How n is dependent on conductor …

In metals, n i.e., the number of electrons in unit volume of the conductor is almost independent of temperature. However, t i.e., the relaxation time does vary with temperature. When temperature increases, the thermal speed of the electrons increases as well as, the amplitude of vibration of the positive ions inside the metal conductor also increase, about their mean positions. Thus, the collisions between the electrons and the positive metal ions become more frequent and this decreases the relaxation time, t, leading to an increase in the resistivity of the conductor.
Also, the temperature coefficient of metals is positive.

The number of free electrons in a unit volume of the semi-conductor increases exponentially with an increase in the temperature. This more than compensates the small decrease in t, the relaxation time. Also, the temperature coefficient is negative. Thus the resistivity decreases with a temperature increase in semi-conductors.