Resistivity of Various Materials

The classification

• Materials are classified as conductors, semiconductors and insulators in increasing order of resistivity.
• Metals have low resistivities, in the range $10^{-8}\ \Omega\,\text{m}$ to $10^{-6}\ \Omega\,\text{m}$.
• At the other end, insulators such as ceramic, rubber and plastic have resistivities about $10^{18}$ times greater than metals, or more. (NCERT's chapter Summary quotes the figure for glass and rubber as $10^{22}$ to $10^{24}$ times that of a metal — either number is accepted, since the point being examined is only the enormous ratio.)
• Semiconductors lie in between, roughly in the middle of the range on a logarithmic scale. Si and Ge are the standard examples.

What distinguishes a semiconductor

• Semiconductors have resistivities that characteristically decrease as the temperature rises, the opposite of a metal.
• Their resistivity can also be decreased by adding a small amount of a suitable impurity. It is this feature that is exploited in electronic devices.
• The reason for both, from $\rho = m/ne^2\tau$: in a semiconductor the free-carrier density $n$ rises steeply with temperature (or with doping), and that increase in $n$ more than compensates the fall in $\tau$.

Alloys, and why standard resistors are made of them

• Nichrome (an alloy of nickel, iron and chromium), manganin and constantan show a very weak dependence of resistivity on temperature.
• They are therefore used for wire-bound standard resistors: the resistance value hardly changes as the resistor warms in use.
• The second reason CBSE marks is that alloys have a high specific resistance, so a comparatively short length of wire gives the required resistance.
• So: low temperature coefficient of resistivity together with high specific resistance — that combination is the answer to the standard MCQ.
• Nichrome is also why a toaster or heating element is made of it: a high $\rho$ gives a high $R$, and $H = I^2Rt$ then produces plenty of heat.

Reading a resistivity-temperature figure

Standard results

• $\rho_{\text{metal}}$: $10^{-8}$ to $10^{-6}\ \Omega\,\text{m}$; insulators about $10^{18}$ times greater or more; semiconductors in between.
• Resistivity depends only on the material and its temperature — never on length, area or shape.
• Metals: $\alpha$ positive. Semiconductors and insulators: $\alpha$ negative. Alloys: $\alpha$ nearly zero.
• Nichrome, manganin, constantan for standard resistors: low $\alpha$, high $\rho$.
• Adding a suitable impurity lowers the resistivity of a semiconductor.