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Which of the following represents the correct order of band gap energies for Germanium (Ge), Silicon (Si), and Gallium Arsenide (GaAs) at room temperature?
E(Ge) < E(Si) < E(GaAs)
E(Si) < E(Ge) < E(GaAs)
E(GaAs) < E(Si) < E(Ge)
E(Ge) < E(GaAs) < E(Si)
E(Ge) < E(Si) < E(GaAs)
The band gap energy (EgтАЛ) is the energy difference between the valence band and the conduction band. At room temperature (300┬аK), the band gap values are approximately 0.66┬аeV for Germanium (Ge), 1.12┬аeV for Silicon (Si), and 1.42┬аeV for Gallium Arsenide (GaAs).
The band gap energy (EgтАЛ) is the energy difference between the valence band and the conduction band. At room temperature (300┬аK), the band gap values are approximately 0.66┬аeV for Germanium (Ge), 1.12┬аeV for Silicon (Si), and 1.42┬аeV for Gallium Arsenide (GaAs).
EgтАЛ(T)тЙИEgтАЛ(0)тИТT+╬▓╬▒T2тАЛ тАФ Varshni's empirical relation for temperature dependence of band gap
f(E)=1+ekBтАЛTEтИТEFтАЛтАЛ1тАЛ тАФ Fermi-Dirac distribution function governing electron occupancy
The band gap is determined by the interatomic bond strength in the semiconductor crystal lattice. Stronger covalent bonds or higher ionicity result in a larger energy gap required to excite an electron from the valence band to the conduction band.
Ge is a narrow band gap semiconductor, ideal for infrared detectors.
Si is a moderate band gap material, the industry standard for VLSI.
GaAs is a direct band gap semiconductor, widely used in optoelectronics and high-frequency applications.
As atomic size increases down the periodic table, bond strength usually decreases, narrowing the band gap.
Higher band gap materials like GaAs allow operation at higher temperatures.
Direct band gap materials (GaAs) are highly efficient for light emission.
Lower band gap materials (Ge) exhibit higher leakage currents due to thermal generation of carriers.
Si: Integrated circuits and solar cells.
GaAs: LEDs, Laser diodes, and high-speed satellite communication.
Ge: Fiber optics and radiation detectors.
| Feature | Germanium | Silicon |
|---|---|---|
Band Gap (eV) at 300K | 0.66 | 1.12 |
Germanium (Z=32) has the smallest band gap among the three.
Silicon (Z=14) has an intermediate band gap.
Gallium Arsenide (Z=31,33) has the largest band gap.
Option B, C, and D are incorrect as they misrepresent the energy ordering determined experimentally.
A is correct тАФ The correct ascending order of band gap energies at room temperature is E(Ge)<E(Si)<E(Ga┬аAs) with values 0.66┬аeV<1.12┬аeV<1.42┬аeV.
Remember the sequence 'Ge < Si < GaAs' as it frequently appears in exams involving photodetectors and LED efficiency.
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