How do holes and electrons have different mobility?

[nandu]

carrier mobility

How do holes and electrons have different mobilty. it cant be because holes are heavier than electrons or anything like that, since holes are only vacant spots and are imaginary charges, and logically they move as fast as electrons but the other way.

 

[SkyHigh]

Re: carrier mobility

Holes and Electrons have different mobilities due to:

1. The material and state of matter in specific.
2. The band, shell or energy level the carriers are concerned.
3. The field effect at which these carriers are subjected to pull and push.

In Silicon, the average mobility of electrons have 2.71 times faster than holes, sometimes approximated to 2.5 or even 3.0 for simplicity. The reasons, as highlighted above, are:

a. Electrons travel in the conduction band of any solid-state matter, conductor, insulator or semiconductor. Since Silicon is a semiconductor, electrons travel in the conduction band. In any solid-state matter, conduction band is the overlapped shells, formed by the outermost shells farthest from the nucleus of any atom, thus having higher energy level than innermost shells. Therefore due to inter-atomic forces, electrons are highly mobile.

b. Holes are not doubt the vacant charge, or opposite (positive) charge when electrons moved. However this is a crude concept. Holes are in fact created because of the elevation of electrons from innermost shells to higher shells or shells with higher energy levels. Since holes are locked or subjected to the stronger atomic force pulled by the nucleus than the electrons residing in the higher shells or farther shells, holes have a lower mobility.

c. Electric field asserted to the material accelerates the velocity of the electrons, not holes. In long-channel MOS transistor, it is theoretically correct to assume constant mobility of electrons to be 2.71 faster than holes. But not in short-channel MOS transistor since the electric field is so strong that engulfs the effective channel length, the constant mobility does not hold anymore, mobility increases with distance closer to the field source. Conversely, hole mobility decreases.

You can read more about semiconductor physics on topics such as carrier transport, mobility, energy levels and solid-state matter from books written by S. M. Sze, Michael Shur, Tyagi, Benjamin Streetmen, Kasap, Neaman etc.


PhD MSc DIC BEng (Hon) Imperial College
Analog Devices Inc (Ireland)

Added after 1 minutes:

BTW, holes are not imaginary charges. Holes are real charges.

 

[Karthikeya]

Re: carrier mobility

SkyHigh
the information given by you is a known fact and given in books...but the last sentence was something that i hadnt heard of. no one has seen an electron but is considered to be real ...is it in the same sense that u say holes are real?

regards

 

[SkyHigh]

Re: carrier mobility

LoL~ I haven't seen myself too.

Physicists working in the areas of nuclear physics, quantum physics, atomic physics and plasma physics are very likely to have seen it. "Seen" it as in electron is plotted and characterized as a constant energy. This energy is constant in all elements known to us today.

I know some guys working with quantum computing at Rutherford Appleton and Cavendish. They manipulate electrons to perform some quantum logic gates by subjecting it to controlled E-fields in a novel substrate that has holes and electrons in there. It is interesting! They can probably tell you the same thing they had told me before. Electrons close to the nucleus have the same mobility as holes and the only way to to differentiates them is more than just understanding polarity and mass. However Pauli Exclusion Principle doesn't hold well when electrons are highly mobile at outermost shell, differentiation between electrons and holes become more apparent using mass and polarity principles and techniques to plot their energies, masses and polarities.

Electron, no doubt it is scientifically proven as an energy, it exists because it has mass and polarity, it is a charged particle. Since it is the smallest thing known to us, there is no optical instrument that can help us see it. Even the world's strongest magnifying instrument is nothing more than an Scanning Electron Microscope which in fact uses electron to probe and plot the energy of materials under probe.

At the moment, we can only "see" electron as a plotted energy. That's the best we can unless someone can discover something smaller than electron and manipulate it to probe electron.

Added after 5 minutes:

Holes on the other hand is a plotted energy, found to be the same mass as electron, but demonstrates opposite charge and also having lower energy level than electron. Why lower energy? Well... Hole demotes to lower energy level so that electron can promote to higher energy level. This explains why hole is less mobile. Since electrons and holes can be plotted for polarity, mass and energy, they are real.

 

[A.Anand Srinivasan]

Re: carrier mobility

if you read the basics of electronics you would be able to realise that holes move in valence band and electrons in conduction band and the movement of hole requires an electron to change position in the valence band

 

[nonlinear]

carrier mobility

Hi!
Movement of hole requires movement of electron. However, movement of electron does not always cause motion of hole. Definitely, over a finite interval of time, total distance travelled by hole would be less than that of the electron. Hence we can conclude that velocity of electron is greater than that of the hole in the prsence of the same electric field. Clearly, electrons are lighter than the holes.