What property of an LED's semiconductor material determines its forward voltage drop?

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Current flows in an LED only once the applied voltage is enough to lift electrons across the semiconductor's band gap, so the forward drop follows that band gap — and so does the color, which is why red LEDs run near 1.8 V and blue ones near 3 V. Bulk resistance, junction capacitance, and junction depth affect other behavior but not the voltage the material demands.