Quantum-confined Stark effect (QCSE)

The Stark effect is the energy shift of atomic or molecular states under an applied electric field. In bulk semiconductors, the analogous Franz–Keldysh effect produces a small absorption-edge shift with field. In quantum wells, confinement amplifies the effect dramatically — and the band-edge absorption becomes a strong function of applied field.

Mechanism in a quantum well under transverse electric field. Applied field $F$ perpendicular to the well layers:

1. Tilts the band edges — electrons drift toward the high-potential well wall, holes toward the low-potential wall, reducing electron–hole overlap and shifting the effective transition energy downward (red shift)
2. Reduces oscillator strength — the spatial separation of electron and hole envelope functions reduces the matrix element for optical transitions
3. Polaron broadens the absorption peak — the heavy-hole exciton remains bound at moderate fields where bulk excitons would already be ionized, preserving sharp absorption features

The combination produces strong field-dependent absorption near the band edge: at zero field, the well is transparent slightly above the bandgap; at moderate field ($\sim 100$ kV/cm), absorption at the same wavelength becomes very strong.

Typical absorption change for an InGaAsP MQW at 1550 nm:

Implementation in EAMs. An electro-absorption modulator places a MQW stack inside a reverse-biased p-i-n diode. Photons at the design wavelength pass through with low loss at zero bias. Applying reverse bias creates a strong transverse electric field across the i-region, activating the QCSE and dramatically increasing absorption. Modulation depths exceeding 20 dB are achievable with $\sim 2$ V swing.

Drawbacks.

• Chirp. QCSE produces simultaneous absorption and index change (Kramers–Kronig related). The associated frequency chirp during modulation is typically smaller than for direct laser modulation but larger than for ideal Mach–Zehnder modulators. EAM chirp parameter $\alpha_H$ is typically 0.5 – 1.5, vs $\sim 0$ for push–pull MZMs.
• Wavelength sensitivity. The strong wavelength dependence of QCSE means the EAM operates over only $\sim 20 - 30$ nm range. The wavelength must be specified at design time; the same chip cannot serve different wavelengths.
• Polarization sensitivity. QCSE differs for TE and TM polarizations because the heavy-hole–electron overlap differs in the two polarizations. Polarization-insensitive operation requires careful strain engineering.

QCSE-based EAMs are widely used in electro-absorption-modulated lasers (EMLs) — monolithically integrated DFB laser + EAM transmitters that are the dominant 10/25/100 Gb/s telecom source for short to medium reach.