A parallel implementation of the direct coupling of InGaP/GaAs HBT transport equations has been included in an Harmonic Balance simulator. Several results such as a class AB amplifier for mobile communication study and a stability analysis of “crunch effect” in multi-finger HBT have been performed

Lopez, D.

Quéré, R.

Sommet, R.

English

AMS Acta

ELECTROTHERMAL HARMONIC BALANCE SIMULATION OF AN INGAP/GAAS HBT BASED ON3D THERMAL AND SEMICONDUCTOR TRANSPORT  MODELSR. Sommet, D. Lopez, R. QuéréI.R.C.O.M. - C.N.R.S. U.M.R. n° 6615, I.U.T. G.E.I.I.,7, rue Jules Vallès 19100 Brive la Gaillardesommet@brive.unilim.frABSTRACTA parallel implementation of the direct coupling of InGaP/GaAs HBT transport equationshas been included in an Harmonic Balance simulator. Several results such as a class AB amplifierfor mobile communication study and a stability analysis of “crunch effect” in multi-finger HBThave been performed.INTRODUCTIONCircuit and device interaction determination appears to be one of the major challenge ofmobile communication engineering in the next few years [1]. The ability of co-designingsimultaneously devices and circuits will be a major feature of CAD tools for the design of MMICcircuits [2]. However, current simulation tools used to simulate the steady state of microwavecircuits are based on the Harmonic Balance (HB) technique and require lumped models for theactive devices which are not based on numerical solution of the semiconductor equations and as aconsequence are not predictive. They require the active semiconductor components to becharacterized in advance and fitted to a lumped equivalent model. The approach presented heredeals with the integration of the physical system of semiconductor equations of a III-V HBT in ageneral circuit simulator [3].PARALLEL SIMULATORThus, the popular HB formulation has been adopted in the proposed approach coupled to afully implicit discretization scheme of one dimensional device equations. The resulting softwareallows the optimization of circuit performances in terms of physical and geometrical deviceparameters as well as in terms of terminating impedance’s. This result has been achieved by makinguse of dedicated techniques for convergence improvement including the exact Jacobian matrixcalculation of the nonlinear system that has to be solved [4]. In order for the simulator to be usablein term of CPU computation time, especially for multi finger HBT, we have realized a coarse grainparallel implementation of the simulator base on the scheme presented in figure 1. One “master”process solves by a Newton-Raphson iterative method the HB equations resulting from Kirchofflaws at each node of the global circuit. In order to get nonlinear current values and their derivativesversus applied commands, it sends requests to slave process which solve transport equations foreach emitter finger and collects data currents and their derivatives to build the Jacobian matrixuseful to convergence algorithm. The fact that computation time is mainly due to physicalsimulation implies that if we consider a “n” fingers amplifier circuit, the speedup is about “n” on theparallel machine compared to the serial machine. The actual implementation relies on a cluster of 9PCs controlled by the LINUX operating system. A fast Ethernet HUB at 100 Mbits/s enablesconnection between each computer. The communication library between machines is based on thestandard MPI [5] providing a complete portability of the software. The feature of the completeparallel computer is about 1 GO of RAM and 20 GO of Hard Disk.RESULTSSeveral results concerning a InGaP/GaAs HBT have been obtained. Figures 2 and 3 presentfirst a comparison between simulated and pulsed measurements characteristics for a one finger 2µm* 30µm HBT. We can see a good agreement between measurements and models which first validateour one dimensional DD approach.Results concerning the optimization of a class AB power amplifier for mobilecommunication at 1.8 GHz have already been presented in [3] and are just remember here. With theactual coupling method, optimization of the amplifier becomes feasible in terms of devicecharacteristics or embedding impedance’s for a particular device as the total CPU time required forthe simulation of the steady state regime takes less than 4 min per power point. Moreovercomplementary results such as internal carrier densities evolution inside the device during theloadline cycle may be extracted which is very interesting for the co-design of circuits and activecomponentsThe second kind of results concern the study of thermal instability on multi fingers HBT.We have simulated the “crunch” effect which appears in a 2 or more fingers HBT. Figure 4 exhibitsfirst the Ic curve versus Vbe for fixed Vce corresponding to the thermal solution of the DD for onefinger. The two possible solutions for a given Vbe and a fixed Vce value show the potentialinstability for the Ic current. The schematic of the simulated circuit is presented in figure 5. A probegenerator is introduced in order to force a temperature gap between finger 1 and finger 2. Thesolution is computed for several values of Vprobe until Iprobe equal zero is reached meaning thatthe probe generator do not perturb the steady state equilibrium [6]. Figure 6 shows the current Ic ineach transistor. For Vce greater than about 4V the temperature in each transistor vary. The currentin the hot finger increases rapidly whereas this of the cold one decreases. Some results concerning astudy of the effect of the ballast resistor Reext and the thermal resistor Rth in the two fingers HBThave been realized.(an internal integrated ballast layer is already present in the transistor). They willbe presented at the conference. The shift of critical Vce where the “crunch” phenomena appears iscompatible in each case with the Liu formula (1) [7].Vce crit = 1/φRth * (ηkT/qIc + re) (1)The originality of the implemented electrothermal model relies also on the way the thermalnetwork is obtained. A three dimensional thermal analysis is performed first with the Finite Elementsoftware MODULEF.A cutplane of the HBT 3D mesh is presented in figure 7. Then the thermalresistor network is extracted according the temperature profile. This thermal network is composedby linear elements such as finger thermal resistor and thermal coupling resistor. The second stagewill consist of integrating more precisely thermal effects by means of model reduction techniqueapplied to the K rigidity and the M stiffness matrix provide by the finite element software.CONCLUSIONWe have presented a parallel implementation of the direct coupling of InGaP/GaAs HBTtransport equations in an Harmonic Balance simulator which enable to study power amplifier formobile communication and thermal stability analysis of “crunch effect” in multi-finger HBT.Moreover the thermal resistor network is extracted from 3D thermal analysis. This simulator is alarge step to a full physical coupled simulator with predictive capabilities.REFERENCES[1] R.W. DUTTON, Z. YU "Architecture of TCAD For High Frequency Application" Workshopon Nonlinear CAD MTT-S 96, San Fransisco, June 17 1996, pp 2-26.[2] Z. YU, R. W. DUTTON "Large Signal Analysis of RF Circuits in Device Simulation"Workshop on Nonlinear Modeling and Characterization of Microwave Devices MTT-S 99, L. A.,June 1999.[3] R.SOMMET, Y. PERREAL, R.QUERE "A direct coupling between the semiconductorequations describing a GaInP/GaAs HBT in a circuit simulator for the co-design of microwavedevices and circuits" GaAs  97 – Bologna, sept. 1997[4] R. SOMMET, E. NGOYA "Full Implementation of Implicit Nonlinear Model with Memory inan harmonic Balance Software", IEEE on Microwave and Guided Letters, Vol. 46, n° 7,  june 1997[5] M. SNIR, S.OTTO, S. HUSS-LEDERMAN, D. WALKER, J. DONGARRA “MPI : TheComplete Reference”, The MIT Press, Massachusetts London, England 1996[6] T. PEYRETAILLADE, M. PEREZ, S. MONS, R. SOMMET, Ph. AUXEMERY, J.C.LALAURIE, R. QUÉRÉ "A Pulsed-Measurement based Electrothermal Model of HBT withThermal Stability Prediction Capabilities" IEEE, MTT-S 97, DENVER, june 1997[7] W. LIU, A. KHATIBZADEH “The Collapse of Current Gain in Multi-Finger HeterojunctionBipolar Transistors : its Substrate Temperature Dependence, Instability Criteria, and Modelling”,IEEE Trans. On Electron Devices N° 10, oct.1994FIGURESFigure 1 : Implementation of the parallel circuit simulatorKirchoffEquationsSolverMASTERFinger 1Semiconductor equations Solver( )( ) [ ]− ∇ ⋅∇ = − + −= ∇ + −= − ∇ + −= + ∇= − ∇x x D Ax nx pn n n n xp p p p xq p n N Nnt qJ G Rpt qJ G RJ qn E qD nJ qp E qD pε ψ∂∂∂∂µµ11SLAVE 1Finger 2SemiconductorequationsSolverSLAVE 2commandscurrents,derivativesvs commands...SLAVE N3D thermal« reduced »model[ ]thR-0.00500.0050.010.0150.020.0250.030.0350 1 2 3 4 5 6 7 8 9 10JC (A)VCE(V)simulatedmeasuredFigure 2 : Simulated and measured outputcharacteristics Ic(Vce)11.11.21.31.41.51.61.70 1 2 3 4 5 6 7 8 9 10VBE (V)VCE (V)simulatedmeasuredFigure 3 : Simulated and measured inputcharacteristics Vbe(Vce)0.11101001.2 1.25 1.3 1.35 1.4 1.45Ic(Vbe) mAVbeVCE = 8VVCE=6V VCE=4V VCE=2VFigure 4 : Ic(Vbe) characteristic for one fingercollectorecbaseRe1ext=0 Re2ext=0Pdiss1 Pdiss2Rth1=800 Rth2 =800RthcT11 T2VprobFigure 5: Two fingers HBT and its thermalcircuit05101520253035404550Ic2(Vce)0 1 2 3 4 5 6 7 8Vce(V)Ic, Ic1, Ic2 (mA)Ic1(Vce)Figure 6: Collector currents versus VceVia HoleActive areaGold bridgeAsGa substrateFigure 7 : Cutplane of the HBT 3D mesh

Electrothermal harmonic balance simulation of an INGAP/GAAS HBT based on 3D thermal and semiconductor transport models

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