⭐ 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: Carrier Distribution and Fermi Level Identification

Objective

Study carrier distribution vs energy plots and identify the relationship between Fermi level position and doping type.

Steps

Step 1: Access the Interactive Simulation

1. Click on the "Simulation" tab if not already active
2. The main visualization displays:
   • DOS Plot: Density of states function with energy bands
   • Carrier Distribution: Real-time carrier concentration visualization
   • Fermi Level Indicator: Dynamic Fermi level position marker
   • Energy Band Diagram: Conduction and valence band edges

Step 2: Analyze Different Doping Scenarios

1. Material Selection:

   • Choose semiconductor material from dropdown (Si, Ge, GaAs)
   • Each material has different band gap and effective masses
   • Observe how material properties affect DOS shape

2. Doping Type Analysis:

   • Intrinsic Semiconductor:

     • Set doping concentration to minimum
     • Observe Fermi level near midgap
     • Note symmetric carrier distribution

   • n-type Doping:

     • Select n-type from doping type dropdown
     • Increase donor concentration using slider
     • Watch Fermi level move toward conduction band

   • p-type Doping:

     • Select p-type from doping type dropdown
     • Increase acceptor concentration using slider
     • Observe Fermi level shift toward valence band

Step 3: Fermi Level Position Identification

1. Plot Analysis:

   • Three carrier distribution plots are displayed with different Fermi level positions
   • Plot A: Fermi level near midgap (intrinsic)
   • Plot B: Fermi level above midgap (n-type)
   • Plot C: Fermi level below midgap (p-type)

2. Matching Exercise:

   • Identify which plot corresponds to intrinsic, n-type, or p-type semiconductor
   • Use the interactive interface to match plots with doping types
   • Consider carrier concentration asymmetry around the Fermi level

Key Observations

• Fermi level position indicates majority carrier type
• Higher doping concentration moves Fermi level closer to respective band edge
• Intrinsic semiconductors have Fermi level near midgap
• Carrier distribution reflects Fermi-Dirac statistics

Task 2: Interactive Parameter Effects on Carrier Density

Objective

Explore how different parameters affect carrier density plots and understand the underlying physics.

Steps

Step 1: Temperature Effects Study

1. Low Temperature Analysis (0K - 100K):

   • Set temperature to low values using the slider
   • Observe sharp Fermi-Dirac cutoff at T ≈ 0K
   • Study carrier freeze-out effects in doped semiconductors
   • Note incomplete ionization at low temperatures

2. Room Temperature Behavior (250K - 350K):

   • Adjust temperature to room temperature range
   • Observe thermal broadening of distribution
   • Study complete ionization of dopants
   • Analyze equilibrium carrier concentrations

3. High Temperature Effects (400K - 600K):

   • Increase temperature to high values
   • Watch intrinsic carrier generation dominate
   • Observe Fermi level approach toward midgap
   • Study thermal carrier excitation across band gap

Step 2: Doping Concentration Effects

1. Light Doping (10^14 - 10^15 cm^-3):

   • Set low doping concentrations
   • Observe small Fermi level shifts
   • Study non-degenerate semiconductor behavior
   • Note Maxwell-Boltzmann approximation validity

2. Moderate Doping (10^16 - 10^17 cm^-3):

   • Increase doping to moderate levels
   • Watch significant Fermi level movement
   • Observe increased majority carrier concentration
   • Study dopant ionization effects

3. Heavy Doping (10^18 cm^-3 and above):

   • Set high doping concentrations
   • Observe Fermi level approach band edges
   • Study degenerate semiconductor behavior
   • Note band tailing and bandgap narrowing effects

Step 3: Material Property Comparisons

1. Band Gap Effects:

   • Compare wide bandgap (GaAs) vs narrow bandgap (Ge) materials
   • Study how band gap affects intrinsic carrier concentration
   • Observe temperature dependence differences

2. Effective Mass Impact:

   • Analyze how different effective masses affect DOS
   • Compare electron vs hole effective masses
   • Study asymmetric carrier distributions

Step 4: Real-time Interactive Analysis

1. Dynamic Visualization:

   • Enable thermal carrier animation to see carrier generation/recombination
   • Observe dynamic redistribution with parameter changes
   • Use animation speed controls for detailed observation

2. Quantitative Analysis:

   • Monitor real-time parameter values in the data display
   • Record carrier concentrations at different conditions
   • Study numerical relationships between parameters

Interactive Features

• Real-time Updates: All plots update instantly with parameter changes
• Animation Controls: Start/stop/speed control for thermal effects
• Plot Tools: Zoom, pan, reset for detailed examination
• Hover Information: Detailed values on mouse interaction

Task 3: Challenge-Based Learning Assessment

Objective

Test understanding through comprehensive interactive challenges covering DOS and carrier density concepts.

Steps

Step 1: Access Challenge Module

1. Click on the "Challenges" tab
2. Five challenge categories are available:
   • Rapid Fire Quiz
   • Fill in the Blanks
   • Calculations
   • Advanced Concepts
   • Matching Exercise

Step 2: Rapid Fire Quiz

1. Question Types: Multiple-choice questions on carrier density and DOS

2. Topics Covered:

   • DOS mathematical expressions (∝ √E dependence)
   • Fermi-Dirac distribution function
   • Temperature effects on carrier statistics
   • Doping influence on Fermi level position
   • Material property relationships

3. Assessment Process:

   • Select answers by clicking on options
   • Questions randomly selected from comprehensive bank
   • Use "Check Answers" to verify responses
   • "Show Hints" provides guided assistance

Step 3: Fill in the Blanks Challenge

1. Concept Completion: Complete key statements about carrier density physics

2. Topics Include:

   • DOS function definitions
   • Fermi level properties and significance
   • Temperature and doping dependencies
   • Effective mass and band structure relationships

3. Interaction:

   • Type answers directly into blank fields
   • Real-time validation with color-coded feedback
   • Multiple attempts allowed for learning

Step 4: Calculation Challenge

1. Numerical Problem Solving: Quantitative carrier density calculations

2. Problem Categories:

   • Calculate effective DOS at band edges
   • Determine carrier concentrations from Fermi level
   • Compute temperature coefficients
   • Analyze doping ionization fractions

3. Features:

   • Enter numerical answers with appropriate units
   • Automatic validation with engineering tolerance
   • Progressive hint system for complex problems

Step 5: Advanced Concepts Assessment

1. Complex Physics Topics:

   • Quantum mechanical aspects of DOS
   • Degenerate semiconductor statistics
   • Band structure modifications under heavy doping
   • Temperature-dependent effective mass

2. In-depth Analysis:

   • Multi-part questions requiring detailed understanding
   • Conceptual reasoning about physical mechanisms
   • Application of theoretical knowledge to practical scenarios

Step 6: Matching Exercise

1. Concept Association: Connect related DOS and carrier density concepts

2. Interaction Method:

   • Click on items to select and create pairs
   • Visual connection lines indicate relationships
   • Multiple simultaneous connections possible

3. Content Areas:

   • Physical parameters and their mathematical expressions
   • Material properties and their effects
   • Temperature regimes and characteristic behaviors