Drift Current Density (Interactive)

In doped semiconductors at equilibrium, electron and hole densities satisfy $$ n\,p = n_i^2,\quad n - p = N_D - N_A, $$ where $N_D$ and $N_A$ are donor and acceptor concentrations and $n_i$ is the intrinsic carrier density (material dependent). Under an electric field $E$, the drift current density is $$ J = q\,(n\,\mu_n + p\,\mu_p)\,E, $$ with $q$ the elementary charge and $\mu_n,\mu_p$ the electron and hole mobilities, respectively. Using cm-based units: $N_D,N_A,n,p,n_i$ in cm$^{-3}$, $\mu$ in cm$^2$/Vs, $E$ in V/cm ⇒ $J$ in A/cm$^2$.

Interactive widget

Edit the inputs to see how $J$ and the total current $I = J\,A$ scale with material properties, field, and cross-section.

Material:

Intrinsic density $n_i$ (cm^-3): 1e10

Donor concentration $N_D$ (cm^-3):

Acceptor concentration $N_A$ (cm^-3):

Electron mobility $\mu_n$ (cm²/Vs):

Hole mobility $\mu_p$ (cm²/Vs):

Electric field $E$ (V/cm):

Electron density $n$ (cm^-3): 0

Hole density $p$ (cm^-3): 0

Conductor width (µm):

Conductor height (µm):

Cross-sectional area $A$ (µm²): 10000

$J_n$ (A/cm²): 0

$J_p$ (A/cm²): 0

Total $J$ (A/cm²): 0

$I = J\,A$ (A): 0

3D view of a rectangular conductor (length fixed). Adjust width and height above to rescale the cross-section. Grid spacing: 100 µm.

3D scale: 10.0×

Carrier rate: 10×

Sphere size (µm): 0.100 µm

Total spheres: 200

Background and notes

$\mu_n,\mu_p$ depend on material and doping; at room temperature and low doping in Si, $\mu_n \sim 1350\,\mathrm{cm^2/Vs}$ and $\mu_p \sim 480\,\mathrm{cm^2/Vs}$ (order of magnitude).
At high fields, velocity saturation and other effects reduce the validity of the linear drift relation $J = q\,(n\,\mu_n + p\,\mu_p)\,E$.
Assumptions: 300 K, full ionization, and mass-action $np=n_i^2$ with charge neutrality $n-p=N_D-N_A$ to determine $n$ and $p$ from $N_D,N_A,n_i$.
Units: $N_D,N_A,n,p,n_i$ in cm$^{-3}$, $\mu$ in cm$^2$/Vs, $E$ in V/cm ⇒ $J$ in A/cm$^2$. Geometry is in µm and area $A$ is displayed in µm$^2$; internally $A$ is converted to cm$^2$ to compute $I$ (A).

Use this calculator to build intuition for how carrier concentration, mobility, field, and geometry influence conduction.