What is the Shockley equation?

The Shockley ideal diode equation describes the current-voltage relationship of a PN junction: I = I0(e^(V/nVT) - 1), where I0 is the reverse saturation current, n is the ideality factor (1–2), and VT = kT/q is the thermal voltage (~26 mV at 300 K). Under forward bias, current rises exponentially; under reverse bias, it saturates at –I0.

What is the difference between Silicon and Germanium diodes?

Silicon has a reverse saturation current I0 of roughly 1 pA (10^-12 A) and a forward voltage drop of about 0.6–0.7 V. Germanium has a much larger I0 (~1 μA) and a lower forward drop of about 0.2–0.3 V. Germanium was preferred for early transistors and high-frequency applications, but silicon dominates modern electronics.

How does temperature affect diode characteristics?

As temperature rises, the thermal voltage VT = kT/q increases and I0 grows exponentially. This means less forward voltage is needed to conduct the same current. For silicon, the forward voltage decreases by about 2 mV/K. Thermal runaway in power diodes occurs when this positive feedback is not managed by proper heat sinking.

What does the ideality factor n represent?

The ideality factor n (1–2) indicates which transport mechanism dominates. n = 1 means ideal diffusion-dominated current; n = 2 means recombination-dominated current. Real silicon diodes show n ≈ 2 at low currents and n ≈ 1 at higher currents. A larger n produces a shallower I-V curve slope in log scale.

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Semiconductor Simulator

PN Junction Diode I-V Characteristic Simulator

Compute diode current using the Shockley equation $I = I_0(e^{V/nV_T}-1)$. Adjust material, ideality factor, and temperature to explore how semiconductors behave across operating conditions.

Material & Parameters

Material Preset

Reverse Sat. Current I₀ (A)

10⁻¹⁵10⁻³

Ideality Factor n

Temperature T (K)

Summary

Results

25.9

VT (mV)

0.617

Vf @ 1 mA (V)

3.42e-4

I @ 0.5 V (A)

—

Breakdown Est.

I-V Characteristic (Log Scale)

Temperature Comparison (250K / 300K / 350K / 400K)

Theory & Key Formulas

$$I = I_0\left(e^{V/nV_T}- 1\right)$$ $$V_T = \frac{kT}{q}\approx 25.9\,\text{mV at 300 K}$$

k = 1.381×10⁻²³ J/K, q = 1.602×10⁻¹⁹ C. n = 1: diffusion-dominated; n = 2: recombination-dominated.

What is a PN Junction Diode?

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What exactly is a PN junction, and why does it only let current flow one way?

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Basically, it's a sandwich of two semiconductor types: P-type (with extra "holes") and N-type (with extra electrons). Where they meet, electrons and holes recombine, creating a "depletion region" that acts like a built-in barrier. To get current flowing, you need to apply a forward voltage to lower this barrier. Try moving the voltage slider in the simulator above to see how the current suddenly shoots up after a certain point.

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Wait, really? So the curve isn't perfectly sharp? I see a parameter called the "Ideality Factor" (n). What's that for?

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Great observation! In a perfect, textbook diode, the turn-on is described by a simple exponential. In practice, real diodes have imperfections. The ideality factor, n, accounts for this. If n=1, current is dominated by pure diffusion of charges. If n=2, it means recombination in the depletion region is significant. Slide the "Ideality Factor" control between 1 and 2 to see how it smears out the knee of the curve.

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Okay, and what about temperature? I see it's set to 300K. What happens if the diode gets hot?

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Temperature is huge! It affects two key things: the thermal voltage $V_T$ and the reverse saturation current $I_0$. As you increase the temperature with the slider, you'll see the curve shift left—the diode turns on at a lower voltage. This is critical for circuit design because a hot diode can behave very differently from a cold one.

Physical Model & Key Equations

The core model for an ideal PN junction diode's current-voltage relationship is given by the Shockley diode equation:

$$I = I_0\left(e^{V/(nV_T)}- 1\right)$$

I is the diode current (A). V is the voltage across the diode (V). I₀ is the reverse saturation current, a tiny constant dependent on the material. n is the ideality factor (1 to 2). V_T is the thermal voltage.

The thermal voltage is not a fixed number; it's set by the absolute temperature and fundamental constants:

$$V_T = \frac{kT}{q}$$

k is Boltzmann's constant (1.381×10⁻²³ J/K). T is the absolute temperature in Kelvin (K). q is the elementary charge (1.602×10⁻¹⁹ C). At room temperature (T=300K), $V_T \approx 25.9$ mV. This equation shows why temperature is a key control in the simulator.

Real-World Applications

Rectifiers in Power Supplies: The one-way current flow is used to convert alternating current (AC) from your wall outlet into direct current (DC) needed by electronics. The sharpness of the I-V curve determines how efficiently this conversion happens.

Voltage Clamping & Protection: Diodes can be used to limit voltage spikes. For instance, a Zener diode (a special type) uses the reverse breakdown region—which you can simulate by extending the voltage to negative values—to provide a stable reference voltage or protect sensitive circuits.

Temperature Sensing: Since the forward voltage drop has a known, predictable dependence on temperature (as you explored with the T slider), diodes are often used as inexpensive and accurate temperature sensors in integrated circuits.

Solar Cells & Photodiodes: A PN junction is the heart of a solar cell. When light hits it, it generates a current. This simulator shows the "dark" characteristic; under light, the entire I-V curve shifts down, allowing power to be extracted from the device.

Common Misconceptions and Points of Caution

There are several important points to keep in mind when using this simulator, especially from a practical design perspective. First, the misconception that "the forward voltage Vf is always 0.7V (for silicon)". This is a significant misunderstanding. The 0.7V in a datasheet is merely a "typical value" at a specific current (e.g., 10mA or 100mA). Try switching the current scale in the simulator from logarithmic to linear and compare the voltage drop at 1mA and 100mA. Even when the current increases tenfold, the voltage only increases by about 60mV (for n=1 at room temperature), but the absolute value changes substantially. In low-current circuits, it can be around 0.4V, and in high-current rectification, exceeding 1V is not uncommon.

Next, the handling of the reverse saturation current I₀. While it's a fixed value in the simulator, actual components have significant manufacturing variations, and datasheets often only list a "maximum" value. For example, a silicon diode's I₀ might be listed as 1nA (typical) at 25°C, but the maximum could be 50nA, and at high temperatures, this value can swell by a factor of 1000 or more. In high-impedance circuits where reverse leakage current must be strictly considered, this variation can make or break your design.

Finally, it's crucial to understand the "applicability limits" of the Shockley diode equation. While this equation explains mid-current region behavior very well, real diodes have many effects not included in this model. In the high forward current region, the voltage drop due to internal semiconductor resistance (bulk resistance) becomes non-negligible, making the graph slope steeper. Conversely, at very low forward voltages or in the reverse region, effects like surface leakage and recombination become dominant, causing simulation and actual measurements to diverge. It's essential to use it strictly as a "beautiful first-order approximation model" and move to higher-order models (like SPICE models) as needed.

How to Use

Set reverse saturation current I₀ using the exponent sliders (range: 10⁻¹² to 10⁻⁶ A) to match your semiconductor material—silicon typically 10⁻¹² A, germanium 10⁻⁶ A.
Adjust ideality factor n (1.0–2.0) where n=1 represents ideal diffusion current and n=2 indicates recombination in depletion region; most silicon diodes operate at n≈1.3.
Modify junction temperature T (200–400 K) to observe thermal effects on threshold voltage and reverse leakage current; thermal voltage VT = kT/q changes from 17.3 mV at 200 K to 34.5 mV at 400 K.
Read output statistics: forward voltage at 1 mA, saturation current at 0.5 V, and estimated breakdown voltage characteristic of your diode configuration.

Worked Example

Silicon power diode at 300 K (27°C): I₀ = 10⁻¹² A, n = 1.2. Thermal voltage VT = 25.9 mV. At forward bias of 0.7 V, the Shockley equation yields I = I₀[exp(qV/nkT)−1] = 10⁻¹² [exp(0.7/(1.2×0.0259))−1] ≈ 1.0 mA. Forward voltage at 1 mA matches observed 0.68–0.72 V typical for silicon rectifiers. Increasing temperature to 350 K reduces Vf by approximately 2.1 mV per degree Celsius due to increased I₀ and higher VT.

Practical Notes

Ideality factor n varies with current regime: at low forward currents (<100 µA), generation-recombination dominates (n≈2); at higher currents (>1 mA), diffusion current controls (n≈1). Use simulator to identify your operating region.
Reverse saturation current doubles approximately every 5–6 K for silicon; use temperature slider to predict leakage at elevated ambient conditions (automotive, industrial applications).
Breakdown voltage estimation assumes avalanche multiplication; actual breakdown for 1N4007 rectifier diode occurs around 1000 V, but your custom junction depth and doping profile will shift this value significantly.
Schottky diodes exhibit lower forward voltage (0.3–0.4 V at 1 mA) and higher I₀ (10⁻⁸ to 10⁻⁶ A) than PN junctions; adjust I₀ and n parameters to simulate Schottky behavior for comparison.