RONGO UNIVERSITY PHY 411: SOLID STATE 1.An intrinsic semi-conductor has 8.9times 10^19 conducting electrons per cubic metre. It is doped to form an n-type semi- conductor resulting into 125% increase in the number of conducting electrons . Determine; a) The number of charge carries per cubic metre of the n-type semiconductor. (5 marks) (1) mainl b) The number of charge carriers contained in 12cmtimes 10mmtimes 0.5m of the new material. CAT

a) To determine the number of charge carriers per cubic meter of the n-type semiconductor, we need to calculate the increase in the number of conducting electrons.<br /><br />Given that the intrinsic semiconductor has $8.9 \times 10^{19}$ conducting electrons per cubic meter, and the doping results in a $125\%$ increase in the number of conducting electrons, we can calculate the number of charge carriers in the n-type semiconductor as follows:<br /><br />Number of charge carriers = Initial number of conducting electrons + Increase in number of conducting electrons<br />Number of charge carriers = $8.9 \times 10^{19}$ + $1.25 \times 8.9 \times 10^{19}$<br />Number of charge carriers = $8.9 \times 10^{19}$ + $11.125 \times 10^{19}$<br />Number of charge carriers = $20.025 \times 10^{19}$<br /><br />Therefore, the number of charge carriers per cubic meter of the n-type semiconductor is $20.025 \times 10^{19}$.<br /><br />b) To determine the number of charge carriers contained in a specific volume of the new material, we need to calculate the volume in cubic meters and then multiply it by the number of charge carriers per cubic meter.<br /><br />Given the dimensions of the material as $12cm \times 10mm \times 0.5m$, we can convert these values to meters and calculate the volume:<br /><br />Volume = Length x Width x Height<br />Volume = $0.12m \times 0.01m \times 0.5m$<br />Volume = $0.0006m^3$<br /><br />Now, we can calculate the number of charge carriers contained in this volume:<br /><br />Number of charge carriers = Number of charge carriers per cubic meter x Volume<br />Number of charge carriers = $20.025 \times 10^{19} \times 0.0006$<br />Number of charge carriers = $12.015 \times 10^{16}$<br /><br />Therefore, the number of charge carriers contained in $12cm \times 10mm \times 0.5m$ of the new material is $12.015 \times 10^{16}$.