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In electronics, the fact that mobility of electrons is higher than the mobility of holes is frequently used. How can we explain this using effective mass of electrons and holes ?

Arinjoy Pramanik
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  • I think this is a very good electrical engineering question, but the answer might be very short, out very long, depending on how you are taught sold state electronics at university! I'm a bit hesitant to just write "since effective hole mass is just the negative effective mass of an absentee electron, and since these are usually described at the extremes of the valence band in typical III-V semiconductors, it follows that the average hole has larger inertia than the average electron in that band; approximating the scattering time to be the same, that would indicate that holes are less mobile", – Marcus Müller Mar 16 '23 at 06:55
  • but as RoyC has written that's a bit backwards, as we need the scattering time to relate inertia to mobility, and that is just another magic constant with a priori no better explanation than "well it makes the formula work". I do agree, hence, that looking at effective mass to infer mobility is probably not taking you far. But: I have no idea which way you learn things at your institution! Your courses might build from a Drude model upwards, and scattering time might be very intuitive to you, and my explanation very confusing. – Marcus Müller Mar 16 '23 at 06:59

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Effective mass is not a good way of thinking about this.

Conduction in both N and P type semiconductors occurs due to the movement of electrons. Holes do not exist as an entity they are the absence of an electron in one of the bonds in the silicon crystal.

In a N type semiconductor the electrons move as free electrons in the conduction band with little impedance to their movement.

In a P type semiconductor the electrons move from bond to bond within the crystal matrix, it takes more energy to achieve that than to move a free electron.

At a simplistic level I think of this as throwing a ball through open air as compared to trying to throw a ball through light twigs.

RoyC
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  • Holes do not exist is a bit strong. At the level required to fully describe what's going on, ie quantum mechanics, holes are every bit a fully paid-up member of the particle zoo as electrons. Electrons jumping from bond to bond might sound like an intuitive stretch of the Drude model, but it's not adequate to describe effective mass and mobility quantitatively, it's not a good 'Lie to Children'. The best would be to say that those figures need to be plugged into the model to make it work, and if you want the reality, then learn QM. – Neil_UK Mar 16 '23 at 08:33
  • Considering only n type semiconductors only, still the mobility of electrons is greater than holes. Even in transistors I am told npn is used over pnp just due to the fact that mobility of electrons is greater than 2 times the mobility of holes. – Arinjoy Pramanik Mar 16 '23 at 15:08
  • @Neil_UK I am an engineer not a physicist. I have a mental model which explains the disparity in mobility. For my purposes this gives a ratio of about 3:1. This will lead me to make an engineering decision to use N channel devices where I can. If you wish to discuss QM take it to Physics SE. Your assumption that I need to learn QM is erroneous. – RoyC Mar 16 '23 at 17:28