Download Note to EE 312 Students

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