulsed-power field. While breakdown voltages of individual IGBT die are starting to encroach on territory typically occupied by SCR thyristors, they have rela-tively lagged in current handling capacity. Part of the reason for this stems from a limitation in the IGBT silicon manufacture that sets the maximum die size at « l c m 2 ; many modern SCRs and IGCTs can be constructed on single 91mm diameter wafers (Figure 1.1 Figure 1.1 [10]). Due to the limitation in die size, high-power IGBT devices are con-structed in modules of several IGBT die in parallel. This introduces the problem of ensuring uniform current sharing. Under DC or slow transient conditions, current sharing is dominated by the relative on-state resistances of the various IGBT die within a module. However, under high speed switch-ing conditions, it has been shown that the internal layout of IGBT modules has a marked effect on the current distribution within the module, and cor-5 Chapter 1. Background respondingly also the performance and lifetime of the module [2]. Further analysis of IGBT module geometry has identified that parasitic inductances and coupling to the gate circuit within the packaging are largely to blame for current imbalances in some types of module[13][14]. IGBTs are of continued interest for designers of a thyratron replacement switch, but it is apparent that more attention needs to be paid to IGBT module design if such an application is to be realized. ABB manufactures a thyratron replacement that uses stacked IGBT modules, but it's relatively slow switching speed (maximum of 1.5kA//^s) is a testament to the challenge that faces designers of IGBT based solutions [15]. It is possible to boost di/dt performance of a slower switch by adding a saturating magnetic core in series with the switch. This "saturating reactor" will initially appear very inductive and limit the rise of current, until satu-ration occurs, which results in an effective short circuit. The disadvantage of this approach, to pulsed power applications, is that it adds a consider-able amount of parasitic inductance to the circuit and can contribute to impedance mismatches in the system. Additionally, as the characteristics of the non-linear magnetic material are fixed, lower operating voltages will result in slower saturation of the magnetic material, and therefore a signif-icantly reduced di/dt: limiting the useful dynamic operating voltage of the switch. 1.3 Switch Selection 1.3.1 Electrical Criteria Electrically, the switch must be capable of meeting the requirements already outlined in Section 1.1, specifically the requirements for kicker-magnets out-lined in Table 1.1. 1.3.2 Form Factor IGBT modules come in several different types of packages. Two of the main approaches to package design are shown in Figure 1.2; on the left is a "brick 6 Chapter 1. Background < k m i i1 Figure 1.2: Comparison of IGBT module packaging options type" package manufactured by Mitsubishi, on the right is a "hockey puck" style of press-type package from Westcode. Brick Type Modules In the brick-type package the IGBT die are flow-soldered onto a PCB that contains traces for the collector, emitter and gate. Additional interconnections are made with individual wire bonds. This type of arrangement, the most common for power IGBT modules, offers easy connection to external circuits via bolt-on terminals, and is relatively cheap to manufacture. However, for pulsed power applications, this ease of connection comes at a price. [2] [13] [14] illustrate the difficulties associated with achieving uniform current distribution using this design. Additionally, low inductance series configuration is difficult, as these modules take up a considerable amount of space, and both emitter and collector terminals are on the same side of the device. One significant advantage of this type of module is that they can be configured such that the return path has a minimal effect on the current distribution within the module. As much of the work detailed in this doc-ument deals with this particular subject, it is apparent that this is not of small importance. 7 Chapter 1. Background Press Pack Modules Devices of this design, are constructed such that the emitter and collector terminals make up the top and bottom of the module. The term 'press pack' comes from the way in which individual die are sandwiched inside the module between the collector and emitter terminals. Electrical contact is achieved by compressing the module under a considerable amount of force (between 20kN and 70kN, depending on the design and application). Series connection is relatively simple as modules can be stacked one upon the other, and the entire structure compressed to make electrical contact both between and within each individual module. This series configuration also lends itself well to low inductance designs, for the return current path can be constructed to surround the stack: creating a coaxial structure. One aspect where press pack designs have a distinct advantaged is cool-ing. Heat is conducted away from both sides of the silicon by the emitter and collector contacts. Cooling solutions can then be applied at these terminals. Another advantage, perhaps more important to pulsed power applica-tion, of the press pack design concerns the mode of failure for the IGBT die. Press pack IGBTs fail to short circuit. This means that, with proper redundancy in a series stack of modules, that a failure in one module (or device within a module) is rarely catastrophic, and the stack usually remains functional[16]. In contrast, brick-type IGBTs often fail violently, severing the wire-bonds within the module and resulting in an open circuit[2]. For even a few individual IGBT die to fail in this fashion would render the entire stack useless. 1.3.3 P r i o r W o r k S L A C Experiments TRIUMF's initial investigations into IGBT based thyratron replacements began in conjunction with researchers at the Stanford Linear Accelerator Center (SLAC) [14]. In their attempts to develop a switch to replace thyra-trons for klystron modulators they experienced catastrophic failure in some IGBT modules when they were exposed to soft short-circuit conditions [2]. 8 Chapter 1. Background In their attempt to determine the cause of the failures, they performed F E M analyses of the geometry of the device and attributed the failures to an asymmetry of path inductances: contributing to an imbalance of device currents. T R I U M F Current Distribution Analysis TRIUMF continued the analysis from where SLAC left-off. The TRIUMF contribution was to perform a coupled-circuit element extraction of the IGBT module, and to simulate the conditions which lead to the failure of the device in PSpice. The results of this analysis showed conclusively that, while asymmetric path inductances were a factor, it was inductive coupling to the module's internal gate trace that was largely to blame for the cur-rent imbalance and resulting failure of the module. [14] and [17] detail this process. 1.3.4 Westcode Module Specifics One of the other modules available to the SLAC researchers, and to TRI-UMF was a prototype Westcode module designed specifically for pulsed-power applications. This device features a redesigned gate trace, and other, undisclosed improvements for high di/dt switching. The device is rated at 5.2kV, and 900A DC. However, for the intended application of a thyratron replacement, it is likely to be operated at 60% of the rated blocking voltage, and pulsed at almost lOx the DC current (3.1kV and >8kA, respectively). Figure 1.3[18] shows a rendering of the internals of this specific mod-ule. The image is an exploded view of the device which illustrates the 14 IGBT "cassettes" that house the IGBT silicon die (detailed in the inset, bottom-right), the copper stand-off "posts" that locate the die, and the aforementioned redesigned gate trace. 9 Chapter 1. Background Figure 1.3: Rendering of a Westcode press pack IGBT module intended for pulsed power applications In the course of the research detailed in this thesis, it was necessary to dismantle one of these IGBT modules. Figure 1.4 is a series of photos documenting this process. There are 14 IGBT die within the Westcode module. For the rest of this document they will be referred to by number, as labelled on the illustration in Figure 1.5. 10 Chapter 1. Background (a) Opened Westcode IGBT module showing 14 parallel IGBT "cas-settes" . (b) Detail of Westcode IGBT internals. Visible are the copper posts, IGBT die (in cassettes), and the gate trace. Figure 1.4: Photos of a dismantled Westcode module Chapter 1. Background Figure 1.5: Rendering of the internals of a Westcode press pack IGBT mod-ule with numbered current paths 12 Chapter 1. Background 1.4 Focus of this Thesis Westcode publishes in their documentation the assertion that, as all of the paths through the IGBT module are of equal-length, that they exhibit equal inductances. Figure 1.6 is an equivalent circuit of the IGBT module, includ-ing parasitic inductances, as supplied in their documentation [19]. In this figure these parasitic inductances are lumped into just two parameters, one at the emitter and one at the collector of the device. Figure 1.6: Westcode provided equivalent circuit of press pack module When assessing the suitability of this module for a thyratron replacement at TRIUMF, this assumption was called into question. It was suspected that there might be significant issues with uniform current sharing under pulsed conditions, and that these issues might also be strongly influenced by the geometry of the return current path. The research documented in this thesis covers the creation, simulation and testing of a coupled-circuit model of the Westcode module that explic-itly takes into account the inductive coupling that exists, both between the separate current paths through the device and to the return path. It is hoped that this circuit model will be of great help in the future for the process of prototyping a thyratron replacement switch. One of the 13 Chapter 1. Background biggest advantages of such a circuit is that it allows for new geometries to be quickly and easily tested in PSpice, along with the external circuit and any non-linear switching elements. As PSpice is already used to simulate existing pulsed switches [20], as well as their loads [6], this is the preferred method of implementing the characteristics of the IGBT module 14 C h a p t e r 2 Simulation of Current Distribution In order to ascertain how the current is distributed within the IGBT module, I undertook to model and simulate the internal structure of the Westcode press pack IGBT module. Simulation Objective The goal of these efforts was to produce a versa-tile circuit model of the Westcode IGBT geometry that could be employed in PSpice to predict the current distribution under a wide variety of conditions in a minimal amount of time. Additionally, as the requirements of a thyra-tron replacement would likely involve pushing any switch to it's physical limits, an accurate model of the IGBT geometry would be of great benefit later in the thyratron-replacement design process to avoid costly failures. 2.1 Simulation Methods Each electrical path within the hockey-puck IGBT module consists of an IGBT die and a copper post. The ideal software tool to analyse and pro-duce a current distribution for this geometry would be a 3D electromagnetic code, capable of also simulating the non-linearity of the semiconductor die. However, to the author's knowledge, no such code is available. Hence the circuit analysis code PSpice, the de-facto standard for non-linear circuit simulation, is used to simulate the electrical current paths within the IGBT module. For this, inductance and resistance values are required for each of the electrical paths in the IGBT module: these values are derived from an elec-15 Chapter 2. Simulation of Current Distribution tromagnetic code. Initially a 3D F E M code was used to simulate each IGBT die (as a linear element with the appropriate on-state resistance, see Appendix A) and the copper posts of the module. However, meshing of the model was overly prob-lematic: due both to the excessive number of elements required to perform a high-frequency simulation, and the difficulties associated with meshing mating regions with very different material properties. This approach was abandoned. Hence, instead, a 2D code is used to model the IGBT. Firstly, the cop-per post was modelled, with the same current distribution throughout its length, and the inductance per unit length and resistance per unit length, of each post, was determined. The same procedure was used to calculate the inductance per unit length of each on-state IGBT die; and the results are used to assign component values to a PSpice model of the IGBT module to provide a complete model. Such parasitic extractions are performed in the frequency domain. In order to produce the circuit model, and to be assured of its accu-racy, I undertook to model and simulate the Westcode module via several different approaches. As described in the subsequent sections, different soft-ware tools were used, and employed several different modelling techniques. These tools were organized into discrete "workflow" which produce a current distribution, given a geometric model of the IGBT module, under certain conditions. 2.1.1 Software Tools Different software packages were used throughout this process, these are de-tailed in Table 2.1. Using different software packages with dissimilar solving techniques to solve the same geometry provided us with confidence in the final outcome. This is especially important in our case, where physical mea-surements to determine the current distribution within the IGBT module, especially under switching conditions, while not impossible, are themselves difficult and prone to error. 16 Chapter 2. Simulation of Current Distribution Software Package Usage Vector Fields Opera 2D • 2D-FEM Modelling. • AC steady state and transient simu-lation. Integrated Engineering Soft-ware (IES) OERSTED • 2D-BEM/FEM modeling. • AC steady state simulation. • Circuit parameter extraction. Fasthenry • 3D-Magnetoquasistatic Multipole modeling. • Circuit parameter extraction. OrCAD PSpice Flexible time domain and frequency do-main simulation of extracted circuit pa-rameters. Matlab • Scripts to convert impedance ma-trixes into resistances and coupled inductors. • Scripts to extract current densities from simulation tool log files. Table 2.1: Modelling and simulation software. 17 Chapter 2. Simulation of Current Distribution 2.1.2 Simulation Geometries Return Path Geometry As has been pointed out previously in this document, the geometry and effect of the return path on the current distribution should not be neglected. To attempt to produce the least biased current distribution within the simulated Westcode module, and to lower the inductance of the circuit, a coaxial structure was modelled. For practical reasons, a fully coaxial return path is unfeasible: there is no way to easily access the device, and the connection of gate drives would become problematic. As such, an array of six rods in a circular shape was simulated, approximating a coaxial structure. The number six was cho-sen because it has been shown that this number of return rods minimizes the inductance for a geometry[21]. Adding additional paths to further ap-proximate a fully coaxial structure yields little to no benefit to the overall inductance. The rods are spaced some distance away from the IGBT module (10cm-12cm), as this is indicative of the spacing required for the potential appli-cation of a stack of modules, where the voltage difference between the top of the stack and the return path may exceed 75kV. 2D Model In the following simulations, a 2D model of the Westcode module appears as a cross-sectional slice, viewed from above, of the IGBT module's 14 forward paths, surrounded by the six return paths. Figures 2.2 and 2.5 illustrate how this was implemented. With the first of these taking advantage of the symmetry of the arrangement, and the second modelling a complete 2D 'slice'. 3D Model The 3D model of the Westcode IGBT module described in Section2.2.4 is an extruded version of the 2D model described above. The device is modelled 18 Chapter 2. Simulation of Current Distribution as having 100cm long posts, rather than the actual length of sslcm. The reason this was done was to minimize the effect of fringing of magnetic field that might be simulated at the ends of the rods. In the actual device these fields would be excluded by the highly-conductive copper emitter and collector contacts. 2.2 Simulation Workflow Using various permutations of the tools from the section above, I developed several different workflows to determine the current distribution within the Westcode module. Each of these workflows was capable of producing a solution to one or more scenarios from of a set of test cases. Exploiting the features and capabilities of the different software packages, we were able to cross-check the solutions between workflow techniques, and software packages. The current distribution within the IGBT was examined for the following test scenarios: Frequency domain solution with single excitation frequency. domain solution with multiple excitation frequencies (AC-sweep analysis). c Time domain solution with a single-frequency sine wave drive. d Time domain solution with an arbitrary current pulse. Time domain solution with non-linear circuit elements. 19 Chapter 2. Simulation of Current Distribution 2.2.1 Workflow 1: Opera 2D Field Solution This technique involves using the Opera2D software package for both mod-eling, and for solving for the individual die currents at discrete AC drive frequencies. • 2D Modeling. External circuit definition Pre-processor V • Multiple single-frequency AC simulations AC B-field solver V Opera2D V • Integration of current density for each die Post-processor V • Current distribution at a single / frequency, and over a range of ( frequencies ^ 3 + 9 Figure 2.1: Opera2D Field Solver workflow The geometry simulated is a cross sectional slice of one half of the sym-metrical IGBT module (top, centre); complete with half of the corresponding return path (surrounding), as shown in Figure 2.2. Normal B field bound-ary conditions were applied to the top edge of the model, and the solver set to regard this as the axis of symmetry. The solver considers the device to be infinitely 'long', however a length in the Z-direction is specified for the device, so that the results may be scaled accordingly. Being a 2D model, the material simulated is assumed to be homogeneous over the entire length. Simulating just half of the IGBT module allowed for a denser mesh to be used while still retaining the same total number of elements. This is important when doing a high-frequency analysis on a highly conductive material, as the skin effect crowds current to a very thin depth along the edge of each conductor, and correspondingly small elements must be used. 20 Chapter 2. Simulation of Current Distribution Equation 2.1 illustrates how the skin depth (5) depends inversely on both the frequency of simulation (/) and the conductivity (cr). For the materials under consideration (silicon, copper), the relative permeability (fir) is near unity, so the total permeability (/z = iir/un) will be fixed. S = l/y/2nflMT (2.1) As an extreme example: for a copper bar (a = 5.96 * 10 75m~l) with a 10MHz drive frequency, 6 is a mere 15/xm. With an accepted minimum of three elements per skin-depth [22], this amounts to an extremely high element count, even when when a graded mesh is employed (as it is in this model). Figure 2.2: Modelled geometry - Opera 2D This workflow performs the F E M analysis of the module at a specific frequency while assuming that the geometry being modelled is part of a larger external circuit (detailed in Figure 2.3). The resistance in the external circuit is arbitrarily chosen to be large compared to the impedance of the module. The voltage source can then be scaled to give the appropriate current. In this case, a peak current of lOkA for a complete module was modelled: although, as the model is linear, and we are only concerned with the relative distribution of current, the actual value of the peak current, as 21 Chapter 2. Simulation of Current Distribution modelled in the electromagnetic simulation, is not important Forward Current Path Return Current Path Figure 2.3: External circuit for Opera2D AC analysis External Resistor lOkVac 1 Ohm I ran the simulation with a series of frequencies starting at 1Hz, and extending to 10MHz. Using Opera2D's built-in scripting ability, the current density for each of the die was integrated and extracted at each simulated drive frequency. Matlab was then used to parse the resulting Opera2D log-file, retrieve the die currents, and then normalize these to the total simulated module current. Simulation Time To perform a single-frequency analysis on this model takes just over five minutes to simulate on a Pentium IV 3.0GHz machine with 2GB of R A M . An additional few minutes is required to perform the post-processing and obtain the current distributions from the model. Summary With proper implementation, this workflow should be able to produce some of the most accurate simulations of the current density un-der steady state conditions. However, the length of time required to do a complete F E M simulation at each simulation frequency, combined with the inability to simulate a device that is heterogeneous along its length limits the utility of this workflow to verifying the results produced by other workflow. 22 Chapter 2. Simulation of Current Distribution 2.2.2 Workflow 2: IES OERSTED Field Solver IES OERSTED features an integrated AC steady state field solver which utilizes the boundary element method, finite element method, or a hybrid combination of the two. IES has integrated their software such that model-ing, simulation, and analysis are all performed in the same interface. • 2D Modeling. • Detinition of conductors • Assignation of current densities ' • 2D B E M / F E M A C Analysis • Integration oi region current density Integrated modeller / solver TES > OERSTED V •j • Current distribution at a single frequency, and over a range of frequencies. (9 + t±W Figure 2.4: Workflow 2 - IES OERSTED Field Solver To simulate the IGBT in OERSTED, a two-dimensional model repre-senting a complete cross-section of the IGBT module was created that did not take account of symmetry (Figure 2.5). Otherwise, the geometry rep-resented by this model was identical to the Opera2D rendering. This was possible as OERSTED's use of ID boundary elements at the periphery of each conductor negated the necessity for a large number of F E M elements resulting from skin effect (see Section 2.2.1 for an example) . As with the Opera2D simulation, the module simulated must be assumed to be made of homogeneous material along its length. Once the geometry was established, it was a relatively simple matter to assign the total current density in the forward and return conductors, define the drive frequency and set the self-adaptive solver running. Once the solver had finished, the current density was produced for the entire module and integrated over individual regions. To obtain the current distribution over a range of frequencies, it is nec-essary to set up a parametric analysis within IES OERSTED. OERSTED 23 Chapter 2. Simulation of Current Distribution Figure 2.5: Modelled geometry - IES OERSTED, IGBT die are shown in red, return paths in blue has an advantage over Opera2D in that a number of post-processing options can be specified to be run for each parametric case without any additional scripting required. For our model, the post-processing options calculated the total current present in each path at each specified drive frequency. S u m m a r y The OERSTED field solver is very similar to the Opera2D field solver, and has the same set of advantages and disadvantages. The ease of use of the IES unified environment is a benefit, but, as with Opera, this method is useful mainly as a comparison tool for the other workflow. 24 Chapter 2. Simulation of Current Distribution 2.2.3 Workflow 3: OERSTED Extraction with PSpice Simulation This method employs IES OERSTED as an extraction tool that produces an impedance matrix at a single extraction frequency. This matrix is converted into mutually coupled circuit parameters which can then be analysed in any PSpice circuit. 2D Modeling Definition of conductors Assignation of current densities 2D B E M / F E M single-frequency A C Analysis Extraction of impedance matrix Convert impedance matrix into mutually coupled inductances Integrate circuit parameters into PSpice Capture schematic Simulate any of a number of scenarios with PSpice A/D Current distribution derived from: a) Single SS A C frequency b) A C frequency sweep c) Transient analysis with single frequency sine drive d) Transient analysis with arbitrary drive waveform e) Nonlinear analysis using PSpice models for IGBT die. Integrated modeler / solver Mutual inductance extraction script PSpice A/D IES OERSTED MATLAB OrCAD PSpice Figure 2.6: Workflow 3 - OERSTED extraction and PSpice simulation The circuit parameter extraction solver uses nearly the same geometric model in OERSTED as the field solver. The only major difference to this model is a result of the method that OERSTED uses to produce circuit parameters: For x forward paths, and y return paths, OERSTED produces an x * x impedance matrix. This matrix represents the complex impedances 25 Chapter 2. Simulation of Current Distribution Distant return path Figure 2.7: OERSTED geometry for circuit parameter extraction of the forward conductors in the presence of the return conductors. As a result, the return paths are not explicitly represented and expressed as circuit parameters (this is in contrast to Fasthenry; see Section 2.2.4 - below). To render the PSpice model more flexible, it was decided to model all of the conductors in the existing geometric model as forward current paths, and include a separate return path which is relatively distant from the model (Figure 2.7). This permits the actual return path to be modelled from within the circuit simulator, and allows some alterations to be made without requiring re-extraction of parameters. The impedence matrix, as well as circuit parameters, are produced using BEM/FEM/Hybr id analysis (as with the OERSTED field solver, above) at a single extraction frequency which is determined at the time of simulation. Extracting circuit parameters at a single frequency, and then using them as linear elements over a wide range of frequencies in PSpice can be problem-atic, as these values are, in fact, frequency dependent (this effect is covered in Appendix B). Inductance ladders can be constructed to simulate this 20 Chapter 2. Simulation of Current Distribution effect and have been employed successfully by others[23]. However, con-struction of these inductance ladders adds considerably to the complexity of the PSpice model and may not be considered necessary. As shown in the aforementioned appendix, it is possible to achieve greater accuracy from a single set of extracted circuit elements by combining resistive and inductive components generated from the same model at different extraction frequen-cies. The resistive portion is taken from a low frequency extraction, and the inductive portion from a high frequency extraction. The process of rendering the extracted impedance matrix into coupled circuit parameters is detailed in Appendix C. This conversion process gen-erates a PSpice .include file that contains .PARAM statements for each of the self inductance and resistance values. Also included in this file are the coupling coefficients between each inductor. Attaching this file to a PSpice schematic with appropriately labelled resistors and inductors produces a circuit that electrically mimics the geometric effects of the different current paths. For a composite structure such as the Westcode module, where different materials (silicon, copper, molybdenum) are layered to make up the com-plete module, modelling can be accomplished by performing a separate 2D extraction for each distinct layer in the device. The resulting .include files can be included in the PSpice simulation, with the circuit elements for each path are arranged in series within the schematic, thus emulating the previously attempted 3D simulation. The circuit parameters extracted are per unit length. To adapt these values to represent the real module, the resistances and inductances are lin-early scaled accordingly (terms RatioCuR & RatioCuL in Figure 2.8). The coupling terms are expressed as a ratio of the self- and mutual-inductances, and therefore remain independent of the length of the extruded model and need no adjustment. Simulation Time Each single frequency parasitic extraction in OER-STED 2D takes just over 11 hours on the same machine as used for Sec-tion 2.2.1. 27 Chapter 2. Simulation of Current Distribution ,{L2 * RatioCuL} L3 {13 1 Ratio CuL} {L13 "RatioCuL} - 0 -iokvac {114" RatioCuL} R1 {R1 • RatioCuR} {R2 * RatioCuR} < {R3 " RatioCuR} R13 {R13 • RatioCuR} RI4 [Rt4' RatioCuR} Figure 2.8: PSpice AC Analysis with OERSTED Circuit Parameters Summary The real advantages of this particular workflow are in the flex-ibility that PSpice simulation offers: • It is possible to represent a device that is made of composite materials along its length (as is the case with the Westcode module) by modelling 2D slices of the various materials separately. The resulting circuit parameters are then arranged in series within PSpice and scaled to the appropriate length to simulate the entire device. • Both AC and transient analyses can be performed much faster than with F E M / B E M analysis alone. • Non-linear circuit elements can be introduced to represent the IGBT die portions of the module, and switching behaviour can then be ex-plicitly assessed. • In non-linear analyses the effect of inductive coupling to the gate traces from main current paths can also be simulated. This has been shown to have the potential to significantly alter the current distribution during switching[14]. However, there are drawbacks inherent with this workflow: • The technique described above to model a composite device by layer-ing the results from independent simulations, works only for specific 28 Chapter 2. Simulation of Current Distribution geometries. In the case of the Westcode module, it is effective because virtually all the current flow is orthogonal to the 2D plane(s) modelled. This means that there will be very little (magnetic) coupling between layers, and that each set of extracted inductances can be considered coupled only within themselves. For other geometries, this may not be the case. • Extracting circuit parameters at a single frequency, and then using them as linear elements over a wide range of frequencies may lead to inaccuracy in the simulation. This can be mitigated with additional processing of the extracted circuit elements. 29 Chapter 2. Simulation of Current Distribution 2.2.4 Workflow 4: Fasthenry Extraction with PSpice Simulation This workflow uses the "free of charge" 3D parasitic inductance extraction tool Fasthenry to produce impedance matrixes. These matrixes are then converted into PSpice resistors and coupled inductors which can then be inserted into a PSpice schematic and simulated [24]. 3D modeling (text entry) Definition of external nodes Definition of frequency range 3D magnetoquasistalic field solver Extraction of impedance matrices for a range of extraction frequencies Convert impedance matrix into resistances and mutually coupled inductances Integrate circuit parameters into PSpice Capture schematic Simulate any of a number of scenarios with PSpice A/D Current distribution derived from: a) Single frequency A C SS analysis b) A C SS analysis over a frequency sweep c) Transient analysis with single frequency sine drive d) Transient analysis with arbitrary drive waveform e) Nonlinear analysis using PSpice models for IGBT die. 3 D modeler Magnetoquasi static field solver Mutual inductance extraction script PSpice A/D FastModel FastHenry MATLAB GrCAD PSpice Figure 2.9: Workflow 4 - Fasthenry extraction and PSpice simulation Fasthenry is a magnetoquasistatic multipole parastitic inductance ex-traction program developed in the mid-90's at MIT [24]. Models are created 30 Chapter 2. Simulation of Current Distribution Figure 2.10: Fasthenry 3D geometry for circuit parameter extraction from a text input file by defining nodes and then connecting these nodes with rectangular conductors. The software also has the capability to create conducting planes by meshing together conductors. Augmenting the text entry system is another, currently free of charge, software product called FastModel 1. FastModel provides a real-time display of the geometry as it is entered, and can also be used to configure and launch FastHenry. The text entry system, while ill-suited to geometries not constructed entirely of straight-segments, is surprisingly efficient in creating simple models. External nodes are defined representing ports for the network solver. The solver commences to analyze the effect of an AC drive applied to one port, on all the other ports. What contributes to make FastHenry unique among our solvers is its use of "partial inductances". Partial inductances 1 Available from 31 Chapter 2. Simulation of Current Distribution are a mathematical abstraction that permits inductances to be calculated without an explicitly defined return path[25]. Instead, the 'return path' is considered to be infinitely far from the conductor, and the conductor's self-and mutual-inductances are calculated accordingly. Defining conductors in this fashion requires that the mutual terms be considered whenever PSpice simulations are run, as it is through mutual coupling that the effect of the actual return paths are considered. The result of a simulation in FastHenry is an n * n complex impedance matrix, where n represents the number of external ports present in the model. Following from the example given in OERSTED circuit parameters section (section 2.2.3, above): for a FastHenry model with x forward paths, and y return paths, n = x + y. Each impedance matrix is valid for a single extraction frequency (see Appendix B). To convert the impedance matrix to a PSpice include file, a M A T L A B script was written. This script is virtually identical to the script used to convert the OERSTED derived impedances and also produces a similar PSpice. include file. Simulation of the Fasthenry extracted circuit elements in PSpice also fol-lows the same procedure, and they can be used in the same circuits as those generated by OERSTED. While Fasthenry is a 3D simulation program, and therefore able to simulate heterogeneous structures, it is also possible to combine the extracted circuit elements from independent simulations in the same way as with the OERSTED workflow. For the Westcode geometry, we chose to implement the model using the latter of these techniques. This permitted us to examine the silicon and copper regions of the module sep-arately within PSpice and yet avoid forcing Fasthenry to solve the much larger matrix that would result from attempting to include these (largely uncoupled) regions together in one composite model. Simulation Time The time taken to produce an impedance matrix in Fasthenry varies with the number of ports, conductors and filaments in the model. For our model (20 ports, 20 filamented conductors) of the Westcode module this came to f«15m per extraction. For each additional material 32 Chapter 2. Simulation of Current Distribution layer, or desired frequency, a separate extraction must be performed. PSpice is able to produce either transient or AC solutions to simple circuits that make use of these extracted circuit elements in <1 minute on average. Summary As this workflow employs PSpice as a simulation tool and uses identically formatted circuit parameters to the previous workflow it follows that it shares all the corresponding advantages. Additionally, being a 3D solver, Fasthenry is capable of modelling geometries that are difficult or impossible for 2D solvers to render [14]. Circuit elements derived by Fasthenry are, like those from OERSTED, produced for a single frequency and have similar limitations and mitigation techniques. ) 33 Chapter 2. Simulation of Current Distribution 2.3 Simulation Results This section compares the results of simulations run using the techniques and models described above. As the simulation techniques are themselves experimental, much of the focus of this section is on comparing the results of these techniques. We are especially interested in determining the de-pendability of the two workflows which use PSpice as a simulation engine (Workflows 3 and 4), for it is these techniques that are the most flexible. 2.3.1 A C Steady State Results The following simulation results compare the AC magnitude of the current distribution, as derived by the above techniques, over a swept frequency range from 1Hz to 10MHz. The first section below considers a hypothetical scenario of a "pure cop-per IGBT module; this simulation allows us to directly compare the results from all of the workflows. The second section details results from a more complex model, which includes a small slice of a material with the resistivity of silicon to represent the sandwiched IGBT die. "Copper Only" Frequency Sweep Field Solvers Initially the module was modelled using the F E M and B E M field solvers as a hypothetically pure copper device. It was anticipated that these tools would provide the most accurate distribution of the current for this limited model as they perform a complete simulation for each frequency step specified. Figure 2.11 presents the results from the field solvers. 34 Chapter 2. Simulation of Current Distribution I — Conductors 1 & 12 Frequency (Hz) (a) Opera 2D (Workflow 1) prediction for an "all-copper" Westcode IGBT module. Red - Opeta2D 1 10 100 1000 10000 100000 1 x 1 0 6 1 x 1 0 7 Frequency (Hz) (b) Comparison: Opera 2D (Workflow 1) and OERSTED Field Solver (Work-flow 2). Figure 2.11: Field solver predictions of steady state current distribution for an "all copper" module 35 Chapter 2. Simulation of Current Distribution Figure 2.11(a) is a plot of the proportion of the module current predicted to flow through each path by Opera 2d as a function of drive frequency (Note: due to symmetry within the module, each plotted line represents two cur-rent paths, refer to Figure 1.5 for numbering). At low frequencies (<10Hz, in this case), the distribution is near-uniform and each conductor assumes l/lAth of the total module current («7.14%). As the frequency increases, the inductive portion of the impedance begins to dominate, and the distri-bution becomes increasingly less uniform; conductors near the edge of the device take more current as the drive frequency increases while innermost conductors take less. Above a certain frequency (wl kHz in this example) the current distribution becomes almost entirely determined by the relative values of the coupled inductances of the module. At the higher frequencies the innermost conductors (Conductors 5 & 9, and 6 & 10) conduct little to no current, while the conductors at the corners of the device (Conductors 1 & 12) conduct almost twice as much as they do at low frequencies. The second portion of this figure, 2.11(b), illustrates the very good agree-ment between the two types of field-solver. Additionally, as the OERSTED model explicitly defines all 14 forward paths through the module without taking advantage of symmetry, and yet still presents only seven discernible lines on the plot, it can be assumed that the assumption of symmetry in the Opera 2D model was correct. As such, for the remainder of this document, reference will only be made to the lower half of the IGBT module (Conduc-tors 1 7), with the symmetric top portion assumed to exhibit the same characteristics. The only.readily apparent difference between the distribution as pre-dicted by Opera 2D and the OERSTED field solver, is at very low frequen-cies (w2Hz). Here, some anomalies are present in the OERSTED simulation. This is most likely attributable to the solver's use of ID boundary elements at the surface of the conductors to solve for what is likely to be, at these low frequencies, a bulk distribution of current. For such distributions, F E M modelling is much more appropriate. However, as the discrepancy is small, localized and explainable, it is not considered to be problematic. 36 Chapter 2. Simulation of Current Distribution Circuit Solvers The plots in Figure 2.12 compare the distribution ob-tained through PSpice simulation of extracted circuit parameters to the field solver solution. Figure 2.12(a) presents the distribution obtained from sim-ulating Fasthenry extracted circuit elements, and Figure 2.12(b) the results using OERSTED derived parameters2. The following observations can be drawn from Figures 2.11 & 2.12: • The four plots all share the same general shape when transitioning from one extreme to the other. • Additionally, this transition takes place over a similar frequency range for all four techniques: approximately two decades. • Al l four workflow produce similar distributions at simulation drive frequencies below approximately 10 Hz; the predicted distributions also plateau to similar values above approximately 10 kHz. • If the distribution predicted by the field solvers can be assumed to be the most correct, then the two PSpice solved techniques under-estimate the magnitude of the imbalance in this hypothetical "copper only" module for approximately one and a half decades spanning up-wards in frequency from approximately 10 Hz. • In both PSpice simulations, Conductors 2 and 4 are predicted to take a considerably higher proportion of the module current between 100Hz and 1kHz (see circled regions). This is notable, as it is the only loca-tion where the shape itself of the distribution, as it transitions from resistively dominated to inductively dominated, differs significantly between workflow. 2 It is of note that the extracted circuit elements simulated to produce the following plots (and, unless otherwise specified, all subsequent PSpice-derived results) are amalgamations of two separate extractions. One of these extractions was performed at a low frequency (1Hz), and the other at a high-frequency(lMHz). The circuit elements used combine the resistive values from the low frequency extraction with the inductances and coupling terms of the high frequency extraction, as it was found that this particular combination gave the best 'fit' over the simulated frequency range without resorting to ladder networks. Applendix B details the rationale and methodology behind this decision. 37 Chapter 2. Simulation of Current Distribution 0.14 e ' CL 0.02 0 • Red (dotied). Opera 2D — rT \ •."•I ' I I 1 1 1 i 1 m l 1 10 100 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 x 1 0 6 1 x 1 0 7 Frequency (Hz) (a) Comparison: Opera 2D field solver (Workflow 1) with PSpice model using Fasthenry extracted parameters (Workflow 4). • Red (dotted) - Opera 2D [ Grsen - PSpica w/ O E R S T E D ParGmele/a.. 0 .14 - / 1 10 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 i»106 1 x 1 07 Frequency (Hz) (b) Comparison: Opera 2D field solver (Workflow 1) with PSpice model using OERSTED extracted parameters (Workflow 4). Figure 2.12: PSpice simulated predictions of steady state current distribu-tion for an "all copper" module 38 Chapter 2. Simulation of Current Distribution At the extreme ends of the spectrum, the different workflow appear to agree well. In Figure 2.13 a comparison between the simulation techniques is made at 1Hz, and then again at 1MHz. As these particular distributions represent the lower and upper asymptotes, respectively, they are applicable over the majority of the spectra, excepting the two decades of transition mentioned above. The low frequency distribution in Figure 2.13(a) is identical to well within l/100*k of 1% of the total module current. It is interesting to note that, at low frequencies, the PSpice predicted currents are more uniform between die than the field solver values. This is possibly a result of accu-mulated error from integration in the field solvers, but is too small to be of any concern. At 1MHz, Figure 2.13(b), the predicted current distribution is also sim-ilar across the various workflow. The largest spread is for the predicted current through Conductor 4, and is less than 0.2% of the total module current. Choice of Workflow If the field solver solutions produced by Workflow 1 and Workflow 2 are to be considered accurate representations of the current distribution within this hypothetical pure-copper IGBT module, then they can be used to determine which of the PSpice simulation workflow is best suited for continued investigation of the Westcode module. There is relative insignificance in the variation of predicted current dis-tribution in the low and high frequency plateau regions of the AC sweep analysis. Therefore it follows that the choice of extracted parameters should be those that most closely follow the transition from resistively dominated to inductively dominated. It was thus decided to use the Fasthenry parame-ters, adjusted as described in Appendix B, to perform further analysis of the Westcode IGBT module. Fasthenry is also attractive as an extraction tool as it is much faster than OERSTED in performing extractions, making it easier to prototype new designs. Additional attractions of FastHenry are its ability to handle 3D geometries, and its low price (free). 39 Chapter 2. Simulation of Current Distribution Figure 2.13: Comparison of workflow predicted distributions at low fre-quency and high frequency AC drives 40 Chapter 2. Simulation of Current Distribution 2.3.2 Resistive Module Results With a simulation methodology chosen, it was decided to perform simula-tions more representative of the actual IGBT module characteristics, while retaining a simple, linear model. This involved performing a second set of parasitic extractions of the same geometry used for the above copper module, this time with the resistivity of the simulated material adjusted to match that of an IGBT die in the linear on-state. Initially, as neither detailed specifications, nor a dismantled device was yet available, an estimation was made of this value from manufacturer datasheet information then combined with a estimate as to the IGBT die dimensions. Later, the on-state resistance was determined experimentally, the dimensions of the die measured and the models revised. This process is detailed in Appendix A. As described in Sections 2.2.3 and 2.2.4, the coupled parameters ob-tained from this second set of extractions are combined with the previously extracted copper elements. The composite structure is then simulated in both the frequency domain, with an AC sweep, and in the time domain, with current pulses of varying rise-times. Since the measured and calculated values obtained for the IGBT linear on-state resistance exhibit some differences, and are only applicable to IGBT die already conducting a significant amount of current (>w40A/die), a range of die resistances was analysed. These were derived by scaling the resistive portions of the originally extracted parameters in PSpice to produce an appropriate value for the die resistance. This provides a convenient method to quickly asses the effect on the current distribution of changes in on-state resistance (for example, resulting from an altered gate voltage), or to examine the distribution earlier in the switching process when the IGBT die has not fully turned-on. This approach is also considered valid because the length of the copper post is significantly longer than the length of the IGBT die: hence the effect of the self-inductance of the post is much greater than that of the die. Therefore, the slight change in inductance of the die (at a given frequency), resulting from the altered resistivity, is a comparatively 41 Chapter 2. Simulation of Current Distribution small effect. 2.3.3 A C Steady State Results In Figure 2.14(a), the effect of changing the value of the simulated "die" resistance on the steady state current distribution is examined. The resis-tance values simulated were chosen to represent the possible range of IGBT on-state resistances (the 12.5mfi, and 25mQ traces), and to characterize the transition from the copper-only distribution ( the 0.25mf2, and 2.5rml traces). From this plot, it is apparent that each 10-fold increase in die resis-tance results in the shifting of the transition point, from a resistively deter-mined distribution to an inductively determined one, by one decade. This is confirmed by examining the phase angle of the module. The frequency at which the phase angle becomes 45°, indicating the inductive portion of the impedance is equal to the resistive portion, also shifts linearly as the die resistance is increased. This is borne out by theory: 9 = t an - 1 (27 r /L / i ? ) (2.2) Therefore a increase in R produces the same effect on the phase 9 as a proportional increase in / . This frequency also corresponds to the point at which the first sign of divergence in the module current is visible in Figure 2.14(a). An immediate corollary from this is: increasing the on-state resistance of each path through the IGBT module improves the distribution of current throughout the module. An additional conclusion that can be reached from looking at these plots is that the value of the simulated die resistance has no effect on the final high-frequency current distribution; this distribution appears to be inductively determined by the geometry. 42 Chapter 2. Simulation of Current Distribution (a) Effect on current distribution of varying resistance of Si region. Re-sistances shown on plot are per-path. (b) Phase angle of module impedence as a function of Si region impedance. Red dots indicate 45° phase angle Figure 2.14: Effect of introducing resistive Si region to model current dis-tribution 43 Chapter 2. Simulation of Current Distribution 0.16 buiJ i ' i i i ' i I 1 10 100 1000 10000 100000 i x 1 0 6 1 x l 0 7 Frequency (Hz) Figure 2.15: Simulation tool comparison with 2.5mf2 Si region resistance Figure 2.3.3 revisits the choice of workflow. On this plot the current distribution is analysed for the following: • Workflow 3 & Workflow 4, the two PSpice workflows, using OERSTED and Fasthenry as extraction tools respectively, are compared. Both are using so-called "mixed" parameters with inductive and resistive values combined from 1Hz and 1MHz extractions, respectively. • A PSpice simulation of a single set of Fasthenry-extracted parameters that represents the combination of the copper and silicon regions. This simulation models the silicon region as a separate slice within the Fasthenry 3D model of the IGBT module. • An Opera 2D predicted current distribution with a uniform conduc-tivity calculated to reflect a total resistance of 2.5m£) (the average resistance of the post and IGBT die) for each current path. The value of the conductivity used to create this was 434Sm _ 1. • A PSpice simulation using circuit elements extracted from a Fasthenry 44 Chapter 2. Simulation of Current Distribution model with this same value of conductivity. In this model, the IGBT die and post combination is modelled as being one homogeneous vol-ume. Workflows 3 & 4 and the Unified Fasthenry model, all produce nearly identical current distributions. This hints that the shift in the frequency of divergence, observed between workflows illustrated in Figure 2.12, is likely a result of differences in the extracted resistance values for each copper conductor. Given that any resistance value chosen to represent the IGBT die, will swamp the extracted value for the copper post, this source of error can be considered to be insignificant for this particular application of these circuit elements. The Opera 2D and PSpice simulations that use homogeneous uniform resistivities, both predict divergence at a lower frequency than the other simulations. These can be viewed as less-correct. The rationale for this is as follows: The current in regions simulated as highly conductive copper is able to redistribute itself within each conductor; it will fringe to the outer-most edge. When a uniform resistivity is assumed, the skin depth for this same region is much larger, and the current will fringe much less. This re-distribution of current has the effect of reducing the coupling between the IGBT posts and to the return path (by approximately 5%, as predicted by Fasthenry), shifting the divergence point downward in frequency. 2.3.4 Pulsed Time Domain Results This section investigates the simulated current distribution within the IGBT as it is driven by a current pulse of varying rise-times. The pulse is generated in PSpice by discharging a 5Q coaxial cable through the PSpice model of an IGBT module, and into a matched load. Figure 2.16 shows a circuit diagram of this idealized pulse forming network as implemented in PSpice. The length of the pulse is determined by the delay time of the transmis-sion line. In this case, the line is comprised of two 2.5/US segments connected together to form one 5/iiS long cable which will deliver a pulse ICtyxs wide. The rise and fall times of the pulse are determined by the transit time (TTRAN) 45 Chapter 2. Simulation of Current Distribution R3 100k V2 68kVdC ~=±=-TCLOSE = 0.5u TTRAN = {SWTran} TD = 2.5US Z0 = 5 TD = 2.SUS ZO - 5 Figure 2.16: Pulse forming circuit used for time domain pulsed distribution analyses of the switch U l . This parameter was adjusted for each simulation case to produce the requisite 10%—>90% rise-time. The amplitude of a current pulse from a PFN into a matched load is 1/2 of the PFN voltage divided by the characteristic impedance. Here, an 8kA pulse was desired, and was obtained after a small (10%) increase in the PFN voltage from the anticipated 80kV to accommodate for a voltage drop established across the lOOkf) resistor by the initial DC bias-point calculation. Figure 2.17 shows the simulated current in each conductor during turn-on when a module with 12.5mf2 on-state resistance is pulsed by an 8kA pulse with a 10%—>90% rise-time of 300ns. Again, as in the simulations described in the previous section, a linear resistive element was used in place of the IGBT die. As predicted by the frequency domain measurements, Conductor 1 takes a significant amount more current than the other die during the switching period. In fact, the current in this conductor is predicted to overshoot what would (ideally) have been it's maximum current by «180A, (30%). The 8kA pulse requires the switch to conduct a peak di/dt of 30kA/jUS. This is an ambitious figured that, as pointed out in the background portion of this document, has not yet been realized with IGBT switches. The plots in Figure 2.18 illustrate effect that altering rise-time has on the current distribution within the simulated Westcode module. Also in-vestigated in these plots is the effect of adjusting the simulated on-state resistance of the IGBT die. 46 Chapter 2. Simulation of Current Distribution Figure 2.17: Current distribution for simulated module with 12.5mfi on-state resistance and a 10% to 90% rise-time of 300ns Figure 2.18(a) confirms the results of the frequency domain analyses in Figure 2.14. The linear relation to the on-state resistance observed in the frequency domain plots is again seen here: doubling the on-state resistance permits the rise-time to become halved, while still maintaining the same distribution. 47 Chapter 2. Simulation of Current Distribution (a) Comparison: Module current spread for different pulse rise-times. Data for 12.5mfi and 25mf2 on-state resistances shown. Solid traces indicate most-conducting current path, dashed traces indicate the least-conducting path. 0 I i i i i I i i i 1 , 1 , 1 1 1 1 0 1 2 3 4 5 6 Time (us) (b) Relative proportion of die current within module for various pulse rise-times. 12.5mf2 on-state resistance data shown. Figure 2.18: Effect of varying rise-time and on-state resistance on current distribution for a 8kA pulse 4 8 Chapter 2. Simulation of Current Distribution . This follows from the relationship between the rise-time and edge band-width of a signal. For.a single pole circuit such as this, the equivalent edge bandwidth for a given 10%—>90% rise-time can be estimated from the following approximation [26]: B W ~ ^ (2.3) Here, BW represents the equivalent edge bandwidth, and Tr the rise-time of the pulse. This approximation is a rule-of-thumb used for deter-mining the choice of measurement equipment for measuring pulses. What is important to note is again the linear relationship between the rise-time and frequency content of the pulse. In Figure 2.18, we can see that, as the rise-time of the pulse decreases, the relative distribution of current within the device tends towards the induc-tively dominated distribution: for a 100ns pulse, the distribution is nearly completely inductively determined. Up until this point, we have assumed that the geometry of the model was fixed. However, as it is a simple matter to investigate in PSpice, illustrating the effect of reducing the height of the copper region in the IGBT module is presented in Figure 2.19. In this plot the numbers are indicative of the copper stand-off post height in the simulated device relative to the actual post height of the Westcode module. Shortening the height of each post has the effect of reducing L in Equation 2.2 by an equivalent amount. This shifts the frequency of diver-gence higher, and has the corresponding effect on the rising-edge distribution of the pulse. Conclusion The results of simulations performed of the Westcode IGBT module present a largely consistent picture of the current distribution within the device. The results of the frequency and time domain simulation cor-roborate each other well, and the different workflow produce distributions that are largely in agreement. The sensitivity of the predicted current distribution within the module 49 Chapter 2. Simulation of Current Distribution Figure 2.19: Predicted current distribution for simulated 12.5mfi module with scaled post-heights. has been established with regards to: pulse rise-time, die on-state resistance, A C drive frequency and copper post height. It has been found that there is a linear relationship between these factors and the uniformity of the distribu-tion. In the case of the pulse rise-time and the die on-state resistance, this relationship is direct. For the remaining two factors, AC drive frequency and copper post height, the relationship is inverse. 50 Chapter 3 Experimental Verification The final step in confirming the simulated model was to subject the physical module to experiments to determine the current distribution within the module. Measurement Goals As the IGBT module is a compact, closed device, acquiring the current distribution is not a simple procedure. This chapter details the equipment and procedures necessary to produce results that can be compared to the simulations. 3.1 Method of Analysis 3.1.1 Frequency Domain It was decided to initially perform measurements in the frequency domain. While the focus of the research is inherently a time-domain problem, in that it is concerned with transients occurring during fast switching, a frequency domain analysis of the problem is advantageous for two major reasons: 1. It greatly simplifies the process of acquiring measurements. 2. It also aides interpretation of the measurements: allowing the experi-mental results to be directly compared to simulation results. One of the reasons frequency domain measurements are easier to perform than time domain measurements is related to our choice of measurement equipment. Rogowski coils produce an output voltage that is proportional to the derivative of current flowing through the 'loop', and as such usually require some form of integration. 51 Chapter 3. Experimental Verification However, when the current source is a single frequency AC drive, the output of the Rogowski coil is directly proportional to the current, albeit phase shifted and scaled linearly by the frequency (see Section 3.1.3). Measurements are further simplified with a frequency-domain analysis, in that the capacitive energy storage and fast gate drive circuits required for fast turn-on of the IGBT module are not required. While this document is only concerned with the frequency domain analy-sis of the Westcode module, it is important to note that all of the equipment (e.g. the test jig and the Rogowski coils) have been explicitly designed for use in any subsequent time domain analyses that may be performed. 3.1.2 Resistive Elements (IGBT Replacements) Experimental determination of the IGBT on-state resistance revealed that a minimum of approximately 40A was required, per die, to put the IGBT into the linear region of its V / I relationship (Applendix A). This was unfeasible, as it would require a stable DC current of almost 600A be flowing through the complete Westcode module for the entire time that measurements were being performed. While current supplies of this magnitude are available at TRIUMF, the amount of power that would be dissipated by the module (in the order of 300W+), plus the complexity of measuring what would be a relatively tiny AC signal in the presence of such a large DC current, forced the development of a different solution. To introduce a series resistance for each post, and to attempt to assure consistency, it was decided to solder four parallel low-tolerance (5%) surface mount resistors between two layers of copper foil. These sit upon the copper posts within the IGBT module. Uniform contact is assisted by bending up the corners of each resistive element so that the force of the top brass spacer (Figure 3.7(c)) comes in contact with each of them as it is placed upon the module and the corners flatten. Figure 3.1 illustrates 14 of these deployed in the Westcode module. It is worth noting that the module is not compressed in any way with the resistive elements in place. 52 Chapter 3. Experimental Verification Figure 3.1: Resistive elements to replace IGBT die, in place within the Westcode module 3.1.3 Current Sensing Measurements required a means of sensing how the current was distributing itself within the IGBT module. The requirements called for a current sensor with an inside diameter that was large enough to be able to fit around each post (approximately 1cm across), but an outside diameter small enough to permit two adjacent sensors to share the space between each post (inter-post spacing « 5mm). Additionally, as it is hoped to perform time domain measurements of the IGBT switching characteristics in the future, it was a requirement that the current sensor must be able to fit in the very limited space between each IGBT cassette and the gate trace in the Westcode mod-ule (a space of just over 1mm). To the author's knowledge, no such sensor is commercially available. 53 Chapter 3. Experimental Verification Rogowski Coils Rogowski coils are air-cored current transducers. They consist of a series of windings around a non-ferritic former, usually flexible. Rogowski coils are a favourite current sensing tool for those wishing to measure high-power tran-sients as they do not saturate with large currents, and can be constructed in such a fashion so that they may be 'opened' and wrapped around an in-place conductor (i.e. a bus-bar) [27]. Rogowski coils exploit Ampere's law, in that the windings around the former act to perform a piece-wise closed line integral of the magnetic field flowing around a conductor. It further follows from Ampere's law that it doesn't matter what shape this path takes, as long as it completely circles the conductor. Unlike a conventional CT, rogowski coils are not self-integrating, and produce an output voltage proportional to the derivative of the current flowing through the loop. hrive = I Sin(wt) Vcoil = KIUJ cos(ut) Where K is a single frequency constant related to the Rogowski coil response. Rogowski coils have been employed for very similar applications to this in the past[28], and can be fabricated without highly specialized equipment. The photographs in Figure 3.2 detail the Rogowski coils that I constructed, and those in Figure 3.3 show the coils in-place within the module. The output of the Rogowski coil can be expressed as the following: _ HQAN di c m l ~ I dt Where A is the cross-sectional area of the former, N is the number of winding turns, and I the length of the former. The coils made at TRIUMF had 480 turns, a cross sectional area of just under 1mm2, and a length of 4.8mm. Seven such coils were constructed. 54 Chapter 3. Experimental Verification (a) Winding of a Rogowski current-sensing coil. (b) Finished Rogowski coil. Figure 3.2: Rogowski coil construction 55 Chapter 3. Experimental Verification Figure 3.3: Rogowski coils in-place within Westcode module Chapter 3. Experimental Verification Instrumentation Amplifier As the output from the Rogowski coils is extremely small, especially at low frequencies, an instrumentation amplifier was designed with a gain of «10,000. Figure 3.4 shows the schematic for the instrumentation amplifier circuit used. The circuit implemented had R i =51.1kfi, R G =10.5f&,- and R2 h R3 =10k£l The expression for the gain of this amplifier is: Four identical channels of this amplifier were built. A photo of the con-structed four-channel amplifier is shown in Figure 3.5. G = 1 + 2 RG With the values listed above, the gain of the amplifier is equal to 9963. Figure 3.4: Instrumentation amplifier circuit diagram 57 Chapter 3. Experimental Verification 3.2 Test J ig 3.2.1 Requirements In all of the simulations described in this document, a geometry for the IGBT and the corresponding return path is presented. This design is intended to reflect a potential electrical layout for a thyratron replacement switch. As such, it is designed to: • Exhibit low inductance: the geometry of the return path is intended to act as a coaxial structure. • Produce an unbiased distribution of current within the module. • Allow for large blocking voltages that would be attained by series connections of modules. The test jig also needs to exhibit these same electrical characteristics. It is also necessary that the test jig help to facilitate measurements on the IGBT module. This entails having a relatively short assembly/dissassembly cycle, allowing sufficient space for possible measurements, and, as the pro-cess will involve some relatively high-frequency signals (with components >lMHz), a readily accessible common ground for all measurement and sup-ply equipment. Another concern is that the materials used be non-magnetic 58 Chapter 3. Experimental Verification to prevent non-linearities. Additionally, to be a general purpose appara-tus, the test jig must be mechanically able to compress an IGBT mod-ule with sufficient force to make electrical contact, as per manufacturer's specifications[19]. 3.2.2 Design Prevessin Design After considering the above criteria, and examining the apparatuses already in use to compress presspack IGBT modules and other similarly packaged semiconductors^, 9], it was decided to use a modified version of a design already in use at CERN Prevessin [1]. The Prevessin design is shown in Figure 3.6. In this design, which has been developed for pulsed measurements only, energy is stored in ten parallel 50fi coaxial cables rated at 8kV DC. These cables attach to the bottom aluminium plate of the apparatus, where the outside sheaths of the coaxial cables are also electrically connected. The centre conductors of these ten cables then go on to form the 'return' path that surrounds the DUT. The Prevessin design has several advantages, especially when it comes to time-domain pulsed measurements. These include the direct connection of the energy storage devices, and, most importantly, a single ground comprising the base of the module. However, as our intention is to perform frequency domain measurements (at least initially), this design is not ideal in that it is difficult to supply from a single source. T R I U M F Design Components Figure 3.7 illustrates the components that make up the test jig assembly used at TRIUMF. As with the Prevessin jig, this test apparatus is designed such that the IGBT module is compressed between two aluminium plates (top and bottom illustrated in Figures 3.7(a) and 3.7(c), respectively) with six brass 59 Chapter 3. Experimental Verification Figure 3.6: CERN Prevessin test jig for presspack IGBTs (Note: "MuliCon-tacf'(sic) should read "MultiContact")[l] conducting rods making up the return path (Figure 3.7(b)). The geometry of this return path is consistent with the simulated models presented in Figures 2.2, 2.5 and 2.10. Electrical Layout As mentioned above, the design of the test jig reflects the simulation models, and is also a conceptual design for a thyratron replacement. The frequency domain measurements were carried out at low voltage, and hence did not require HV insulation anywhere in the apparatus to perform. Figure 3.8 illustrates how this was implemented in the test jig, the ar-rows show the direction of positive current flow. Further description of the labelled portions of the figure follows: i . Current enters the jig from the external connection pictured in Fig-ure 3.7(e) (right). i i . Connection is made to the top brass spacer, which is insulated from the top aluminum plate. 60 Chapter 3. Experimental Verification (a) Jig top plate with 6 conducting rods, and 3 clamping rods. Absent: electrical connection plate featured in (f) (c) Components comprising module stack: (from left to right) bottom spacer, Westcode IGBT module (with IGBT die), centring ring, top conducting spacer, insulating shim. Background: jig bottom plate. (e) A C source electrical connections to top aluminium plate of jig. Connection point for forward current at right, source return contact at left. (b) Conducting rod (foreground) and in-sulated clamping rod (background, left). (d) Insulation for compressing rods. (f) Side view of assembled jig. 61 Figure 3.7: TRIUMF test jig assembly photos Chapter 3. Experimental Verification Figure 3.8: Current path through TRIUMF test jig Figure 3.9: Test setup electrical layout i i i . The current gets distributed through the 14 parallel paths within the Westcode IGBT module. i v . The bottom aluminium plate redistributes the current to the return conductors. v . The brass rods (two of six shown) return the current to the top plate. v i . Current goes via the top aluminium plate to the return connector: Fig-ure 3.7(e) (left). Figure 3.9 illustrates a schematic view of the test layout used for fre-quency domain analysis. 62 Chapter 3. Experimental Verification Mechanical Structure For measurements that require the IGBT module be compressed, clamping is achieved through the use of either three or, if necessary, six non-magnetic stainless steel rods that are electrically insulated from the top A l plate. These rods are segments of 5/16", 304 grade, stainless steel reddi-rod; the insulation is provided by machined G10 (FR4) epoxy spacers that insulate the rod throughout the entire thickness of the top plate (Figure 3.7(d)). In the TRIUMF design this insulation is not nearly as critical as it is with the Prevessin design because the top and bottom plates are electrically con-nected at all times via the brass rods. In the Prevessin apparatus, the clamping insulation must withstand the full voltage across the device. The test apparatus was constructed from non-ferromagnetic materials (i.e. brass, stainless steel, aluminium) such that the return current path would take the same form as the simulated model. For the frequency domain analyses described in this document, the mechanical clamping rods were unused, and the jig was used for the geometry of its return path. 3.3 A C Measurement Results The measurements were made by exciting the module with a 10V peak AC signal from a 50f2 output impedance function generator, and measuring the output of the Rogowski coils as amplified by the instrumentation amplifier. To remove non-periodic noise, the averaging functionality of the oscilloscope was employed. A 5fi resistor was placed in series with the test jig and the function generator, and the voltage across this resistor measured for current sensing purposes. 3.3.1 Purely Copper Module Measurements of the current distribution for the purely copper module proved to be exceedingly difficult. The low-frequency distribution, being dominated by the resistance of each path, is almost entirely determined by the contact resistance to each post. Attempts to get a uniform, or even 63 Chapter 3. Experimental Verification I PSpice - Fasthenry Mixed Parameters Experimental Measurements Canductor Conductar Cpnductor Conductor Conductor Conductor Conductor 6 7 Figure 3.10: Experimental results for high-frequency (2MHz) distribution with copper-only module consistent, measurement of the low frequency distribution were thwarted by the difficulty of acquiring uniform electrical contact. Attempts were made to improve the distribution by improving the electrical contact to the device (i.e. by the application of conducting paste, and by compressing the mod-ule) , but these proved fruitless. In some cases these attempts actually made the problem worse as it took even less of an absolute variation in contact resistance to effect the relative distribution of current. However, even though measurements at low- and intermediate-frequencies were problematic, the copper module did allow us to examine the high-frequency current distribution. This is illustrated in Figure 3.10 where the experimentally determined current distribution at 2MHz is compared with the high frequency asymptote values from simulation. The agreement for this experimentally determined distribution with the simulation results is good, although not perfect. The largest error is for Conductor 7, where the difference between the simulated and experimentally determined distributions is approximately 1.2% of total module current. 64 Chapter 3. Experimental Verification 3.3.2 Resistive Module When attempting measurements on the IGBT module, it soon became ob-vious that there was an upper-limit of approximately 2MHz to our measure-ments. Beyond this point, capacitive interference from the module began to dominate the measurements. This was problematic, as simulations showed that, with resistive modules inserted to appropriately reflect the on-state resistance of an IGBT die, the distribution would not fully reach it's induc-tively determined asymptote by this frequency. Keeping in mind the potential effect that the contact resistance might have on the distribution, simulations were performed to determine what the maximum value of series resistance could be inserted and while per-mitting the entire transition from a resistively-dominated to an inductively-dominated distribution to be examined. The results of the simulation pointed to a series resistance of 2.5mfi per path. The results of measurements with this value of on-state resistance and their comparison to theory are shown in Figure 3.11. Again, it is likely that the effect of contact resistances played a large role in determining the distribution of current within the module. Figure 3.11(a) shows the comparison to the original PSpice simulation. The low-frequency current distribution is significantly altered by the effect of the contact resis-tances, which also have the effect of shifting the resistive-inductive transition point upwards in frequency. A revised PSpice model was made, this time with different values of con-tact resistance inserted into each path to match the simulation to the exper-imental low-frequency distribution. The average "contact resistance" added to the PSpice model was 0.6mf2. The results are shown in Figure 3.11(b). With the effect of the contact resistances added to the PSpice model, the experimental data correlates much more strongly with the simulation. There are significant discrepancies: most notably the transition point for Conductors 5 Sz 6, and the high-frequency asymptotes for Conductors 2 & 4. However, it can be said that the agreement between the,experimental and simulated results is acceptable. . 65 Chapter 3 . Experimental Verification Frequency (Hz) (a) 2.5mf2 comparison with PSpice simulation neglecting contact resis-tances Frequency (Hz) (b) 2.5m$7 comparison after accounting for contact resistances in the PSpice simulation Figure 3.11: Comparison of simulated and measured current distribution within the IGBT module with 2.5mfl of series resistance 66 Chapter 3. Experimental Verification It is interesting to note that the "bump" predicted by the PSpice simu-lation for the relative current in Conductor 2 (as highlighted in Figure 2.11) appears to be present in the experimental results. This is interesting as it was not predicted by either of the field solvers, which are considered to be 'more correct'. 67 Chapter 4 Conclusions and Recommendations for Future Work This document details the successful design and testing of a methodology to model the geometry of a press-pack semiconductor device as a set of cou-pled circuit parameters. In the process of creating this methodology, the geometry of a Westcode IGBT module was analysed as to its suitability for application in a thyratron replacement. This analysis concludes that the module design exhibits a high-frequency current imbalance that is in-extricably tied to its layout. As has been shown, it is possible to mitigate this imbalance by either increasing the on-state resistance of the IGBT die, or shortening the overall height of the stand-offs upon which these die are placed. However, increasing the on-state resistance also effects losses in the device, and decreasing the post height would increase capacitive coupling to the gate trace from the collector. Additionally, there is a lower limit to the height of the posts imposed by the DC break-down voltage of the the module. While the model generated appears to be remarkably accurate, especially considering its simplicity (just two coupled inductors and two resistors per current path), there is definitely room to improve its accuracy. This is es-pecially true at intermediate frequencies, where the module distribution is defined by both its resistive and inductive components. In this frequency range, the current model over-estimates the uniformity of the current distri-bution. I suggest that a method of converting several Fasthenry extractions, 68 Chapter 4. Conclusions and Recommendations for Future Work from over a range of frequencies, to a coupled-inductance ladder network be investigated. Given the relatively short amount of time that each Fasthenry extraction consumes (wl5 minutes), and the ability of PSpice to rapidly simulate circuits of far higher complexity than our current model, it is au-thor's opinion that this would be a worth-while endeavour, and would not significantly impact prototyping speed. Using the existing methodology, there is much future work that can be performed to examine the effects of modifying any combination of internal die layout, or return path configuration. A future model of the IGBT might also introduce non-linear models of IGBT die and consider the effects asso-ciated with coupling to the gate trace. Considering the simplicity and speed modifying and simulating the existing model, these should be a relatively simple tasks. 69 Bibliography [1] Private communication with M . Barnes June 30, 2006. [2] R. Cassel and M . Nguyen, "A new type short circuit failures of high power IGBT's," Pulsed Power Plasma Science, 2001. PPPS-2001. Di-gest of Technical Papers, vol. 1, 2001. [3] M . Barnes and G. Wait, "Solid State Switch Alternatives For Klystron Modulators," in 1995 Second modulator klystron workshop: A Modula-tor klystron workshop for future colliders, ser. SLAC : 481, A. Donald-son, Ed. The Center, Stanford, Calif, 1996. [4] A. Dunlop, "Prototype thyratron replacement using semiconductors [pulsed power switch]," IEE Symposium Pulsed Power 2001 (Ref. No. 2001/156), 2001. [5] E2V Technologies Ltd. Hydrogen thyratrons preamble. [Online]. Available: http://www.e2v. com/download. cfm?type= document&document=613 [6] M . Barnes and G. Wait, "(tri-dn-05-15) pspice analysis of the ags alO kicker magnets," TRIUMF, Tech. Rep., 2005. [7] M . Barnes, G. Wait, E. Carlier, L. Ducimetiere, U. Jansson, G. Schroder, and E. Vossenberg, "Operation Modes of the Fast 60 kV Resonant Charging Power Supply for the LHC Inflectors," Proc. of 11 thIEEE Pulse Power Conference, Baltimore, plS09-pl314, June, 1997. [8] G. Wait and M . Barnes, "Thyratron Lifetimes, A Brief Review," in 1995 Second modulator klystron workshop: A Modulator klystron workshop for future colliders, A. Donaldson, Ed., 1996. 70 Bibliography-Id] A. Welleman, E. Ramezani, and U. Schlapbach, "Semiconductor switches replace thyratrons & ignitrons," Pulsed Power Plasma Sci-ence, 2001. PPPS-2001. Digest of Technical Papers, vol. 1, 2001. [10] A. Welleman, J. Waldermeyer, and E. Ramezani, "Solid State Switches For Pulse Power Modulators," LIN AC 2002, Proceedings of, pp. 709-711, 2002. [11] M . Nguyen, "Short circuit protection of high speed, high power IGBT modules," Pulsed Power Conference, 2003. Digest of Technical Papers. PPC-2003. 14th IEEE International, vol. 2, 2003. [12] P. Palmer and A. Githiari, "The series connection of IGBTs with active voltage sharing," Power Electronics, IEEE Transactions on, vol. 12, no. 4, pp. 637-644, 1997. [13] G. Leyh, "A critical analysis of IGBT geometries, with the intention of mitigating undesirable destruction caused by fault scenarios of an ad-verse nature," Particle Accelerator Conference, 2003. PAC 2003. Pro-ceedings of the, vol. 2, 2003. [14] M . Barnes, E. Blackmore, G. Wait, J. Lemire-Elmore, B. Rablah, G. Leyh, M . Nguyen, and C. Pappas, "Analysis of High-Power IGBT Short Circuit Failures," Plasma Science, IEEE Transactions on, vol. 33, no. 4, pp. 1252-1261, 2005. [15] S. Scharnholz, R. Schneider, E. Spahn, A. Welleman, and S. Gekenidis, "Investigation of IGBT-devices for pulsed power applications," Pulsed Power Conference, 2003. Digest of Technical Papers. PPC-2003. 14th IEEE International, vol. 1, pp. 349-352, 2003. [16] S. Gunturi and D. Schneider, "On the operation of a press pack igbt module under short circuit conditions," Advanced Packaging, IEEE Transactions on, vol. 29, no. 3, pp. 433-440, August 2006. [17] B. Rablah, "An analysis of the effects of parasitic inductance in internal IGBT module geometry," 2004, TRIUMF Co-op Student Report. 71 Bibliography [18] Westcode Semiconductors Ltd. High power press-pack igbts: Extended range. [Online]. Available: [19] F. Wakeman, K. Billett, R. Irons, and M . Evans, "Electromechanical characteristics of a bondless pressure contact IGBT," Applied Power Electronics Conference and Exposition, 1999. APEC'99. Fourteenth Annual, vol. 1, 1999. [20] L. Ducimetiere, U. Jansson, G. Schroder, E. Vossenberg, M . Barnes, G. Wait, S. Div, and G. CERN, "Design of the injection kicker magnet system for CERN's 14 TeVproton collider LHC," Pulsed Power Con-ference, 1995. Digest of Technical Papers. Tenth IEEE International, vol. 2, 1995. [21] M . Barnes and G. Wait, "High current 66kv tests on high stability pfn discharge capacitors for cern lhc," IEEE PULSED POWER CONFER-ENCE, vol. 2, pp. 773-776, 1999. [22] A. Loth and F. Lee, "Two-dimensional skin effect in power foils for high-frequencyapplications," Magnetics, IEEE Transactions on, vol. 31, no. 2, pp. 1003-1006, 1995. [23] S. Kim and D. Neikirk, "Compact equivalent circuit model for the skin effect," Microwave Symposium Digest, 1996., IEEE MTT-S Interna-tional, vol. 3, 1996. [24] M . Kamon, M . Ttsuk, and J. White, "FASTHENRY: a multipole-accelerated 3-D inductance extraction program," Microwave Theory and Techniques, IEEE Transactions on, vol. 42, no. 9, pp. 1750-1758, 1994. [25] A. Ruehli, C. Paul, and J. Garrett, "Inductance calculations using partial inductances and macromodels," Electromagnetic Compatibility, 1995. Symposium Record. 1995 IEEE International Symposium on, pp. 23-28, 1995. 72 Bibliography [26] Tektronix. Understanding oscilloscope bandwidth, rise time and signal fidelity. [Online]. Available: TechnicaLBriefs/bw_rt/55_18024_0.pdf [27] D. Ward and J. Exon, "Using Rogowski coils for transient current mea-surements," Engineering Science and Education Journal, vol. 2, no. 3, pp. 105-113, 1993. [28] J. Joyce, "Current Sharing and Redistribution in High Power IGBT Modules;" Ph.D. dissertation, PhD thesis, University of Cambridge, UK, May 2001. [29] M . Evans, F. Wakeman, R. Irons, G. Lockwood, and K. Billett, "DESIGN CONCEPTS OF A BONDLESS PRESSURE CONTACT IGBT," EPE'99, Lausanne, September 1999. [30] Westcode Semiconductors Ltd. T0900ta52e 5.2kv igbt datasheet. [Online]. Available: 73 Appendix A IGBT On-state Resistance A survey of Westcode documentation showed that the average on-state re-sistance, as determined from V-I plots showing the slope resistance of sim-ilar IGBT modules in their linear regions, varied from lOmfi to 15mfi per die[29][30]. As the module TRIUMF is examining is a prototype device, and, as such, has no datasheet information available, measurements were made to determine the on-state resistance. Using a single Westcode IGBT die as a switch, the gate was pulsed with a voltage of 15V. The IGBT was set-up to switch a bank of capacitors (10x470/zF) into a short-circuit. Measurements of the voltage across the IGBT and the current were made as the charging voltage on the capacitors was increased. A plot of these measurements is shown in Figure A . l . Also on this plot are low current measurements made using a DC power supply with a maximum output of 1.5A. These measurements are intended to confirm the results of the pulsed measurements. The measurement of the current through the IGBT was achieved using a Pearson 410 CT, with a Tektronix 7401 oscilloscope used to measure the collector-emitter voltage and read the output from the CT. The current pulses, typically less than 3/iS wide, were measured from the mean of the flat-top value. A photograph illustrating the set-up is in Figure A.2 featuring: the capacitor bank (left), clamped IGBT die (right), charging supply (top right) and CT probe (bottom middle). 74 Appendix A. IGBT On-state Resistance Collector Current (A) Figure A . l : V-I relationship for Westcode IGBT die to determine on-state resistance (Vg a ^ e = 15V) Figure A.2: Measurement set up for IGBT die on-state resistance measure-ments 75 Appendix A. IGBT On-state Resistance The IGBT does not enter the linear region until the collector current is above R S 4 0 A . The slope-resistance of the IGBT was calculated from the slope of the plotted data to be 23.3mfi. This value is between 1.6x and 2x the values obtained from the manufacturer's curves for commercially available devices. Given the relationship between the on-state resistance and the internal module current distribution that has been established in Section 2.3.4, it is quite possible that this is an intentional modification on the part of the manufacturer to improve the response of the module to pulsed switching. 76 Appendix B Frequency Dependance of Parameters It is well known that parasitic resistance and inductance values are frequency dependent [22]. As a rule, resistance values increase as the drive frequency is increased. This follows from the skin-effect (Equation 2.1), where, as the current fringes to the outside of the conductor, the cross-sectional area of the conductor available for conduction decreases, increasing the effective resistivity of the conductor material. To a lesser degree, inductance values are also effected by drive frequency. At higher frequencies, the magnetic field is excluded from the inside of the conductor by induced-eddy currents, resulting in a decrease in overall inductance. To determine the effect that the frequency of extraction might have upon the accuracy of the simulations, Fasthenry was set to run a series of extrac-tions for a purely copper model of the Westcode module from 1Hz to lMhz. Plots of the resistance, self-inductance, along with the mutual coupling terms relating to Conductor 1, are shown in Figure B . l . The resistance of each conductor is highly frequency dependant, and rises about 1.5 orders of magnitude before plateauing near 1MHz. There is variation between the forward conductors («2%) with the conductors closest to the inside of the module having a higher extracted resistance. 77 Appendix B. Frequency Dependance of Parameters (a) Conductor resistance (b) Conductor self-inductance Frequency (Hz) (c) Subset of K-value coupling terms (coupling to Conductor 1 shown) Figure B . l : Extracted resistance, inductance and mutual coupling terms for a "copper only" model of the Westcode IGBT module as a function of frequency 78 Appendix B. Frequency Dependance of Parameters The self-inductance values decrease, on average, approximately 20% be-fore plateauing. There is also a significant spread between the self-inductances at the high-end of the frequency range («5%). It is interesting to note that this high-frequency spread in self-inducatance values acts to enforce a more uniform current distribution, as conductors towards the centre of the mod-ule have lower self-inductance terms than those at the outside, for higher frequencies. This is due to the magnetic field being excluded from neigh-bouring conductors, due to induced eddy-currents, and being forced out to the fringes of the module. From the shape of these plots, it was decided to mix the extracted circuit parameters from high- and low-frequency simulations to produce a single set of circuit elements. Inductance values, as well as the associated cou-pling terms, would be taken from the high-frequency simulation, resistive values from the low-frequency simulation. The rationale was: at low fre-quencies, the resistances would dominate and determine the distribution of current, while at high-frequencies, the inductances would be dominant. At both extremes, the distribution would be 'correct'. It was hoped that, for intermediate frequencies, the distribution would be close enough to be accurate. Figure B.2 shows the extraction frequencies considered, and their effect on the current distribution. For legibility, only Conductor 1 is shown. Opera 2D simulation results are included as a reference for what is to be considered an accurate estimation of the distribution. From this analysis, it was decided to perform the PSpice simulations with the 1Hz R - 1MHz L parameters, as they provided the best combination of high- and low- frequency fit, as well as an acceptable match over the entire frequency range. If it is deemed necessary to have an improved fit, it is recommended that inductance ladder-networks be constructed. 79 Appendix B. Frequency Dependance of Parameters Figure B.2: Different extraction frequencies and their effect on module cur-rent distribution 80 Appendix C Coupled Inductors From Impedance Matrixes The following Matlab code performs the conversion of a single-frequency impedance matrix into a set of resistor and inductor values, as well as a set of coupling terms for the inductors. function [M_R,M_L,K_val] = GetMutual(X,freeq) % Calculates resistance, self inductance, mutual inductances, and coupling values. "/, Takes an n X 2*n matrix with separated real and imaginary components in alternat % columns. [m,n] = size(X) ; M_L = zeros(m); M_R = zeros(m); K_val = zeros(m); '/.Omega omega = 2*pi*freeq; i =1; j =2; while i <=.m while j <= n %Set the diagonal of M_L equal to the self-inductances. %" M_R 11 " " resistances. if j == 2*i M_L(i,i) = X(i,j)/omega; 81 Appendix C. Coupled Inductors From Impedance Matrixes M_R(i,i) = X ( i , j - D ; else °/,set up a l l the mutual inductances M_L(i,j/2) = X(i,j)/omega; end J=J+2; end j= 2 ; i = i+1; end i = l ; j = i ; f o r i = l:m-l f o r j = i+l:m i f s q r t ( M _ L ( i , i ) * M _ L ( j , j ) ) ~= 0 K _ v a l ( i , j ) = M_L(i,j) / s q r t ( M _ L ( i , i ) * M _ L ( j , j ) ) ; end end end M_R; M_L; K_val; 82 


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