Theory

A PN junction is formed by the combination of a doped p- type and n-type semi conductors that are in contact. The p-type is usually doped with B or Al, while the n-type is usually doped with P, As, or Sb. The interface between these two types of doped semiconductor (p-type, n-type) materials is also known as a P-N junction. P-N junctions are very important in making most semiconductor electronic devices such as integrated circuits, LED’s and transistors. This is because all electronic action in the above devices takes place at the P-N junctions. For example there are two p-n junctions in series in the bipolar junction transistor, which is a type of transistor.

[pic]
Figure 1: An example of a P-N Junction.

Objectives

The objectives of this experiment were to investigate the DC current-voltage characteristics of the PN junction diode, Experimentally verify theoretical model developed in lecture and extract ideality factor, and reverse saturation current. Produce a piece-wise linear model for the diode and Compare closed form, piece-wise linear model, and PSPICE simulations with experiment. A set of formulae was given in order to aid in the process of solving variables within the experiment. Some useful formulae in our experiment can be given the equations below.

[pic] (1) [pic] (2)
And the diode equation is: [pic] (3)
Where Id given in Equation 1 is DC current through diode, and Vd given in Equation 2 is the voltage across the diode. Additionally: lo given in Equation 3 represents reverse saturation current, q stands for electron charge (1.6 x 10-19 C), k is the Boltzmann's constant (1.38 x 10-23 J/K), T stands for absolute temperature in Kelvin degree and finally n is the ideality factor, 1 ≤ n ≤ 2

Experiment For the experiment, the first thing that needed to be done was to set up the circuit required to proceed with the lab. The circuit can be seen in Figure 2.
[pic]
Figure 2: Circuit setup for the lab experiment.

Once that was done, a varying DC power supply was input as the Vs manually. By varying the Vs, measurements were taken for each increment of voltage that was input into the circuit. That process was a manual procedure for testing the values obtained. Once that was taken, an automated method was used in order to get similar values. A program called CurveTracer was used. CurveTracer obtained measurements given the boundary inputs that were put into the program. It generated a plot to graphically represent the data Vd vs Id given in Figure 3.
[pic]
Figure 3: The plot generated by CurveTracer representing Vd vs Id.

From the data that was obtained from the CurveTracer, the reverse saturation current Io and n can be determined. Once that process was complete, the experiment had to be ran again, but this time under a simulation. This simulation would give near perfect values for what should have been obtained. The simulation would be conducted with the use of PSPICE. The procedures above will be completed almost the same way, only this time it will be completed virtually.

Data and Results This lab involved multiple different methods of proving accurate measurements. The first method that was tested was taking measurements of the circuit. This involved manually varying the voltage applied into the circuit and taking measurements by reading the voltage and current across a certain point of the circuit. The measurements yielded a graph that can be seen in Figure 4.

[pic]
Figure 4: Plot of Id(mA) and Vd(V) against each other.

The Id and Vd are found by taking these measurements. These points can be seen in Table 1. Note that the plot starts to develop a slope after a certain point, which can be estimated around .505 Vd.

Table 1: Measured results of Vd and Id(mA).

|Vs |Vd (V) |Id (mA) |
|0 |0.000027 |0.0003 |
|0.1 |0.0983 |0.0002 |
|0.2 |0.20207 |0.0003 |
|0.3 |0.29913 |0.001 |
|0.4 |0.38373 |0.008 |
|0.5 |0.43595 |0.0339 |
|0.6 |0.46186 |0.0698 |
|0.7 |0.4791 |0.1107 |
|0.8 |0.49231 |0.1563 |
|0.9 |0.50218 |0.2008 |
|1 |0.5076 |0.2476 |
|2 |0.55398 |0.7271 |
|3 |0.5769 |1.2181 |
|4 |0.59266 |1.7128 |
|5 |0.60413 |2.2102 |
|6 |0.61374 |2.7091 |

These values then had to be compared with the use of a lab software called CurveTracer, which ultimately does the same thing as varying the voltage by hand, but has the ability to define a set number of parameters such as starting and end Vs as well as the number of steps. The graph of the CurveTracer can be seen in Figure 5.
[pic]
Figure 5: Measured Id(mA) vs Vd from the use of CurveTracer

The second method of proving values for Vd and Id involved simulating the circuit through PSPICE and taking measurements through the simulation. The simulation yielded results similar to the measurements that were taken by hand, but since PSPICE simulates all simulations under perfect conditions, the results were much more accurate. Figure 6 shows the plot of the obtained results of the PSPICE simulation.

[pic]
Figure 6: PSPICE Simulation plot of results.

As seen, the PSPICE model gives more accurate measurements of all the values due to its perfect environment simulation. Based in the information given above, a linear model can also be developed for this plot, which can be seen in Figure 7.
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Figure 7: Original PSPICE plot with a linear model

By looking at this linear model, a piecewise function can be determined. From 0 to around an estimated 0.61, it can be said that Id is 0. However even though realistically there were values that were able to be measured, because they were so small, it is going to be said that they’re 0. For values greater than 0.61, it can be said that the function for this area can be given as the slope. So for values greater than 0.61, the function can be said as 77.5*x. Given the slope, the value of Rd can be determined. V0 can also be determined by looking at the value intersecting the x-axis. Rd can be calculated through the use of Equation 4.
[pic] (4)
By inserting the slope, the value of Rd can be given by .013 mΩ or 13 Ω.

The measurements obtained through the lab can be confirmed even further by plugging in the variables that were obtained through the lab into a diode equation. With the use of Equation 5 and Equation 6, further clarification of the results can be seen.
[pic] (5)

[pic] (6)

Equation 5 is given as the diode equation, while Equation 6 is the loop equation. For Equation 5, there are many variables that are already determined from the lab. Value are given as: q is the electron charge, k is given as Boltzmann’s constant, T is given as the absolute temperature in Kelvin degrees, I0 given as the reverse saturation current, n given as the ideality factor. All of the above are known except for I0 and n. However, taking the natural log of Equation 5 allows I0 and n to be calculated. When the natural log of both sides are taken, the exponent goes away and the values within the exponents are brought down. Id however becomes ln(Id). By plotting ln(Id) vs Vd allows I0 to be solved. This plot can be seen in Figure 7.

[pic]
Figure 8: Plot of the natural log of Id vs Vd.

I0 would be the value intersecting the y-axis. That intersecting value would be the natural log of I0, so by taking that value to the exponential gives the real value of I0, which would be 5.87*10^-9 A. Now that I0 is calculated, all the variables within the equation are solved except for n. By plugging in all the variables and solving for n yields the value of n as 1.762.

Summary and Conclusions In this lab students investigated the DC current-voltage characteristics of the PN junction diode. The students plotted I-V and created a piecewise linear model of I-V. The PN junction was then simulated in PSICE. The measured results showed that as the voltage, Vd, increased, so did the current, Id. The function increases exponentially. The simulated results also showed that the same relationship between Vd and Id. Equation 5 above accurately predicts the behavior of the current for the measured and simulated results in the diode. Table 2 below shows the range in which the behavior is similar to Equation 4.
Table 2: Range of values where measured and simulated results agree with ideal results

|Results |Starting Vd (V)|Ending Vd (V) |
|Measured |0 |0.65 |
|Simulated |0 |0.65 |

A semiconductor in high injection means that the number of generated carriers is large compared to the background doping density of the material. In this case minority carrier recombination rates are proportional to the number of carriers squared. This means that in high‐level injection it takes a larger increase in diode voltage to produce a given increase in diode current. This is seen in the ideal, measured, and simulated results. As the voltage is increased, the current eventually becomes harder and harder to increase. This is seen in the exponential shape of the I-V curve. Eventually the curve in the lab begins to level out instead of approaching infinity. In summary, the model given is not a high level injection regime. This is due to the I-V curve leveling out a certain point. Although the student data does not show the leveling out of the curve, this behavior can be predicted .If the model were truly a high level injection regime, the I-V curve would continue to approach infinity.