2 1.The concentration of conduction electrons in pureSi at 300K is 1016 m-3. Assume that by doping thelattice with phosphorus, you want to increase thisnumber by a factor of a million (106). What fractionof the silicon atoms must you replace withphosphorus atoms?(At room temperature, the thermal agitation iseffective enough so that essentially every phosphorusatom donates its “extra” electron to the conductionband).
3 Answer:concentration of phosphorus atoms(1016 m-3) x (106) = 1022 m-3 = npconcentration of silicon atoms in a pure silicon latticeNA = Avogado’s number 6.02 x 1023 mol-1A = molar mass of silicon 28.1g/mol= density of silicon = 2330 kg/m3
4 = 5 x 1028 m-3The ratio of the concentration of Si atoms and theconcentration of P atoms is the fraction of Si atomsthat need to be replaced with P atomsThis says that if only one silicon atom in fivemillion is replaced by a phosphorus atom, thenumber of electrons in the conduction band willbe increased by a factor of 106.
5 2. Solution A Si sample contains 1016 cm-3 In acceptor atoms. The In acceptor level is 0.16 eV above Ev, and EFis 0.26 eV above Ev at 300 K. How many (cm-3) Inatoms are unionized (i.e. neutral)?SolutionNa = 1016 cm-3Not all of them are ionized. The concentration of ionized atoms isgiven by Naf(Ea), where f(Ea) is the probability of electrons beingfound in energy state Ea.
6 The concentration of unionized atoms is 1016 – x 1016 = 2.1 x 1014 cm-3