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The energy of a photon of sodium light (lambda = 589 nm) equal to the band gap of a semiconducting material . ( a ) Find the minimum energy E required to create a hole - electron pair . ( b ) Find the value of E / KT at a temperature of 300 K. |
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Answer» SOLUTION :The energy of the photon in `EV=(12400)/(lambda)` Wavelength of photon `=589nm=5890Å` `=(12400)/(5890)=2.1eV` Thus the band gap is 2.1 eV . This is also the minimum energy E required to push an electron from the valence band into the conduction band . Hence , the minimum energy required to create a hole - electron pair is 2.1eV . (b) At `T=300K, KT=(8.62xx10^(-5)eV//K)/(300K)` `=25.86xx10^(-3)eV`. Thus, `(E)/(kT)=(2.1eV)/(25.86xx10^(-3)eV)=81` The available thermal energy is nearly 81 times LESS than that of the required energy to create electron hole pair . So it is difficult for the thermal energy to create the hole - electron pair but a photon of light can do it EASILY . |
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