Quick Summary:  A schematic and operational instructions are given for a device to measure the Saturation Current and Ideality Factor of a diode.

The Saturation Current and Ideality Coefficient of a diode can be determined by measuring an applied DC voltage along with the resultant current flow, at two different voltages.  These two data pairs are then substituted into the Schottky diode equation to create two simultaneous equations in Is and n. The equations are then solved for Is and n.  Since the equations include exponential functions, they can not be solved by ordinary algebra.  Numerical methods must be used. 

The Schottky diode equation at 25 degrees C. is:  Id = Is*(exp(Vd/(0.0257*n))-1) Amps.  Id = Diode Current,  Is=Saturation Current,  Vd = Diode Voltage,  n = Ideality Coefficient.  Measurements have shown that the Is and n of point contact germanium diodes can vary with current, but are relatively constant when the current is under six times Is.

A convenient set of measuring currents is about 6*Is and 3*Is.  Substituting Id = 6*Is, then Id = 3*Is into the equation and solving for Vd yields:  For Id = 6*Is, Vd = 0.05000*n volts.  For Id = 3*Is, Vd =  0.03561*n volts.  The value of n will probably be between 1.0 and 1.2 for the type of diodes used in crystal sets, so use 1.1 in determining the applied voltage to use.  The actual voltages to use are about 0.055 and 0.039 volts, respectively.
 

S1 is a triple pole double throw switch, S2 is a push button momentary-contact SPST switch,  S3 is a range switch that enables greater precision when measuring diodes of low Is,  DVM is a digital voltmeter with 10 Meg input resistance on the 200 mV range and the 20k pot is a ten-turn precision potentiometer such as part  # 594-53611203 from Mouser.

Procedure for Measuring Is and n:

1. Take Data Set #1:  Set S1 to V and S3 to LC (low current).  Push S2 and adjust the 20k pot. to obtain a reading of about 0.055 volts  = V1 on the DVM.  Set S2 to I, read the DVM and call that voltage V2.
2. Take Data set #2:  Set S1 to V.  Push S2 and adjust the 20k pot. to obtain a reading of about 0.039 volts = V3 on the DVM.  Set S2 to I, read the DVM and call that voltage V4.
3. The diode voltage (Vd1) from Data Set #1 is V1.  The diode current (Id1) is (V2/1,000,000)-(V1/10,000,000) Amps.  The diode voltage (Vd2) from Data Set #2 is V3.  The diode current (Id2) is (V4/1,000,000)-(V3/10,000,000) Amps.
4. The two data sets Vd1, Id1 and Vd2, Id2 must now be entered into the Schottky diode equation shown above in paragraph 2, in order to make two simultaneous equations in Is and n. Solving them will yield values for Is and n, measured at an average current of about four to five times Is.

There is currently available on the Web, a program from Polymath Software at: http://www.polymath-software.com/.  This program has many capabilities, and among them is a non-linear equation solving capability.  A free demo copy of the latest program is available for download, but is limited to 20 uses.  After that, for more usage, you have to buy it.

Some programmable pocket calculators include a non-linear equation solver.  One calculator that has one is the HP 32S Scientific Calculator.  The program to solve for n and Is takes only 28 steps of program memory and is here. 

Mike Tuggle posted on 'The Crystal Set Radio Club' the following simple procedure for determining Is and n by using a spreadsheet.  "In lieu of an equation solver package, the Schottky parameters can be solved for by simple trial-and-error. This is easily done with an ordinary spreadsheet, like Excel or Lotus. For the two measurement points, (Id1, Vd1) and (Id2, Vd2), set up the spreadsheet to calculate:  Id2[exp(Vd1/0.0257n) - 1] and, Id1[exp(Vd2/0.0257n) - 1].  Then plug in different trial values of n, until the two terms become equal.  This gives the correct value of n.  Now, plug this value of n into:  Is = Id1 / [exp(Vd1/0.0257n) - 1] or, Is = Id2 / [exp(Vd2/0.0257n) - 1] to get the correct value of Is."  An Excel spreadsheet constructed as Mike suggested is here.  An example from data taken on an Agilent HBAT-5400 is entered, for reference, on line 2.  Line 3 may be used for calculations using data from other diodes.  Column H automatically calculates a value for Is each time n is changed.  All one has to do is enter the values as described above in columns A through E and hit enter. 
 
 

• If the Is of the diode under test is too high, 0.055 volts will not be attainable for V1 in step 1.  The solution is to set switch S3 to HC (high current).  The calculations for current then become: Id1=(V2/100,000)-(V1/10,000,000) Amps and (Id2=V4/100,000)-(V3/10,000,000) Amps.
• If the voltage readings seem to unstable, try placing the measuring setup on a ground plane and connect the common lead of the DVM to it.  A sheet of household aluminum can be used for the ground plane.  Use shielded cable from the lead from the DVM to the test setup.
• The voltage readings are quite sensitive to diode temperature.  You can see this easily by grasping the diode body with thumb and forefinger and noting the change in the voltage reading when measuring V1 or V3.  Don't take data until the readings stabilize.
• The actual reverse leakage current of a diode may be compared to that of one that matches the theoretical V/I curve of the Schottky diode equation shown in paragraph two.  If the reverse current, at a low applied voltage, is appreciably greater than the equation specifies, DX reception will probably be compromised.  To make the check, reconnect the diode so that it is reverse biased.  The reverse current (Ir) should be 50% of Is at an applied voltage, Vr, of -0.0178*n volts, 90% of Is at -0.0592*n volts and 99% at -0.1184*n volts.  To calculate Ir, take Data Set #3:  Set S1 to V and S3 to LC (low current).  Push S2 and adjust the 20k pot. to obtain a reading of 0.0178*n, 0.0592*n or 0.1184*n volts = V5, on the DVM.  Set S2 to I, read the DVM and call that voltage V6.  The reverse current can now be calculated as Ir = (V6/1,000,000)-(V5/10,000,000) Amps.

Published: 03/28/01  Revised: 04/14/01

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