The diode is a fundamental circuit device used in a variety of RF and microwave applications, from switching to attenuation, limiting, mixing, frequency multiplication and protection against electrostatic discharge, to name a few. The diode is also a highly nonlinear device, as the voltage across it, V_{d}, will induce one of two states: ON (V_{d} > 0), where it generally acts like a variable resistor and OFF (V_{d} < 0), where it acts like a variable capacitor. As a result, a nonlinear model is required to predict the diode’s behavior and some very accurate ones have been developed over the years. These models are generally well understood, so this tutorial does not discuss changes or updates to such earlier work. Instead, in this two-part tutorial, procedures to extract the pertinent parameters of these models from device measurements using Excel are discussed. Part 1 focuses on the ON region and Part 2 discusses the OFF region. Part 1 begins by considering the Shockley diode model and reducing it into a workable equation. Then, DC I-V measurements are presented for a silicon 1N4148 diode and the procedure to extract the pertinent parameters using Excel is described in detail. Finally, the result of this extraction and its limitations, especially concerning Schottky diodes fabricated on GaN, are discussed.

**THE DIODE MODEL**

A fundamental relationship between the voltage across and current through a diode in the forward or ON region is given by the well-known Shockley equation shown in **Equation 1:**^{1}

Where:

I_{d} = current through the diode

I_{s} = diode saturation current

K = Boltzmann’s constant (1.38e-23 Joules per Kelvin)

n = diode ideality factor

q = charge of an electron (1.602e-19 coulombs)

R_{s} = ON resistance of the diode

T = temperature (in Kelvin)

V_{d} = voltage across the diode

Of these parameters, V_{d} and Id are measured directly as the I-V curve; q, K and T are known beforehand and n, I_{s} and R_{s} are the unknowns that must be determined to complete the model.

Before discussing how to extract these parameters, there is a complication with the Shockley equation: the diode current on the left side of Equation 1, I_{d}, is a nonlinear function of the same diode current on the right side of the equation. In other words, Equation 1 cannot be used in its present form to relate directly the diode current to the applied voltage, V_{d}. Some algebraic manipulation is required to transform Equation 1 into an equation that can be utilized in an optimization routine.

Readers familiar with Equation 1 will recognize that the contribution of the parallel conductance, G_{x}, which describes the leakage current through the diode at very low voltages, has been discarded. In almost all circumstances, the diode is operated at voltage levels where this leakage current can be ignored. Some circuit simulation tools do not include G_{x} in their intrinsic diode model. Additionally, including the conductance term in Equation 1 does not allow for separating the diode voltage from the diode current. As a result, the conductance parameter, G_{x}, will be ignored for this tutorial.

Reducing Equation 1 into a form that will be useful for optimization is relatively straightforward. It starts by performing some simple algebra and then takes the natural log of both sides. The result is shown in Equation 2:

For simplicity, a new variable, *β*, which is a function of temperature and has units of 1/Volt, is introduced in **Equation 3:**

Solving Equation 2 for V_{d} as a function of I_{d}, the known parameter,* β* and the unknown parameters, n, I_{s} and R_{s}, results in **Equation 4:**

Equation 4 is useful since the diode voltage, V_{d}, has been separated from the diode current, I_{d}. This is precisely the form that will be implemented in the Excel optimization routine.

**DIODE MEASUREMENTS, COMPLETE WITH WARNINGS**

Although the diode is described mathematically by a complicated-looking equation, measuring the device’s DC I-V relationship is very straightforward, one of the simplest to perform and understand. Since numerous methods exist to accomplish this task, no particular measurement approach will be discussed, except to say that do not let the simplicity fool you.

Plenty of problems can creep up due to the following issues:

- Not calibrating out the resistance of the leads, cables, probes, etc.
- Taking too little data, such as measuring only a single device or using too few voltages
- Not keeping the temperature constant
- Keeping the lights on when measuring devices directly on a semiconductor wafer
- Using bias tees, which often have high leakage current and skew the measurement
- Not setting a maximum current for the voltage source can lead to device destruction.

Issues with keeping the temperature constant can be the hardest to spot unless you can sense the diode temperature in real-time. This is not an issue for most automated measurement systems because the measurement is quick enough to avoid self-heating in the diode. In other words, you can assume the temperature is constant during the measurement unless the data tells you otherwise. For example, look to the temperature if you get a poor fit to the diode equation shown in Equation 4 and cannot understand why.