Question

A p-type Si semiconductor is made by doping an average of one dopant atom per \( 5 \times 10^7 \) silicon atoms. If the number density of silicon atoms in the specimen is \( 5 \times 10^{28} \, \text{atoms/m}^3 \), find the number of holes created per cubic centimetre in the specimen due to doping. Also, give one example of such dopants.

Hint:

In p-type semiconductors, dopants like boron create holes, and the number of holes is equal to the number of dopant atoms introduced into the material.

Answer 1

Number of Holes Created in P-Type Silicon Semiconductor Due to Doping

Doping a p-type silicon semiconductor introduces holes (positive charge carriers) by replacing silicon atoms with dopant atoms. This section calculates the number of holes generated per cubic centimetre through doping.

Given Data:

• Doping concentration: 1 dopant atom for every \( 5 \times 10^7 \) silicon atoms.
• Number density of silicon atoms: \( 5 \times 10^{28} \, \text{atoms/m}^3 \).

Step 1: Determine the Number of Dopant Atoms per Unit Volume

The number of dopant atoms per unit volume is found by multiplying the doping concentration by the silicon atom number density:

\[ \text{Number of dopant atoms per unit volume} = \frac{1}{5 \times 10^7} \times 5 \times 10^{28} \, \text{atoms/m}^3 \]

This results in:

\[ = 1 \times 10^{21} \, \text{atoms/m}^3 \]

Step 2: Determine the Number of Holes per Cubic Metre

In a p-type semiconductor, each dopant atom yields one hole. Consequently, the number of holes per cubic metre equals the number of dopant atoms per cubic metre:

\[ \text{Number of holes per cubic metre} = 1 \times 10^{21} \, \text{holes/m}^3 \]

Step 3: Convert to Cubic Centimetres

Given that 1 cubic metre equals \( 10^6 \) cubic centimetres, the number of holes per cubic centimetre is calculated as:

\[ \text{Number of holes per cubic centimetre} = \frac{1 \times 10^{21}}{10^6} = 1 \times 10^{15} \, \text{holes/cm}^3 \]

Conclusion:

The doping process in the p-type silicon semiconductor results in \( 1 \times 10^{15} \, \text{holes/cm}^3 \).

Example of Dopants:

Boron (B) is a common dopant used to create p-type silicon. Boron has one fewer valence electron than silicon, which creates a hole in the semiconductor lattice.