Experiment 2 2 Current Flow in the BJT 2.1 Summary In this experiment, the HP4145 Semiconductor Parameter Analyser (SPA) test instrument is used to measure the current-voltage characteristics of a commercial bipolar transistor. This data will be used to extract the parameters of a common bipolar transistor model, the Ebers-Moll equations. Please refer to the detailed instructions in Appendix A, provided online at the course website and in the lab, for more information if required. 2.2 Theory One of the most commonly used models for the bipolar transistor is a set of relations known as the Ebers-Moll equations. This model is derived by assuming "low-level" injection (i.e. an amount of extra injected minority charge which is much less than the inherent majority charge) in each of the emitter, base and collector regions. Solving the relevant equation in each area, and applying boundary conditions at each of the junctions yields three equations, one for each of the emitter, base and collector currents. Although the most general form of the equations contains physical transistor parameters such as the width of the "neutral" base region, a more commonly used form collects these physical parameters into a smaller number of constants. In this form, the Ebers-Moll equations are I E = I ES e qv BE n ( kt E 1) α R I CS e qv BC n ( kt C 1) (2.1) I C = α F I ES e qv BE n ( kt E 1) I CS e qv BC n ( kt C 1) (2.2) I B = ( 1 α F )I ES e qv BE n ( kt E 1) + ( 1 α R )I CS e qv BC n ( kt C 1) (2.3) where: V BE, V BC = the base to emitter and base to collector voltages (V) I E, I C, I B = the emitter, collector and base currents (A) I Es, I Cs = the emitter and collector saturation currents (A) 1
α F, α R n E, n C = the forward and reverse collector to emitter current ratios = emitter and collector ideality (or slope) factors Note that the collector to emitter current gains α F and α R are less than one, and are related to the collector to base current gains β F and β R by β F = α F 1 α F, β R = α R 1 α R (2.4) Extraction of the parameters for the model is in principle quite straightforward. A measurement of I C, I B and I E in the forward and reverse active regions can be used to calculate α F and α R simply by calculating the appropriate ratios. Referring to (2.1), if V BC is set to zero by shorting the collector and base together, then the exponential term involving V BC will be 1, and the second term on the right hand side of (2.1) will vanish. If the value of V BE is greater than a few times n E kt/q, which is about 26mV at room temperature so that this will be true for any V BE greater than a very small value, then the exponential will be much greater than 1, and the emitter current will be given approximately by I E I ES e qv BE n E kt (2.5) thus a measurement of I E vs V BE at V BC =0, plotted as ln(i E ) vs V BE will give the value of n E (from the slope) and I Es (from the intercept). Using equivalent arguments for equation (2.2), if V BE is zero, the second term on the right hand side will vanish, and if V BC is at least a few times greater than n C kt/q, then the exponential term will be much greater than 1 and the collector current will be approximately given by I C I CS e qv BC n C kt (2.6) and thus a measurement of I C vs V BC, plotted as ln(i C ) vs V BC will give the value of n C and I Cs. The accuracy of this model for small terminal voltages is quite good, with the accuracy falling off at higher values due to the breakdown of the low-level injection assumption. Although mathematically this process is straightforward, in practice the measurements can be difficult to perform accurately. A modern bipolar transistor has a forward collector to base current gain in excess of 300, which implies that for a collector current of 300 µa the base current is only 1 µa, which is small enough to require specialized measurement equipment. In addition, the intrinsic series resistance of a current meter causes a voltage drop between the voltage source and the device terminals, necessitating another accurate measurement. To allow these measurements to be made accurately and easily, the lab will be performed using a Hewlett-Packard (newer versions are Agilent rather than HP) test instrument, the HP4145 Semiconductor Parameter Analyser. In addition to having the requisite measurement accuracy, this unit also has other features that make the measurements and analysis easy to perform. 2
ELEC 3908 Experiment 2 Appendix A gives a detailed description of the general steps required to configure the equipment for measurement this can be used to refresh your memory of the details of operation of the 4145 that you learned during the Lab Tutorial. If you encounter difficulty in any aspect of the lab, please consult a TA. 2.3 Experiment 1. Connect the transistor to the test connection box with SMU1, SMU2 and SMU3 connected to the emitter, base and collector respectively as shown in the Figure below. 2. In the CHANNLE DEFINITION menu name the voltages and currents associated with the emitter, base and collector VE, VB, VC, IE, IB and IC. 2.3.1 Ebers-Moll Parameters of BC Junction Perform the measurements necessary to extract the Ebers-Moll parameters. First extract the parameters of the BC junction. 4. In the CHANNLE DEFINITION menu change the channel definitions so that both the emitter and base SMUs are functioning as grounds (VBE = 0), and set the collector SMU to be a variable current source. Also define two user functions, one called VBC, which in this case is simply the negative of VC, since the base is held at ground, and the other called LNIC as the natural logarithm of the negative of the collector current, LN(-IC). Although, as we have seen, it is possible to plot the current on a log scale automatically, the user function method avoids possible problems with taking the natural logarithm of a negative number. 5. From the Ebers-Moll equations, we note that for the case VBE = 0, the current will turn out to be negative, for reasons that we will discuss in class. Anticipating this set the collector current to 3
sweep from -1 µa to -1 ma in -5 µa steps in the SOURCE SET UP menu. Set compliance to - 0.9V. 6. In the MEAS & DISP MODE SET UP menu define the plot axes to be VBC and LNIC (note that the EXTN key must be pressed to obtain access to these names), set the axis limits to be about 0.5 to 0.7 V for VBC, and -15 to -5 for LNIC. If desired, the collector current itself may also be plotted. 7. Use the Line Function to fit a line to the plot. Capture this plot with the line parameters - you will need the data to extract the Ebers-Moll coefficients. 2.3.2 Ebers-Moll Parameters of BE Junction The Ebers-Moll parameters of the BE junction are extracted in a similar manner 8. In the CHANNLE DEFINITION menu change the channel definitions so that both the collector and base SMUs are functioning as grounds (V BC = 0), and set the emitter SMU to be a variable current source. Define two user functions, VBE = (-VE) and LNIE = LN(-IE). 9. In the SOURCE SET UP menu set the emitter current to sweep from -1 µa to -1 ma in -5 µa steps. Compliance should be set to -0.9V 10. In the MEAS & DISP MODE SET UP menu define the plot axes to be VBE and LNIE, set the axis limits to be about 0.5 to 0.7 V for VBC, and -15 to -5 for LNIC. If desired, the emitter current itself may also be plotted. 11. Use the Line Function to fit a line to the plot. Capture this plot with the line parameters - you will need the data to extract the Ebers-Moll coefficients. 2.3.3 Forward and Reverse Current Gains This section will complete the measurements necessary for the parameter extraction. It remains only to measure the forward and reverse current gains, which is easily done using the userdefined functions. The easiest way to measure α F and β F is to measure the forward active characteristic and have the 4145 evaluate a function which computes the ratio of collector to base currents and collector to emitter currents. Since the current gains are a weak function of base emitter voltage, and since our eventual aim will be to compare the prediction of the model with a measured characteristic, we will measure the current gains at a known value of base emitter voltage. 4
12. In the CHANNLE DEFINITION menu set the emitter SMU to ground. Set the base SMU to be a constant voltage source, and the collector SMU to be a sweeping voltage source. Define an ALPHA user function as IC/(-IE) and a BETA user function as IC/IB. 13. In the SOURCE SET UP menu set VB = 0.67 V for the base emitter voltage; try this value, but if the currents are exceedingly large, resulting in low current gains, reduce this value slightly and record the new value for your report. Set the VC sweep to be 0 to 1 V. Use a STEP of 0.01V. Set compliance to 20mA 14. In the MEAS & DISP MODE SET UP menu define the x-axis to be VC and y-axes to be the ALPHA and BETA user functions, and perform the measurement. Use the MARKER to obtain the exact values somewhere on the flat portion of the characteristic, and capture the plot for the report. 15. The procedure for measuring the reverse characteristic is virtually identical, with the exception that the emitter and collector leads must be physically interchanged at the test box, and the scales for ALPHA and BETA must be readjusted. Perform this measurement, use the MARKER to obtain the exact values somewhere on the flat portion of the characteristic, and capture the plot for the report. Put the transistor back into the forward active configuration. 2.3.4 BJT I-V Characteristics We now have enough data to do the parameter extraction, and the last measurement step will be to measure some data for comparison with the model. For ease of plotting, since we are interested in the prediction of the model as a function of V BC, V BE being held constant, but we are actually varying V CE (since V E is zero) 16. In the SOURCE SET UP menu the collector voltage sweep may be left as 0 to 1 or slightly reduced to give a greater fraction of the axis to the low voltage level characteristic. 17. In the MEAS & DISP MODE SET UP menu define the x-axis to be VC and y-axes to be the IB and IC, and perform the measurement. Capture the plot for your report. 18. In the SOURCE SET UP menu change the step size for VC to get 10 data points. 19. In the MEAS & DISP MODE SET UP select the LIST display and include the columns VC, VB, IC, and IB. Measure and capture the list of data points for analysis. However this is not how you are used to seeing the I-V characteristic. So now a typical active region I C vs. V CE at constant I B plot will be measured. 5
20. In the CHANNLE DEFINITION menu set the emitter (SMU1) as ground (MODE = COM), the collector (SMU3) as a sweeping voltage source (MODE = V, FCTN =VAR1), and the base (SMU2) should functions as a sweeping current source (MODE = I, FCTN = VAR2) 21. Using the SOURCE SET UP menu, set the collector voltage to sweep from 0 to 5 V, and the base current to step by 4 µa. 22. Using the MEAS & DISP MODE SET UP menu, set up the graphics plot to give I C vs V C (which is identical to V CE since V E = 0), with V C from 0 to 5V and I C from 0 to 5 ma, make the measurement and observe the plot on the screen. If necessary, readjust the base current sweep values and/or axis scales until something like the usual I C -V CE plot is obtained (consult a TA if you are not sure of what the plot should look like). 23. The easiest way to observe the reverse characteristic is to physically remove the transistor and reinsert it so that the emitter and collector leads are reversed. Having done this, it is also necessary to readjust the base current sweep parameters, since the current gains are lower in this configuration. Adjust the base current step on the SOURCE SET UP menu to 10 µa (as a first guess), change the current axis scaling to 30 µa max, and redo the measurement, again adjusting parameters as necessary if your device is different. 2.4 Data Analysis 1. We are now in a position to "extract" the Ebers-Moll model parameters from the measured data, however by using the line, marker and user function capabilities of the machine virtually all the work has been done. From the ln(i C ) vs V BC plot, n C kt/q may be read off directly as l/grad (i.e. the slope) of the plotted line. Divide this value by 0.0259 (kt/q at room temperature) to give the value of n C. The intercept of the line, given directly from the data as Y intercept, is the value of ln(i Cs ). Calculate the exponential of this value to give I Cs in amps. Similarly, from the ln(i E ) vs V BE plot, n E kt/q may be read off directly as l/grad (i.e. the slope) of this plotted line. Divide this value by 0.0259 (kt/q at room temperature) to give the value of n E. The intercept of the line, given directly from the data as Y intercept, is the value of ln(i Es ). Calculate the exponential of this value to give I Es in amps. The marker data on the graph of ALPHA and BETA in the forward active region gives α F and β F, and the marker data on the graph of ALPHA and BETA in the reverse active region gives the values of α R and β R. What are those values? 2. Verify that the measured values of α F and β F and α R and β R are related by the expressions in (2.4). 6
3. Evaluate the collector and base currents for a range of values of V BC within the limits of V BC in the measurement of part 2.3.4 of the Experiment section above using the values extracted for I Cs, I Es, α F and α R, and the known value of V BE used in part 2.3.4, plotting the values on the same axes as the measured values. The actual prediction should not be more than 20% off in the flat region of the curve, and the shape should correspond to the measured characteristic. Calculate the actual error in prediction of each current in the flat region. V BC (mv) Meas. I C (µa) Calc. I C (µa) % error Meas. I B (µa) Calc. I B (µa) % error 4. Determine whether a ±0.1 change in the slope of the lines used to determine I Cs and I Es could account for the difference between the measured characteristic and the prediction. 7
2.5 References 1. Streetman, B. G, Solid State Electronic Devices, 3 rd ed., Sections 7.2.1, 7.5.1. 2. Pulfrey, D. and Tarr, N. G., Introduction to Microelectronic Devices, pp. 336-350, pp. 366-367. 3. Muller, R. S. and Kamins, T. I., Device Electronics for Integrated Circuits, p. 280. 4. Sze, S. M., Physics of Semiconductor Devices, p. 140, p. 145. 8