MICROWAVE ENGINEERING VIRTUAL LAB

Gunn Oscillator VIRTUAL LAB

Explore the transferred electron effect and negative differential resistance in GaAs semiconductor devices. Interactive simulation of Gunn diode characteristics, domain formation, and microwave generation.

01 Learning Objectives

Understand TED Principles

Explain the transferred electron effect (Gunn effect) in GaAs and InP semiconductors, including the two-valley model and electron transfer mechanism.

Analyze NDR Characteristics

Study the negative differential resistance region in the V-I characteristics of Gunn diodes and its significance for microwave oscillation.

Domain Formation Dynamics

Investigate the formation, transit, and extinction of high-field domains (Gunn domains) and their relationship to oscillation frequency.

Circuit Design Parameters

Determine the relationship between device length, domain velocity, and oscillation frequency. Analyze power output and efficiency.

02 Theoretical Background

Two-Valley Energy Band Model

The Gunn effect is explained by the Ridley-Watkins-Hilsum (RWH) theory based on the two-valley model of GaAs conduction band.

Key Concepts:

  • Central Valley (Γ): Low energy, high mobility (μ₁ ≈ 8000 cm²/V·s), lower effective mass
  • Satellite Valley (L): Higher energy, low mobility (μ₂ ≈ 200 cm²/V·s), higher effective mass
  • Energy Separation: ΔE ≈ 0.36 eV (greater than thermal energy kT but achievable by electric field heating)
Electron Transfer Mechanism
Energy (eV) Crystal Momentum (k) Γ (Central) L (Satellite) ΔE ≈ 0.36eV

Negative Differential Resistance (NDR)

E < Eth
Electrons in central valley
High mobility, Ohmic behavior
E ≈ Eth
Electron transfer begins
Peak velocity, NDR region starts
E > Eth
Most electrons transferred
Low mobility, saturation
Threshold Field: Eth ≈ 3.2 kV/cm for GaAs
Peak Velocity: vp ≈ 2 × 107 cm/s
NDR Condition: dJ/dE < 0 (differential negative mobility)

Gunn Domain Formation & Transit

Domain Dynamics:

  1. Nucleation: At cathode, accumulation layer forms due to non-uniform doping or field enhancement
  2. Growth: Domain grows as electrons behind move faster (higher field) than those ahead
  3. Transit: Domain drifts toward anode at saturation velocity vs ≈ 107 cm/s
  4. Extinction: Domain disappears at anode, current increases, new domain forms
Oscillation Frequency:
f = vs / L
where L = device active length
Domain Electric Field Profile
E0 Domain Peak Cathode ← Electron Flow Anode

Modes of Operation

Transit-Time Mode

fL ≈ 107 cm/s

Domain forms and transits entire length. Frequency determined by device length.

Quenched Domain Mode

fL > 107 cm/s

RF voltage quenches domain before reaching anode. Higher frequency operation.

Limited Space-Charge Accumulation (LSA)

fL >> 107 cm/s

RF cycle too fast for domain formation. Most efficient mode (up to 20% efficiency).

03 Virtual Experimental Procedure

Note: This virtual laboratory uses interactive simulation controls to replicate physical experiments. Follow the steps below using the Simulation Controls panel in Section 04.

A V-I Characteristics & NDR Region Analysis

  1. 1
    Initialize Simulation: Click the Reset button to set default parameters (L = 10 μm, V = 3.0 V, n = 3×10¹⁵ cm⁻³, vs = 1.0×10⁷ cm/s)
  2. 2
    Set Device Parameters: Using the Device Length slider, select your desired active region length (5-50 μm). Record this value as L. Set Doping Concentration to 3×10¹⁵ cm⁻³ using the respective slider.
  3. 3
    Sweep Bias Voltage: Starting at 0 V, increment the Bias Voltage slider in steps of 0.5 V up to 10 V. At each step:
    • • Click Run Simulation to update plots
    • • Record the operating point current from the V-I Characteristics plot (yellow star marker)
    • • Note the electric field distribution in the Domain Formation plot
  4. 4
    Identify Threshold: Locate the voltage Vth where the V-I curve slope changes sign (transition from positive to negative differential resistance). This corresponds to the threshold field Eth ≈ 3.2 kV/cm.
  5. 5
    Calculate Parameters: Compute static resistance R = V/I at multiple points and differential resistance rd = ΔV/ΔI in the NDR region. Tabulate results showing the transition from positive to negative resistance.

B Frequency Measurement & Domain Velocity Calculation

  1. 1
    Set Operating Point: Adjust the Bias Voltage slider to 6.0 V (above threshold for stable oscillation). Ensure Saturation Velocity is set to 1.0×10⁷ cm/s.
  2. 2
    Measure Frequency: Click Run Simulation and record the Calculated Frequency displayed in the control panel. This value is computed as f = vs/L.
  3. 3
    Analyze Waveform: Observe the Output Waveform plot. Measure the period T between peaks and calculate frequency f = 1/T. Verify it matches the calculated value. Note the sawtooth-like shape characteristic of Gunn oscillations.
  4. 4
    Vary Device Length: Systematically change the Device Length slider to values: 5 μm, 10 μm, 20 μm, 30 μm, and 50 μm. At each setting, run the simulation and record:
    • • The calculated frequency
    • • The domain transit time visible in the Domain Transit Animation
    • • The RF waveform frequency from the Output Waveform plot
  5. 5
    Verify Relationship: Plot f vs. 1/L and verify linearity according to f = vs/L. Calculate the slope to experimentally determine the saturation velocity vs.

C Domain Dynamics & Saturation Velocity Effects

  1. 1
    Observe Domain Formation: Set Bias Voltage to 2.5 V (below threshold) and run simulation. Observe the Domain Formation plot showing uniform electron distribution and the Domain Transit Animation showing no domain activity.
  2. 2
    Threshold Transition: Gradually increase Bias Voltage from 2.5 V to 4.0 V in 0.1 V steps. At each step, observe:
    • • The formation of accumulation layer in the Domain Formation plot
    • • The appearance of high-field domain (red curve peak)
    • • The start of domain transit in the animation
    • • The onset of RF oscillation in the Output Waveform
  3. 3
    Vary Saturation Velocity: Set L = 10 μm and V = 6 V. Systematically vary the Saturation Velocity slider from 0.8 to 1.5 (×10⁷ cm/s). Record how frequency changes and verify the linear relationship in the calculated frequency display.
  4. 4
    Analyze Velocity-Field Curve: Observe the Velocity-Field Characteristic plot. Identify:
    • • Peak velocity point (≈2×10⁷ cm/s)
    • • Threshold field marker (dashed orange line at 3.2 kV/cm)
    • • NDR region where slope is negative
    • • Saturation velocity region at high fields
  5. 5
    Doping Effects: At constant L = 10 μm and V = 6 V, vary the Doping Concentration slider. Observe changes in domain sharpness in the Domain Formation plot. Note how higher doping affects domain formation criteria (n₀L product).

Data Collection Template

Step Length L (μm) Voltage V (V) Doping n (×10¹⁵) Velocity vs (×10⁷) Calc. Freq (GHz) Current I (A) Observations
A-1 10 0-10 (sweep) 3 1.0 — Record from plot V-I curve, find Vth
B-1 5,10,20,30,50 6.0 3 1.0 Record from display — f vs. 1/L relationship
C-2 10 2.5-4.0 3 1.0 — — Domain formation threshold

Simulation Tips

  • • Reset between experiments: Always click Reset when starting a new procedure part to ensure consistent initial conditions
  • • Slider precision: For fine voltage adjustments (0.1 V steps), click on the slider track or use arrow keys after selecting the slider
  • • Plot interaction: Hover over plot points to read exact values. Use the zoom tools in the top-right corner of each plot for detailed examination
  • • Animation speed: The Domain Transit Animation speed is proportional to the bias voltage setting
  • • Multiple runs: You can change parameters and click Run Simulation multiple times without resetting to compare scenarios

04 Interactive Simulation

Simulation Controls

5 10 μm 50
0 3.0 V 10
1 3 10
0.8 1.0 1.5
Calculated Frequency 10.0 GHz
Threshold Field 3.2 kV/cm

V-I Characteristics & NDR Region

Velocity-Field Characteristic

Domain Formation (Space Charge)

Output Waveform (RF Signal)

Domain Transit Animation

Cathode (x=0) Ready to simulate... Anode (x=L)

05 Lab Report Guidelines

Required Sections

  • 1
    Title & Objectives

    Clear statement of experiment goals

  • 2
    Theory

    Two-valley model, RWH theory, domain dynamics (max 2 pages)

  • 3
    Simulation Procedure

    Step-by-step description of slider adjustments and parameter settings used

  • 4
    Results & Analysis

    Tabulated data from simulation runs, plotted characteristics, screenshots of key plots

  • 5
    Discussion

    Physical interpretation of simulation results, comparison with theoretical predictions

  • 6
    Conclusion

    Key findings, validation of f = vs/L relationship, limitations of virtual model

Key Calculations to Include

Threshold Field: Eth = Vth / L Compare with theoretical 3.2 kV/cm using voltage slider data
Domain Velocity: vs = f × L Verify using calculated frequency display and length slider
Frequency Scaling: f ∝ 1/L Verify linearity by plotting f vs 1/L from Part B data
Doping-Length Product: n0L > 1012 cm-2 Calculate for your simulation parameters

Grading Rubric

Criterion Weight
Theoretical Understanding 25%
Simulation Data Quality 30%
Analysis & Calculations 25%
Presentation & Interpretation 20%

Sample Discussion Questions

  1. Why does the Gunn effect not occur in silicon or germanium?
  2. Explain the difference between Gunn oscillators and IMPATT diodes in terms of noise performance.
  3. How does the simulation demonstrate the two-valley model through the V-I characteristics?
  4. What happens to domain formation when the bias voltage is exactly at threshold (3.2 V for 10 μm)?
  1. Calculate the required device length for 30 GHz operation using the velocity slider.
  2. What limitations does this virtual simulation have compared to a physical Gunn diode experiment?
  3. How would you modify the simulation controls to study LSA (Limited Space-Charge Accumulation) mode?
  4. Discuss the relationship between doping concentration and domain stability as observed in the simulation.