Solving Current-Voltage Characteristic of P-N Diodes with ln i = ln i˚ + eV/2kT

In summary: By using this method, you can plot the data on semilog paper with i on the log scale and determine T without any prior knowledge or understanding of physics. In summary, to plot the current-voltage characteristic of a p-n diode that is forward biased, you can use a curve-fitting software package to calculate T and plot the data on semilog paper without needing to know the value of i˚.
  • #1
tallin_grady
1
0
For the current-voltage characteristic of a p-n diode which is foward biased:

ln i = ln + eV/2kT

where i˚ = a constant current
e = electronic charge
k = Boltzmann constant
T = absolute electron temperature
i and v are current and voltage respectively, for which I have a series of values

I am supposed to plot i against v on semilog paper with i on the log scale, with T calculated from the graph without knowing i˚. Admittedly physics isn't my storng suit and I have thought about this for a long time and have gotten nowhere. I was wondering if somebody could tell me how I am supposed to do this?

Thanks,

Tallin
 
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  • #2
The simplest way to plot the current-voltage characteristic of a p-n diode that is forward biased is to use a curve-fitting software package, such as Origin or MATLAB. This will allow you to easily enter your values of current and voltage and then fit a curve to the data. The equation for the curve (ln i = ln i˚ + eV/2kT) will be automatically calculated by the software, so you won't need to know the value of i˚. Additionally, the software will calculate values for T, k, and e from the fitted curve.
 
  • #3


Firstly, the equation ln i = ln i˚ + eV/2kT is known as the Shockley diode equation and is used to describe the current-voltage characteristic of a p-n diode. This equation shows that the natural logarithm of the current is directly proportional to the applied voltage, with a slope of e/2kT. This slope is dependent on the temperature, where a higher temperature will result in a smaller slope and vice versa.

To plot i against v on semilog paper, you will need to plot the natural logarithm of i (ln i) on the y-axis and the voltage (v) on the x-axis. Since the equation is in logarithmic form, plotting on semilog paper will result in a straight line. The slope of this line will give you the value of e/2kT, which can then be used to calculate the temperature T.

To calculate T from the graph, you will need to know the value of e/2k, which is a constant. Once you have this value, you can use the slope of the line (e/2kT) to calculate the temperature T. This can be done by rearranging the equation to T = e/2k(slope). This value of T can then be used to determine the absolute temperature of the diode without knowing i˚.

I hope this helps in understanding how to plot and interpret the current-voltage characteristic of a p-n diode using the Shockley diode equation. If you have any further questions, please do not hesitate to ask. Good luck with your experiment!
 

1. How does the current-voltage characteristic of a P-N diode relate to ln i = ln i˚ + eV/2kT?

The formula ln i = ln i˚ + eV/2kT is known as the Shockley diode equation, which describes the relationship between the current and voltage of a P-N diode. This equation shows that the current (i) is directly proportional to the voltage (V) and temperature (T) and is also dependent on the constant e (electron charge) and k (Boltzmann constant). This equation is used to solve for the current-voltage characteristic of a P-N diode.

2. What is the significance of ln i˚ in the equation ln i = ln i˚ + eV/2kT?

The term ln i˚ represents the reverse saturation current of the diode, which is the current that flows when the diode is in reverse bias. This current is typically very small and can be ignored in most cases, but it is important to include in the equation for accurate calculations.

3. How does the temperature affect the current-voltage characteristic of a P-N diode?

The temperature is a crucial factor in the Shockley diode equation, as it is directly proportional to the current. As the temperature increases, the current also increases, resulting in a higher current-voltage characteristic. This is due to the fact that the movement of charge carriers is affected by temperature, and an increase in temperature leads to more charge carriers being available to flow through the diode.

4. Can the Shockley diode equation be used for other types of diodes?

While the Shockley diode equation is specifically used for P-N diodes, it can also be applied to other types of diodes that have a similar structure and behavior. This includes Schottky diodes and Zener diodes, which have their own variations of the equation.

5. How is the current-voltage characteristic of a P-N diode used in real-world applications?

The current-voltage characteristic of a P-N diode is used in various electronic devices, such as rectifiers, voltage regulators, and switches. By understanding and analyzing the characteristic, engineers can design and optimize these devices for specific purposes. Additionally, the characteristic can also be used to test and troubleshoot diodes in circuits.

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