Question

What is the need of doping of intrinsic semiconductors? Ideal diodes are used in the given circuits. Find the value of current in both the circuits.

Hint:

An ideal diode is a short when forward biased and an open when reverse biased. A series diode string conducts only if all diodes are forward; then \(I=V/R=2/10=0.2\) A, otherwise 0.

Answer 1

Step 1: Need of doping.
A pure (intrinsic) semiconductor has very few free charge carriers at room temperature, so its conductivity is very low and it is of little practical use. Doping means adding a small, controlled amount of a suitable impurity to greatly increase the number of charge carriers and hence the conductivity:
- Adding a pentavalent impurity (P, As) supplies extra electrons \(\to\) n-type semiconductor.
- Adding a trivalent impurity (B, Al) supplies extra holes \(\to\) p-type semiconductor.
Doping lets us control conductivity and make useful devices such as diodes and transistors.

Step 2: Rule for an ideal diode.
An ideal diode has zero resistance when forward biased (behaves like a closed switch) and infinite resistance when reverse biased (behaves like an open switch, no current).

Step 3: Left circuit.
All three diodes point the same way as the current driven by the 2 V cell, so all are forward biased and behave like plain wires. Only the \(10\,\Omega\) resistor limits the current: \[ I_1 = \frac{V}{R} = \frac{2}{10} = 0.2\ \text{A} \] Step 4: Right circuit.
Here the third diode is connected opposite to the other two. Whatever the direction of current, at least one diode is reverse biased and blocks it, so the circuit is open: \[ I_2 = 0\ \text{A} \] \[\boxed{I_1 = 0.2\ \text{A},\qquad I_2 = 0}\]