How can electrons travel from the valence band into the conduction band?

I'm currently studying Introductory Semiconductor Device Physics by Parker.

In band-theory, we know that if an electron is at the top of an energy band, then there are no allowed states immediately above it, since the forbidden band lies immediately above the top of an allowed band. See the following figure (from the same textbook) for illustration: Given this, in the above figure, how can electrons travel from the valence band into the conduction band? It seems to me that it would have to somehow traverse the forbidden band, no?

I would greatly appreciate it if people could please take the time to clarify this.

• Those bands aren't places between which an electron can "travel." Those bands define sets of discrete energy levels that an electron can (or can not) occupy. An electron "jumps" from one energy level to another by absorbing or emitting a discrete amount of energy. – Solomon Slow Apr 2 at 13:54
• @SolomonSlow Yes, I am describing all of this in the quantum mechanical sense, not in the macroscopic sense. The author says that, if an electron is at the top of an energy band, then there are no allowed states immediately above it, since the forbidden band lies immediately above the top of an allowed band. Given this, and given that the valence band and the conduction band have a forbidden band between them, then by the logic of the author's statement, how can electrons go from the valence band to the conduction band? [...] – The Pointer Apr 2 at 14:06
• [...] I'm asking because, it seems to me that if we use the logic of the author's first statement, then electrons cannot go from the valence band to the conduction band, since there is a forbidden band between them? This is what I'm seeking clarification on. – The Pointer Apr 2 at 14:07
• Consider the hydrogen atom with discrete energy levels - how does an electron ‘travel’ from one to another? – Jon Custer Apr 2 at 14:43

The idea that the electron travels on the energy axis is a misconception. Every state in the valence band $$\phi_{VB}$$ corresponds to a wave function and thus a probability distribution in space. The same is true for the conduction band states $$\phi_{CB}$$.
You can imagine the excitation of an electron as an change from $$\phi_{VB}$$ to $$\phi_{CB}$$. But also here there is an instant change of the wavefunction and thus the probability of finding the electron at a given position in the crystal.