Acceptor level definition
You've arrived at the seeming contradiction because you think in the direction opposite to what is productive from the pragmatic point of view, I mean, what you are doing when computing the eigenstate shift caused by a lattice imperfection due to an acceptor atom. Think the other way round: rather than a &quot;stolen&quot; electron, you have a positive hole localised &quot;outside&quot; the boron atom and weakly held by the negative charge of the acceptor atom enriched with an excessive electron, and it is this quasi particle (hole) that is exchanged with adjacent bonds.
You can read a tolerable explanation of this mechanism in Chapter 9, page 6 of https://pages.hep.wisc.edu/~prepost/623/transistor/pnlecturenotes.pdf with a hole mass and the silicon permittivity participating in the binding energy formula. The &quot;Hydrogen atom model analogy&quot; is acceptable because a potential well that gives the binding energy of 0.1eV is really shallow. I admit the last statement smells a logical fallacy of begging the question; the strict proof is left to OP.
UPDATE in response to comments:
Let us apply your consideration of covalent bond formation with participation of the acceptor atom to computation of wavefunctions and energy levels. Suppose, in computation we decided to directly address the &quot;stolen&quot; electron, participating in covalent bonds. But the acceptor atom is surrounded by multiple silicon atoms, so which one donates the electron? Even with a classical physics consideration, we have at least four nearest candidates. You consider one &quot;frustrated silicon atom which has 3 covalent bonds&quot;, but there are a good few &quot;frustrated silicon atoms&quot; that share their loss, totaling one electron minus, within their group. Notice that any silicon atom, participating in the formation of covalent bonds with the acceptor atom, still forms all four covalent bonds, despite one electron missing. More precisely, there are no individual &quot;frustrated&quot; silicon atoms, but all four covalent bonds, formed with the acceptor atom, are &quot;frustrated&quot;, because the acceptor atom has only three valence electrons, and the &quot;collective&quot; wavefunction of these four covalent bonds is deficient of one electron.
Therefore, you cannot trace just one individual electron when solving the problem of the acceptor atom in the silicon lattice. There are many electrons with essentially overlapping individual wavefunctions. This category of physical problems is called &quot;many body problems&quot;, the &quot;collective&quot; wavefunction being a many body wavefunction. These problems are hard to solve brute-force.
Fortunately, the problem of lattice imperfections is amenable to solution with a Schroedinger equation for individual particles, where the collective motion of participating covalent electrons is modeled as an equation of motion for a quasi particle. Strictly speaking, the contribution of a mobile carrier donated by the donor atom is also computed as a quasi particle called &quot;electron quasiparticle&quot;, with an effective mass different from the electron mass, slightly for Si and not-so-slightly for the other semiconductors. The mobile carrier donated by the acceptor atom is called a hole.
One more reference with excellent visuals: http://ee.sc.edu/personal/faculty/simin/ELCT566/03%20Semiconductors%20II-Doped,%20transport.pdf .
As an exercise, re-draw the slide &quot;Concentration-temperature dependence in doped semiconductors&quot; (page 6) to illustrate the case of p-Si.