Silicon has some special chemical properties, especially in its crystalline form. An atom  of silicon has 14 electrons, arranged in three different shells. The  first two shells -- which hold two and eight electrons respectively --  are completely full. The outer shell, however, is only half full with  just four electrons. A silicon atom will always look for ways to fill up  its last shell, and to do this, it will share electrons with four  nearby atoms. It's like each atom holds hands with its neighbors, except  that in this case, each atom has four hands joined to four neighbors.  That's what forms the crystalline structure, and that structure turns out to be important to this type of PV cell.
The only problem is that pure crystalline silicon is a poor  conductor of electricity because none of its electrons are free to move  about, unlike the electrons in more optimum conductors like copper. To  address this issue, the silicon in a solar cell has impurities  -- other atoms purposefully mixed in with the silicon atoms -- which  changes the way things work a bit. We usually think of impurities as  something undesirable, but in this case, our cell wouldn't work without  them. Consider silicon with an atom of phosphorous here and there, maybe  one for every million silicon atoms. Phosphorous has five electrons in  its outer shell, not four. It still bonds with its silicon neighbor  atoms, but in a sense, the phosphorous has one electron that doesn't  have anyone to hold hands with. It doesn't form part of a bond, but  there is a positive proton in the phosphorous nucleus holding it in  place.
When energy  is added to pure silicon, in the form of heat for example, it can cause  a few electrons to break free of their bonds and leave their atoms. A  hole is left behind in each case. These electrons, called free carriers,  then wander randomly around the crystalline lattice looking for another  hole to fall into and carrying an electrical current. However, there  are so few of them in pure silicon, that they aren't very useful.
But our impure silicon with phosphorous atoms mixed in is a  different story. It takes a lot less energy to knock loose one of our  "extra" phosphorous electrons because they aren't tied up in a bond with  any neighboring atoms. As a result, most of these electrons do break  free, and we have a lot more free carriers than we would have in pure  silicon. The process of adding impurities on purpose is called doping, and when doped with phosphorous, the resulting silicon is called N-type  ("n" for negative) because of the prevalence of free electrons. N-type  doped silicon is a much better conductor than pure silicon.
The other part of a typical solar cell is doped with the element  boron, which has only three electrons in its outer shell instead of  four, to become P-type silicon. Instead of having free electrons, P-type ("p" for positive) has free openings and carries the opposite (positive) charge.

 
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