Equilibrium Carrier Concentration

Introduction

Semiconductors have majority carriers and minority carriers. The charge carriers more abundant are the majority carriers; while the minority carriers are the charge carriers less abundant. Doping can increase the equilibrium carrier concentration. Equilibrium carrier concentration is the total number of carriers in the conduction and valence bands. A constant is the product of the minority and majority charge carriers. Equilibrium carrier concentration is the number of carriers in the conduction and valence band with no externally applied bias. The equilibrium carrier concentration for majority carriers is equal to the intrinsic carrier concentration plus the free carriers number added by doping the semiconductor. In most cases, doping of the semiconductor is several orders of magnitude greater than the intrinsic carrier concentration, so that the majority carriers number is nearly equal to the doping.

Equilibrium

An important equation for determining the carrier concentrations in a material is defined by the Law of Mass Action, we must first understand the description of thermal equilibrium before further discussing. Thermal equilibrium is a relationship between the concentrations of charge carriers at a certain temperature. Described differently, at a given temperature, there is an equilibrium between both generation - formation of pairs of electron-hole as a result of thermal excitation or photon absorption - and recombination which is the natural destruction of pairs that happen when electrons from conduction band fall back again into valence band. In the intrinsic case, the bound electrons number is much higher than the free electrons number, thus the charge carriers generation is independent of the electron-hole pairs number which have been already formed. Though, as soon as generation occurs, recombination happens and it depends on the charge carriers concentration in the material. In fact recombination is directly proportional to the charge carriers number.

Law of Mass action Equations

The product of the majority and minority carrier concentration at equilibrium is a constant, which is mathematically expressed by the Law of Mass Action. n_op_{o =}n_i² where n_i: is the intrinsic carrier concentrationn₀: electron equilibrium carrier concentrations.p_0: the hole equilibrium carrier concentrations. By using the Law of Mass Action above, the majority and minority carrier concentrations can be expressed in the following equations: n-type: n_o = N_D,p_{o =}n_i² / N_Dp-type: p_o = N_A,n_{o =}n_i² / N_A where N_D: donor atoms concentration N_A : acceptor atoms concentration. The equations above show that the minority carriers number decrease with the increase of the doping level. As an example, in the n-type material, some of the extra electrons which are added by doping the material will occupy the empty spots (the holes) which are in the valence band, thus lowering the number of holes.