Drift Current

Drift current is one of the two fundamental mechanisms by which charge carriers move inside a semiconductor. It arises whenever an electric field is applied across the material, causing electrons and holes to accelerate in opposite directions. Understanding drift current is essential for analyzing resistors, diodes, and transistors in both DC and AC operating conditions.

Core Concept Explanation

The following diagram illustrates how electrons and holes move in opposite directions when an electric field is applied to a semiconductor material.

When an electric field E is applied to a semiconductor, free carriers experience a force. Holes, being positive, accelerate in the direction of E. Electrons, being negative, accelerate opposite to E. Despite moving in opposite directions, both carriers contribute to current in the same direction because of their opposite charges.

The average velocity acquired by carriers under the field is called drift velocity, denoted vd. It is proportional to E for moderate field values. The proportionality constant is called mobility (mu), measured in cm2/V·s. For electrons, vdn = mun × E. For holes, vdp = mup × E.

Mobility is a material property that reflects how easily a carrier moves through the lattice. In silicon at room temperature, electron mobility (~1350 cm2/V·s) is significantly higher than hole mobility (~480 cm2/V·s). This asymmetry has direct consequences in MOSFET design where NMOS devices are inherently faster than PMOS.

Mathematical Expression

The total drift current density J_drift is the sum of electron and hole contributions. Each component is the product of carrier charge, carrier concentration, and drift velocity. Since drift velocity equals mobility times electric field, the expression simplifies to a conductivity-based form.

The complete expression is: J_drift = q(n·mun + p·mup)·E. The term inside the bracket has units of conductivity (sigma), so J = sigma × E, which is simply Ohm's law in differential form. This confirms that drift current obeys ohmic behavior at low to moderate field strengths.

Resistivity rho = 1/sigma = 1/(q·(n·mun + p·mup)). For an n-type semiconductor with n >> p, this simplifies to rho = 1/(q·n·mun). This formula is frequently tested in GATE problems involving doped semiconductor resistance calculations.

Practical Understanding

At low electric fields, drift velocity increases linearly with E and the ohmic relationship holds. However, at very high fields (above ~10^4 V/cm in silicon), the carrier velocity saturates due to increased phonon scattering. This is known as velocity saturation and it limits the speed of short-channel MOSFETs.

Temperature also affects drift current. As temperature rises, lattice vibrations (phonon scattering) increase, reducing carrier mobility. For bulk semiconductors, mobility decreases roughly as T^(-3/2) for lattice scattering. This means resistivity increases with temperature for metals, a behavior also seen in doped semiconductors where impurity scattering is secondary.

Given:
Silicon n-type sample: n = 5 x 10^16 cm^-3, p negligible
mun = 1350 cm^2/V·s, q = 1.6 x 10^-19 C
Applied Electric Field E = 100 V/cm

Why this formula applies:
Dominant carrier is electron; drift current density = q·n·mun·E

Formula:
J_drift = q · n · mun · E

Substitution:
J_drift = (1.6 x 10^-19) x (5 x 10^16) x (1350) x (100)

Calculation:
= 1.6 x 10^-19 x 5 x 10^16 x 1.35 x 10^5
= 1.6 x 5 x 1.35 x 10^(-19+16+5)
= 10.8 x 10^2
= 1080 A/cm^2

Final Answer: J_drift = 1080 A/cm^2

Exam Tip: In GATE problems, when only one carrier type dominates (n-type or p-type), always drop the minority carrier term from J_drift. Also remember: sigma = q·n·mun for n-type and sigma = q·p·mup for p-type. Resistivity is the reciprocal of conductivity, not mobility.

Quick Revision

• Drift current is caused by an applied electric field; carriers move to minimize potential energy.
• Drift velocity: vd = mu × E. Mobility mu has units cm^2/V·s.
• Total drift current density: J = q(n·mun + p·mup)·E = sigma·E (Ohm's law form).
• Electron mobility in Si (~1350) is about 2.8x higher than hole mobility (~480).
• At high fields, velocity saturates; ohmic behavior breaks down.
• Mobility decreases with temperature due to increased phonon scattering.
• Exam trap: Do not confuse resistivity (1/sigma) with mobility. They have different units and physical meaning.