Why a free electrons the majority carriers in n-type semiconductors

[petert]

Hello,

This is more of a physics question, so I am not sure which category fits best.

I understand that n-type semiconductors have more free electrons than holes, but I don't get why from the way they are constructed by doping.

To explain, let me quote from https://www.halbleiter.org/en/fundamentals/doping/:

The dopants are positively charged by the loss of negative charge carriers and are built into the lattice, only the negative electrons can move. Doped semimetals whose conductivity is based on free (negative) electrons are n-type or n-doped. Due to the higher number of free electrons those are also named as majority charge carriers, while free mobile holes are named as the minority charge carriers.

So on one hand the dopants, for example phosphorus, will provide the free electrons. Yet this will also make the dopant/donor positive. How can you have more free electrons than holes (which appear in the dopant)? I don't see how this would not balance out to be of neutral charge overall.

[rfeecs]

So on one hand the dopants, for example phosphorus, will provide the free electrons. Yet this will also make the dopant/donor positive. How can you have more free electrons than holes (which appear in the dopant)?

The phosphorous atoms provide the free electrons.  The ionized phosphorous atoms are positively charged, but they are fixed charges.  They are not holes.

As you say, overall the N-type material is neutral.  With each phosphorous atom you add a (mobile) free electron and a (fixed) positive charge.

[kosine]

Semiconductors - however doped - are electrically neutral. For every proton, there's an electron. So no net charge. Period. (If there was any residual charge they'd attract each other like magnets, pick up fluff, be used as batteries etc.)

What the doping does is create dangling atomic bonds. In pure silicon, each atom forms 4 bonds, but when doped it can't quite do that because some atoms will want to make 3 or 5 bonds instead. When there's an excess of 5-bond atoms it's N type. These dangling electrons are still attracted to their parent atom, but because they're not forming a complete bond with the surrounding silicon (or germanium) they are relatively easy to dislodge. They then become a mobile charge carriers which give rise to a current.

Their parent atoms are now positively charged ions and will try to grab a electrons from somewhere nearby. The application of a voltage therefore causes a leap-frog of electrons through the crystal, and that's roughly how it works. Swap the electrons for holes for P type.