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Report: Experiment No. 5 DIODES AND RECTIFIERS James J. Whalen September 30, 2000 Note to EE 312 Students I am providing part of the report on Experiment No. 5 DIODES & RECTIFIERS. I am providing the Introduction and Part 3: Reverse Characteristics in the Breakdown Region. You are to provide Part 1: Forward Characteristics and Part 5: Temperature Characteristics. You are to incorporate my Introduction and Part 3: Reverse Characteristics in the Breakdown Region in your report.. You should organize Part 1: Forward Characteristics, and Part 5: Temperature Characteristics just as I organized Part 3: Reverse Characteristics in the Breakdown Region. Both Part 1 and Part 5 should be self-contained with sections on Procedure, Measurements, Discussion, & References. This facilitates grading by the Staff. I am providing a very detailed Introduction. Specifically, I am providing the equations needed for Parts 1 & 5 because the report warrants doing so. Introduction In the EE 310 textbook, Sedra/Smith, Microelectronic Circuits, the current-voltage characteristic of a junction diode is given by Eq. (3-1) which is re-numbered as Eq. (I-1). I where IS{exp( V / nVT ) 1} ( I 1) I is the diode current, V the diode voltage, IS the saturation current, n the ideality factor, and VT = kT/q which has a value 0.02586 V at T = 300 K. Equation (I-1) can be used to develop two methods for determining IS the saturation current. At reverse bias when V/nVT -5, Equation (I-1) may be written as I IS ( I 2) At forward bias when V/nVT +5, Equation (I-1) may be written as I IS exp(V / nVT ) ( I 3) Equation (I-2) suggests that all that needs to be done is to reverse bias a junction diode and measure the current I which will equal the magnitude of IS. The problem is that the values for IS are in the pA range for silicon junction diodes. The current measured at reverse bias may not be a diode junction current, but a leakage current through a path other than the junction. This is almost always true for silicon diodes. For that reason the reverse bias technique is not used to measure IS. Instead a forward bias method based upon Eq. (I-3) is used to measure IS. Values of the diode current I and diode voltage V are measured at forward bias. Typical values selected for the diode current I are 10 A, 100 A, 1 mA, 10 mA, & 100 mA. The corresponding values for the diode voltage V should be in the range 0.0 to 0.8 V. Junctions diodes have a parasitic series resistance RS. At the higher current levels the internal series resistance RS of the diode may cause an additional voltage drop. By plotting values of the diode current I on the log axis and values of the diode voltage V on the linear axis of semi-log graph paper, it is possible to identify the current range where the voltage drop caused by RS is negligible. The equations given in the EE 310 textbook, Sedra/Smith, Microelectronic Circuits, on pp. 133-134 are valid for the current range where the voltage drop caused by RS is negligible. These equations are V nVT ln( I / IS ) ( I 4) V 2 V 1 nVT ln ( I 2 / I1) ( I 5a) V 2 V 1 2.3nVT log ( I 2 / I1) ( I 5b) where V2 & I2 and V1 & I1 are two pairs of values for V & I. First the value of the ideality factor n is determined using either Eq. (I-5a) or Eq. (I-5b). Then the values for V2 & I2 are inserted into Equation (I-4) to determine IS. The forward bias method will be used to determine values for IS at room temperature (~ 22 C or 295 K), ~45 C (318 K) and ~70 C (343 K). From the temperature dependence of IS, a value for the energy gap EG can be determined using EG IS CT 3 exp kT ( I 6) The equations for the pn-junction diode given in the EE 310 textbook “Microelectronic Circuits” by Sedra/Smith are based upon the standard Shockley diffusion theory. After processing the data for the 1N4004 silicon rectifier diode, it was discovered that the standard Shockley diffusion theory did not apply. The ideality factor n was in the range 1.84 to 1.91, and the value for the energy gap was EG = 0.5 eV. The value for n was twice as large as expected. The value for EG was approximately 50% of what was expected for a silicon diode. The data sheets for the 1N4004 silicon diode were consulted. The 1N4004 data sheets gave values for the forward recovery time in the 150 to 250 ns range. These times are sufficiently short so that the 1N4004 silicon diode can be switched on and off at a rate up to 100 kHz. To achieve 150 to 250 ns recovery times the manufacturer often intentionally adds impurities such as gold which act as recombination centers. The contribution of the recombination centers must be taken into account. Recombination centers can affect both the forward and reverse current. Their effect upon the forward current is important in Experiment No. 5. One of the best references on semiconductor devices is “Physics of Semiconductor Devices”, 2nd ed. by S. M. Sze. More advanced topics for pn-junction diodes are discussed in some detail in Chapter 2, pn-Junction Diode. Among the topics discussed are the contributions of recombination-generation processes to the reverse and forward current for pn-junction diodes. The exact information needed is given on pp. 91-92. S. M. Sze writes “At forward bias, where the major recombination-generation processes in the depletion region are the capture processes, we have a recombination current in addition to the diffusion current…. Similar to the generation current in the reverse bias, the recombination current in forward bias is also proportional to ni. The total forward current (per unit area) JF can be approximated by … JF Dp ni 2 qV q exp p ND kT qW qV vth Nt ni exp 2 2kT ( I 7) where q is the electronic charge, Dp the hole diffusion constant, p the hole lifetime, ni the intrinsic carrier concentration, ND the donor concentration, W the depletion width, a capture cross section, vth the carrier thermal velocity, Nt the trap density, k Boltzmann’s constant, T the temperature in K, and V the forward voltage. The first term in Eq. (I-7) is the standard Shockley diffusion theory current with an ideality factor n = 1. The second term in Eq. (I-7) is recombination current with an ideality factor n = 2. Since an ideality factor n very close to n = 2 was determined from the I-V data for the 1N4004 silicon diode, the second term in Eq. (I-7) is the dominant term. The silicon diode saturation current IS is obtained by multiplying the second term by the area A. IS A qW qV vth Nt ni exp 2 2kT ( I 8) Since the saturation current IS is proportional to ni and not ni2, the temperature dependence of IS is given by EG IS CT 2 exp 2kT 3 ( I 9) where C is a constant and EG is the energy gap. By plotting either logIS or lnIS versus 1/T (or 1000/T as is more conventional), a value for EG can be determined. The new formulas are lnIS = ln(C X T1.5 ) - EG/2kT (I-10) log IS = log(C1 X T1.5 ) - EG/2kT X loge (I-11) where log10e = 0.43429.The temperature dependence term T1.5 can either be treated as a constant or a correction can be made for it. Initially it was treated as a constant. However, the plot of logIS versus 1000/T was not quite a straight line. A correction for the T1.5 term was made, and a better straight line was obtained. The correction term was developed as follows: log IS = log(C1 X T1.5 ) - EG/2kT X loge (I-11) log IS = log(C1 X T1.5 ) + log(C1 X T11.5) - log(C1 X T11.5 ) - EG/2kT X loge log IS = log{(T/T1)1.5} + log(C1 X T11.5) - EG/2kT X loge (I-12 log IS = 1.5log(T/T1) + log(C1 X T11.5) - EG/2kT X loge (I-13) log IS - 1.5log(T/T1) = log(C1 X T11.5) – EG/2kT X loge (I-14) where log10e = 0.43429. The corresponding formula for lnIs is lnIS - 1.5ln(T/T1) = ln(C1 X T11.5) – EG/2kT (I-15) The temperature T1 was set equal to the lowest temperature for which I-V data were collected. That temperature was T1 = 294.5 K. The term log IS - 1.5log(T/294.5) may be plotted versus 1/T. The slope of the resulting straight line is set equal to - EG/2kT X loge. It is conventional to plot the term log IS - 1.5log{(T/294.5) versus 1000/T. The factor 1000 is frequently used because the values for 1000/T lie in the range 2.5 to 4.0 for values of T in the range 400 K to 250 K. Of course the factor of 1000 must be accounted for when determining EG. The forward I-V characteristics were also measured for the silicon Zener diode at room temperature. The ideality factor was much closer to 1 than to 2. It is believed that standard Shockley diffusion theory is probably appropriate for the silicon Zener diode. Since its I-V characteristics were not measured as a function of temperature, the formulas for its temperature dependence are not needed. However, it is straightforward to modify Eq. (I-14 ) or Eq. (I-15 ) for a silicon diode . The factor 1.5 is replaced by the factor 3.0, and the factor EG/2kT is replaced by the factor EG/kT. This report is organized in the following manner. In Part 1 data are given for the forward I-V characteristics for the 1N4004 silicon rectifier diode and the silicon Zener diode at room temperature. Values for the ideality factor n and saturation current IS are determined for each diode. In Part 3 data are given for the reverse I-V characteristics for the silicon Zener diode. The breakdown voltage VZ was determined. Also determined was a value for the dynamic resistance RZ in the breakdown region. In Part 5 data are given for the forward I-V characteristics for the 1N4004 silicon diode at ~40 C & ~70C. These data are labeled IVT data. Values for the ideality factor n and saturation current IS are determined at each temperature. Values of logIS – 1.5log(T/294.5) were plotted versus 1000/T(K). Equation (I-14) was used to determine a value for the energy gap EG. Part 3. Reverse Characteristics in the Breakdown Region 3.1 Procedure The I-V characteristics of the silicon Zener diode are measured beginning at 0 VDC and extending into the breakdown region. In the breakdown region values for the current I were selected to be 0.1 mA, 0.2 mA, 0.5 mA, 1.0 mA, 2.0 mA, 5.0 mA & 10 mA. Values larger than 10 mA were not used in order to avoid power dissipation greater than 300 mW in the Zener diode. The schematic diagram for the measurement circuit is shown in Fig. 3-1. The dc power supply was the Tektronix PS 503A. It was connected to provide 0 to 40 VDC. The Fluke 8010A DMM was used to measure the current I. The Fluke 8000A DMM was used to measure the voltage V. Note that the current I consists of the diode current ID + IVM. The current IVM (IVM = V/10M) is the current through the Fluke 8000A DMM that was used to measure the voltage V. The resistor R1 was a 2-watt carbon composition resistor. The ground shown in Fig. 3-1 is optional because none of the equipment terminals in use was at ground potential. Figure 3-1 Circuit for reverse characteristic measurement. 3.2 Measurements The values for I and V are recorded in Table 3-1. The voltage V equals the diode voltage VD. The diode current is given by ID = I - IVM where IVM = V/10M. The diode current ID was identically zero until voltage breakdown at VD = 28.1 V occurred. To facilitate the plotting of ID vs VD using EXCEL Chart Wizard, the columns containing VD & ID were copied to the last two columns in Table 3-1. The plot of ID vs VD obtained is shown in Fig. 3-2. 3.3 Discussion The Zener diode breakdown voltage VZ was determined to be 28.1 V. If the Zener diode has a maximum power dissipation rating PDMAX of 0.5 W, the maximum diode current IDMAX can be calculated as follows: IDMAX = PDMAX/VZ = (0.5W)/(28.1V) = 17.8 mA It was also desired to determine the Zener diode dynamic resistance RZ = VD/ID. Note how rapidly the diode current ID increases as VD increases in the breakdown region. The Fluke 8000A DMM resolution at VD = 28.1 V was 0.1 V. Therefore, the minimum error is 0.1 V. Using the data listed in Table 3-1, the following value was calculated for RZ = VD/ID. RZ = VD/ID = (29.0 0.1 V – 28.5 0.1 V) (9.95 mA – 5.00 mA) = (0.5 0.2 V) (4.95 mA) RZ = 101 40 The values for VZ = 28.1 V and RZ = 101 can be used to simulate the Zener diode I-V characteristic. 3.4 References 1. K. Etemadi, Laboratory Manual for EE 312 Basic Electronic Instruments Lab. & EE 352 Introductory Electronic Circuits Lab. Buffalo (NY): 1999, pp.45-53. 2. J. Whalen, Lecture Slides on Experiment No. 5: Diodes & Rectifiers. Buffalo (NY):2000. (Slides available at htttp://www.ee.buffalo.edu/~whalen/ee312). 3. A. S. Sedra and K. C. Smith, Microelectronic Circuits. New York: Oxford University Press, 4th ed., 1998, pp. 131-134. 4. S. M. Sze, Physics of Semiconductor Devices. New York: John Wiley & Sons, 2nd ed., 1981, pp. 84-92. TABLE 3-1 ZENER DIODE I-V DATA V = VD V -0.0015 1.001 5.00 10.08 15.0 20.0 25.0 28.0 28.1 28.1 28.1 28.1 28.2 28.5 28.7 28.8 29.0 29.0 I mA 0.0001 0.0002 0.0005 0.001 0.0015 0.002 0.0025 0.0028 0.1000 0.202 0.505 1.000 2.04 5.05 6.99 8.00 9.00 9.95 V/10M mA 0 0.0001 0.0005 0.001 0.0015 0.002 0.0025 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0029 0.0029 0.0029 0.0029 ID mA 0 0 0 0 0 0 0 0 0.1000 0.202 0.505 1.000 2.04 5.05 6.99 8.00 9.00 9.95 V = VD V 0.000 1.001 5.00 10.08 15.0 20.0 25.0 28.0 28.1 28.1 28.1 28.1 28.2 28.5 28.7 28.8 29.0 29.0 ID mA 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1000 0.202 0.505 1.000 2.04 5.05 6.99 8.00 9.00 9.95 Fig 3-2 Zener Diode I-V Characteristics 12.0000 10.0000 Diode Current (mA) 8.0000 6.0000 mA 4.0000 2.0000 0.0000 0.000 5.000 10.000 15.000 20.000 25.000 -2.0000 Diode Voltage VD(V) Figure 3-2 Zener diode I-V characteristic. 30.000 35.000