Animated Solution for Physics - Semiconductors: Which of the following statements is not true ?

That's a semiconductor for you! In its pure form, known as an intrinsic semiconductor, it behaves almost like an insulator at absolute zero. But as you turn up the heat, something magical happens. The thermal energy excites electrons, allowing them to break free from their covalent bonds and jump from the valence band to the conduction band. Every time an electron makes this leap, it leaves behind a vacancy called a hole. Both the free electrons and the holes act as charge carriers. So, as temperature increases, the number of charge carriers increases, which means the conductivity shoots up. And what happens to resistance when conductivity goes up? It goes down! So, the resistance of an intrinsic semiconductor decreases with an increase in temperature.

To make them useful, we introduce impurities in a process called doping. If we take pure Silicon, which has 4 valence electrons, and dope it with a trivalent impurity (like Boron or Aluminum, which have 3 valence electrons), the impurity atom forms covalent bonds with three neighboring Silicon atoms. But it falls short by one electron to bond with the fourth Silicon atom. This missing electron creates a vacancy, or a hole. Since we are creating an abundance of holes (which act as positive charge carriers), this type of material is called a $p$-type semiconductor.

On the flip side, what if we dope Silicon with a pentavalent impurity (like Phosphorus or Arsenic, which have 5 valence electrons)? Four of these electrons will form bonds with neighboring Silicon atoms, but the fifth electron is left loosely bound and becomes a free electron. Because we are introducing an abundance of free electrons (negative charge carriers), this material is called an $n$-type semiconductor. So, in an $n$-type semiconductor, the majority carriers are electrons, and the minority carriers are holes.

At the junction, electrons from the $n$-side diffuse into the $p$-side and recombine with holes, creating a depletion region that acts as a barrier. If you apply a voltage such that the positive terminal is connected to the $p$-side and the negative to the $n$-side (forward bias), the barrier shrinks, and current flows easily. But if you reverse the connections (reverse bias), the barrier widens, and almost no current flows. This ability to allow current in only one direction is the exact definition of a diode. Therefore, a $p$-$n$ junction acts as a semiconductor diode.

As we've just discovered, $n$-type materials are teeming with extra electrons donated by pentavalent impurities. Therefore, electrons are the majority carriers, making statement (c) the false statement we were looking for!