Let △E denotes 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−△$$E/2kT$$ . Find the ratio of the concentration of conduction electrons in diamond to that in silicon at room temperature $$300$$ K . △E for silicon is $$1.1$$ eV and for diamond is $$6.0$$ eV.

Question

Let △E denotes 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−△$$E/2kT$$ . Find the ratio of the concentration of conduction electrons in diamond to that in silicon at room temperature $$300$$ K . △E  for silicon is $$1.1$$ eV and for diamond is $$6.0$$ eV.

Infinity Learn · Accepted Answer

Given  η$$=e$$−△$$E/2kT$$    △E  (diamond) $$=$$ $$6$$ eV             △E  (Si)  $$=$$ $$1.1$$ eV Now, η$$1$$ $$(Diamond)=e$$−△$$E12kT$$     $$=e$$−$$6$$ $$eV2$$×$$1.38$$×$$10$$−$$23$$×$$300$$ $$=e$$−$$6$$×$$1.6$$×$$10$$−$$192$$×$$1.38$$×$$10$$−$$23$$×$$300$$,η$$1=e$$−$$62$$×$$300$$×$$8.62$$×$$10$$−$$5$$ $$=$$ e−$$116=4.14722$$×$$10$$−$$51$$                                     Similarly , η$$2$$  $$(Silicon)=e$$−△$$E22kT=e$$−$$1.12$$×$$1.38$$×$$10$$−$$23$$×$$300$$ $$=e$$−$$1.1$$×$$1.6$$×$$10$$−$$192$$×$$1.38$$×$$10$$−$$23$$×$$300$$ $$=e$$−$$1.12$$×$$8.62$$×$$10$$−$$5$$×$$300$$ $$=$$ e−$$21.2683=$$ $$5.7979$$×$$10$$−$$10$$∴ratio $$=$$ η$$1$$η$$2=4.14722$$×$$10$$−$$515.7979$$×$$10$$−$$10=7.15$$×$$10$$−$$42$$

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