This tutorial visualizes the push-pull of electrons and holes at a PN junction and how applied voltage changes the depletion region and energy bands. You see the physical picture (carriers and lattice) and the band diagram in one view.

 

Mathematical foundation

1. PN junction

In N-type silicon, majority carriers are electrons (blue dots). In P-type, majority carriers are holes (red circles). At the junction, electrons diffuse into the P side and recombine with holes, leaving a depletion region with few free carriers and a built-in potential V_bi (about 0.7 V for Si).

2. Bias and depletion width

Forward bias (V > 0) reduces the barrier: the depletion region shrinks, carriers cross and recombine, and current flows. Reverse bias (V < 0) increases the barrier: the depletion region widens, carriers are pulled away from the junction, and only a tiny saturation current flows.

3. Energy bands

The conduction band E_c and valence band E_v bend near the junction. The offset between P and N sides is q V_bi. With forward bias the "hill" flattens; with reverse bias it becomes a steep cliff.

4. Diode equation

The current is I = I_s (e^{qV/(n k T)} − 1). Forward: I grows exponentially with V. Reverse: I ≈ −I_s. The I–V graph in the separate canvas below shows this curve and the operating point as you move the voltage slider.

 

Usage

Follow these steps to explore the diode mechanism:

1. Source: Choose DC (constant voltage), Sinusoidal, Pulse, or Triangle. The Magnitude (V) slider sets the voltage in DC mode and the amplitude (peak value) for the other sources. The readout shows the instantaneous voltage.
2. Magnitude (V) slider (−5 V to +5 V): In DC mode this is the applied voltage. For Sinusoidal/Pulse/Triangle it is the amplitude. Move right for forward bias; the depletion region shrinks, blue electrons and red holes move toward the center and recombine (flash), and the energy band "hill" flattens. Move left for reverse bias; the depletion region widens, carriers are pulled toward the terminals, and the band diagram shows a steep barrier.
3. Wave speed (Hz): For Sinusoidal, Pulse, and Triangle sources, this sets how fast the voltage changes (frequency in Hz). Use a low value (e.g. 0.1–0.2 Hz) to see electrons and holes move and recombine in slow motion; use a higher value (e.g. 1–2 Hz) for faster cycles.
4. Top half (PN junction): N-type (light blue) on the left, P-type (light red) on the right. Gray overlay = depletion region. Blue dots = electrons, red circles = holes. Gray dots = silicon lattice. Polarity markers at the left and right ends show +/− in circles (blue fill = negative, red fill = positive); they update with applied voltage (forward: − left, + right; reverse: + left, − right). Watch carriers cross and recombine in forward bias and the center empty in reverse.
5. Bottom half (Energy band): Conduction band E_c (blue) and valence band E_v (orange) bend at the junction. Forward bias lowers the barrier; reverse raises it.
6. I–V curve: Plots the diode I–V curve. The green dot is the operating point. Forward: point moves up; reverse: near bottom (saturation current).
7. Input/output vs time: Time-domain plot with shared vertical and horizontal center lines. V (input) (blue) and V (output) (orange, half-wave rectified) in the top half; I (output) (green) in the bottom half. Voltage traces are drawn at 2× scale for visibility.
8. Show Depletion labels: Check to show "Depletion Region" and N-type / P-type; uncheck to hide.

Tips: Set voltage to 0 to see zero bias (moderate depletion, small barrier). Then move to +1 V or +2 V to see strong forward behavior (recombination, flat bands). Then move to −2 V or −3 V to see reverse (wide depletion, steep bands, almost no current).

Parameters

• Source: DC (constant), Sinusoidal, Pulse (50% duty), or Triangle. Magnitude slider sets DC value or peak amplitude.
• Wave speed (Hz): Frequency of the time-varying source (0.05–2 Hz). Lower = slower voltage change so carrier movement is easier to see.
• Magnitude (V): Applied bias amplitude from −5 V to +5 V. Forward (> 0) allows current; reverse (< 0) blocks it (except tiny I_s).
• Polarity markers: ± in circles at the ends of the material; blue circle = negative, red circle = positive. They reflect applied voltage polarity and swap in reverse bias.
• Depletion region: Width grows with reverse bias and shrinks with forward bias. Built-in potential V_bi ≈ 0.7 V (Si) sets the band offset.
• I–V curve: I = I_s(e^{qV/(n k T)} − 1). Logarithmic vertical scale; display clamped for large forward current.
• Time-domain plot: Last 5 s of V (input), V (output) = max(0, V), and I (output). Voltage traces use 2× gain for visualization only.