Drift current
Drift current is the component of electric current in semiconductors arising from the directed motion of charge carriers, such as electrons and holes, under the influence of an applied electric field, distinct from diffusion current which stems from concentration gradients.[1] This phenomenon is fundamental to charge transport in semiconductor devices, where the drift velocity of carriers is proportional to the electric field strength and their mobility, typically yielding current densities expressed as J_{drift} = q (n \mu_n + p \mu_p) E, with q as the elementary charge, n and p as electron and hole concentrations, \mu_n and \mu_p as their respective mobilities, and E as the electric field.[2] In semiconductors like silicon and gallium arsenide, drift current dominates in regions with strong electric fields, such as depletion layers in p-n junctions or Schottky barriers, enabling the operation of diodes, transistors, and photodetectors.[1] Carrier mobility, a key parameter, varies with material and temperature— for instance, electrons in silicon exhibit \mu_n \approx 1400 cm²/V·s at room temperature, while holes have \mu_p \approx 450 cm²/V·s— and is limited by scattering mechanisms including phonons and impurities.[2] At high fields exceeding approximately 10⁴ V/cm, drift velocity saturates around 10⁷ cm/s in silicon due to optical phonon scattering, impacting device speed and efficiency in applications like MOSFETs and microwave diodes.[2] The interplay between drift and diffusion currents governs overall carrier transport, with equilibrium occurring when they balance, as in the built-in field of a p-n junction.[1] In optoelectronic devices, such as photodetectors, drift current facilitates rapid carrier collection under reverse bias, contributing to photocurrents proportional to generation rates and field strength, while in high-speed transistors, velocity saturation effects must be accounted for to model performance accurately.[2] Understanding drift current is essential for designing efficient semiconductor technologies, from integrated circuits to solar cells.Fundamentals
Definition and Basic Principles
Drift current refers to the electric current arising from the directed movement of charge carriers—such as electrons or holes—within a material under the influence of an applied electric field, distinguishing it from the random, thermally driven motion of these carriers.[3] In solid-state materials like conductors and semiconductors, free charge carriers respond to the electric field by acquiring a net directional velocity, resulting in a flow of charge that constitutes the current.[4] This phenomenon forms a foundational aspect of charge transport in solids, where carriers exist as mobile electrons in the conduction band of semiconductors or as conduction electrons in metals. The basic principles of drift current stem from the interaction between the electric field and charged particles, imparting a force that biases their otherwise isotropic thermal motion toward a preferred direction. In semiconductors, this leads to a net charge displacement, enabling the material to conduct electricity when doped to increase carrier concentration. The concept gained prominence in the mid-20th century, particularly after the 1947 invention of the point-contact transistor by John Bardeen and Walter Brattain at Bell Laboratories, which relied on understanding carrier drift for device operation, followed by William Shockley's theoretical advancements in 1945 on field-effect amplification.[5] The 1949 Haynes-Shockley experiment further validated these ideas by directly measuring carrier drift mobility in germanium, marking a key milestone in semiconductor physics.[6] Charge carriers in solids include electrons, which are negatively charged and drift opposite to the electric field direction, and holes—effective positive charges arising from missing electrons in the valence band—which drift in the same direction as the field. Mobility, a material-specific parameter, quantifies the ease with which these carriers move under the field, influencing the magnitude of the drift current; higher mobility indicates less resistance to directed motion due to scattering by lattice vibrations or impurities.[1] In intrinsic semiconductors, both electrons and holes contribute equally to drift, while in extrinsic types, the majority carrier dominates. This carrier transport contrasts with diffusion current, which occurs due to concentration gradients rather than fields.[3]Physical Mechanism
In semiconductors, charge carriers such as electrons and holes experience a force due to an applied electric field, given by \mathbf{F} = [q](/page/Q) \mathbf{E}, where [q](/page/Q) is the carrier charge and \mathbf{E} is the field; this force accelerates the carriers in the direction opposite to the field for electrons and along the field for holes, superimposing a directed motion on their random thermal velocities.[7][8] However, this acceleration is frequently interrupted by scattering events, where carriers collide with lattice vibrations (phonons), impurity atoms, or other defects, randomizing their momentum and preventing unbounded speed increase. These collisions balance the field's accelerating effect, leading to a steady-state average motion known as drift, where the net carrier displacement occurs despite the absence of a continuous straight-line path.[7][8] The paths of carriers under an electric field are characteristically zigzag: between collisions, a carrier accelerates linearly along the field direction, gaining momentum proportional to the field strength and the time elapsed since the last scattering; upon collision, its velocity is altered randomly, often losing the directed component while retaining thermal energy.[7] The mean free time \tau, defined as the average interval between such collisions, governs this steady-state motion by determining how long carriers can accelerate before scattering resets their trajectory; longer \tau allows greater average directed velocity, while frequent scattering diminishes the net drift.[7][8] Scattering mechanisms vary: phonon interactions dominate in pure crystals at room temperature, while impurities become significant in doped materials, collectively setting the relaxation time \tau that underlies the observed drift. Temperature influences this mechanism primarily through its effect on scattering rates, as higher thermal energy intensifies lattice vibrations, increasing phonon density and thus shortening \tau, which reduces the efficiency of drift for a given field in both semiconductors and metals.[7] In semiconductors, this temperature-induced rise in scattering competes with the exponential increase in intrinsic carrier concentration, but the core drift process—field-driven acceleration moderated by collisions—remains more sensitive to phonon effects than in metals, where carrier density is largely temperature-independent and metallic bonding leads to similar but often stronger lattice scattering. In intrinsic semiconductors, where electron and hole concentrations are equal, both carrier types undergo this same drift mechanism under bias, contributing to the total current with their respective responses to the field.[7] This average directed motion manifests as the drift velocity, a key outcome detailed mathematically elsewhere.[8]Mathematical Formulation
Drift Velocity
The drift velocity v_d represents the average velocity acquired by charge carriers in a material when subjected to an electric field, superimposed on their random thermal motion.[1] This net directed motion arises because the electric field imparts a consistent force on the carriers, leading to a small but measurable average drift despite frequent collisions that randomize their velocities.[9] The derivation of the drift velocity begins with Newton's second law applied to a charge carrier. For a carrier with charge [q](/page/Q), effective mass [m](/page/M), and velocity v, the net force under an electric field \mathbf{E} includes the driving force q\mathbf{E} and a frictional drag force -\frac{m\mathbf{v}}{\tau}, where [\tau](/page/Tau) is the relaxation time (average time between collisions). This yields the equation of motion: m \frac{d\mathbf{v}}{dt} = q\mathbf{E} - \frac{m\mathbf{v}}{\tau}. In steady state, the acceleration \frac{d\mathbf{v}}{dt} = 0, so the equation simplifies to q\mathbf{E} = \frac{m\mathbf{v}_d}{\tau}, where \mathbf{v}_d is the steady-state drift velocity. Solving for \mathbf{v}_d gives: \mathbf{v}_d = \frac{q\tau}{m} \mathbf{E}. This linear relationship holds at low electric fields, where the drift velocity is much smaller than the thermal velocity.[10][1] For electrons, with charge q = -e (where e > 0 is the elementary charge), the drift velocity is \mathbf{v}_{d,n} = -\frac{e\tau_n}{m_n^*} \mathbf{E}, directed opposite to the electric field. For holes, with effective positive charge q = +e, it is \mathbf{v}_{d,p} = +\frac{e\tau_p}{m_p^*} \mathbf{E}, aligned with the field. The relaxation times \tau_n and \tau_p differ due to distinct scattering mechanisms for electrons and holes.[9] The proportionality constant in the drift velocity expression is the carrier mobility \mu, defined as \mu = \frac{|q|\tau}{m^*}, so \mathbf{v}_d = \mu \mathbf{E} (with direction depending on carrier type). Mobility quantifies how easily carriers move under a field and is influenced by factors such as lattice scattering (via phonons), impurity scattering, and temperature; higher \tau or lower m^* increases \mu. In silicon at room temperature (300 K), electron mobility \mu_n is approximately 1400 cm²/V·s, significantly higher than hole mobility \mu_p at about 470 cm²/V·s, reflecting electrons' lower effective mass and reduced scattering.[1][9][10]Drift Current Density
The drift current density represents the macroscopic flow of charge carriers in a material driven by an applied electric field, extending the microscopic concept of drift velocity to bulk transport. The drift velocity describes the average directed motion of carriers, with electrons moving opposite to the field and holes in the same direction, leading to a net current when considering carrier concentrations. For electrons, the drift current density is derived as \vec{J_n} = (-q) n \vec{v_{dn}}, where q is the elementary charge, n is the electron concentration, and \vec{v_{dn}} = -\mu_n \vec{E} is the electron drift velocity, with \mu_n the electron mobility and \vec{E} the electric field; the negative sign in the charge reflects the electron charge, yielding \vec{J_n} = q n \mu_n \vec{E}. Similarly, for holes, \vec{J_p} = q p \vec{v_{dp}} = q p \mu_p \vec{E}, where p is the hole concentration and \mu_p the hole mobility. The total drift current density is the vector sum \vec{J_{\text{drift}}} = \vec{J_n} + \vec{J_p} = q (n \mu_n + p \mu_p) \vec{E}.[8] This formulation links directly to electrical conductivity, defined as \sigma = q (n \mu_n + p \mu_p), such that \vec{J_{\text{drift}}} = \sigma \vec{E}, establishing the connection to Ohm's law in materials where drift dominates transport.[8][11] In metals, high electron concentrations (n \approx 10^{22} \, \mathrm{cm^{-3}}) compensate for lower mobilities (\mu_n \approx 10{-}50 \, \mathrm{cm^2/V \cdot s}), resulting in conductivities on the order of $10^5{-}10^7 \, \mathrm{S/cm}; for example, in copper, \sigma \approx 5.96 \times 10^5 \, \mathrm{S/cm} arises primarily from electron drift despite modest \mu_n. In contrast, semiconductors exhibit tunable conductivity through doping, with carrier concentrations adjusted to $10^{15}{-}10^{18} \, \mathrm{cm^{-3}} and higher mobilities (\mu_n \approx 1000{-}1500 \, \mathrm{cm^2/V \cdot s}, \mu_p \approx 400{-}500 \, \mathrm{cm^2/V \cdot s}) in materials like silicon, enabling \sigma values from $10^{-6} \, \mathrm{S/cm} (intrinsic) to over $10^2 \, \mathrm{S/cm} (heavily doped).[12] This drift current density equation was pivotal in William Shockley's 1950s semiconductor models, particularly in his book Electrons and Holes in Semiconductors, which integrated it into analyses of carrier transport and early transistor designs.Comparison with Other Currents
Drift versus Diffusion Current
In semiconductors, charge carrier transport is governed by two distinct mechanisms: drift current, which arises from the motion of charged particles under an applied electric field, and diffusion current, which results from the random thermal motion of carriers tending to equalize concentration gradients. Drift current is directly proportional to the electric field strength and carrier density, leading to a linear current-voltage characteristic in uniformly doped materials, consistent with Ohm's law.[13] In contrast, diffusion current depends on the spatial gradient of carrier concentration, driving net flow from regions of higher to lower density, and exhibits non-linear behavior due to its equilibrium-driven nature. Qualitatively, drift current aligns carrier motion with the electric field direction—electrons opposite to the field and holes along it—while diffusion current flows independently of the field, solely dictated by concentration differences, and can oppose or reinforce drift depending on the setup.[14] Drift typically dominates in biased, uniform doping scenarios where the electric field is significant, such as in bulk conduction regions, whereas diffusion prevails in non-uniform doping or high-injection conditions, like near contacts or interfaces.[15] Material dependencies further differentiate them: drift is influenced by carrier mobility, which varies with scattering mechanisms and temperature, while diffusion relates to the diffusion coefficient via the Einstein relation, tying it closely to thermal properties. The following table summarizes key distinctions:| Aspect | Drift Current | Diffusion Current |
|---|---|---|
| Driving Force | Electric field (E) | Concentration gradient (∇n or ∇p) |
| Direction | Along E for holes, opposite for electrons | From high to low concentration |
| Material Dependency | Mobility (μ), carrier density (n or p) | Diffusion coefficient (D), gradient |
| Typical Dominance | High bias, uniform doping | Injection, non-uniform doping |