I have been taking serious look into diode modeling and measurement recently in an attempt to better understand these solid-state successors to the humble crystal and cat's whisker detector. There is much good information on diodes to be found in many excellent web sites of course, but there is nothing quite like actually making the measurements and working with them to get a good feel. This page reports some of my protocols and test setups which I have found to be useful.
Most probably the single best web article for the measurement of diode Is and n parameters is given by Ben Tongue in his Article 16. In this article he describes an interesting circuit for the measurement as well as protocols for making them. For my purposes I did not wish to make this a construction project and felt I might get along with good quality meters and my already-built "Diode Test Jig". Essentially Ben Tongue's method consists of making two precision measurements of Voltage and Current through a diode at small signal levels, essentially about 3 and 6 times Is (sufficiently low that the voltage drop across the series resistance Ro can be ignored). The measurements are then substituted into the Shockley equation Is*{exp[(qe/(n*k*T))*(V-I*Rs)]-1} and solved simultaneously for the two data pairs. Mike Tuggle has provided a nice excel spreadsheet to do the math. This spreadsheet, Cal_n_Is.xls forms the basis of my technique and I am thus indebted to both Ben Tongue and Mike Tuggle for making this project feasable.
In addition to simply calculating the main parameters Is and n, I also wished to measure enough points to plot a characteristic curve, and to compare the measured curve with one calculated directly from the Shockley equation. My first spreadsheet then combined Tongue/Tuggle calculation protocol and a graphical view of the match between measured and theoretical. I did make a few methodology modifications which I thought/hoped would allow added accuracy:
1) Using the full Shockly equation without simplifing for an assumed 25dC room temperature. While the 25dC assumption is generally good and probably within the measurement error (or perhaps not), including the actual measured temperature eliminates doubts of innacuracies due to this parameter. With the power of PC's and spreadsheets there is no reason simplify the equation.
2) Used Vd = 0.04 and 0.05 V (adequately close to Ben Tongue's recommended 0.039 and 0.055 V) whenever possible. Note for some diodes with significantly different forward voltage drops, Si diodes in partictular I had to use higher values for Vd.
3) Reporting: I decided that, as there is no unique solution to n and Is, each is dependant on the valuse Vd and Id, I feel that reporting both Vd and Id is necessary for repeatability. Naturally I also include the ambient temperature in the report as well, and
4) I included a calculation for Ro (or Rg if you are using Tongue's reference) as that is the goal of the exercise.
A screen shot shown below:
To use the sheet one need only adjust the voltage Vd to that shown in the first column and record the current Id. If only Vd1/Vd2 and Id1/Id2 are measured then the next step is to adjust the value for "n" until the match between the two equations is exact. I even provided a simple ratio calculation to easily test for a match.
While the math is good and results excellent, I quickly found a couple deficiencies in my method,
1) measurements require high precision and its nearly impossible to land EXACTLY at the voltage required. I needed only to get quite close, let the meters stabilize for 2 - 5 minutes, and then record BOTH Vd and Id.
2) the work is rather tedious and, for a large number of diodes it pays dividends to measure only the needed Vd and Id and let the plot aside. My second spreadsheet thus dispenses with the plot. It is with my second spreadsheet that all my data tables and results are posted.
3) better comparisons between diodes can be made if one targets specific Currents rather than Voltages, discussion on this below.
A view of my current data reporting spreadsheet showing ALL input parameters as well as determined values of n, Is, and Rd.
Data input fields in blue: (target Id1 close to 1.0 uA and Id2 close to 0.5 uA).
Calculated fields in red and black.
Adjustment field "n" in green: (adjust value of n until the ratio of the two calculations = exactly 1).
(Note: the engineers in the crowd will have noticed in the above report than I am carrying a degree of precision not justified by the level of accuracy in my measurements. The final results of n, Is, and Rd should be rounded off to not more than three significant figures.)
A copy of my spreadsheet can be downloaded here: Cal_n_Is_Rd.xls
While measuring a good number of diodes, both Germanium, Schottky, Silicon, and even a few LED's, I noted that Tongue's recommended measurements at Vd = 0.039 and 0.055 V resulted in current reports spread out over more than two orders of magnitude. As the determination of Is and n is not unique but a function of Id, I felt uneasy by this method. While most Germanium diodes I have measured have a fairly narrow range of Forward Voltage drops, (Vf), that of Schottky's can range up to a tenth of a volt. This is the factor responsible for the huge range of measured Id values, see the following plot of I/V characteristics for some selected diodes:
In order to get what I feel is a better comparison between diodes, I have decided to target not some pre-determined voltage, but rather target currents of Id = 0.5 and 1.0 uA. On the above plot on the right (with Log Id vs Vd scale) it will be clear that I am aiming at the same part of the characteristic curve regardless of Vf. Hopefully this will allow good comparison between diodes with rather different Vf, even as far as including Silicon and LED's in my mix. Still, on study of the plot above, I must note that the Germanium characteristic at 0.5 to 1.0 uA appears to be curving towards its zero-crossing. Perhaps targeting an amp range between 3.0 and 5.0 uA would have been better, still thinking here, on va voir....
Shockley equation Id = Is*{exp[(qe/(n*k*T))*(V-I*Rs)]-1}
where:
n = ideality factor
Is = Saturation current in Amps
Id = Diode Current in Amps
Vd = Diode Voltage
k = boltzmann = 1.38E-23 J/K
T = temp K = 300
K = dC + 273.15 Kelvin
qe = electron charge = 1.609E-19 cmb
Often simplified to:
Id = Is*(exp(Vd/(0.0256789*n))-1)
Diode Resistance Rd = VT * n / Is
Where:
T = 300K
VT = k*T/qe = 0.0256789
SO: Rd = k * T / qe * n / Is
Ebers-Moll equation Vf = m (kTq) ln [(If / Is) +1]
Kevin
Diode n Is Rd nA k Ohm Germanium Diodes FO-215 ITT 1.11 175 163 FO-215 ITT 1.10 196 144 1N277 black 1.50 2293 17 1N277 black 1.60 2296 18 1N270 bonafide 1.28 915 36 1N270 blue 1.26 857 38 1N270 blue 1.66 2310 19 D18 russia 1.20 194 160 D18 russia 1.27 193 170 GAZ 51 Tesla 1.14 140 211 GAZ 51 Tesla 1.52 617 64 OA 5 Tesla 1.85 3384 14 OA 5 Tesla 1.48 1996 19 D9E russia 1.42 2161 17 D9E russia 1.54 2414 16 1N34A bonafide 1.82 2153 22 1N34A bonafide 1.25 1392 23 1N34A green 1.57 1389 29 1N34A green 1.30 1185 28 1N34A green 1.32 1554 22 1N34A 37 orange 1.10 1458 19 1N34A 37 orange 1.36 1370 26 1N34A red 1.34 833 42 1N34A red 1.32 993 34 D310 russia 1.01 1215 21 GD 402A russia 1.55 970 41 GD 402A russia 1.71 1360 33 UK A russia 1.56 1565 26 UK A russia 2.00 5766 9 UK B red russia 1.64 2049 21 UK B red russia 1.85 3777 13 UK C ora russia 1.92 3462 14 UK C ora russia 1.95 3354 15 UK D blk russia 2.00 4901 10 UK E blk russia 2.00 5862 9 UK F blk russia 1.82 3523 13 UK G blue russia 1.86 3123 15 Average 1.39 1334 54 Schottky Diodes HP 5082-2835 1.07 12 2206 1N5711 blue 1.07 6 4541 1N5711 blue 1.07 6 4816 1N60 1.09 178 158 1N60 1.10 161 176 BAT 46 1.12 141 204 BAT 46 1.18 172 177 1N34A ? schottky 1.11 317 90 1N34A ? schottky 1.24 482 66 1N5819 1.19 750 41 1N5819 1.14 807 36 1SS16 1SS16 Average 1.13 276 1137 Silicon Diodes 1N914 1.95 5 9293 1N914 2.02 7 7618 1N4148 2.00 6 8934 1N4148 2.00 6 9323 1N4007 1.51 1 64311 1N4007 1.51 1 77954 6A10 1.57 2 19275 6A10 1.54 2 20379 1N4736A Zener 1.15 0 1.91E+09 1N4736A Zener 1.14 0 2.50E+09 KB 130 russian 1.14 0 5.83E+08 KB 130 russian 1.16 0 4.36E+08 UK H russian 1.94 8 6263 UK H russian 1.77 4 12548 UK I russian 1.78 0 260253 KD 401A russian 1.51 0 232930 KD 401A russian 1.38 0 1539619 D 220 russian 1.26 0 322405 D 220 russian 1.24 0 537707 D 223A russian 1.20 0 10262661 D 223A russian 1.20 0 8565213 UK J russian 1.46 4 9849 UK J russian 1.40 2 20013 Average 1.52 2 2.37E+08 Light Emitting Diodes Red 2.15 0 1.70E+12 Red 2.07 0 5.52E+12 Amber 1.56 0 2.09E+17 Amber 1.62 0 6.46E+16 Yellow 1.59 0 8.03E+17 Yellow 1.38 0 2.87E+20 Green 2.05 0 4.23E+13 Green 2.07 0 4.34E+13 Water Green 3.27 0 4.85E+13 Water Green 1.93 0 5.79E+19 White-Gn 1.44 0 1.05E+20 White-Gn 3.04 0 6.88E+09 Average 2.01 0 3.76E+19
