ShaneLogic/drift-diffusion-current-analysis

Drift and Diffusion Current Analysis

When to Use

Apply this skill when:

• Analyzing individual current components (drift vs diffusion) in a semiconductor junction
• Calculating current density in bulk semiconductor regions
• Examining current behavior at doping interfaces
• Verifying equilibrium conditions in unbiased junctions
• Investigating how applied bias affects current components

Prerequisites

Before applying this skill, ensure you have:

• Electric field profile (dψ/dx) for the region
• Carrier density gradient information
• Doping profile of the junction
• Applied bias voltage (if any)

Core Workflow

1. Calculate Drift Current in Bulk Regions

For regions 1 and 2 (bulk semiconductor regions):

jn,drift = σn * dψ/dx

Where:

• jn,drift = drift component of electron current density
• σn = electron conductivity
• dψ/dx = gradient of electrostatic electron potential

Action: Compute the drift current density using the electric field profile and material conductivity.

2. Analyze Diffusion Current at Doping Interface

At the doping interface between regions:

• Diffusion current becomes very large (typically ~10^4 A/cm²)
• Diffusion current changes little with applied bias
• Magnitude is driven by carrier density gradient

Action: Identify the interface location and evaluate the diffusion current magnitude based on the doping gradient.

3. Compare Drift and Diffusion Distributions

Observe the relationship:

• Drift current distribution matches diffusion current in shape
• Drift current is shifted parallel to the current axis
• The shift results in a constant net current

Action: Plot or compare the spatial distributions of both current components to verify their relationship.

4. Verify Equilibrium Condition

For zero bias (V = 0):

• Total current jn = 0
• Drift and diffusion currents are equal in magnitude
• Currents cancel each other out: jn,drift = -jn,diffusion

Action: Confirm that at equilibrium, the drift and diffusion components sum to zero.

Key Variables

| Variable | Type | Description | |----------|------|-------------| | jn,drift | Current Density | Drift component of current | | jn,diffusion | Current Density | Diffusion component of current | | ψ | Potential | Electrostatic electron potential | | dψ/dx | Field | Electric field (potential gradient) | | σn | Conductivity | Electron conductivity |

Output Interpretation

The analysis yields:

• Magnitude of drift current in bulk regions
• Magnitude of diffusion current at the interface
• Spatial distribution of both components
• Net current (sum of components)
• Verification of equilibrium condition

Common Patterns

• Bulk regions: Drift current dominates due to electric field
• Interface region: Diffusion current peaks due to sharp doping gradient
• Applied bias: Primarily affects the balance between components, not individual magnitudes
• Equilibrium: Perfect cancellation of drift and diffusion