CHAPTER 5MD 1999.2 Confidential and Proprietary 5-1Draft 7/28/99NPN BipolarTransistor Examples5Example SpecificationsThe use of Medici is illustrated by going through some of the analysis that mightbe performed on an NPN bipolar transistor. The analysis is divided into six parts.• The input file mdex2 develops the simulation structure.• The input file mdex2f then simulates the forward current characteristics for thedevice.The results of this simulation are examined with the input file mdex2fp.• The input file mdex2p modifies the emitter region of the device and specifiesdifferent material properties for the modified region.• The forward current characteristics are then repeated for the modified device.• The results of the simulation with the modified emitter are examined with theinput file mdex2pp.• The input file mdex2m illustrates a one-dimensional analysis of a bipolar tran-sistor.Generation of the Simulation StructureThe input file mdex2 creates the simulation structure for an NPN bipolar device.The output associated with the execution of Medici for the input file mdex2 isshown in Figures 5-1 through 5-5.Defining the Initial MeshAs with the MOS example in Chapter 4, the first step in creating a device structureis to generate an initial mesh. Since this initial mesh will be refined, it needs to beNPN Bipolar Transistor ExamplesMedici User’s Manual 5-2 Confidential and Proprietary MD 1999.2Draft 7/28/99adequate for defining the structure, but does not need to be fine enough to performa solution on.The mesh generation is initiated with the MESH statement at line 4 of the input fileshown in Figure 5-1.MeshSpecificationsThe X.MESH and Y.MESH specify how the initial rectangular mesh is generated.• The X.MESH statement that follows creates a grid section extending from x=0microns (the default starting location) to x=6 microns.• A uniform spacing of 0.25 microns is specified with the H1 parameter.• The first Y.MESH statement creates a 0.5 micron grid section at the top of thedevice that has a uniform spacing of 0.125 microns.Figure 5-1 Output of the simulation input filemdex2 1... TITLE Avant! MEDICI Example 2 - NPN Transistor Simulation 2... COMMENT Grid Generation and Initial Biasing 3... COMMENT Specify a rectangular mesh 4... MESH 5... X.MESH WIDTH=6.0 H1=0.250 6... Y.MESH DEPTH=0.5 H1=0.125 7... Y.MESH DEPTH=1.5 H1=0.125 H2=0.4 8... COMMENT Region definition 9... REGION NAME=Silicon SILICON 10... COMMENT Electrodes 11... ELECTR NAME=Base X.MIN=1.25 X.MAX=2.00 TOP 12... ELECTR NAME=Emitter X.MIN=2.75 X.MAX=4.25 TOP 13... ELECTR NAME=Collector BOTTOM 14... COMMENT Specify impurity profiles 15... PROFILE N-TYPE N.PEAK=5e15 UNIFORM OUT.FILE=MDEX2DS 16... PROFILE P-TYPE N.PEAK=6e17 Y.MIN=.35 Y.CHAR=.16 ... + X.MIN=1.25 WIDTH=3.5 XY.RAT=.75 17... PROFILE P-TYPE N.PEAK=4e18 Y.MIN=0 Y.CHAR=.16 ... + X.MIN=1.25 WIDTH=3.5 XY.RAT=.75 18... PROFILE N-TYPE N.PEAK=7e19 Y.MIN=0 Y.CHAR=.17 ... + X.MIN=2.75 WIDTH=1.5 XY.RAT=.75 19... PROFILE N-TYPE N.PEAK=1e19 Y.MIN=2 Y.CHAR=.27 20... PLOT.2D GRID TITLE=”Example 2 - Initial Grid” SCALE FILL 21... COMMENT Regrid on doping 22... REGRID DOPING LOG RATIO=3 SMOOTH=1 IN.FILE=MDEX2DS 23... PLOT.2D GRID TITLE=”Example 2 - 1st Doping Regrid” SCALE FILL 24... REGRID DOPING LOG RATIO=3 SMOOTH=1 IN.FILE=MDEX2DS 25... PLOT.2D GRID TITLE=”Example 2 - 2nd Doping Regrid” SCALE FILL 26... COMMENT Extra regrid in emitter-base junction region only. 27... REGRID DOPING LOG RATIO=3 SMOOTH=1 IN.FILE=MDEX2DS ... + X.MIN=2.25 X.MAX=4.75 Y.MAX=0.50 OUT.FILE=MDEX2MS 28... PLOT.2D GRID TITLE=”Example 2 - 3rd Doping Regrid” SCALE FILL 29... COMMENT Define models 30... MODELS CONMOB CONSRH AUGER BGN 31... COMMENT Solve for Vce=3 volts 32... SYMB CARRIERS=0 33... METHOD ICCG DAMPED 34... SOLVE V(Collector)=3.0 35... COMMENT Switch to Newton and two carriers - save solution 36... SYMB NEWTON CARRIERS=2 37... SOLVE OUT.FILE=MDEX2SMedici User’s Manual Generation of the Simulation StructureMD 1999.2 Confidential and Proprietary 5-3Draft 7/28/99• The next Y.MESH statement adds a 1.5 micron grid section beneath this witha grid spacing that increases from 0.125 microns at y=0.5 microns to 0.4microns at the bottom of the structure (y=2.0 microns).Device Regions The entire structure is defined as silicon with the REGION statement. TheELECTR statements are used to place the contacts. The base and the emitter areplaced on the surface, and the collector is placed along the entire bottom of thestructure.Impurity Profiles The impurity profiles for the device were specified using analytic functions,although they could also have been read from Avant! SUPREM-3, TSUPREM-4, or 1D and 2D formatted files.The first PROFILE statement specifies a uniform n-type background concentra-tion. The next two PROFILE statements specify p-type impurities for forming thebase. High concentration n-type profiles are then used to form the emitter and bur-ied collector for the structure.The specification of an output file on the first PROFILE statement saves the pro-files to be used whenever the grid is refined. This should always be done to avoidhaving to interpolate impurity concentrations from the nodes of an unrefined gridto the nodes of a refined grid.Regrid In lines 22 and 24, the grid is refined based on impurity concentration. During theregrids, a triangle is subdivided into four congruent triangles whenever the impu-rity concentrations at the nodes of the triangle differ by more than three orders ofmagnitude.In line 27, a third refinement based on impurity concentration is performed. Thisregrid is confined to the vicinity of the emitter-base junction. Confining the regridin this manner allows a fine grid to be placed in this important region and at thesame time keeps the total node count from becoming excessive.The final mesh is saved in a file for use in later simulations.The various stages of the mesh refinement are shown in Figures 5-2 through 5-5.Models andInitial SolutionThe MODELS statement at line 30 is used to select various physical models thatare included during the solution phase.At this point it is desired to obtain a solution with =3V and =0V which canbe used as a
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