1. The number density of conduction electrons in pure silicon at room temperature is about 11016m3. By doping with phosphorous, you desire to increase this number by a factor of 1 million(106). At room temperature, assume that the thermal energy is sufficient that all of the extraelectrons from the P doping enter the conduction band. What fraction of silicon atoms must youreplace with phosphorous atoms

This question is incomplete, the complete question is;

The number density of conduction electrons in pure silicon at room temperature is about 10¹⁶ m⁻³. By doping with phosphorous, you desire to increase this number by a factor of 1 million (10⁶). At room temperature, assume that the thermal energy is sufficient that all of the extra electrons from the P doping enter the conduction band. What fraction of silicon atoms must you replace with phosphorous atoms

the  fraction of silicon atoms we must replace with phosphorous atoms is 4( 10⁶  - 1 )

Explanation:

Given that;  

the number density no =  10¹⁶ m⁻³

Required no =  (10¹⁶ × 10⁶) = 10²² m⁻³

Each silicon atom has 4 valence electron,

Hence; Silicon density =  10¹⁶/4

now, if x = No of silicon atoms to be replaced with phosphorous, then;

(10¹⁶/4 - x)4 + 5x = 10²²

10¹⁶ - 4x + 5x = 10²²

10¹⁶ + x = 10²²

x = 10²² - 10¹⁶

Fraction of silicon atoms will be;

⇒ 10²² - 10¹⁶ / 10¹⁶/4

⇒ 4( 10²² - 10¹⁶ / 10¹⁶ )

⇒ 4( 10²²/10¹⁶  - 10¹⁶/10¹⁶ )

⇒ 4( 10⁶  - 1 )

Therefore, the  fraction of silicon atoms we must replace with phosphorous atoms is 4( 10⁶  - 1 )

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