Concepts Of Physics MCQ Edition [Volume 2]PhysicsSemiconductors and Semiconductor Devices
Let E designate the energy gap between the valence band and the conduction band. The population of conduction electrons (and of the holes) is roughly proportional to e^ - E/2kT . Determine the approximate ratio of the concentration of conduction electrons in diamond to that in silicon at room temperature 300 K . The gap E for silicon is 1.1 eV and for diamond is 6.0 eV . Also, how many conduction electrons are likely
Options
- ARatio 1.8 10⁻¹⁹ , almost zero
- BRatio 2.3 10⁻³³ , almost zero
- CRatio 7.6 10⁻⁴² , almost zero
- DRatio 4.2 10⁻⁵¹ , almost zero
Correct answer
C. Ratio 7.6 10⁻⁴² , almost zero
Step-by-step solution
The concentration of conduction electrons is given by n e^ - E / 2kT . The ratio of the concentration of conduction electrons in diamond to that in silicon is: n_ diamond n_ silicon = e^ - E_ diamond / 2kT e^ - E_ silicon / 2kT = e^ -( E_ diamond - E_ silicon ) / 2kT Given E_ diamond = 6.0 eV and E_ silicon = 1.1 eV . E_ diamond - E_ silicon = 6.0 - 1.1 = 4.9 eV At T = 300 K , the thermal energy kT in electron-volts is: kT = 1.38 10⁻²³ 300 1.6 10⁻¹⁹ eV 0.025875 eV 2kT = 2 0.025875 = 0.05175 eV Substituting these va