Question

Explain the effect of biasing on the depletion region of a p-n junction. Using a p-n junction diode, draw the circuit diagram of a half-wave rectifier and show the shape of the input and output voltage.

Hint:

Forward bias lowers the barrier and narrows the depletion region; reverse bias widens it. A half-wave rectifier uses one diode that conducts only in the positive half cycle, giving a pulsating DC output.

Answer 1

Step 1: Depletion region and barrier potential.
At an unbiased p-n junction, diffusion of majority carriers leaves a thin region of uncovered immobile ions (negative on the p-side, positive on the n-side). This region has almost no free carriers and produces a barrier potential of about \(0.3\) V for germanium and \(0.7\) V for silicon.

Step 2: Forward biasing shrinks it.
Applying an external voltage with p at the higher potential pushes majority carriers toward the junction, neutralising some of the immobile ions. The depletion width and the barrier both decrease, and once the applied voltage exceeds the barrier, the current rises sharply.

Step 3: Reverse biasing widens it.
Applying the voltage the other way pulls majority carriers away from the junction, exposing more immobile ions. The depletion width and barrier both increase, and only a tiny reverse saturation current (due to minority carriers) flows.

Step 4: Half-wave rectifier arrangement.
Connect the AC source (through a step-down transformer) to a single diode in series with the load \(R_L\). The diode acts as a one-way valve for the current.

Step 5: Output description and quality.
Because the diode conducts only when its anode (p-side) is positive, current passes during one half of each AC cycle and is blocked during the other. Hence the graph of output versus time shows only the upper (positive) humps of the input sine wave, with gaps where the negative halves were. This pulsating DC has the same frequency as the input, an average value \(V_{dc} = V_m/\pi\), and needs a filter to smooth it.

\[\boxed{\text{Forward bias: thinner depletion layer; reverse bias: thicker; half-wave rectifier passes one half cycle}}\]