E3 Doping: Donors and Acceptors

Topic

A donor impurity introduced into the crystal lattice of this semiconductor material donates an electron to the material's conduction band—a process governed by an ionization energy described by a hydrogen-like model. The additional electron contributed by the donor impurity is bound to it much more weakly than an ordinary valence electron; according to that same hydrogen-like model, the additional electron orbits the donor impurity just as it would a hydrogen nucleus—albeit within the semiconductor material rather than in a vacuum—meaning the ionization energy required to release it into the conduction band is far lower than the material's full bandgap. Because the donor impurity's ionization energy is lower, a larger fraction of these donor impurities will donate their additional electrons to the conduction band at any given temperature.

The concentration of ionized donor impurities—along with the concentration of any ionized acceptor impurities present in the lattice—must satisfy the condition of overall charge neutrality for the semiconductor material, in conjunction with the concentrations of free electrons and holes. Each ionized donor impurity leaves behind a fixed positive charge in the lattice after donating its additional electron, whereas each ionized acceptor impurity leaves a fixed negative charge; consequently, the sum of these fixed charges and the charges of the free electrons and holes must exactly cancel out. A higher concentration of ionized donor impurities in the lattice results, in turn, in a higher concentration of free electrons in the semiconductor material in order to maintain this charge neutrality. Consequently, this model—characterized by the donor impurity and charge neutrality present at its inception—demonstrates that such doping shifts the free-electron concentration of the semiconductor material well above the intrinsic concentration established by another model in this set; notably, achieving this shift does not require intense thermal excitation across the full bandgap. While intrinsic charge-carrier concentration necessitates exciting electrons directly from the valence band to the conduction band across the entire bandgap, this doping achieves the same shift in free-electron concentration using the significantly lower ionization energy of the donor impurity. A higher concentration of donor impurities within the crystal lattice drives the free-electron concentration—already shifted well above the intrinsic level—even further away from that intrinsic value; furthermore, it ensures that the semiconductor's Fermi level (described in greater detail by a separate model in this set) is determined by the concentration of these donor impurities.

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