The band-to-band and excitonic absorption of the quantum-well modulator under and external electric field is calculated by using the k.p model. This derives a variety of characteristics including the bias-dependent extinction ratio and the chirp behavior, and allows optimized design for desired device performances.

The source code is done by using Python. The calculation consists of the following steps:

• The k.p model is employed and solved by using numerical methods to calculate the electron and hold wavefunctions, and the conduction and valence energy bands;

• Calculate the absorption and its bias dependence by using the Fermi's golden rule;

• In terms of calculated absorption, the extinction ratio vs bias is obtained;

• The chirp parameter is calculated by using the Kramers-Kronig relation.

The absorption curve of the electro-absorption modulator is measured experimentally, and then fitted by applying a Levenberg-Marquardt fitting algorithm (source coding by C++). The chirp and absorption curve are linked by the Kramers-Kronig relation. From fitted absorption model curve, the chirp parameter can be calculated over a range of the temperature. This approach is applicable to individual chips, and allows for characterizing chip-to-chip difference in the chirp.

C++ is used as the programming language core engine of retrieving data from different testing data files. The front-end GUI is implemented using Qt.

The spectral response of common optoelectronic photodetectors is restricted by a cutoff wavelength limit λ_c that is related to the activation energy (or bandgap) of the semiconductor structure (or material) (Δ) through the relationship λ = hc/Δ. This spectral rule dominates device design and intrinsically limits the long-wavelength response of a semiconductor photodetector. Here, we report a new, long-wavelength photodetection principle based on a hot–cold hole energy transfer mechanism that overcomes this spectral limit. Hot carriers injected into a semiconductor structure interact with cold carriers and excite them to higher energy states. This enables a very long-wavelength infrared response. In our experiments, we observe a response up to 55 µm, which is tunable by varying the degree of hot-hole injection, for a GaAs/AlGaAs sample with Δ = 0.32 eV (equivalent to 3.9 µm in wavelength).

Internal photoemission refers to such a case where carriers are photoexcited and transferred from one material to another by passing through an interface. Photoexcitation occurs in the absorber (referred to as emitter) before photoemission. The photoexcited holes with high energies originate from those at the states around the Fermi level. By having higher energy than the photoemission threshold, these carriers can come across the penitential barrier; in other words, photocarriers must be transferred from the energy band of the emitter to that of the barrier material. This process typically involves scatterings through which the excited holes are directed to pass over the emitter-barrier interface.

Optical excitation includes direct and indirect transitions. The type of transitions that contributes to quantum yield (defined as number of carriers being collected per incident photon) relies on the energy of the incident photon. In the vicinity of the photoemission threshold, carriers must stay at states with energies nearly at the same level of the potential barrier before emission. This results in a higher probability of the occurrence of indirect transitions. However, under the excitation of photons with energies much greater than the threshold energy, direct transitions dominate over the indirect transitions in contributing the quantum yield significantly.

In terms of the principle of the internal photoemission, its use lies in at least the following areas: (1) studying the band parameters of materials, such as the band structure; (2) studying the band offset at the interface of a heterostructure; (3) development of internal photoemission-based photodetectors.

The real (ε₁) and imaginary (ε₂) components of the dielectric function (DF) must satisfy the Kramers-Kronig (K-K) relation, i.e.,.

where P denotes the principal value of the integral. To obtain a universal DF independent of particular optical processes and materials or structures, multiple oscillator-like mathematical functions are used to construct the DF. The idea is that the DF of individual optical process, such as the BB and IVB transitions, can be expanded into basic functions, for example, with the following form:

where ε₁ is the high-frequency dielectric constant; N and M are the number of functions, determined by the fitting. The second and third terms correspond to the Lorentz and localized functions, respectively.

An optical spectrum is usually a result of various optical processes associated with the material itself and other influences from, for example, the dopants or impurities. In most of the cases, only those that have the dominating effects are considered. By using a comprehensive DF, all of the features shown on the spectrum are able to be taken into account, and therefore, a “perfect” fitting can be achieved. This DF model is basically a mathematical manipulation and does not have the corresponding physical processes. Nevertheless, this approach is very useful and serves as the way of converting the experimental data (transmission and reflection) into a DF. Apparently, the advantage lies in the inclusion of all of possible optical processes such as the BB and IVB transitions, the transitions involving impurity levels or bands, and the doping-induced band tailing states, intra-band free-carrier (FC), and phonon absorption.

The Lorentz oscillators have the global effects on the entire spectral range and cannot replicate fine features. One of the approaches for this is to limit the number of Lorentz oscillators being used, as well as adding localized functions which are handled by the third term, where A_k is the amplitude. Here, ε₁^k(ω) is obtained by carrying out the K-K transformation on ε₂^k(ω); ε₂^k(ω) consists of localized functions, as constructed with the following triangle function:

which is defined in the spectral region of [ω_k-1, ω_k+1]. It is apparent that the triangle function should be limited to a reasonably small range to mimic the experiments.

To fit the experimental spectra, all of the unknown parameters are taken as fitting parameters and determined by using the Levenberg-Marquardt method. The fitting accomplished in this study is divided into two steps: (1) determining the global Lorentz oscillators and then (2) refining the localized functions. Usually, it is necessary to include a great number of oscillators or localized terms to achieve a “perfect” fitting, which means a great deal of computation time is required. A better implementation is to repeat the fitting iteratively, i.e.,

where ε_m-1(ω) is obtained from the prior fitting, and ε_m(ω) is the new DF.

The fittings include the complex index of refraction of each stratified layer derived from the DF, and then the calculation of the reflection and transmission for the sample, consisting of a thin film on a substrate. The calculation is carried out based on an intensity- transfer-matrix method (ITMM). A TMM is used to take into account the coherence of the forward and backward traveling waves due to the interfacial reflection in the film. However, non-coherence should be considered to deal with the substrate, since its thickness is of the order of magnitude of 10 µm.

The development of 1310 nm VCSELs is hindered by the poor performances of InP-based distributed Bragg reflectors (DBRs). To solve this problem, several methods such as InP/GaAs hetero-integration, epitaxy of InP-based Sb-compound DBRs and GaAs-based active materials are applied to the fabrication of 1310 nm VCSELs. We designed a composite structure of 1310 nm VCSELs in which InP-based InAsP/InGaAsP strain-compensated multi-quantum wells (SC-MQWs) are sandwiched between SiO2/TiO2 dielectric DBRs and GaAs/AlAs DBRs. The lasers have been fabricated by structure design, materials growth, wafer direct-bonding and device processing. Main research works are as follows:

1. We designed the structure of VCSELs in three aspects: active region, resonant cavity and effective carrier injection. First, energy bands of InAsP/InGaAsP SC-MQWs are calculated by employing effective mass model, and structure parameters such as thickness and element component of the well and barrier are optimized so that maximum electron–confinement energy can be obtained. Second, we provide an intuitive method to qualitatively evaluate the reflectivity of periodic structures. The cavity length and DBRs’ sequence of VCSELs with the structure of SiO2/TiO2 DBR-cavity-GaAs/AlAs DBR are then determined by this method for obtaining Fabry-Pérot (F-P) resonance and effective reflection from DBRs. The resonance features are confirmed by calculating optical distribution using transfer-matrix method. The threshold conditions of VCSELs are analyzed and the relationships of DBR reflectivity and well numbers are obtained to achieve lower threshold current. We then provide an optimizing scheme for high device performances. The carrier injection efficiency is of vital importance for VCSELs. Based on the self-consistent solution to Poisson equation and carrier diffusion, we calculate carrier distribution in active layer under different structures of current-injection region, and propose the approaches for effective carrier injection into the active region.

2. To obtain lower optical absorption and higher conductivity of materials, we optimized the doping of n-GaAs/AlAs DBRs. Then we grow GaAs/AlAs DBRs and InP-based resonant cavities including InAsP/InGaAsP MQWs using gas-source molecular-beam epitaxy (GSMBE). Considering the requirement of precisely control of DBR central wavelength and resonant cavity length, we can easily adjust the DBR central wavelength by employing F-P resonators, and grows InP/InGaAsP superlattice in the InP-based cavity so that specific resonance wavelength can be realized in device processing.

3. We developed the technologies of InP/GaAs wafer direct-bonding. By designing a experimental fixture and optimizing the process of wafer-bonding, we fabricate uniformly bonded InP/GaAs wafer-pairs. In process, infrared-spectra method and high-resolution X-ray diffraction (HRXRD) are used to characterize bonding quality and the InP epilayer on GaAs substrate respectively. Results show that 0.044% of residual strain and 0.11° of <001> tilt angle exist in the sample with bonding process of (001) InP layer and GaAs substrate. This result confirms uniform bonding between InP and GaAs materials.

4. We evaluated the effects of high-temperature bonding process on material performances. Experimental results show that the barrier height of bonded InP/GaAs hetero-junction is close to the theoretic value. By employing superlattice structures in InP-based materials and higher bonding temperatures, electrical performances of bonding samples can be improved. Owing to the high-temperature stability, InAsP/InGaAsP MQWs upon bonding process has comparable luminescent performances with those of as-grown ones even when the bonding process is up to 650 °C. Thus this material system is adapted to hetero-integration using wafer direct-bonding techniques. However, high-temperature annealing triggers the disordering of InP/GaAs interface, which introduces excess optical loss and blue-shift of cavity mode in VCSELs. We evaluate optical loss by using wafer-bonded F-P structures. Simulated Results show that the value of optical loss introduced by bonding interface is comparable to the loss of tunnel junction and aperture scattering etc. Lowering annealing temperatures and employing superlattice at the interface is beneficial to lower optical loss of bonding interface.

5. Bottom-emitting devices of 1310 nm VCSELs were fabricated by device processing including high-temperature wafer direct-bonding of InP-based active layer and GaAs-based DBRs, circular mesa etching, current aperture definition, metal contact and dielectric DBRs’ deposition. The CW submilliampere threshold current as low as 0.54 mA and maximum optical power of 1.9 mW have been achieved. The slope efficiency is between 0.27 and 0.32 W/A. The 5 mm-aperture device exhibits single-transverse mode emission with a maximum SMSR of 43 dB. These results indicate that the InAsP/InGaAsP QW active region is attractive as an optional gain medium to the AlGaInAs QWs for high-performance long-wavelength VCSELs.