Extraction Algorithms

This section describes the extraction algorithms used for DC, capacitance, parasitic resistance, and AC model parameters of the bipolar transistor.

DC Parameter Extractions

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, which 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 an 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. This measurement holds the base-collector voltage at approximately 0V and drives the emitter with a negative bias sweep. The bias should produce Ic in the range of less than 1nA to more than 10 mA 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 optimization 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 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 problem. The example file npnwpnp.mdl includes a compound structure of both an 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 Circuit Parameter Extraction for more information on using this file to characterize the reverse active mode of operation.

Capacitance Parameter Extractions

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.

Parasitic DC Parameter Extractions

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 peak 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.

AC Parameter Extractions

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. The H11 data 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 H21 measurement has not calibrated out the stray capacitance (from bond pads, package, probe, or others) 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 on any unaccounted stray capacitance in the small signal model.

The reverse transit time parameter TR is extracted from measurements of the common-collector current gain H21.

IC-CAP supports two different methods of calculating the Q1 component of the base charge during the extractions.

    (default method)

    (alternate method)

The alternate method can be selected by defining a model parameter or variable named GPQ1 and setting it equal to 0. If GPQ1 is not defined or non-zero, the default method is used.