The spin-singlet and the Pauli exclusion principle

Figure 1 illustrates this process by recalling that a certain amount of energy (of thermal origin) is required to break a covalent bond. Without loss of generality, let us refer to a Si sample of unit volume.

The single trivalent impurity that acquires an electron then becomes a negative ion as illustrated in Figure 2. Compared to the three remaining electrons, the excess electron is less deeply bound to the ion, so it occupies an energy level slightly higher than the top of the valence band. The presence of a macroscopic number of trivalent impurities generates an extremely dense spectrum centered at −εa = −εg+∆, where εg> 0 is the bandgap while 0 < ∆ ≪ εg. According to the Pauli exclusion principle, each level is occupied by at most two electrons with antiparallel spins.

A functional equation for chemical potential

Conclusion

We conclude this partial analysis, however rich in physical content, by highlighting the role played by the formation of spin-singlet states that reflect the Pauli exclusion principle. We are therefore in the presence of typically quantum effects, which escape our perception essentially based on classical mechanics.