Question

Increasing the temperature of a semiconductor breaks covalent bonds. For each broken bond, two electrons become free to move and transfer electrical charge. (a) What fraction of valence electrons are free to move and (b) what fraction of the covalent bonds must be broken in order that 5 × 1015 electrons conduct electrical charge in 50 g of silicon? (c) What fraction of the total silicon atoms must be replaced by arsenic atoms to obtain one million electrons that are free to move in one pound of silicon?

Answer 1

Part a

Mass of Si = 50 g

Molecular weight of Si = 28.08 g/mol

Avogadro number = 6.023 x 10^23 atoms/mol

Atoms of Si = mass x Avogadro number /molecular weight

= 50 g x 6.023 x 10^23 atoms/mol / 28.08 g/mol

= 1.072 x 10^24 atoms

valence electrons = 4 electrons/atom x 1.072 x 10^24 atoms

= 4.288 x 10^24 electrons

fraction of valence electrons = 5 × 10^15 / 4.288 x 10^24

= 1.17 x 10^-9

Part b

One covalent bond has = 2 electrons

covalent bonds must be broken per electron

= 5 × 10^15 / 2

= 2.5 x 10^15

fraction of the covalent bonds = 2.5 x 10^15/1.072 x 10^24

= 2.33 x 10^-9

Part C

Mass of Si = 1 lb x 454g/lb = 454 g

Number of atoms

= 454g x 6.023 x 10^23 atoms/mol / 28.08 g/mol

= 9.733 x 10^24 atoms

Replaced atoms = 1 million = 10^6

fraction of the total silicon atoms must be replaced by arsenic atoms

= 10^6/9.733 x 10^24

= 1.03 x 10^-19