Objectives

Diodes can operate under two conditions: forward bias and reverse bias. In this laboratory the reverse bias state of a number of typical diodes were examined, and such characteristics as their built in voltage (Vbi), doping concentrations, and the temper ature dependence of breakdown were determined. Techniques employed during this laboratory included the taking of current - potential (I-V) plots, as done in previous laboratories, and the new technique of measuring how the capacitance of a diode varies w ith a changing potential (a C-V plot.)

Procedure

This laboratory was dived into two major sections, the taking of the C-V-V and the I-V characteristics. The reverse bias C-V data, taken first, was for a 1N4007 diode and was obtained using a Hewlett - Packard 4194A Impedance / Gain-Phase Analyzer. The diode was inserted into the front panel terminals of this largely automated instrument, which was then configured to measure and record the capacitance of the diode at fifty equally spaced data points between 1 and 10 V. So as to produce the most repres entative data, these measurements were to be the average of several samples at each data point, and all data was manually recorded from the instrument's display into a text file. An important note is that the diode was inserted into the instrument such t hat its cathode was attached to the cathode terminal of the instrument, and its anode to the anode terminal. This insured that the C-V data taken was for the diode's reverse bias range and not its forward. The data recorded during this section is shown in Table 1.

The second part of this laboratory consisted of obtaining the I-V characteristics of a 1N4728A diode and a 1N4736A diode. These were obtained using the differential amplifier / oscilloscope method developed in Laboratories 1 and 2 (see Laboratory Handou ts 1 and 2). Individual I-V plots of the two diodes appear in Figure 5 and Figure 6, and a superimposed plot of both in Figure 7. Indicated on all of these diagrams are t he approximate breakdown voltages (the potentials after which a noticeable current begins to flow in the reverse bias state) of each diode. These values are compared to those values listed on the component data sheets in Table 2 .

For the final part of the laboratory the I-V curves of each diode were observed while each diode was heated with a 20 W soldering iron. At the point of maximum deflection each of the two plots were recorded and a superimposed plot of the unheated-state and heated-state I-V curves appear in Figure 8 and Figure 9. Heating caused the I-V curve of the 1N4728A diode to shift in the positive direction by approximately 212.5 mV and the 1N4736A to shift 8 37.5 mV in the negative direction. These values also appear on Figure 8 and Figure 9 respectively.

Analysis

The data from the first section of the laboratory (shown in Table 1) was plotted using the data analysis package Matlab. The first plot made was a log-log plot of capacitance as a function of potential (this plot is shown in Figure 1, and the Matlab script used to produce it in Figure 2.) Capacitance in p-n junction diodes is known to be proportional to the applied potential raised to a power m (see Equation 1.) The valu e of m is important because m-values around 0.33 indicated a semiconductor junction with a linearly graded doping concentration, while values around 0.5 indicate a step junction. By taking the log of both sides of the proportion the slope of the line of the resulting graph becomes equal to m, and whether a step or linearly graded junction exists can be determined. In Figure 1 a best-fit line through the data points possesses a slope of 0.43, indicating that the diode had a st ep junction.

Equation 1

The second plot made was a linear plot of inverse squared capacitance versus potential (this plot is shown in Figure 3, and the Matlab script used to produce it in Figure 4.) For a p-n step junctio n, the x-intercept of this type of plot is known to be approximately equal to the built-in Voltage (Vbi) of the junction. A best fit line, the equation of that line, and the x-intercept of the line are all indicated on Figure 3 and reveal a Vbi of approximately 0.57 V. The doping concentration of the junction was determined by assuming that the 1N4007 diode is a N+P junction (a junction with a much higher acceptor than donor concentration) in which case equation 2 applies. T his equation can be solved for inverse squared capacitance as a function of applied potential (see Equation 3,) in which case the acceptor concentration can be solved for by substituting in a measured data point. Performing this calculation resulted in a value of 1.09 x 10^19 cm^-3 for the acceptor concentration. This value is similar in magnitude to the values for acceptor concentration which given in the homework problems for silicon, lending credibility to our results.

Equation 2

Equation 3

These values for Vbi and the acceptor concentration are both based upon linear approximations made to a small number of data points of observed data which varied greatly. This simplification was probably the single largest source of error in the lab, bu t unfortunately also one whose influence upon our calculations cannot be determined. Because the approximation may have under or overemphasized any of our data points, the influence upon our calculations for Vbi and the acceptor concentration is untracea ble. Other possible sources of error were the fact that a large amount of data was recorded from the Phase Analyzer by hand, providing ample opportunity for data to be incorrectly recorded.

Since a temperature increase caused the 1N4728A diode to shift in the positive direction, we know that its breakdown method is tunneling. This is because if its method was avalanche, increased random kinetic energy of individual carriers would make it m ove difficult for free carriers to descend down the potential energy ramp crossing the depletion region due to their increased ability to travel to different parts of their source semiconductor. As increasing temperature does shift the I-V curve of the 1 N4736A in the negative direction, it can be seen that its breakdown method is avalanche.

Conclusion

In this laboratory the variation of capacitance with potential for the reverse bias region of a diode was observed, and also employed to calculate certain characteristics of the diode. The effects of increased temperature upon the reverse breakdown pote ntial upon two different diodes were also observed, and these observations where used as evidence of the two different reverse breakdown methods.

Suggestions for Improvement

Our lab group produced significantly larger deflections in the I-V curves of our diodes through use of a soldering iron in a far shorter time than those groups which used hair dryers. While safety (and odor) concerns do exist for soldering irons, the ef fects of heating are far easier to observe using an iron than a hair dryer, making it a good idea to make soldering irons available to all students in the lab in the future.

Another suggestion is to implement a Phase Analyzer to PC connection, via GPIB. The ability to transfer data automatically would allow a far greater number of data points to be collected, improving the accuracy of the lab. An interesting idea for the future may be to publish all lab handouts on the World Wide Web. This would have obvious environmental benefits, and would also allow students to read farther ahead into the lab schedule.


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