Figure 4-1: DUTs and Setups for the Bipolar Model
This chapter contains step-by-step procedures for using the bipolar transistor model supplied with the IC-CAP system. It includes a description of model setup, instrument connections, and model parameters.
This chapter describes the University of California at Berkeley (UCB) bipolar transistor model supported in SPICE, and the techniques used to extract model parameters. Using the Model file named bjt_npn.mdl, this chapter provides step-by-step instructions for making DC, capacitance, and high frequency AC measurements and their corresponding extractions. You also can use the Model file as a template for creating custom Model configurations, which you can save under names of your own definition.
HP Application Note 1201-4, Advanced Bipolar Transistor Modeling Techniques, provides comprehensive descriptions of how to use the bipolar transistor extractions described here [1]. The theory of each extraction is discussed, as are topics such as temperature dependence, area scaling, and possible model improvements. The complete set of model equations for the UCB bipolar transistor model is also provided. Refer to this application note for advanced topics that are beyond the scope of this chapter.
The UCB bipolar transistor model is a hybrid of the Ebers-Moll [2] and Gummel-Poon [3] models. With a minimum parameter specification of IS, BF, and BR, the model defaults to the more simple Ebers-Moll model. The Ebers-Moll model is ideal because it neglects base width modulation, parasitic resistances, and high current injection effects.
Inclusion of additional parameters activates elements of the Gummel-Poon integral charge control model, which can provide greater accuracy. The Gummel-Poon model provides superior presentation of the current flow in the transistor' s base. It also provides accurate representation of parasitic resistances at all terminals, capacitance across all junctions, current-frequency effects, and temperature effects.
The UCB bipolar model is supported by all SPICE simulators currently included with IC-CAP. These include the HPSPICE, SPICE2(G6), and SPICE3 simulators.
NOTE: These simulators are provided with IC-CAP as a courtesy to the IC-CAP users, and are not supported by Hewlett Packard.
Note that the default nominal temperature for HPSPICE is 25 degrees C. For SPICE2 and SPICE3 it is 27 degrees C. To force a nominal temperature, set the TNOM variable under the Utilities menu to the desired value.
Bipolar parameter extraction is divided into the four categories of DC, Capacitance, Parasitic Resistance, and AC. Each of these corresponds to the required supporting measurements. The required instruments are described under Test Instruments. Measurement types and corresponding model parameters are listed in table 4-1. Table 4-2 summarizes the DUTS, Setups, and their attributes. The physical connections to the test device are described under Instrument to Device Connections.
The Model, bjt_npn.mdl, provides DUTs and Setups that correctly bias a typical device for the measurements needed to perform the associated parameter extractions. See chapter 1, Introduction, for definitions of the terms DUT and Setup.
Setups are provided for measuring and extracting the properties of the internal transistor (not including parasitic resistances). These are called fearly, rearly, fgummel, and rgummel. The fearly and rearly Setups measure forward and reverse Early voltage characteristics. The Early voltage parameters VAF and VAR are extracted simultaneously in the rearly Setup, using measurements taken from both fearly and rearly. The fgummel and rgummel Setups perform the forward and reverse Gummel plot measurements. The parameters IS, BF, NE, IKF, ISE, and NF are extracted by the fgummel Setup, while the extractions in the rgummel Setup produce the BR, NR, IKR, ISC, and NC parameters. Note that the model uses the saturated current parameter IS to simulate current flow in both directions.
Measuring the bipolar transistor's capacitance characteristics requires three DUTs. This is because each p-n junction is a physically different one-port connection. The base-emitter, base-collector, and collector-substrate junctions each have a different DUT and Setup. While you will perform all three measurements on the same physical device, each measurement requires different instrument connections for the corresponding DUT and Setup. The DUTs and instrument connections for each measurement are listed in table 4-3.
Each p-n junction is measured from a small forward bias to a large reverse bias. The extractions are performed using the Program Transform set_CJ to find the initial value of CJ0 then optimizing the parameters of the general p-n junction capacitance equation to the measured data. This produces the capacitance, built-in voltage, and grading factors for each DUT. These are: CJE, VJE, MJE; CJC, VJC, MJC, CJS, VJS, MJS. For the most accurate extractions, calibrate out stray capacitance from cables, probes, and bond pads before taking each p-n junction capacitance measurement.
Three parasitic resistances are connected to the bipolar transistor: RE, RC, and RB. RE and RC are constant value components, while RB is a function of base current. RE is measured by the Setup named reflyback. This Setup saturates the transistor, then measures the differential voltage drop from collector to emitter (with Ic = 0) versus the differential base to emitter current.
RC is measured by the Setup named rcsat, which measures the parameter as the DC resistance from collector to emitter at the onset of saturation. Alternately, the rcactive Setup can be used to measure the collector resistance in the active region of device operation. However, this extraction is very dependent on the operating point, which must be specified by manually placing a box on the Plot contained in the Setup. For complete information on using this extraction, refer to Application Note 1201-4, Advanced Bipolar Transistor Modeling Techniques.
The fourth Setup, rbbib, does not actually measure or extract RB. Instead, it produces a characteristic curve of base to emitter bias versus DC base current. The resulting curve is used when the base resistance is measured and extracted using S-parameters as shown below.
The AC DUT uses Setups that measure S-parameters with a network analyzer. The quality of the measured S-parameters depends heavily on the calibration of the network analyzer. IC-CAP does not perform error correction. It relies totally on the measuring instruments for the correction of errors. Note that making high frequency measurements on packaged transistors can lead to unexpected results. This is due to the stray capacitance and inductance that are a part of the package. You should measure S-parameters with a high quality microwave wafer probe.
The AC Setup named rbbac measures H11 of the transistor in the common emitter mode. This input impedance is then used in the extraction to produce the model parameters RB, IRB, and RBM.
The AC Setup named h21vsvbe measures H21 of the transistor in the common emitter mode. The measured current gain is then used to extract a small signal model that produces the parameters TF, ITF, VTF, XTF, and PTF.
The AC Setup named h21vsvbc measures H21 of the transistor in the common collector mode. The measured current gain is then used to extract the parameter TR.
The model parameter extractions are based on the concept that under steady state conditions, specific sets of parameters uniquely simulate the performance of the device. This lets you perform extractions over isolated regions of the device' s electrical response.
The forward and reverse DC bias extractions and junction capacitance characteristics are virtually independent of each other. The series resistances and small signal high frequency extractions, however, depend heavily on the DC and capacitance parameters.
Model parameter extractions produce parameters that are referenced to a temperature of 27 degrees C. To perform extractions at other temperatures, change the system variable TEMP to the correct value. TEMP is in the table of system variables, accessed through the Utilities Menu.
Table 4-1 summarizes the measurement types for the bipolar model by operating region, and the parameters that have the greatest effect on each type.
MEASUREMENT TYPE CONTROLLING MODEL PARAMETERS
DC Large Signal forward bias IS, BF, IKF, ISE, NE, NF, VAF
DC Large Signal reverse bias BR, IKR, ISC, NC, NR, VAR
Series Resistance RE, RC, RB, IRB, RBM
Capacitance CJE, VJE, MJE,
CJC, VJC, MJC, XCJC,
CJS, VJS, MJS, FC
Small Signal High Frequency TF, ITF, XTF, VTF, PTF, TR
Temperature Effects EG, XTB, XTI
IC-CAP Temperature Specification TNOM (system variable)
Table 4-1: Summary of UCB Bipolar Model Parameters by Measurement Type
Refer to tables 4-4 through 4-9, at the end of this chapter, for the definitions and SPICE default values of the bipolar model parameters.
Table 4-2 summarizes all of the DUTs, Setups, Inputs, Outputs, Transforms and Extractions in the bipolar transistor model.
DUT SETUP INPUTS OUTPUTS TRANSFORM FUNCTION ACTIONS
dc fearly vb,vc,ve,vs ic none none extraction in rearly
dc rearly vb,vc,ve,vs ie evextract BJTDC_vaf_var VAF,VAR
dc fgummel vb,vc,ve,vs ib,ic beta equation: ic/ib none
isextract BJTDC_is_nf IS,NF
fgextract BJTDC_fwd_gummel BF,IKF,ISE,NE
optiml Optimize IS,NF
optim2 Optimize BF,IKF,ISE,NE
dc rgummel vb,vc,ve,vs ib,ie beta equation: ie/ib none
nrextract BJTDC_nr NR
rgextract BJTDC_rev_gummel BR,IKR,ISC,NC
optimize Optimize BR,IKR,ISC,NC
cbe cj vbe cbe extract Optimize CJE,VJE,MJE
cjfunc PNCAPsimu none:simulates c vs v
set_CJ Program initial zero bias CJE
cbc cj vbc cbc extract Optimize CJC,VJC,MJC
cjfunc PNCAPsimu none: simulates c vs v
set_CJ Program initial zero bias CJC
ccs cj vcs ccs extract Optimize CJS,VJS,MJS
cjfunc PNCAPsimu none:simulates c vs v
set_CJ Program initial zero bias CJS
prdc reflyback ib,ic,ve,is vc extract BJTDC_re RE
prdc rcsat vb,vc,ve,vs ic extract BJTDC_rc RC (saturation)
prdc rcactive vb,vc,ve,vs ib,ic RC_active Program RC (active)
prdc rbbib vb,vc,ve,vs ib rbb RBBcalc none:calc rb vs ib
ac rbbac vb,vc,ve,vs,freq h extract BJTAC_rb_rbm_irb RB,RBM,IRB
h11corr H11corr corrects H11 for Zout
htos TwoPort none:h-par to s-par
ac h2lvsvbe vb,vc,ve,vs,freq h acextract BJTAC_high_freq TF,ITF,XTF,VTF,PTF
scale_params Program none:scales AC params
ac h21vsvbc vb,vc,ve,vs,freq h extract_TR Optimize TR
Table 4-2: Setup Attributes for the UCB Bipolar Model
The following sections explain the general procedure for extracting model parameter data from the UCB Bipolar Transistor. The procedure applies to all types of parameters: DC, Capacitance, and AC. The differences between extracting one type of parameter and another lie primarily in the types of instruments used to measure the data and the specifications within the DUTs and Setups.
Model parameters are typically extracted from measured data but may also be extracted from simulated data. To extract from measured data, make sure that the Outputs specified in the extraction Transforms use the '.m' suffix. For example, IS and NF are extracted using the BJTDC_is_nf function. To extract from measured data, IC-CAP uses log10(ic.m) as the specification of the forward collector current. (Use the .s suffix when extracting from simulated data.)
When performing an extraction, accurate results depend on the sequence of steps you follow. The top-to-bottom order of DUTs and Setups in a Model file is the suggested order of measurements and extractions. In the bjt_npn.mdl Model file, the large signal DC and junction capacitance parameters are independent of each other. However, for the parasitic resistances and AC parameters to be accurately extracted, the preceding two groups must be successfully extracted first. The Setups in the bjt_npn.mdl file are desired for use with a typical bipolar transistor. You may be able to improve results with your own devices by modifying these Setups to more closely conform to your needs.
The following procedure is recommended for measuring and extracting parameters from a typical bipolar transistor. Once the test device is installed in the test fixture and test instruments connected, all subsequent functions can be performed from the DUT-SETUP in the Model Editor.
This completes the procedure. By selecting the proper DUT and Setup, you can measure and extract parameter data of any desired type.
NOTE: The most effective procedure is to execute measurements and extractions from the DUT level (using the commands in the DUT popup menus). This assures that each Setup will be used in the correct order. If Setups are not executed in the correct order, incorrect results may be produced.
This section lists the instruments to use for measuring the characteristics of bipolar transistors. For more detailed information refer to chapter 11, Measurement.
DC model parameters are derived from measured DC voltage and current characteristics, using the HP4141, HP4142, or HP4145.
Capacitance model parameters are derived from measured capacitance characteristics at the device junctions, using the HP4271, HP4275, HP4280, HP4284, or HP4194.
AC model parameters are derived from measured S-parameters converted to the H-parameter domain, using the HP8753 or HP8510 network analyzers.
Install the device in a test fixture. Verify the correct connection to the device nodes by checking the Setup Editor specifications.
Table 4-3 is a cross reference of the connections between the terminals of a typical bipolar transistor and various measurement units. These connections and measurement units are defined in the Model file bjt_npn.mdl, and can be modified.
The Input and Output tables in the various Setups use the following abbreviations for the bipolar transistor nodes:
These nodes are defined in the Circuit Editor and can be modified as desired. The measurement units, which also can be modified, are defined in the Hardware Unit Table with the following abbreviations:
In table 4-3, DUT is the name of the DUT as specified in the DUT-SETUP tile. COLLECTOR, BASE, EMITTER, and SUBSTRATE are the names of the bipolar transistor terminals. As an example of how to read the table, the first line indicates that DUT dc has the DC measurement unit SMU1 connected to its collector, SMU2 connected to its base, SMU3 connected to its emitter, and SMU4 connected to its substrate.
DUT COLLECTOR BASE EMITTER SUBSTRATE COMMENTS dc SMU1 SMU2 SMU3 SMU4 none cbe open CM(H) CM(L) open calibrate for stray capacitance cbc CM(L) CM(H) open open calibrate for stray capacitance ccs CM(H) open open CM(L) calibrate for stray capacitance prdc SMU1 SMU2 SMU3 SMU4 none ac NWA(Port2)&SMU1 NWA(Port1)&SMU2 ground SMU4 calibrate for reference plane
Table 4-3: Instrument-to-Device Connections
The following section includes the recommended steps for measuring and extracting model parameters from a typical bipolar transistor.
In this example, you read in the bjt_npn.mdl Model file, perform measurements and model extractions, and save the completed Model to a name you define. All measurement and extraction functions are performed from the Model Editor, using the Setup names in the DUT-SETUP tile. The instructions assume that IC-CAP is running. If it is not, refer to chapter 3, Startup and Operation.
In summary, you execute the following procedures:
This sets IC-CAP to the directory that contains the bjt_npn.mdl Model file.
A Dialog Box showing all *.mdl files will be displayed.
Move the mouse pointer to the line that contains bjt_npn.mdl and click LEFT.
This selects the file and places its name in the Selection field at the bottom of the Dialog Box.
It takes several seconds to read the file and configure IC-CAP.
When complete, the npn Model Editor appears. You are now ready to begin measurement and extraction operations.
The DC extractions must be done exactly in the order in which they are listed:
This assures accuracy, because the parameter extractions are dependent on each other. Do all of the measurements, followed by all ofthe extractions, and finally, the simulations.
All DC model parameters have now been extracted and their values placed into the Parameter Editor. To view these values, move the mouse pointer to the Parameter Set title on the Model window title bar, press LEFT to display the pulldown menu and release on Edit. A list of the current model parameters appears in the Parameter Set Editor.
Figure 4-1: DUTs and Setups for the Bipolar Model
Place the device to be measured into the test fixture to be used. Make sure that the Capacitance Meter (CM) units connected to the device correspond to the same CMs in the table of Instrument-to-Device Connections for each of the next three measurements. Be sure to calibrate the capacitance meter before taking each measurement.
The extractions of the three junction capacitance parameter sets are independent of each other. However, perform them in the order listed in the Model window:
NOTE: When the bipolar transistor has only three terminals (no substrate such as in a discrete process) omit the step for measuring and extracting the substrate capacitance.
Place the device to be measured into the test fixture to be used. Make sure that the SMUs connected to the device correspond to the same SMUs in the table of Instrument-to-Device Connections.
Note that the series resistances to be measured are sensitive to any contact resistance between the device and test fixture. The extractions of the resistances are also dependent upon the prior successful extraction of the DC parameters.
This completes the DC parasitic resistance extractions. No extraction is performed on the rbbib Setup.
Use a network analyzer to make the next set of measurements. S-parameter measurements are highly sensitive, so it is important that the instrument be properly calibrated.
Place the device to be measured in the test fixture. For each of the next two measurements, make sure the SMUs connected to the network analyzer's port bias connections correspond to the same SMUs in the table of Instrument-to-Device Connections.
S-parameter measurements can take up to several minutes, depending on the number of data points specified. The extraction of the base resistances and transit time parameters are highly dependent upon successful model parameter extraction of all the preceding parameters.
This completes the AC extractions. The extracted set of model parameters is now complete.
The instructions in previous sections showed how to execute IC-CAP commands from Setups. You also can execute these same commands from a DUT. In this case they are executed on all of the Setups in the DUT. To do this, place the mouse pointer on a DUT name, press LEFT, drag to and release on one of the commands in the pop up menu. Since this lets you measure, extract, optimize, or simulate several Setups at a time, it is the most efficient way to operate. However, it is not suggested that Optimization be routinely performed on the ac DUT. Optimization of S-parameters can take considerable time when there are a large number of data points in the Setup.
Simulation of each of the Setups is performed exactly as the measurement and extractions are. Move the mouse pointer to the Setup name, press LEFT to display the pop up menu, drag the pointer to Simulate, and release the mouse button. Simulations may be performed in any order once all of the model parameters have been extracted. For further information on simulation, refer to chapter 12, Simulation.
Display Plots of measured and simulated data the same way you execute measurements, extractions, or any other IC-CAP command. In a typical IC-CAP session, execute Display Plots from a Setup pop up menu. Doing this from the DUT can place numerous Plot Windows on the screen. Viewing Plots is an ideal way to compare measured and simulated data, for determining whether further optimization is useful. For additional information on Plots, refer to chapter 15, Plots.
The optimization operation uses a numerical approach to minimize the error between measured and simulated data. As with the other IC-CAP commands, select optimization at either the DUT or Setup level.
Optimization should be performed from Setups rather than from DUTs, since optimization for all Setups under a DUT is rarely required. Optimization is typically interactive in nature, with the best results obtained when you specify the characteristics of the optimization function. For further information on optimization, refer to chapter 13, Optimization.
The IC-CAP bipolar modeling module provides a set of Setups that may be used for general measurement and model extraction for bipolar technology. The IC-CAP system has the flexibility to modify any measurement or simulation specification. The model extractions provided are also intended for general bipolar IC processes. If you have another method of extracting specific model parameters, IC-CAP offers the facilities to do this with the Program function or the ability to write a function in C and link it to the Function List.
All of the measurements and extractions described in the preceding sections have been performed from the Setup level. At that level, the details of the measurements are not visible. You can gain full access to, and control over, the operations of a Setup by opening the Setup window. To do so, move the mouse pointer to the desired Setup name, press LEFT, drag to the Edit command, and release the button. The Setup window appears, providing access to all of the measurement and extraction capabilities.
Typical customization includes modifying bias voltages and measurement frequencies that correspond to the performance of the device under test. All parasitics in a test circuit should either be included in the circuit description or in the Test Circuit Editor under the DUT. Typical components might be series resistances in probes or series inductances from packages. When modifying any of the Setup names, remember that these names must be manually modified if they are specified as an input to a Transform (extraction) or referenced in a Program or Macro. For detailed instructions on modifying Setups, refer to chapter 10, Model Creation and Modification.
The model extractions provided with IC-CAP are designed for general bipolar processes. If a different model extraction is desired, IC-CAP provides the tools for writing them. For example, use IC-CAP's Program function and Parameter Extraction Language to write tailor-made extraction Transforms. Refer to chapter 14, Transforms and Functions for more details on the Program function. For more in-depth extractions, IC-CAP lets you write and compile extraction functions using the C programming language. Writing user defined C language routines is also covered in chapter 14, Transforms and Functions.
An example custom extraction for IS and NF is shown in figure 4-2.
! Extraction for IS & NF ! Note: print statements go to the ! window that started IC-CAP print "Example Custom Extraction for IS & NF" index = 0 !array index ! pick two low current points v1 = -ve[index] WHILE v1 < 0.4 ! get a point near Vbe = 0.4 index = index + 1 v1 = -ve[index] END WHILE i1 = ic.m[index] v2 = -ve[index] WHILE v2 < 0.5 ! get a point near Vbe = 0.5 index = index + 1 v2 = -ve[index] END WHILE i2 = ic.m[index] ! extract IS & NF vt = 8.62e-5 * (TNOM + 273.15) ! thermal voltage NF = 1 / vt * (v2 - v1) / log(i2 / i1) IS = sqrt(i1 * i2) / exp((v1 + v2) / (2 * NF * vt)) print "IS = ";IS;" NF = ";NF print "... end of custom extraction ..."
Figure 4-2: Custom Model Extraction for IS and NF
The following suggestions may you help achieve more successful model extractions. You can incorporate some or all of these into the procedures described above.
Before starting a measurement, you can quickly verify the instrument options settings. Save the current instrument option settings by saving the Model file to <your_file name>.mdl from the Model List. Some of the Instrument Options specify instrument calibration. For most accurate results, you must calibrate the instruments before taking IC-CAP measurements. Typical DC and CV instrument options are listed below.
When taking AC measurements with a network analyzer, several instrument settings are critical. In addition, the calibration must be performed on structures that have impedances similar to the stray parasitics of the device under test. Typical AC instrument options are listed below.
Experiment with the other network analyzer options to obtain the best results with specific devices.
Make sure that the measuring instruments (specified by unit names in the Inputs and Outputs) are correctly connected to the device under test (DUT). Refer to table 4-3 for a list of nodes and corresponding measurement units. Note that the quality of the measuring equipment (instruments, cables, test fixture, transistor sockets, and probes) can influence the noise level in the measurements.
The series resistance in test fixtures can also be critical when making high current measurements. For example, a 1 ohm resistance in series with the emitter at an Ic = 20 mA can cause a factor-of-two error in the measured versus simulated DC performance. Series resistances which are not accounted for in the device model can be included by adding them to the Test Circuit for the DUT.
Make sure that all characteristics of the measurement stimulus and corresponding measured response are specified in the respective Input and Output tables.
For some measurements it is essential to calibrate the instruments or test hardware to remove non-device parasitics from the DUT. For bipolar devices, stray capacitance due to probe systems, bond pads, and so on should be calibrated out prior to each measurement.
In making high frequency two-port measurements with a network analyzer, the reference plane of the instrument must be calibrated out to the DUT. IC-CAP relies on the internal calibration of the instruments for full error corrected data. It is critical that calibration using OPEN, SHORT, THRU, and 50 ohm LOADS be properly done.
IC-CAP's extraction algorithms exist as functions. They are in the Function List, under the title Extractions. The extraction Transforms for a given Setup are listed in the Transform tile for the Setup.
When selecting the Extract command from the Setup level pop up menu, all extractions in the Setup are performed. Each one is executed in the same left-to-right order in which it is listed in the Setup. This order is usually critical to proper extraction performance. The extractions are typically completed in a few seconds. The newly extracted model parameter values are placed in the Parameter Editor.
Simulation uses model parameter values current1y in the Parameter Editor. A SPICE deck is created and the simulation performed. The output of the SPICE simulation is then read into IC-CAP as simulated data.
To select a simulator, use the Utilities pulldown menu in the IC-CAP Main Menu or define a SIMULATOR variable. Simulations vary in the amount of time they take to complete. DC simulations generally run much faster than CV and AC simulations.
If simulated results are not as you expected, use the Simulation Debugger to examine the input and output simulation files. The debugger is listed under the Utilities menu. Note that the output of manual simulations is not available for further processing by IC-CAP functions (such as Transforms and Plots).
The Display Plots function displays all graphical Plots defined in a Setup. The currently active graphs are listed in the Plots tile in each Setup. After the Plot Windows are displayed, their curves are automatically updated each time a measurement or simulation is performed.
Measured data is displayed as a solid line on the Plots. Simulated data is indicated by a dashed or dotted line of the same color. After an extraction and subsequent simulation, make sure to view the Plots for agreement between the measured and simulated data.
The optimization of model parameters improves the agreement between measured and simulated data. The bipolar model typically requires very little optimization, since most of the extraction algorithms have some optimization built into them. Optimizations are listed under the Transform tile.
Capacitance parameter extractions are actually done through optimization. An Optimize Transform whose Extract Flag is set to Yes is automatically called after any extraction that precedes it in the Transform list.
NOTE: Optimizing the AC parameters can be very time consuming because of the number of SPICE simulations required.
A PNP Model file is included with IC-CAP and is named bjt_pnp.mdl. PNP transistors are measured, extracted, and simulated in a manner similar to NPN transistors. The critical difference with a PNP device is that the bias voltages are of opposite polarity from an NPN device.
To aid extracting the two models using the same algorithms, set a variable in the Model level Variable Editor to the proper value. The variable POLARITY should have the value PNP. If this variable is not defined, the default in the extractions is NPN. Using an NPN extraction on PNP data will result in incorrect parameter values or extraction errors.
Another variable convenient for displaying PNP Plots is inv_plot. This variable can invert the Plots in the bjt_pnp.mdl file so they plot in the same direction as the NPN Plots. Set inv_plot to -1 to do this.
This section describes the extraction algorithms used for DC, Capacitance, Parasitic Resistance, and AC model parameters of the bipolar transistor.
The Early voltage extractions produce the model parameters VAF and VAR. The output conductance of Ic versus Vce for steps of Vb is used in the calculation. Both Early parameters are extracted simultaneously. This requires both forward and reverse measurements prior to extraction. The actual extraction is performed under the rearly Setup. The substrate bias should be held at a negative (positive) voltage for a NPN (PNP) transistor. For the extraction to function correctly, the device must be completely out of saturation at the 20 percent point of each curve, and the forward and reverse curves must have the same number of steps.
The forward Gummel measurement is used to extract IS, NF, BF, IKF, ISE, and NE. The measurement holds the base-collector voltage at approximately zero volts and drives the emitter with a negative bias sweep. The bias should produce Ic in the range of less than 1nA to more than 10mA for a typical IC transistor. First IS and NF are extracted from the low current region of the Ic versus Vbe data using a least-squares fit. The very low current region of the Ib versus Vbe data is used to obtain ISE and NE, the base recombination parameters. An internal option in the extraction algorithm is then used to produce BF and IKF and fine tune the ISE and NE parameters. If insufficient high current data is available, IKF will be set to a default value of 10A. To guarantee that IKF is extracted, measure until beta has rolled off to approximately half of its peak value.
The reverse Gummel measurement is used to extract NR, BR, IKR, ISC, and NC. This measurement and extraction is analogous to the forward measurement except that the transistor is now in the reverse active mode. If the measurement is made on an IC structure that has a substrate of opposite polarity to the collector, it is quite possible that the plot of reverse Beta versus Ie will not fit well. This is because the parasitic transistor formed by the base-to-collector-to-substrate begins to conduct, thus robbing current from the base of the transistor being modeled. There is a solution to this classical problem in the Model file npnwpnp.mdl. This file includes a compound structure of both a NPN transistor and its parasitic PNP device. This Model allows you to produce an excellent fit of the NPN transistor operating in the reverse bias region. Refer to chapter 9, Circuit Modeling for more information on using this Model file to characterize the reverse active mode of operation.
The capacitances are split into three different DUTs. The measurement is performed over a range of small forward bias (where v < VJ*FC) to at least several volts of reverse bias. The parameter extraction is accomplished through optimization of the controlling parameters in the characteristic equation for the junction capacitance. The extraction from each produces the zero bias capacitance CJx, the built-in potential of the junction VJx, and the grading factor of the junction MJx. The forward bias coefficient FC is set to the SPICE default value of 0.5. The purpose of this parameter is to switch the capacitance in the simulator into a linear model before the junction bias approaches VJx.
This set of Setups uses DC measurements to obtain the emitter resistance RE, the collector resistance RC, and a DC I versus V relationship to be used later in the base resistance extraction. RE is extracted from a measurement of the differential of collector voltage with respect to base current with the transistor biased into saturation. A linear fit is performed on the part of the curve that is most sensitive to the effects of RE.
In the rcsat Setup RC is extracted from a measurement of Ic versus Vce with the base biased so that the transistor is near its Beta point and well into saturation. The extraction uses a linear fit along with the known RE. In the rcactive Setup RC is extracted at a bias selected by placing a box on the Plot of Ic versus Vce.
The Setup rbbib is not actually used to extract any model parameters directly but is used by the following AC measurements in the extraction of the base resistance parameters. The base voltage bias specification used in this Setup and in the rbbac Setup must be the same. To facilitate this, the start value, stop value, and number of points are set using four variables in the Model level Variable table. These are rbbstart, rbbstop, rbbnpts, and rbbvc. The start and stop bias voltages should sweep the transistor' s operating point from near peak Beta to well into Beta roll-off.
Base resistance and transit time parameters are extracted from network analyzer measurements of the transistor's S-parameters converted to H-parameters. Both of these sets of model parameters are highly dependent upon the prior extraction of the DC, Capacitance, and Parasitic resistance parameters.
The base resistance is extracted from h11 data versus frequency and bias. h11 traces a circular path on a Re-Im axis system versus frequency. The measurement frequency should be held low enough so that this circular pattern does not start to become linear. This characteristic is used to obtain the real value of Rbase versus base current. From the characteristic of Rbase versus Ibase, the RB, IRB, and RBM parameters are extracted.
The transit time parameters, TF, XTF, ITF, VTF, and PTF, are extracted from measurements of the common-emitter current gain h21. The measurement frequency should be higher than the -3dB roll-off frequency of the transistor at all bias levels. However, the measurement frequency should also be low enough so that the magnitude of h21 over the bias levels is always greater than 2.0. Regions of the h21 versus Vbe versus Vce data are isolated where each of these parameters has a dominating effect on an extraction performed there. The extractions use an optimization routine that matches the performance of the complete small signal model to the measured data. The extraction assumes that all other model parameters have been accurately obtained. If the h2l measurement has not calibrated out the stray capacitance (eg. from bond pads, package, probe, etc.) the initial extraction may fail and an extraction decoupled from the small signal model will be performed. These resulting parameters may need scaling using the scale_params Transform depending upon the amount of stray capacitance not accounted for in the small signal model.
The reverse transit time parameter TR is extracted from measurements of the common-collector current gain h21.
NOTE:
IC-CAP supports two different methods of calculating the Q1 component of the
base charge during the extractions:
Q1 = 1 / (1 - Vbe/VAR - Vbc/VAF) (default method)
Q1 = 1 + Vbe/VAR + Vbc/VAF (alternate method)
The alternate method can be selected by defining a model parameter or variab1e
named GPQ1 and setting it equal to 0. If GPQ1 is not defined or non-zero, the
default method is used.
Tables 4-4 through 4-9 list the UCB Bipolar Model parameters. These parameters fall into four primary categories: DC, Capacitance, AC, and Temperature Effects. The DC parameters are divided into three categories: DC Forward, DC Reverse, and Series Resistance. These parameters may be reviewed in the Circuit Editor or in the Parameter Editor (refer to chapter 3, Startup and Operation).
Name Description Default
BF Ideal Maximum Forward Beta 100
The basic parameter for both Ebers-Moll
and Gummel-Poon models.
IKF Knee Current for Forward Beta High (Infinity) Amp
Current Roll-off.
Models variation in forward Beta at high
collector currents. Use if device is to be
used with high collector currents.
IS Transport Saturation Current 1x10^-16 Amp
The basic parameter for both Ebers-Moll
and Gummel-Poon models.
ISE Base Emitter Leakage Saturation Current 0 Amp
Models variation in forward Beta at low
base currents. Use if device is to be used
with low base emitter voltage.
NE Base Emitter Leakage Emission Coefficient 1.5
Models variation in forward Beta at low
base currents. Use if device is to be used
with low base emitter voltage.
NF Forward Current Emission Coefficient 1.0
Used to model deviation of emitter base
diode from ideal (usually about 1).
VAF Forward Early Voltage. (Infinity) Volt
Models base collector bias effects. Used to
model base collector bias on forward Beta
and IS.
Table 4-4: UCB Bipolar Transistor DC Forward Parameters
Name Description Default
BR Ideal Maximum Reverse Beta. 1.0
The basic parameter for both Ebers-Moll
and Gummel-Poon models. Use when the
transistor is saturated or operating in
reverse mode.
IKR Knee Current for Reverse Beta High (Infinity) Amp
Current Roll-off.
Specifies variation in reverse Beta at high
emitter currents. Needed only if transistor
is operated in reverse mode.
ISC Base Collector Leakage Saturation Current. 0 Amp
Specifies variation in reverse Beta at low
base currents. Models base current at low
base collector voltage. Use only if
transistor is operated in reverse mode.
NC Base Collector Leakage Emission 2.0
Coefficient.
Specifies variation in reverse Beta at low
currents. Models base current at low base
collector voltage. Use only if transistor is
operated in reverse mode.
NR Reverse Current Emission Coefficient 1.0
Used to model deviation of base collector
diode from the ideal (usually about 1).
VAR Reverse Early Voltage. (Infinity) Volt
Models emitter base bias effects. Use to
model emitter base bias on reverse Beta and
IS.
Table 4-5: UCB Bipolar Transistor DC Reverse Parameters
Name Description Default
IRB Base Resistance Roll-off Current (Infinity) Amp
Models the base current at which the base
resistance is halfway between minimum and
maximum.
RB Zero Bias Base Resistance. 0 Ohm
Maximum value of parasitic resistance in
base.
RBM Minimum Base Resistance RB Ohm
The minimum value of base resistance at
high current levels. Models the way base
resistance varies as base current varies.
RC Collector Resistance. 0 Ohm
Parasitic resistance in the collector.
Important in high current and high
frequency applications.
RE Emitter Resistance. 0 Ohm
Parasitic resistance in the emitter.
Important in small signal applications.
Table 4-6: UCB Bipolar Transistor Series Resistance Parameters
Name Description Default
CJC Base Collector Zero Bias Capacitance. 0 Farad
Helps model switching time and high
frequency effects.
CJE Base Emitter Zero Bias Capacitance. 0 Farad
Helps model switching time and high
frequency effects.
CJS Zero Bias Substrate Capacitance. 0 Farad
Helps model switching time and high
frequency effects.
MJC Base Collector Function Grading Coefficient 0.33
Models the way junction capacitance varies
with bias.
MJE Base Emitter Function Grading efficient 0.33
Models the way junction capacitance varies
with bias.
MJS Substrate Function Grading Coefficient 0.33
Models the way junction capacitance varies
with bias.
VJC Base Collector Built-in Potential. 0.75 Volt
Models the way junction capacitance varies
with bias.
VJE Base Emitter Built-in Potential. 0.75 Volt
Models the way junction capacitance varies
with bias.
VJS Substrate Function Built-in Potential. 0.75 Volt
Models the way junction capacitance varies
with bias.
XCJC Fraction of Base Collector Capacitance that 1.0
connects to the internal base node.
Important in high frequency applications.
FC Coefficient for Forward Bias Capacitance 0.5
Formula.
Provides continuity between capacitance
equations for forward and reverse bias.
Table 4-7: UCB Bipolar Transistor Capacitance Parameters
Name Description Default
ITF High Current Parameter for Effect on TF. (Infinity) Amp
Models decline of TF with high collector
current.
PTF Excess Phase at FT. 0 Degree
Models excess phase at FT.
TF Ideal Forward Transit Time. 0 Sec
Models finite bandwidth of device in
forward mode.
TR Ideal Reverse Transit Time. 0 Sec
Models finite bandwidth of device in
reverse mode.
VTF Voltage Describing TF Dependence on (Infinity) Volt
Base-Collector Voltage.
Models base-collector voltage bias effects
on TF.
XTF Coefficient for Bias Dependence on TF 0
Models minimum value of TF at low
collector-emitter voltage and high collector
current.
Table 4-8: UCB Bipolar Transistor AC Parameters
Name Description Default
EG Energy Gap for Modeling Temperature 1.11 EV
Effect on IS, ISE, and ISC. Used to
calculate the temperature variation of
saturation currents in the collector, and
base-emitter and collector base diodes.
XTB Forward and Reverse Beta Temperature 0
Exponent.
Models the way Beta varies with
temperature.
XTI Temperature Exponent for Modeling 3.0
Temperature Variation of IS. Models the
way saturation current varies with
temperature.
TNOM This global variable can be assigned 27.0 Celsius
temperature values in degrees C, for use by
extractions and simulations. Enter the
variable in the System Variable Editor, in
the Utilities Application.
Table 4-9: UCB Bipolar Transistor Temperature Effect Parameters