What is Shockley Diode?

Use this calculator to compute Shockley Diode values with step-by-step solutions.

How do I use this calculator?

Enter the required values; results and step-by-step derivation update automatically.

Where is Shockley Diode used?

Electricity, engineering, research, and related scientific disciplines.

What formulas does this use?

All standard shockley diode formulas are applied and shown step-by-step in the results.

Can I get step-by-step solutions?

Yes. The calculator shows a full step-by-step derivation when results are displayed.

How accurate are the results?

Results use standard floating-point arithmetic (~15 significant digits). Suitable for education and professional use.

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ELECTROMAGNETISMElectricityPhysics Calculator

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Shockley Diode Equation and I-V Characteristics

The Shockley equation I = I_s(e^(V/(nV_T)) - 1) describes ideal diode behavior. I_s is saturation current, n is ideality factor (1–2), V_T = kT/q ≈ 26 mV at 300 K. Dynamic resistance r_d = nV_T/I.

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I doubles per ~18 mV increase in V (n=1) at room temperature. Reverse current I ≈ -I_s for V << -V_T. dV/dT ≈ -2 mV/°C for constant current. Series resistance R_s causes voltage drop at high current.

Key quantities

I = I_s(e^(V/(nV_T))-1)

I-V

Key relation

kT/q ≈ 26 mV @ 300K

V_T

Key relation

nV_T/I

r_d

Key relation

~-2 mV/°C

dV/dT

Key relation

Ready to run the numbers?

Why: The Shockley equation models real diodes for circuit design. Ideality factor n accounts for recombination; n=1 for ideal, n≈1.5–2 for Si. Temperature affects V_T and I_s.

How: Enter I_s, V, n, T for current; or I, I_s, n, T for voltage. Thermal voltage V_T = kT/q. Dynamic resistance r_d = dV/dI = nV_T/I for small-signal analysis.

I doubles per ~18 mV increase in V (n=1) at room temperature.Reverse current I ≈ -I_s for V << -V_T.

Sources:IEEE Electron DevicesNIST Semiconductor

Run the calculator when you are ready.

Calculate Diode Current and VoltageShockley equation with temperature and ideality factor

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⚡ Schottky Diode

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Shockley Diode Parameters

Calculation Mode

Saturation Current (Is) - A

Ideality Factor (n)

Temperature

Temperature Unit

Applied Voltage (V) - V

Series Resistance (Rs) - Ω

Reverse Voltage (Vr) - V

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BLOOMBERG TERMINAL - SHOCKLEY DIODE ANALYSIS

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CURRENT: 5.748e-1 A

CURRENT: MODERATE

STATUS: ⚠️ MODERATE - Normal operating range

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Diode Characteristics Visualizations

I-V Characteristics

Current vs Voltage relationship

Temperature Effects

Current variation with temperature

Ideality Factor Comparison

Current vs ideality factor

Logarithmic I-V Plot

I-V characteristics on logarithmic scale

Step-by-Step Calculation

Step 1: Input Parameters

I_s = 1.000e-12 \text{ A}

n = 1.000000

T = 300.000000 \text{ K}

Step 2: Thermal Voltage Calculation

V_T = \frac{kT}{q} = \frac{1.380649e-23 \times 300.000000}{1.602177e-19} = 25.852 \text{ mV}

nV_T = 1.000000 \times 25.852 = 25.852 \text{ mV}

Step 3: Temperature-Dependent Saturation Current

I_s(T) = I_s(T_0) \left(\frac{T}{T_0}\right)^3 \exp\left(-\frac{E_g}{kT} + \frac{E_g}{kT_0}\right) = 1.000e-12 \text{ A}

Step 4: Current Calculation (Shockley Equation)

V = 0.700000 \text{ V}

V_j = V - I \times R_s = 0.700000 - 5.748e-1 \times 0.000000e+0 = 0.700000 \text{ V}

I = I_s \left(e^{\frac{V_j}{nV_T}} - 1\right) = 1.000e-12 \left(e^{\frac{0.700000}{25.852 \times 10^{-3}}} - 1\right) = 5.748e-1 \text{ A}

Step 5: Dynamic Resistance

r_d = \frac{nV_T}{I} = \frac{25.852 \times 10^{-3}}{5.748e-1} = 0.044979 \Omega

G = \frac{1}{r_d} = 2.223e+1 \text{ S}

Step 6: Temperature Coefficient

\frac{dV}{dT} \approx -8.884 \text{ mV/°C}

Step 7: Power Calculations

P = V \times I = 0.700000 \times 5.748e-1 = 4.023e-1 \text{ W}

📚 Official Data Sources

IEEE Electron Devices Society ↗

IEEE standards for semiconductor devices and electronics

Updated: 2026-01-25

NIST Semiconductor Electronics Division ↗

US National Institute of Standards semiconductor measurements

Updated: 2026-01-15

Electronics Tutorials ↗

Comprehensive electronics and diode tutorials

Updated: 2025-12-15

All About Circuits ↗

Educational resource for circuit design and semiconductor physics

Updated: 2025-11-20

⚠️ Disclaimer: This calculator provides theoretical estimates based on the ideal Shockley diode equation. Real diodes exhibit non-ideal behavior including series resistance, reverse breakdown, temperature variations, and manufacturing tolerances. For critical circuit design applications, always consult manufacturer datasheets, perform SPICE simulations, and test prototypes. Thermal management is essential for high-current operation. This calculator is for educational and preliminary design purposes only.

📖 Frequently Asked Questions

What is the ideality factor and why does it matter?

The ideality factor (n) accounts for non-ideal diode behavior. n = 1 for ideal diodes, n = 1.0-1.2 for silicon diodes, and n = 1.5-2.0 for LEDs. Higher ideality factors indicate recombination effects, series resistance, or other non-ideal mechanisms affecting diode behavior.

Why does forward voltage decrease with temperature?

Forward voltage decreases approximately -2 mV/°C for silicon diodes because saturation current increases exponentially with temperature. This temperature coefficient is used in diode-based temperature sensors and requires compensation in precision circuits.

What is dynamic resistance and when is it important?

Dynamic resistance (rd = nVT/I) is the small-signal AC resistance at a specific operating point. It decreases with increasing current, making diodes useful for voltage regulation and signal rectification. Critical for AC circuit analysis and amplifier design.

How does reverse saturation current vary with temperature?

Reverse saturation current increases exponentially with temperature, approximately doubling every 10°C. This is described by Is(T) = Is(T0) × (T/T0)³ × exp(-Eg/kT + Eg/kT0), where Eg is the bandgap energy.

What is thermal voltage and why is it important?

Thermal voltage VT = kT/q ≈ 26 mV at 300K is a fundamental parameter scaling the exponential I-V relationship. It represents the voltage scale at which diode behavior transitions from exponential to linear, critical for understanding diode operation.

How accurate is the Shockley equation for real diodes?

The Shockley equation is accurate for forward bias above the knee voltage (typically 0.5-0.7V for silicon). It doesn't account for series resistance, reverse breakdown, or high-injection effects. For precision applications, use manufacturer SPICE models or measured data.

What causes series resistance in diodes?

Series resistance comes from bulk semiconductor resistance, contact resistance, and lead resistance. It becomes significant at high currents, causing voltage drop and power dissipation. Power diodes are designed with low series resistance for high-current applications.

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

⚡

Shockley derived the equation in 1949; basis of transistor theory.

— IEEE

🌡️

V_T = 25.85 mV at 300 K; scales linearly with T.

— NIST

📐

Ideality n=1 ideal; n≈1–2 for real Si diodes.

— Electronics Tutorials

📊

r_d = nV_T/I; small at high forward current.

— All About Circuits

What is the Shockley Diode Equation?

The Shockley diode equation, also known as the ideal diode equation, is a fundamental relationship in semiconductor physics that describes the current-voltage (I-V) characteristics of a p-n junction diode. Named after William Shockley, this equation provides a mathematical model for understanding how diodes conduct current under forward and reverse bias conditions.

Shockley Equation

The fundamental equation describing diode behavior relates current to voltage through an exponential relationship.

Key Formula:

I = Is(e^(V/nVT) - 1)

Thermal Voltage

Thermal voltage is a fundamental parameter that scales with temperature and determines the exponential behavior of the diode.

Formula:

VT = kT/q ≈ 26mV @ 300K

Ideality Factor

The ideality factor accounts for non-ideal behavior in real diodes, typically ranging from 1 to 2.

Typical Values:

n = 1: Ideal diode
n = 1.0-1.2: Silicon diodes
n = 1.5-2.0: LEDs, some diodes

How Does the Shockley Diode Equation Work?

The Shockley diode equation is derived from semiconductor physics principles, specifically the diffusion of charge carriers across the p-n junction. The equation accounts for both forward and reverse bias conditions, with exponential behavior in forward bias and saturation current in reverse bias.

🔬 Physical Principles

Forward Bias

1Applied voltage reduces the built-in potential barrier
2Carriers diffuse across the junction exponentially
3Current increases exponentially with voltage: I ∝ e^(V/nVT)
4For V >> nVT, I ≈ Is × e^(V/nVT)

Reverse Bias

Applied voltage increases the potential barrier
Current saturates to -Is (reverse saturation current)
For V << 0, I ≈ -Is (constant reverse current)
Reverse current is temperature-dependent

📊 Dynamic Resistance

The dynamic (small-signal) resistance is crucial for AC circuit analysis. It represents the incremental resistance of the diode at a specific operating point.

Dynamic Resistance Formula:

rd = dV/dI = nVT / I

The dynamic resistance decreases with increasing forward current, making diodes useful for voltage regulation and signal rectification.

When to Use the Shockley Diode Calculator

The Shockley diode calculator is essential for electronics engineers, circuit designers, and students working with semiconductor devices. It's particularly valuable for analyzing diode behavior, designing rectifier circuits, and understanding temperature effects.

Rectifier Circuits

Analyze forward voltage drop, power dissipation, and efficiency in AC-to-DC rectifier circuits.

Applications:

Power supply design
Bridge rectifiers
Voltage regulation

LED Forward Voltage

Calculate forward voltage drop for LEDs at specific operating currents, essential for LED driver design.

Benefits:

Driver circuit design
Current limiting
Power efficiency

Solar Cell Analysis

Analyze photovoltaic cell characteristics, including I-V curves and maximum power point tracking.

Applications:

PV system design
MPPT algorithms
Efficiency analysis

Photodiode Analysis

Calculate reverse leakage current and dark current for photodiodes in optical detection systems.

Benefits:

Dark current analysis
Signal-to-noise ratio
Detection sensitivity

Temperature Sensors

Analyze temperature-dependent voltage characteristics for diode-based temperature sensors.

Applications:

Temperature measurement
Thermal compensation
Sensor calibration

Circuit Design

Design voltage regulators, clippers, clampers, and other diode-based circuits with accurate modeling.

Benefits:

Accurate modeling
Power analysis
Thermal design

Key Formulas and Equations

Shockley Diode Equation

I = Is(e^(V/nVT) - 1)

Where I is the diode current, Is is the reverse saturation current, V is the applied voltage, n is the ideality factor, and VT is the thermal voltage.

Thermal Voltage

VT = kT/q ≈ 26 mV at 300 K

Thermal voltage scales linearly with absolute temperature. At room temperature (300 K), it's approximately 26 mV.

Dynamic Resistance

rd = nVT/I = dV/dI

The small-signal resistance decreases with increasing forward current, making diodes useful for voltage regulation.

Temperature Dependence

Is(T) = Is(T0) × (T/T0)^3 × exp(-Eg/kT + Eg/kT0)

Saturation current increases exponentially with temperature, while forward voltage decreases approximately -2 mV/°C.

Inverse Shockley (Voltage from Current)

V = nVT × ln(I/Is + 1)

For forward bias with I >> Is, this simplifies to V ≈ nVT × ln(I/Is).

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⬅️Jump in and explore the concept!

Shockley Diode Equation and I-V Characteristics

🔌 Silicon Rectifier Diode

💡 Red LED Forward Voltage

☀️ Solar Cell Analysis

📷 Photodiode Reverse Leakage

🌡️ Temperature Sensor Diode

⚡ Schottky Diode

Shockley Diode Parameters

Diode Characteristics Visualizations

I-V Characteristics

Temperature Effects

Ideality Factor Comparison

Logarithmic I-V Plot

Step-by-Step Calculation

📚 Official Data Sources

📖 Frequently Asked Questions

What is the ideality factor and why does it matter?

Why does forward voltage decrease with temperature?

What is dynamic resistance and when is it important?

How does reverse saturation current vary with temperature?

What is thermal voltage and why is it important?

How accurate is the Shockley equation for real diodes?

What causes series resistance in diodes?

🔬 Physics Facts

What is the Shockley Diode Equation?

Shockley Equation

Thermal Voltage

Ideality Factor

How Does the Shockley Diode Equation Work?

🔬 Physical Principles

Forward Bias

Reverse Bias

📊 Dynamic Resistance

When to Use the Shockley Diode Calculator

Rectifier Circuits

LED Forward Voltage

Solar Cell Analysis

Photodiode Analysis

Temperature Sensors

Circuit Design

Key Formulas and Equations

Shockley Diode Equation

Thermal Voltage

Dynamic Resistance

Temperature Dependence

Inverse Shockley (Voltage from Current)

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