Carrier Concentration

Definition

Carrier concentration refers to the number of charge carriers (electrons and holes) in a semiconductor material, typically expressed in terms of carriers per cubic centimeter. This concept is crucial as it directly impacts the electrical properties of semiconductors, influencing conductivity, behavior under electric fields, and interactions with defects and impurities.

5 Must Know Facts For Your Next Test

1. Carrier concentration is determined by factors such as temperature, doping levels, and the presence of defects or impurities within the semiconductor.
2. In n-type semiconductors, donor atoms contribute extra electrons, increasing the electron carrier concentration, while in p-type semiconductors, acceptor atoms create holes that increase hole carrier concentration.
3. Carrier concentration plays a significant role in defining the electrical conductivity of semiconductors; higher concentrations lead to increased conductivity.
4. The relationship between carrier concentration and the Fermi level is crucial; as carrier concentration increases, the Fermi level shifts closer to the conduction band for n-type and closer to the valence band for p-type materials.
5. At thermal equilibrium, intrinsic carrier concentration can be calculated using the equation $$n_i = ext{sqrt}(N_c N_v) e^{-E_g/(2kT)}$$ where $$N_c$$ and $$N_v$$ are effective density of states in conduction and valence bands respectively, $$E_g$$ is the energy band gap, $$k$$ is Boltzmann's constant, and $$T$$ is temperature.

Review Questions

• How does carrier concentration affect the conductivity of semiconductors?
  • Carrier concentration has a direct impact on semiconductor conductivity; as the number of charge carriers increases, so does conductivity. In n-type materials, added donor impurities enhance electron concentration, while in p-type materials, acceptor impurities increase hole concentration. This relationship shows how manipulation of carrier concentration through doping can tailor the electrical properties of semiconductors for specific applications.
• Discuss the role of defects and impurities in modifying carrier concentration within a semiconductor.
  • Defects and impurities can significantly alter carrier concentration by acting as either donors or acceptors. Donor impurities introduce extra electrons into the conduction band, increasing electron concentration in n-type semiconductors. Conversely, acceptor impurities create holes in p-type semiconductors by capturing electrons from the valence band. The presence and type of defects can either enhance or reduce overall carrier concentration, affecting device performance and reliability.
• Evaluate how changes in temperature influence intrinsic carrier concentration and overall semiconductor behavior.
  • Temperature has a profound effect on intrinsic carrier concentration due to its influence on thermal excitation of electrons. As temperature increases, more electrons gain sufficient energy to jump from the valence band to the conduction band, thus increasing intrinsic carrier concentration. This elevation in carriers can lead to changes in electrical conductivity and can also shift the Fermi level. Understanding this temperature dependence is vital for predicting semiconductor behavior in varying operational conditions.

Related terms

Doping: The intentional introduction of impurities into a semiconductor to modify its electrical properties, thus increasing carrier concentration.

Intrinsic Carrier Concentration: The number of charge carriers in a pure semiconductor at thermal equilibrium, which serves as a baseline for understanding how doping affects carrier concentration.

Fermi Level: The energy level at which the probability of finding an electron is 50%; it shifts based on carrier concentration, influencing the electrical characteristics of a semiconductor.