Basic Diode Theory
When a single semiconductor crystal is doped with trivalent impurity atoms on one side and with pentavalent impurity atoms on the other side, a p-n junction is formed between the resultant p and n regions. A semiconductor device which utilizes the unique properties that result from such a junction is called a p-n diode.
When the diode is reverse biased (the p and n sides being respectively connected to the -ve and +ve terminals of the battery), the internal barrier field increases (with a corresponding increase in the width of the depletion region), as a result of which the majority charge carriers are further inhibited from crossing the junction and contributing to a current flow. However, the increase in the barrier field helps the minority carriers to cross the junction and contribute to a very small current in the reverse direction. This small current soon attains a constant value with the increase in the reverse bias and is called the reverse saturation current, . It is of the order of nano or pico amperes in Si and micro amperes in Ge. It is important to note that Shockley's equation holds true for the reverse biased diode as well.
Numerical solution for the operating point
The operating point of the diode for a fixed set of circuit parameters given by the supply voltage and the load resistance , can be obtained by solving simultaneously the diode and load-line equations, viz.,
The idea, though simple, is difficult to implement, given the nonlinear nature of the diode equation. A way out of the problem is to look for an iterative numerical solution. At first is eliminated and the above two equations are combined into a single nonlinear equation,
A starting guess for , say 0.5 V, is taken and the solution is iteratively launched till the value of converges appreciably. This converged value of is taken as the solution for the diode voltage for the given fixed value of and . The corresponding diode current is obtained from either of the two equations considered at the outset.
Another approach, though a bit cumbersome, is to plot the two curves and obtain the point of intersection. This point of intersection would give the same operating point of the diode. The accuracy, though, would be somewhat limited.
Effect of temperature on the static curve
One look at Shockley's equation for the diode would tell us that the diode current depends on temperature through its explicit presence inside the exponential. However, we must bear in mind that the reverse saturation current also depends on temperature. The dependence (for Si say) can be expressed through the formula
C is a constant and is the voltage corresponding to the forbidden energy gap for Si and other symbols have their usual meanings. As a rule of thumb, we may say that doubles for every rise in temperature. Interestingly, this implicit dependence dominates the explicit dependence mentioned at the outset. The overall effect is that the diode static curve keeps shifting to the left with rise in temperature.
In this context it may be mentioned that Ge diodes have relatively high values of (of the order of micro amperes), rendering them useless over wide temperature fluctuations.
When a diode is subjected to a dc input voltage, a fixed current results and we get a fixed operating point or Q (Qiescent) point on the static diode characteristic curve. The resistance of the diode at this Q point is called the dc or static resistance and is given by
On the other hand if the diode is subjected to a small signal alternating (ac) voltage oscillating about a fixed dc value, the current also oscillates about the fixed dc value given by the operating point. The resistance that needs to be considered in this case is the ac or dynamic resistance given by
When the ac voltage swing is large, we need to consider another resistance called the average ac resistance of the diode defined between two extreme operating points of the diode given by and as follows:
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