Semiconductors

The number of dopant atoms per silicon atom is . The number of holes created in the specimen per cubic meter is the number of dopant atoms per cubic meter, which is: To find the number of holes per cubic centimeter, we convert from cubic meters to cubic centimeters. Since : Thus, the number of holes created per cubic centimeter due to doping is . An example of a dopant for p-type semiconductors is Boron.

To understand the behavior of a p-n junction diode when it is forward biased, let's explore the concepts of barrier height and depletion layer width:

A p-n junction diode consists of p-type and n-type semiconductors. At the junction, there is a built-in potential barrier that prevents charge carriers from crossing over. The barrier height is the energy level that must be overcome for the charge carriers to move across the junction.

When a diode is forward biased:

• The external voltage reduces the barrier height. This makes it easier for the electrons from the n-side to recombine with holes on the p-side and vice versa.
• The depletion layer, the region devoid of charge carriers, shrinks because the forward bias provides energy that helps the electrons and holes recombine more efficiently, neutralizing the charges in this region.

Thus, under forward bias conditions, the observed effects on the p-n junction diode are: a decrease in both the barrier height and the depletion layer width. The correct answer is:

The barrier height and the depletion layer width both decrease.

Concept: A full-wave rectifier converts both halves of an AC input into pulsating DC output using p–n junction diodes. It provides higher efficiency than a half-wave rectifier.

Circuit Diagram (Centre-tapped full-wave rectifier): Components: 

Centre-tapped transformer 
Two diodes  
Load resistor  
Connections: 

Anodes of diodes connected to the ends of secondary winding 
Cathodes joined together and connected to load 
Centre tap connected to other end of load 
Working: Positive half cycle: 

Upper end of secondary becomes positive 
Diode forward biased → conducts 
Diode reverse biased → off 
Current flows through in one direction 
Negative half cycle: 

Lower end of secondary becomes positive 
conducts, off 
Current again flows through load in same direction 
Thus, both halves of AC are rectified → full-wave rectification. Input–Output Waveforms: Input waveform: 

Sinusoidal AC wave 
Positive and negative halves symmetric 
Output waveform: 

Both halves appear positive 
Pulsating DC with double frequency of input 
Graph description: 

Input: sine wave about zero axis 
Output: series of positive humps (no negative portion) 
Key Features: 

Output frequency =  
Higher efficiency than half-wave rectifier 
Less ripple