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 weaker change: the absorption edge develops a field-dependent tail. In quantum wells, confinement amplifies the effect dramatically. 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. Excitons survive: 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 nearly transparent at photon energies just below the exciton absorption edge (bandgap plus confinement energies); at moderate field ($\sim 100$ kV/cm), absorption at the same wavelength becomes very strong.

For weak fields the shift grows as the square of the field and the fourth power of the well width (second-order perturbation theory), so wider wells shift further for a given field but lose oscillator strength sooner, as the electron and hole separate. An InGaAsP or InGaAlAs MQW for 1550 nm is designed with its zero-field exciton edge at a shorter wavelength than the operating wavelength, so that the operating reverse bias moves the edge onto it. At 1550 nm, a shift of 1 meV corresponds to 1.94 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. A few volts of reverse bias change the transmission by well over 10 dB.

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. The EAM chirp parameter depends on bias: positive at low reverse bias, it falls through zero and turns negative at higher bias, so EMLs are biased where it is small or slightly negative. A push–pull MZM has essentially zero chirp.
• 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 heavy-hole transitions couple only to TE light while light-hole transitions couple to both. Polarization-insensitive operation requires careful strain engineering.

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

References: D. A. B. Miller et al., "Band-edge electroabsorption in quantum well structures: the quantum-confined Stark effect," Phys. Rev. Lett. 53, 2173 (1984); L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012).