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Class 12 physics says hole mobility is lower than electron mobility, often without saying why. The reason: a hole is not a particle travelling on its own. It moves only when electrons still held in bonds hop, one at a time, into a gap. That relay is slower than a free electron drifting through the crystal.
What is a hole in a semiconductor?
In a silicon crystal, each atom shares its four outer electrons with neighbours in covalent bonds. When heat frees one electron, its bond is left one electron short. That vacancy is the hole, and it acts like a positive charge.
The hole moves when an electron from a neighbouring bond fills it, leaving a new vacancy behind, as this University of Liverpool physics explainer on hole flow describes. Repeat the hop and the vacancy travels along the field while the hopping electrons shift the other way. For why a missing electron counts as positive, see our post on why a hole counts as a positive charge carrier.
Why do holes have lower mobility than electrons?
Mobility (μ) is the drift speed a carrier gains per unit electric field, so drift velocity v = μE; our post on the mobility of electrons formula derives it.
In pure silicon, electron mobility is at most 1400 cm²/V·s and hole mobility at most 450 cm²/V·s, according to the Ioffe Institute's silicon data page.
In pure germanium, the same database gives at most 3900 cm²/V·s for electrons and 1900 cm²/V·s for holes (Ioffe Institute, germanium).
The school-level picture explains the gap. A conduction electron has left its bond and drifts on its own until something scatters it. A hole cannot move by itself: each step needs a bound electron, still held by its atoms, to leave one bond and enter the next. The field moves that relay along less easily than it moves a free electron.
What is the deeper reason, beyond the relay picture?
Band theory puts this in numbers: carriers in a crystal respond to a field as if they had an effective mass. The Ioffe Institute's silicon band structure page lists electron masses of 0.98 m₀ along one axis and 0.19 m₀ across it, heavy holes at 0.49 m₀ and light holes at 0.16 m₀. Averaging the electron values over the three directions, 3 / (1/0.98 + 2/0.19), gives about 0.26 m₀, roughly half the heavy-hole mass.
How often carriers scatter matters too. A 2020 theory study by Q.L. Yang and colleagues, posted on arXiv, calls silicon's room-temperature hole mobility abnormally low: the authors use 505 cm²/V·s, about four times lower than in germanium and diamond. They trace it to weak spin-orbit coupling, which leads to strong scattering between valence bands, and to optical phonons taking a large part in scattering holes. The relay picture is a good first answer; the full story adds band shape and scattering.
Worked example: how far does each carrier drift?
Use the silicon values from the Ioffe Institute and a modest field of E = 1000 V/cm.
Electron drift velocity: v = μE = 1400 × 1000 = 1.4 × 10⁶ cm/s, which is 1.4 × 10⁴ m/s.
Hole drift velocity: v = 450 × 1000 = 4.5 × 10⁵ cm/s, which is 4.5 × 10³ m/s.
In 1 nanosecond, the electron drifts 14 μm and the hole drifts 4.5 μm, about a third as far.
In pure silicon, electrons and holes are equal in number, so in σ = e(nμₑ + pμₕ) electrons carry 1400 / (1400 + 450), about 76%, of the current.
Step 4 uses the formula from our post on semiconductor conductivity. Treat v = μE as a low-field rule.
If numericals like this go wrong at the units, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
How should you write this in a board or JEE answer?
For a short-answer question:
Electrons in the conduction band are free and drift directly under the field.
A hole moves only when a bound valence electron jumps from a neighbouring bond into it, so hole motion is a relay of bound electrons.
This relay is slower, so hole mobility is lower than electron mobility.
Common slips to check for:
Calling a hole a heavier particle. Its effective mass is a property of the band.
Saying holes drift against the field. Holes drift along E; the bound electrons hop the other way.
Using one mobility for both carriers in σ = e(nμₑ + pμₕ).
To see how holes, energy bands and doping connect, the Fermi Concept Library gives every concept in physics its own lesson and its place in the map.
