Tools

Carrier Transport

⭐ When you enter the simulation section, a guided tour will appear. It is strongly recommended that you take the tour for the first time, as it provides step-by-step instructions to help you understand the experiment thoroughly. The tour also introduces you to the various controls, features, and interface elements, making it easier for you to navigate and explore the experiment effectively.

Task 1: Interactive Simulation Exploration

1.1 Understanding the Simulation Interface

Main Visualization Area:

  • Device Container: Shows a semiconductor device with:
    • Gold electrodes on left and right sides
    • Blue semiconductor region in the center
    • Moving charge carriers (blue dots = electrons, red dots = holes)
    • Green electric field lines when voltage is applied

Real-time Current Displays:

  • Electron Drift Current (mA/cm²)
  • Electron Diffusion Current (mA/cm²)
  • Hole Drift Current (mA/cm²)
  • Hole Diffusion Current (mA/cm²)

1.2 Control Parameters (Right Panel)

Material Selection:

  • Silicon (Si) - Default material
  • Germanium (Ge) - Higher mobility than Si
  • Gallium Arsenide (GaAs) - Highest electron mobility

Environmental Controls:

  • Temperature: 250-400 K (affects mobility and carrier concentration)
  • Applied Voltage: -5V to +5V (creates electric field for drift)

Doping Controls:

  • N-type Doping: 10¹⁴ to 10¹⁸ cm⁻³ (electron donors)
  • P-type Doping: 10¹⁴ to 10¹⁸ cm⁻³ (hole donors)

Transport Control:

  • Concentration Gradient: 0-100% (drives diffusion currents)

1.3 Simulation Tasks

Task 1a: Drift Current Analysis

  1. Set temperature to 300K
  2. Apply voltage from 0V to 5V in steps of 1V
  3. Observe how drift currents change with voltage
  4. Compare electron vs hole drift currents
  5. Expected Observation: Linear relationship between voltage and drift current

Task 1b: Material Comparison

  1. Set voltage to 2V, temperature to 300K
  2. Switch between Si, Ge, and GaAs materials
  3. Record drift current values for each material
  4. Expected Result: GaAs > Ge > Si for electron mobility

Task 1c: Temperature Effects

  1. Keep voltage at 2V, material as Silicon
  2. Vary temperature from 250K to 400K
  3. Observe mobility changes (shown in current values)
  4. Expected Result: Mobility decreases with increasing temperature

Task 1d: Diffusion Current Study

  1. Set voltage to 0V (no electric field)
  2. Adjust concentration gradient from 0% to 100%
  3. Observe diffusion currents without applied field
  4. Expected Result: Current flows from high to low concentration

Task 2: Advanced Parameter Analysis

2.1 Interactive Parameter Correlation

Combined Effects Study:

  1. Start with default parameters (Si, 300K, 0V, medium gradient)
  2. Systematically vary one parameter at a time:
    • Voltage Effect: Keep all other parameters constant, vary voltage
    • Temperature Effect: Keep all other parameters constant, vary temperature
    • Material Effect: Compare all three materials under same conditions
    • Gradient Effect: Vary concentration gradient with and without applied field

2.2 Current Component Analysis

Understanding Current Equations: The simulation displays four fundamental transport equations:

  • J = J_drift + J_diffusion (Total current)
  • J_drift = qμnE + qμpE (Drift components)
  • J_diffusion = qD_n∇n + qD_p∇p (Diffusion components)

Task 2a: Drift vs Diffusion Dominance

  1. Pure Drift: Set gradient to 0%, apply voltage = 3V
    • Record drift current values
    • Diffusion currents should be near zero
  2. Pure Diffusion: Set voltage to 0V, gradient to 100%
    • Record diffusion current values
    • Drift currents should be zero
  3. Combined Transport: Set voltage to 2V, gradient to 50%
    • Observe competition between drift and diffusion

Task 2b: Einstein Relation Verification

  1. Use Einstein relation: D = (kT/q)μ
  2. At room temperature (300K): D/μ = 26 mV
  3. Compare diffusion and mobility values from simulation
  4. Verify the relationship holds for different materials

Task 3: Challenge Exercises

Navigate to the Challenges tab to access interactive educational content.

3.1 Available Challenges

Challenge 1: Rapid Fire MCQ

  • Multiple choice questions on mobility and transport concepts
  • Test quick understanding of fundamental principles
  • Topics: mobility definitions, temperature effects, material properties

Challenge 2: Fill in the Blanks

  • Complete key transport equations
  • Fill missing parameters in physics formulas
  • Focus on mathematical relationships

Challenge 3: Calculation Challenge

  • Numerical problem solving
  • Calculate mobility, diffusion coefficients, and current densities
  • Apply Einstein relation and transport equations

Challenge 4: Advanced Concepts

  • Deep dive into complex transport phenomena
  • Scattering mechanisms, temperature dependencies
  • Advanced material properties

Challenge 5: Concept Matching

  • Match physics concepts with descriptions
  • Connect theory to practical applications
  • Reinforce understanding of transport mechanisms

3.2 Challenge Strategy

Scoring System:

  • Total Score: Accumulates points from all challenges
  • Challenges Solved: Number of completed exercises
  • Hints Used: Track learning assistance usage

Recommended Approach:

  1. Start with Challenge 1 (MCQ) for concept review
  2. Use simulation to verify answers experimentally
  3. Progress through challenges in numerical order
  4. Use hints sparingly to maximize learning
  5. Reset and retry challenges for mastery

Task 4: Comprehensive Analysis Report

4.1 Data Collection Template

Create a systematic record of your observations:

Material Comparison Table:

| Material | Electron Mobility | Hole Mobility | Drift Current @2V | Notes |
          |----------|-------------------|---------------|-------------------|-------|
          | Si       |                   |               |                   |       |
          | Ge       |                   |               |                   |       |
          | GaAs     |                   |               |                   |       |

Temperature Dependence:

| Temperature (K) | Si e- Mobility | Si h+ Mobility | Observations |
          |-----------------|----------------|----------------|--------------|
          | 250             |                |                |              |
          | 300             |                |                |              |
          | 350             |                |                |              |
          | 400             |                |                |              |

4.2 Analysis Questions

After completing the simulation tasks, answer these questions:

  1. Which material shows the highest electron mobility and why?
  2. How does temperature affect carrier mobility? Explain the physical mechanism.
  3. Under what conditions do diffusion currents dominate over drift currents?
  4. Verify the Einstein relation D = (kT/q)μ using your simulation data.
  5. Explain the difference between intrinsic and extrinsic semiconductor behavior.

Tips for Best Results:

  • Use Chrome or Firefox browsers for optimal performance
  • Allow JavaScript execution for interactive features
  • Take screenshots of interesting parameter combinations
  • Document observations systematically for better learning retention