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 

In a p-type silicon semiconductor, doping introduces **holes** (positive charge carriers) by substituting silicon atoms with dopant atoms. Let's calculate the number of holes created per cubic centimetre due to doping.

Given Data:

• The doping concentration is 1 dopant atom per \( 5 \times 10^7 \) silicon atoms.
• The number density of silicon atoms in the specimen is \( 5 \times 10^{28} \, \text{atoms/m}^3 \).

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

The number of dopant atoms per unit volume can be calculated by multiplying the doping concentration by the number density of silicon atoms:

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

Thus, the number of dopant atoms per unit volume is:

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

Step 2: Finding the Number of Holes per Cubic Metre

In a p-type semiconductor, each dopant atom introduces one hole. Therefore, the number of holes per cubic metre is equal to 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: Converting to Cubic Centimetres

Since 1 cubic metre is equal to \( 10^6 \) cubic centimetres, the number of holes per cubic centimetre is:

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

Conclusion:

The number of holes created per cubic centimetre in the p-type silicon semiconductor due to doping is \( 1 \times 10^{15} \, \text{holes/cm}^3 \).

Example of Dopants:

One common example of a dopant for creating p-type silicon is boron (B). Boron has one less valence electron than silicon, which results in the creation of a hole in the semiconductor.