What is the force that causes electrons to combine with holes? In a PN Junction semiconductor, electrons combine with holes. Electrons in the N region are pretty mobile at room temperature which makes sense. However what is the force that attracts them towards "holes".
As far as I understand "holes" in a P-type semiconductor are because Boron (or any other impurity) has only 3 valence electrons and hence in the crystal formed there is always a possibility of one more electron to make it 8 valence electrons, octet formation. It is not because of an electron that has gone away due to some energy excitation and hence it is electrically neutral.

So what is the force (electromagnetic, gravitational, strong nuclear, weak nuclear) that causes a hole to capture an electron?
 A: First, holes are not neutral, they are positive quasi-particles in the semiconductor corresponding to a missing electron in a full valence band. This missing electron effectively has a positive elementary charge (stemming from the positive atom ions) corresponding to the the missing negative elementary charge of the electron at that location. Electrons and holes exert Coulombic forces on each other and can bind to excitons (similar to a hydrogen atom) in the semiconductor. For the recombination of a hole with an electron, however, such a force is not needed. Considering that the electron is has a quantum mechanical state in the semiconductor, there exists a certain transition probability that an electron recombines with a hole (depending on the concentration of holes), meaning that the electron makes a transition from a state in the conduction band to an electron state in the valence band corresponding to the hole. 
A: This idea of positive charged particles flowing in a semi conductor called "holes" took me ages to accept. Why because my thinking was trapped by early 20th century models. In many ways even today many people who are in the physical sciences still think in this way.
This is understandable as classical models are are much easier to deal with. While Quantum models are highly abstract mathematical equations.
It turns out that when electrons are bound under some potential field they do not behave as classical particles. Once an electron is "free"  it can be modelled as a negative charge with a definite mass and charge via fairly simple classical models.
But when the electron is bound under electromagnetic forces in the valance band for example, the quantum model predicts that the electron gains a weird property called negative mass. That is the electron moves in the opposite direction to the applied force.
Rather than deal with this idea directly it is simpler to consider a "particle" in the valence band as being positively charged, with its own mobility and effective mass.
It really shows just how weird Quantum Mechanics is. The thing is it works. So modern band theory thinks of Classical Electrons in the conduction band and holes in the valance band. Another weird idea is the idea of electron spin once again a Quantum Mechanical effect. The trouble is that we have to stop thinking classically to start to model how things behave at the atomic level.
The classic experiment  the Hall effect can determine if the majority of carriers are "holes" or electrons. Apparently in Iron for example holes can be detected as current carriers. 
