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For an ideal p–n junction, forward current follows the Shockley relationship ID = IS[exp(VD/(nVT)) − 1]. Increasing junction voltage therefore produces a multiplicative increase in current, while voltage rises only logarithmically with current. Real terminal measurements follow this law only over a useful middle range; series resistance, recombination, heating and device construction alter the curve outside it.
What forward conduction means
A p–n diode is forward-biased when its p-side is at a higher electric potential than its n-side. The applied voltage lowers the depletion-region barrier, allowing carriers to be injected across the junction. “Forward-conducting” does not mean that a diode waits for a universal threshold such as 0.7 V. In the ideal equation, some current exists at every finite forward voltage; a circuit designer chooses when that current is significant.
TI describes about 0.6 V as a typical room-temperature silicon forward drop, but the value depends on current, temperature and ideality factor (TI reference guide).
The Shockley diode equation
ID = IS[eVD/(nVT) − 1]
- ID: diode current.
- VD: voltage across the junction.
- IS: saturation-current model parameter.
- n: emission or ideality factor.
- VT = kT/q: thermal voltage, with T in kelvins.
At 300.15 K (about 27 °C), VT is approximately 25.865 mV. TI gives the same equation and its logarithmic form for forward-current analysis and parameter extraction (application report).
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Why the −1 matters
The complete expression gives zero current at zero voltage and approaches −IS under sufficiently large reverse bias before breakdown in the idealized model. It may be dropped only when the exponential term is much larger than one:
ID ≈ ISeVD/(nVT)
Solving this forward approximation for voltage gives VD = nVT ln(ID/IS). This is junction voltage, not necessarily the complete voltage measured at the package terminals.
Why the current is exponential
Forward bias changes the electrostatic potential across the depletion region. Carrier concentrations at the junction boundary vary exponentially with that potential. The resulting minority-carrier injection and diffusion through the neutral semiconductor regions produce the familiar exponential current.
Ideality factor and transport mechanism
Diffusion-dominated current is commonly associated with n ≈ 1. If recombination in the depletion region contributes strongly, the slope often approaches n ≈ 2. The frequently used range 1–2 is an engineering rule of thumb, not an immutable limit; fitted values vary with current range, temperature and device construction (TI; Electronics Letters).
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Thermal voltage
VT increases linearly with absolute temperature and is a scaling voltage inside the exponent, not the diode’s forward drop. At room temperature, a tenfold current increase requires approximately 59.6 mV for n = 1 or 119.1 mV for n = 2.
Reading the relationship on a graph
Taking logarithms produces:
ln ID = ln IS + VD/(nVT)
Thus a plot of ln(I) versus V is approximately straight in the exponential region. For log10(I), the slope is 1/(2.303nVT), and the voltage for a decade of current is ΔV = 2.303nVT. Ordinary axes show a curved knee; semilog axes expose the nearly linear middle section.
Why real diodes depart from the ideal curve
Very low current
Instrument resolution, noise, surface and parallel leakage, offsets and depletion-region recombination can dominate. The diffusion-only equation may not fit this region.
Moderate current
This is usually the best range for demonstrating Shockley behavior: current is measurable, while junction voltage still dominates the terminal voltage. The range depends on part, package, temperature and test setup.
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High current
Measured voltage includes ohmic drops in the semiconductor, contacts, leads and package:
Vterminal ≈ nVTln(1 + ID/IS) + IDRS
The IDRS term bends a semilog plot away from a straight line. At still higher current, high-level injection, conductivity modulation, current crowding, self-heating and thermal runaway may matter.
Temperature feedback
At fixed current, silicon forward voltage generally falls as junction temperature rises. About −2 mV/°C is a common approximation, not a guaranteed coefficient. VT rises with temperature, but IS also changes strongly and usually dominates the fixed-current shift. Junction temperature—not merely ambient or case temperature—is the temperature in the equation. Extra current raises dissipation, heating the junction and potentially allowing still more current.
Worked numerical example
Assume, purely for illustration, IS = 10−14 A, n = 1 and T = 300.15 K. With VT ≈ 25.865 mV, at VD = 0.60 V:
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ID ≈ 10−14 exp(0.60/0.025865) ≈ 12.2 mA
This ignores series resistance and other nonidealities. It is not a universal claim that every silicon diode carries 12.2 mA at 0.60 V; actual IS, n, temperature and construction differ.
Measuring and fitting a diode
Safe resistor-based setup
- Use a variable DC supply, a series current-limiting resistor and the diode.
- Increase supply voltage in controlled increments.
- Measure voltage directly across the diode and resistor voltage separately.
- Calculate current as ID = VR/R.
- Record diode voltage, current, part number, polarity, resistor value, instrument ranges and temperature.
- Plot current on ordinary and logarithmic scales.
Never connect a forward diode directly across an ideal voltage source. Allow thermal stabilization, use current steps for precision work, and use Kelvin connections when extracting low series resistance.
A 1N4148 laboratory study found that the basic model fits only a limited range; adding series and parallel resistance improves agreement (study).
Extracting n and IS
For two valid exponential-region points:
n = (V2 − V1)/(VT ln(I2/I1))
Then IS = I1e−V1/(nVT). Alternatively fit V = a + b ln I; n = b/VT and IS = e−a/b. Do not fit the entire curve: select the straight semilog region, inspect residuals, and add RS or additional current terms only when data justify them.
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Dynamic resistance
Differentiating the forward approximation gives the incremental resistance:
rd = dV/dI ≈ nVT/ID
At room temperature and 1 mA, this is about 25.9 Ω for n = 1 or 51.7 Ω for n = 2. It differs from the DC ratio VD/ID. Including series resistance, rtotal ≈ RS + nVT/ID.
Device types and model limits
| Device | How the equation applies | Main qualification |
|---|---|---|
| Silicon p–n diode | Useful in its moderate forward-current region | Use measured parameters and include RS at high current |
| Schottky diode | Exponential approximation often useful | Metal–semiconductor barrier physics, leakage and parameters differ |
| LED | Nonlinear forward behavior remains | Material, recombination, optical and thermal effects differ |
| Zener/avalanche diode | Forward direction may resemble a p–n diode | Reverse breakdown needs a separate model |
| Solar cell | Diode term appears in illuminated models | Photocurrent and additional recombination terms are required |
Shockley, piecewise and SPICE models
| Purpose | Model | Limitation |
|---|---|---|
| Conceptual explanation | Ideal Shockley equation | Omits most real-device effects |
| Quick hand estimate | Constant-drop or piecewise-linear | Hides exponential and temperature behavior |
| Moderate-current estimate | Shockley with n and IS | Requires a valid fitting range |
| Power design | Shockley plus RS and thermal model | More parameters and thermal coupling |
| Transient simulation | Vendor SPICE model | Parameters are part- and range-specific |
Practical SPICE models add normal and recombination currents, series resistance, high-injection knee current, junction capacitance, transit time, reverse breakdown and temperature dependencies. See the MathWorks SPICE diode documentation. Exponential nonlinearities can also cause simulator convergence problems; realistic source resistance, bounded exponential evaluation and sensible initial conditions help (Ferrite Systems).
Common mistakes
- Calling 0.7 V the diode equation: it is only a rough operating-point heuristic.
- Treating IS as ordinary measured reverse leakage: it is a model parameter.
- Assuming n is always exactly 1 or always between 1 and 2.
- Ignoring series resistance or self-heating.
- Fitting all measured points instead of the appropriate semilog interval.
- Confusing static V/I resistance with incremental dV/dI resistance.
- Using an uncontrolled voltage sweep or connecting a diode directly to an ideal source.
The Bottom Line
The Shockley equation explains why forward diode current rises exponentially, but it describes the junction—not every detail of a real terminal measurement. Use semilog data to identify the valid region, extract n and IS there, and add resistance, thermal and device-specific models when the operating conditions demand them.
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