Drift speed of electrons and holes in semiconductors

[kihr]

I would request for help in understanding why the drift speed of electrons in semiconductors is more than that of holes. Thanks.

 

[SystemTheory]

Post up an equation or two for hole drift versus the electron drift, and someone here might explain. Otherwise I'd have to crack my semiconductors textbook which is laying about somewhere gathering dust ... as I recall the effective mass of a hole is greater than that of an electron when computing the statistical effect on charge carriers due to an imposed electric field.

 

[kihr]

Sorry I do not have the equations for electron / hole drift, or for their effective mass! Maybe someone else could help me. Thanks.

 

[marcusl]

A free electron (in the conduction band) can travel through the bulk semiconductor. It of course scatters off of atoms in the crystal lattice, resulting in the slow net motion known as drift.

It is a bit more difficult for a hole to drift, because a leapfrog action is required. An electron "upstream" of the hole must be excited to the conduction band, drift "downstream", and recombine with that hole. It leaves behind the hole from the atom where it was excited, however, so it looks like the hole has moved upstream. Now the process can repeat, and the hole continues to drift.

Because an electron must happen upon and recombine with a hole, this process happens more slowly (with lower probability) than electron drift. We say that the hole's mobility is lower than the electron's. Because the mobility is lower, a hole has a lower drift velocity in a given applied electric field than an electron.

 

[kihr]

Thanks a lot for your lucid explanation.

 

[palladium]

I have a question regarding this topic. A wire carrying a current is replaced by a semiconductor component, comment upon any change in the drift speeds of the charge carriers, given that the current is kept constant.

 

[Austin0]

A free electron (in the conduction band) can travel through the bulk semiconductor. It of course scatters off of atoms in the crystal lattice, resulting in the slow net motion known as drift.

It is a bit more difficult for a hole to drift, because a leapfrog action is required. An electron "upstream" of the hole must be excited to the conduction band, drift "downstream", and recombine with that hole. It leaves behind the hole from the atom where it was excited, however, so it looks like the hole has moved upstream. Now the process can repeat, and the hole continues to drift.

Because an electron must happen upon and recombine with a hole, this process happens more slowly (with lower probability) than electron drift. We say that the hole's mobility is lower than the electron's. Because the mobility is lower, a hole has a lower drift velocity in a given applied electric field than an electron.

Hi Marcus it sounds in your explanation like electron drift for a free electron is essentially a series of absorbtions and readmissions in which case it seems like the holes created are complementary to that flow. Maybe I am missing something but it seems like if an electron is ousted from an orbit and moves forward to an available hole the distance and time for this event is singular and both the electron and the hole(s) have in effect drifted equally.
It is probably something obvious I am not getting .

 

[SystemTheory]

An intrinsic semiconductor would have the same number of electons and holes generated thermally at room temperature.

Doping with impurities generates n-type (more electrons) or p-type (more holes) in the extrinsic semiconductor.

Electrons in the conduction band have more mobility (ability to drift) than holes in the valence band. The drift in each band depends on the number of n or p carriers and the imposed electric or magnetic field.

For example a copper wire has plenty of electrons acting as carriers in the conduction band with high mobility. No pair generation is necessary to conduct current via electron drift.

A heavily doped n-type material has many electrons acting as carriers in the conduction band with good mobility, but not as good as copper or silver wire. At room temperature it conducts mostly via electron mobility in the conduction band.

A heavily doped p-type material has many holes acting as carriers in the valence band with fair mobility, not as good as n-type material. It conducts current mostly via hole mobility in the valence band. Whether electrons must cross the band gap to help holes drift I do not know.

 

[marcusl]

Austin0, your reasoning is intuitively reasonable. Conduction in semiconductors is not so intuitive, however. The mobility depends on the ratio of relaxation or scattering time to effective mass m*. The effective mass of an electron in a semiconductor depends on the band structure of the material, on phonon interactions, on the electron momentum and on the direction of motion. On average for an electron boosted to the conduction band, m* is about 0.25 of the electron's physical mass. We won't discuss relaxation time here.

You might imagine that the hole's effective mass and relaxation time are also complicated, and differ from, an electron's. In fact, electron mobility is 2 to 4 times as large as hole mobility in intrinsic (that is, pure) silicon and germanium, at room temperature. As a result, electrons dominate conductivity in intrinsic material.

Sorry I don't have a better short answer to this question.

 

[MKp]

hi guys, please tell how come a hole's effective mass is more than that of an electron.

i understand that the net drift velocity is different . so is the relaxation time. but in nutshell ( considering the fact that ew are talking about 'holes' as absence of electrons ) we are talking about net motion of electrons in both the cases.

How does their degree of freedom differs ?

 

[kihr]

My thinking is like this:

A hole is not an independent entity, i.e.for a hole to be created we must have an electron jump from the valence band. Similarly for a hole to disappear an electron must recombine with a hole. In a n- type semiconductor, for example, an electron is free to move in the conduction band and accordingly moves with a drift velocity when under the influence of an electric field. Such motion need not necessarily be associated with motion of holes. In a p- type semiconductor the majority carriers are holes. Here also a hole is created every time an electron jumps to fill the empty position in the lattice of the trivalent atom. The successive electron "jumps" lead to the movement of holes. In this case, however, I am not quite clear as to how the reasoning would be applied to explain the higher mobility of electrons over holes. Similarly in the case of an intrinsic semiconductor the mobility of the thermally generated electrons and holes should be identical given that they are always generated in pairs. Maybe I need to dwell a bit more on the subject.