Evaluate the Shockley diode equation I = I_S(exp(V/nV_T) - 1), the ideal current-voltage relation of a pn junction, in real time. From saturation current, forward voltage, ideality factor and temperature the tool reports the thermal voltage V_T = kT/q, the dynamic resistance r_d = nV_T/I and the power P = V I, and visualizes the semi-log I-V curve and a multi-temperature comparison so the physics of a pn junction can be grasped intuitively.
Parameters
Saturation current log10 I_S
log A
I_S = 1.00 nA
Forward voltage V_F
V
Ideality factor n
Temperature T
°C
With the defaults (I_S = 1 nA, V_F = 0.40 V, n = 1.0, T = 25 C = 298.15 K) V_T is about 25.7 mV, I about 5.7 mA, r_d about 4.5 ohm and P about 2.3 mW. Raising V_F to 0.6 - 0.7 V reaches the typical operating point of a silicon pn junction with current rising exponentially into the hundreds of mA.
Results
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Forward current I
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Thermal voltage V_T
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Dynamic resistance r_d
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Power dissipation P
pn Junction and I-V Operating Point
Left: the triangular diode symbol (anode to cathode) with the applied voltage V and current I. Right: the semi-log I-V curve (voltage V on the x-axis, log|I| on the y-axis). The curve rises exponentially in forward bias and saturates near I = -I_S in reverse bias, with the yellow marker at the present operating point (V_F, I).
Temperature Comparison (25/75/125 C)
Horizontal axis: forward voltage V_F (V, 0 to 1). Vertical axis: current I (A, log10 scale). The three curves correspond to T = 25/75/125 C. Higher temperature raises the thermal voltage V_T so that the same voltage drives more current (in a real pn junction the temperature dependence of I_S also contributes; this tool shows only the V_T effect). The curve at the current temperature is drawn in bold.
Theory & Key Formulas
Shockley diode equation: the ideal current-voltage relation in a pn junction.
Dynamic resistance at the operating point and power dissipation:
$$r_d = \frac{dV}{dI} = \frac{nV_T}{I}, \qquad P = V\cdot I$$
$I_S$ is the saturation current (A), $n$ is the ideality factor (1 to 2, equal to 1 for diffusion-dominated and 2 for recombination-dominated transport), $k = 1.381\times10^{-23}\,\mathrm{J/K}$ and $q = 1.602\times10^{-19}\,\mathrm{C}$. Under forward bias (V > 0) the exponential term dominates and I rises rapidly, while in reverse bias (V < 0) the current saturates at about minus I_S.
What is the Shockley Diode Simulator?
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In my electronics class we learned that a silicon diode "turns on at 0.7 V". What is the Shockley diode equation, and is "0.7 V" really enough?
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Good question. "Silicon diode conducts at 0.7 V" is a handy approximation, but the real voltage-current relation is a smooth exponential described by the Shockley diode equation I = I_S(exp(V/nV_T) - 1). With the tool defaults (I_S = 1 nA, V_F = 0.40 V, n = 1.0, T = 25 C) you already get I about 5.7 mA and r_d about 4.5 ohm, so at V_F = 0.40 V the diode is conducting in the mA range. The "0.7 V" rule is the practical operating point at hundreds of mA — Shockley's equation says V_F is determined logarithmically by current, at about 60 mV per decade when n = 1.
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What is the thermal voltage V_T? The tool shows 25.7 mV; why such a peculiar value?
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The thermal voltage V_T = kT/q comes from Boltzmann's constant k, the elementary charge q, and the absolute temperature T. Think of it as the thermal energy kT of one electron expressed as a voltage. At 25 C (298.15 K) it is about 25.7 mV, at room temperature 27 C (300 K) about 25.85 mV — the industry mnemonic "26 mV at room temperature" comes from there. Drag the temperature slider and you can see V_T about 20 mV at -40 C and about 36 mV at 150 C. Because V_T sits in the denominator, the steepness of the I-V slope depends on temperature.
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How does the ideality factor n change the curve? The slope visibly changes when I move the slider.
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n is an empirical factor that captures which transport mechanism dominates: n = 1 means diffusion-current dominated (an ideal pn junction at medium currents), n = 2 means recombination in the depletion region (low currents). Real diodes show n varying with current. The slope of the semi-log I-V is about 60 mV per decade times n, so n = 1 needs 60 mV to multiply the current by 10 and n = 2 needs 120 mV. Move the slider from n = 1.0 to 2.0 and you can see the current at V_F = 0.4 V drop from about 5.7 mA to roughly the square root, about 75 microamps. LEDs typically have n about 1.5 to 2.0, which is why their forward turn-on is softer than that of a small-signal silicon diode (n about 1.2 to 1.5).
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What is the dynamic resistance r_d = nV_T/I good for? Isn't it just Ohm's law?
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r_d is the small-signal impedance at a chosen operating point, the reciprocal slope of the I-V curve. It is very different from the chord resistance V/I (about 70 ohm with the defaults): the tool shows r_d about 4.5 ohm, an order of magnitude smaller. If you bias the diode with a constant current and add a small AC signal, the AC will see only r_d, which is why diodes work as soft voltage clamps. The same form r_e = V_T / I_E describes the small-signal resistance of a bipolar transistor's emitter — the heart of op-amp input-stage modeling — so r_d is one of the most reused identities in analog electronics, from mixers and detectors to current sources and temperature sensors.
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The curves on the temperature chart shift left as the temperature rises. Does the same thing happen in real diodes?
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Yes — and even more so. In the temperature comparison chart the 25/75/125 C curves shift to the left, meaning the same voltage drives more current at higher T. The tool only includes the V_T term, but in real pn junctions the saturation current I_S itself rises exponentially with temperature (roughly doubling every 10 C), so the forward voltage V_F actually drops by about 2 mV per kelvin. This is why power-supply rectifier diodes get hot at high load and why heat-sink margins matter: V_F is a "room-temperature ballpark", and the full industrial range from -40 to 85 C must be checked separately during design.
Frequently Asked Questions
The Shockley diode equation I = I_S(exp(qV/nkT) - 1) = I_S(exp(V/nV_T) - 1) expresses the current I through a pn junction in terms of the applied voltage V, saturation current I_S, ideality factor n and thermal voltage V_T = kT/q. The current grows exponentially under forward bias (V > 0) and saturates at about minus I_S in reverse bias. With the tool defaults (I_S = 1 nA, V_F = 0.40 V, n = 1.0, T = 25 C) the result is I about 5.7 mA, V_T about 25.7 mV, r_d about 4.5 ohm and P about 2.3 mW.
The thermal voltage V_T = kT/q is set by Boltzmann's constant k = 1.381e-23 J/K, the elementary charge q = 1.602e-19 C and absolute temperature T. At room temperature T = 300 K it is about 25.85 mV, the canonical value in semiconductor physics. The default 25 C (T = 298.15 K) of this tool gives V_T about 25.7 mV. V_T rises linearly with T, but in real pn junctions the strong temperature dependence of I_S dominates, so the forward voltage V_F decreases at about minus 2 mV per kelvin for silicon.
The ideality factor n is an empirical parameter that captures the dominant current-transport mechanism in the diode and lies between 1 and 2. n = 1 corresponds to diffusion-current dominated transport in an ideal pn junction (medium currents) and n = 2 corresponds to recombination in the depletion region (low currents). Real silicon diodes show n near 2 at low current, near 1 at medium current and again above 1 at large current. Larger n flattens the I-V slope so the same voltage drives less current. The slider covers n from 1.00 to 2.00 in 0.05 steps.
The dynamic resistance r_d = dV/dI = nV_T/I is the small-signal impedance of the diode at a given operating point. The larger the bias current I, the smaller r_d, so a diode behaves more like a voltage clamp at high current. With the defaults (I = 5.7 mA, n = 1, V_T = 25.7 mV) r_d is about 4.5 ohm. The quantity is central in LED drive circuits, current sources and diode temperature sensors, and the same formula r_e = V_T / I_E describes the small-signal resistance of the BJT base-emitter junction.
Real-World Applications
Rectifiers in AC-DC converters: Bridge rectifiers in household AC adapters and switched-mode power supplies still rely on silicon pn diodes. At 1 A loads V_F rises to about 0.9 V (outside the Shockley range where bulk resistance starts to matter), and the conduction loss is P = V_F I ≈ 0.9 W per diode, so a bridge of four costs about 3.6 W of heat. Setting V_F = 0.9 V in this tool drives the current into the multi-amp range and makes the need for a heat sink obvious. The same plot also explains why a Schottky diode with V_F about 0.3 V cuts the loss by roughly two-thirds in low-voltage applications.
LED drive-circuit design: A red LED (V_F about 2.0 V, n about 2.0, I = 20 mA) driven from a 5 V supply needs a series resistor R = (5 - 2.0) / 0.02 = 150 ohm. The dynamic resistance r_d = n V_T / I = 2 * 25.7e-3 / 0.02 ≈ 2.6 ohm is about 60 times smaller than R, so the resistor enforces an almost-constant current. Setting n = 2.0 and I_S to about 1e-10 A in this tool reproduces an LED-like I-V. Because rising temperature lowers V_F and pushes current up (which raises temperature further), a series resistor or constant-current driver is mandatory to prevent thermal runaway.
Temperature sensing with a pn junction: A constant-current biased silicon diode drops V_F by about 2 mV per kelvin and is the basis of cheap on-die temperature sensors. With 10 microamps of bias V_F (25 C) is about 0.55 V and V_F (75 C) about 0.45 V — the working principle behind LM35, AD590 and the on-die thermal diodes inside almost every modern CPU and GPU. Set I_S to about 1e-12 A and V_F near 0.55 V in the tool, then sweep the temperature slider from 25 to 75 C to observe V_F dropping linearly.
Mixers and detectors (RF / IF): The non-linear (exponential) I-V curve of a diode contains a quadratic term in its Taylor series, which mixes two frequencies to produce sum and difference components. AM radio detectors, radar IF stages and satellite LNB down-converters all exploit this. Matching the dynamic resistance r_d to the source impedance (often 50 ohm) sets the conversion efficiency, and the bias current needed for r_d = 50 ohm — about 0.5 mA at room temperature — is exactly what this tool computes. Schottky diodes, with their lower V_F and faster recovery, are preferred for high-frequency mixers.
Common Pitfalls and Notes
The most common simplification is "silicon diodes conduct above 0.7 V and not below". As the semi-log plot in this tool shows, the real curve is a smooth exponential and a current in the mA range already flows at V_F = 0.4 V. The "0.7 V threshold" is the operating point at hundreds of mA to 1 A. For precision designs — microamp metrology, maximum-power-point tracking in photovoltaics — Shockley's equation must be used directly. Verify in the tool that meaningful current appears already at V_F = 0.3 to 0.5 V to internalize this.
The next pitfall is "0.7 V stays 0.7 V over temperature". In a real pn junction V_F drops by about 2 mV per kelvin (silicon at 25 C: 0.7 V; at 75 C: about 0.6 V). The temperature-comparison chart in this tool only includes the V_T effect, not the much stronger temperature dependence of I_S (roughly doubling per 10 C). Designs must consider the full V_F variation across the industrial range -40 to 85 C and prefer constant-current biasing (LEDs) or comfortable headroom (linear regulators) over constant-voltage drive.
The last pitfall is "the Shockley equation is the complete model". The real diode adds (1) a series bulk resistance Rs that flattens the I-V slope at large currents, (2) a reverse leakage that slowly grows instead of saturating at -I_S, leading to Zener or avalanche breakdown beyond a critical voltage, and (3) extra recombination current at low V that pushes n toward 2. This tool covers the ideal medium-current forward region and is meant as a teaching model. Real designs need SPICE models with parameters Vto, Rs, Cjo, BV, Eg, Xti or fitting against measured I-V curves.