Name: drift and diffusion in semiconductors
Uploaded: 2024-07-08T13:20:08.000Z
Duration: 1 min 21 s
Channel: JoVE

Carrier transport in semiconductors generates current, through drift and diffusion mechanisms.
Drift current arises when an external electric field causes charged particles to accelerate between collisions.
Considering the electrons, the additional velocity added to the electrons&#39; thermal motion is called the drift velocity. It can be obtained by equating the momentum lost during collisions and the momentum gained from the applied field.
The proportionality factor-mobility- characterizes electron and hole transport due to drift.
The drift current densities for both carriers can be expressed as the product of charge density, mobility, and electric field intensity. The sum of these two gives the total drift current density. Here, the term in parentheses gives conductivity.
Diffusion current results from the random thermal motion of carriers from high to low carrier density regions.
The diffusion current density equals the product of carrier flux and proportionality constant, which includes elementary charge and diffusion coefficient. Its ratio with mobility gives the Einstein relation.
If both an electric field and concentration gradient are present, both the drift and diffusion current contribute to the total current.

carrier transport

The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
<img alt="Drift velocity equation \(v_d = \mu_eE\), formula, electronic transport analysis." src="/files/ftp_upload/15155/15155_Equation_1.svg" style="text-align: center; height: 16px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
Where &#956;e is the electron mobility and E is the electric field intensity.
The current density (J) due to drift for electrons (Jn) and holes (Jp) can be expressed as:
<img alt="Currents in semiconductors, equations: Jn=qn&#956;nE, Jp=qp&#956;pE, electronic transport analysis." src="/files/ftp_upload/15155/15155_Equation_2.svg" style="text-align: center; height: 20px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
Where q is the elementary charge, n and p, are the concentrations of electrons and holes, respectively, and &#956;n and &#956;p are the mobilities of electrons and holes. The total drift current density (Jtotal) is the sum of the electron and hole current densities:
<img alt="Static equilibrium equation J_total=J_n+J_p, symbol, educational concept, physics formula." src="/files/ftp_upload/15155/15155_Equation_3.svg" style="text-align: center; height: 20px;" data-altupdatedat="1762173717000" data-alt="Equation 3" />
 The conductance (&#963;) is then the sum of the products of charge density, mobility for each type of carrier:
<img alt="Electrical conductivity formula, &#963;=q(n&#956;&#8345;+p&#956;&#8346;), symbol for charge carriers in a semiconductor." src="/files/ftp_upload/15155/15155_Equation_4.svg" style="text-align: center; height: 20px;" data-altupdatedat="1762173717000" data-alt="Equation 4" />
Diffusion Current:
 Diffusion occurs due to the thermal motion of carriers, moving from regions of higher concentration to regions of lower concentration. The current density (Jdiffusion) is:
<img alt="Diffusion equations, \(J_{diffusion,n} = -qD_n \frac{dn}{dx}\) and \(J_{diffusion,p} = -qD_p \frac{dp}{dx}\)." src="/files/ftp_upload/15155/15155_Equation_5.svg" style="text-align: center; height: 36px;" data-altupdatedat="1762173717000" data-alt="Equation 5" />
Dn and Dp are the diffusion coefficients for electrons and holes, respectively, and dn/dx and dp/dx are the concentration gradients for electrons and holes.
The Einstein relations link mobility and diffusion coefficient for both electrons and holes:
<img alt="Charge carrier diffusion equations, Dn=kT/q&#956;n and Dp=kT/q&#956;p, semiconductor physics formula" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="text-align: center; height: 36px;" data-altupdatedat="1762173717000" data-alt="Equation 6" />
 Where k is the Boltzmann constant, and T is the absolute temperature.
When both an electric field and a concentration gradient are present, the total current density is the sum of the drift and diffusion components. In real-world applications, these phenomena are analyzed using the semiconductor equations, a set of differential equations that describe the behavior of charge carriers in a semiconductor.

Carrier Transport

Carrier transport in semiconductors generates current, through drift and diffusion mechanisms.
Drift current arises when an external electric field causes ...

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Electrical Engineering

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Basics of Semiconductors

KEY TERMS AND CONCEPTS

drift and diffusion in semiconductors

Drift and diffusion are the two main ways electric current forms in semiconductors. These charge-carrier motions help determine how semiconductor devices work and how well they perform. The carriers involved are electrons and holes.

Drift current begins when an external electric field acts on charge carriers. Electrons and holes move between collisions with lattice atoms, and this motion creates drift velocity. For electrons, drift velocity depends on electron mobility and the electric field strength.

The current density from drift can be written for electrons and for holes. It depends on the elementary charge, the concentrations of electrons and holes, and their mobilities. The total drift current density is the sum of the electron and hole parts. Conductance is then related to the charge density and mobility of each carrier.

Diffusion current comes from thermal motion. Carriers move from regions with higher concentration to regions with lower concentration. For electrons and holes, diffusion current density depends on the diffusion coefficients and the concentration gradients.

Mobility and diffusion are linked by the Einstein relations. These relations connect the electron and hole mobility terms with their diffusion coefficients, along with temperature, the Boltzmann constant, and absolute temperature. When both an electric field and a concentration gradient are present, the total current density is the sum of drift and diffusion. In real semiconductor analysis, these effects are described with semiconductor equations, which are differential equations for charge-carrier behavior.

Drift and Diffusion in Semiconductors

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Drift and diffusion are the two main ways electric current forms in semiconductors. These charge-carrier motions help determine how semiconductor devices work and how well they perform. The carriers involved are electrons and holes. Drift current begins when an external electric field acts on charge carriers. Electrons and holes move between collisions with lattice atoms, and this motion creates drift velocity. For electrons, drift velocity depends on electron mobility and the electric field...

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Explore how electrons and holes create current in semiconductors through drift and diffusion, and see how mobility, concentration, and temperature shape carrier motion.

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electrical engineering

Drift and Diffusion in Semiconductors

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