Chin-Yao Tsai

Nonlinear gain coefficients in semiconductor quantum-well lasers: effects of carrier diffusion, capture, and escape

Effective nonlinear gain coefficients due to the effects of carrier diffusion, capture, and escape are derived from the carrier transport equations. The quantum capture and escape processes between the confined states and the unconfined states are calculated from first principles by evaluating the carrier-polar longitudinal optical phonon interactions. The dc and ac capture times and escape times are derived from evaluating the net capture current of carriers. The differences in capture and escape times between dc and ac operating conditions are numerically investigated. We find that both dc and ac escape times are strongly dependent on the quantum well structure. This differs from the dc and ac capture times that are not sensitive to the quantum well structure. We also find that the dc escape time predicted by the classical thermionic emission theory will no longer be valid for narrow or shallow quantum wells. We show that both dc and ac capture and escape time ratios will increase as the carrier temperature and the carrier density in the quantum well increase. Therefore, we suggest that the possible cause of the resonant frequency degradation and dramatic increase in the damping rate results from the increase of the ac capture to escape time ratio by the effects of carrier heating. Two theoretical models (2N and 3N models) were used to study the effects of carrier diffusion-capture-escape on the modulation response of quantum-well lasers and a distributed model of carrier transport in quantum-well lasers is proposed. Their implications in designing high-speed quantum-well lasers are discussed. >

Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating

Nonlinear gain coefficients due to the effects of carrier heating are derived from the rate equations of carrier energy transfer in semiconductor lasers. We find that, in the modulation responses of semiconductor lasers, stimulated recombination heating will affect the resonant frequency and damping rate in a same form as the effects of spectral hole burning, while free carrier absorption heating will only affect the damping rate. The effects of injection heating and nonstimulated recombination heating are also discussed. The carrier energy relaxation time is calculated from first principles by considering the interactions between carriers and polar optical phonons, deformation potential optical phonons, deformation potential acoustic phonons, piezoelectric acoustic phonons. At the same time, the hot phonon effects associated with the optical phonons are evaluated because their negligible group velocity and finite decay time. We show that the carrier-polar longitudinal optical phonon interaction is the major channel of carrier energy relaxation processes for both electron and holes. We also point out the importance of the longitudinal optical phonon lifetime in evaluating the carrier energy relaxation time. Neglecting the finite decay time of longitudinal optical phonons will significantly underestimate the carrier energy relaxation time, this not only contradicts the experimental results but also severely underestimates the nonlinear gain coefficients due to carrier heating. The effects of spectral hole burning, stimulated recombination heating, and free carrier absorption heating on limiting the modulation bandwidth in semiconductor lasers are also discussed.

Carrier energy relaxation time in quantum-well lasers

Carrier energy relaxation via carrier-polar optical phonon interactions with hot phonon effects in multisubband quantum-well structures is theoretically studied by using both bulk longitudinal optical phonons and confined longitudinal optical phonons. We find that the width and the depth of quantum wells only have moderate effects on carrier energy relaxation rates. Our results also indicate that the difference of energy relaxation rates between the quantum well and the bulk material is not significant. We investigate the effects of longitudinal optical phonon lifetimes on the carrier energy relaxation rate. Neglect of the finite decay time of longitudinal optical phonons will significantly underestimate the carrier energy relaxation time; this not only contradicts the experimental results but also severely underestimates the nonlinear gain coefficient due to carrier heating. The implications of our theoretical results in designing high-speed quantum-well lasers are discussed.

EFFECTS OF SPECTRAL HOLE BURNING, CARRIER HEATING, AND CARRIER TRANSPORT ON THE SMALL-SIGNAL MODULATION RESPONSE OF QUANTUM WELL LASERS

We present an analysis of the high‐speed characteristics of quantum well lasers by simultaneously considering the effects of spectral hole burning, carrier heating, and carrier transport. An exact form of the small‐signal modulation response is obtained. The effects of carrier dephasing time in spectral hole burning, energy relaxation time in carrier heating, and diffusion‐capture‐escape times in carrier transport on the modulation response of quantum well lasers are theoretically investigated.

Carrier capture and escape in multisubband quantum well lasers

Carrier capture and escape processes between quantum wells and barriers via carrier-polar optical phonon interactions are theoretically studied in multisubband quantum well structures. We find that carriers in each subband have their own minimum capture and escape times when the energy difference between the band edges of the subbands and the barrier is equal to the energy of a longitudinal optical phonon. Our results indicate that carrier escape time is more quantum well structure-dependent while carrier capture time is less structure-dependent. Explicit forms for calculating carrier capture and escape times are given which are crucial for designing the quantum well structures with optimal capture or escape efficiencies.<<ETX>>

Breakdown of thermionic emission theory for quantum wells

Carriers escape from quantum wells into barriers via carrier‐polar optical phonon absorption is theoretically studied in multisubband quantum well structures. We find that carriers in each subband have their own minimum escape time when the energy difference between the band edges of the subband and the barrier matches the energy of a longitudinal optical phonon. Compared to the calculations from classical thermionic emission theory, we find that the thermionic emission theory is no longer valid when the width or the depth of quantum wells is small.

Carrier DC and AC capture and escape times in quantum-well lasers

A theoretical model is proposed to study the carrier DC and AC capture and escape times in the small signal modulation response of quantum-well lasers. We derive the DC and AC capture and escape times by calculating the carrier net capture current. Our numerical results indicate that the AC capture and escape times are smaller than the DC capture and escape times. In some cases, they may be even smaller by one order of magnitude. We also find that the AC capture/escape time ratio is larger than the DC capture/escape time ratio by a factor of two. Therefore, conventional theoretical models that do not distinguish the differences between the DC and AC capture and escape times may overestimate the resonant frequency and underestimate the damping rate in the modulation response of quantum-well lasers, i.e., the AC capture and escape times limit the modulation bandwidth of quantum-well lasers more severely than that predicted by the DC capture and escape times.<<ETX>>

Carrier energy relaxation in multisubband quantum well lasers with hot phonon effects

Carrier energy relaxation rates via carrier‐polar optical‐phonon interactions with hot phonon effects are theoretically studied in multisubband quantum well structures. The effects of changing the width and depth of quantum wells on the carrier energy relaxation rate are discussed. Compared to the result of the bulk, we find that the difference in the energy relaxation rate between quantum wells and bulk is rather small. Reducing the lifetime of longitudinal‐optical phonons will effectively enhance the carrier energy relaxation rate. The implications in designing high‐speed quantum well lasers are also suggested.

Effects of hot phonons on carrier heating in quantum-well lasers

The hot phonon effects on carrier heating in quantum-well lasers are theoretically investigated. We show that the neglect of the finite lifetime of LO phonons will significantly underestimate the carrier energy relaxation time and thus underestimate the effect of carrier heating in quantum-wed lasers. We investigate the effects of carrier heating with hot phonons on the saturation and degradation of the resonant frequency in high-speed quantum-well lasers. The implications of the hot phonon effects on the design of high-speed quantum-well lasers are also discussed.<<ETX>>