Carrier Rate Equations Research Articles

The Effect of Electron Escape Rate on the Nonlinear Dynamics of Quantum Dot Lasers under Optical Feedback

When theoretically investigating the nonlinear dynamics of quantum dot lasers (QDLs), the parameter value of the electron escape rate (Ce) is sometimes approximated to zero to simplify the calculation. However, the value of Ce is dependent on the energy interval between the ground state (GS) and the excited state (ES) in the conduction band and is affected by the operation temperature. As a result, such simplified approximation treatments may lead to inaccurate results. In this study, after considering the effect of Ce, we investigate the nonlinear dynamics of QDLs with and without optical feedback based on the asymmetric electron-hole carrier rate equation model. The simulation results show that without optical feedback, the lasing conditions for ES and GS in free-running QDLs are dependent on the value of Ce. A larger Ce is more helpful for the ES emission, and the GS emission will stop lasing if Ce is large enough. Through analyzing the dynamical characteristics of GS and ES in QDLs with optical feedback under different Ce values, it can be found that the dynamical characteristics are strongly correlative with Ce.

Impact of Carrier Transport and Capture on VCSEL Dynamics

Using a vertical-cavity surface-emitting laser (VCSEL) equivalent circuit model based on two carrier rate equations to include effects of carrier dynamics, we study the impact of carrier transport and capture on the small- and large-signal modulation response of high-speed VCSELs. The model also accounts for parasitics, current-induced self-heating, and gain compression. A variation of the effective capture time from 1 to 15 ps is found to have a large impact on the small-signal modulation response, with the 3 dB bandwidth decreasing from 40 to 15 GHz and the response transitioning from under-damped to over-damped. This is primarily due to the increasing low frequency parasitic-like roll-off with increasing effective capture time. A significant effect on the optical waveforms produced by the VCSEL under 56 Gbit/s on-off keying (OOK) non-return-to-zero (NRZ) and pulse-amplitude modulation 4 (PAM4) modulation is observed, with a short effective capture time leading to horizontal eye closure caused by timing jitter (TJ) and intersymbol interference (ISI) and a long effective capture time leading to vertical eye closure caused by long rise- and fall-times. However, for high modulation speed, a short effective capture time is needed and the photon lifetime should be set for clear eye opening. We also show the impact of the effective capture time on the output power vs current characteristics and map the dependence of internal temperature, carrier densities, carrier escape and leakage rates, and spontaneous recombination rates on current for different effective capture times.

Small signal analysis of the modulation bandwidth of light-emitting diodes for visible light communication

We perform a theoretical investigation of the small-signal modulation characteristics of light-emitting diodes (LEDs) for visible light communication (VLC) applications. A comprehensive model for the small-signal frequency bandwidth is developed using a carrier rate equation with the ABC recombination model. Using the obtained general form of the 3-dB bandwidth (f3dB), we analyze the dependence of the bandwidth on various parameters of the LEDs. The internal quantum efficiency (IQE) is found to significantly influence the modulation bandwidth of LEDs. At a high current density, f3dB is approximately inversely proportional to IQE, suggesting the importance of a trade-off between high IQE and fast modulation speed. In addition, we analyze and discuss the effects of the radiative recombination coefficient, current density, and quantum-well thickness on f3dB, comparing the modeling results with previous experimental data. The presented model of the modulation bandwidth can be advantageous in understanding the modulation characteristics of LEDs for high-speed VLC.

Dynamic routing through saturable absorption in graphene photonic resonators: Impact of carrier diffusion and finite relaxation time

We assess the continuous wave and dynamic routing performance of a compact silicon-on-insulator disk resonator overlaid with a graphene monolayer at telecommunication wavelengths. Switching action is enabled by saturable absorption in graphene, controlled by a pump wave of only a few milliwatts. Graphene saturable absorption is modeled through a carrier rate equation that incorporates both the finite relaxation time and diffusion of photo-generated carriers, providing a realistic account of carrier dynamics. The overall nonlinear response of the resonator is evaluated with a rigorous mathematical framework based on perturbation theory and temporal coupled-mode theory. We thoroughly investigate the effects of carrier diffusion and finite relaxation time, both separately and together. We also take into account nonlinear refraction via a Kerr effect term and quantify its impact on the overall response. In order to suppress the Kerr effect, we replace silicon with silicon-rich nitride, allowing for the individual contributions of the resonator core and graphene (of opposite sign) to exactly compensate each other. Our results contribute to the understanding of carrier dynamics and their impact on the performance of practical graphene-based switching components.

Modeling power and linewidth of quantum dot superluminescent light emitting diode

A model for quantum dot (QD) superluminescent light emitting diode (SLED) is presented to study an optical power output and linewidth over a wide range of injection currents. The analysis is based on the photon and carrier rate equations including the effects of homogeneous and inhomogeneous broadening, carrier escape process, and high-current heating. The model is validated using experimental data available from the literature. The results show non-monotonic variations of the output optical power and linewidth of the SLED with the injection current density. It is seen that there exists an optimum injection current density for which the power–linewidth product becomes maximum for a given device length of the QD SLED.

Modeling and improving the output power of terahertz master-oscillator power-amplifier quantum cascade lasers.

A model based on carrier rate equations is proposed to evaluate the gain saturation and predict the dependence of the output power of a terahertz master-oscillator power-amplifier quantum cascade laser (THz-MOPA-QCL) on the material and structure parameters. The model reveals the design rules of the preamplifier and the power extractor to maximize the output power and the wall-plug efficiency. The correction of the model is verified by its agreement with the experiment results. The optimized MOPA devices exhibit single-mode emission at ∼ 2.6 THz with a side mode suppression ratio of 23 dB, a pulsed output power of 153 mW, a wall-plug efficiency of 0.22%, and a low divergence angle of ∼6°×16°, all measured at an operation temperature of 77 K. The model developed here is helpful for the design of MOPA devices and semiconductor optical amplifiers, in which the active region is based on intersubband transitions.

Design of Four-Channel Wavelength-Selectable In-Series DFB Laser Array With 100-GHz Spacing

A four-channel wavelength-selectable in-series DFB laser array with good single-longitudinal-mode (SLM) property is proposed and theoretically analyzed. To realize good SLM property, a linearly chirped Bragg grating with multiple π phase shifts are implemented in the laser cavity. In addition, two reflector sections with chirped Bragg grating are specially designed for reflection compensation at both ends. In our simulation, the split-step time-domain model with coupled-wave equations and carrier rate equations are used. Based on the simulation results, all the channels work with low threshold currents and the SLM properties are considerably enhanced compared with the conventional in-series laser array. Notably a high precision control of grating phase is required in the practical fabrication due to the ultra-small variation of grating period. Therefore, the reconstruction-equivalent-chirp technique is discussed to provide the fabrication of high-precision grating. In addition, the complex heterogeneous integration or butt-joint technique is not required during the whole fabrication process, which simplifies the fabrication and reduces the cost. The proposed wavelength-selectable in-series laser array is deemed to be applied in the dense wavelength division multiplexing technology, especially when fast wavelength switching is needed, such as in the application of NG-PON2.

Carrier escape mechanism in laterally correlated InAs sub-monolayer quantum dots using temperature dependent photoluminescence

We have quantitatively investigated relative effects of photo-carrier escape mechanism upon the quenching of photoluminescence with temperature in an ensemble of embedded InAs sub-monolayer (SML) quantum dots by varying InAs SML coverage from 0.4 ML to 0.8 ML. The mutual interplay of carrier recombination and tunneling throughout the laterally coupled quantum dots for different InAs coverage have been established to determine the temperature dependent photoluminescence (TDPL) spectra. The respective characteristic life times were extracted from the individual TDPL spectra by fitting them with model carrier rate equation. The consequent enhancement of inter-dot tunnel strength with respect to the carrier recombination rate with increasing InAs coverage has been marked out to be responsible for sustainable photoluminescence efficiency at higher temperature. Enhancement of tunneling rate with increasing InAs SML coverage has been physically described as consequence of reduced average inter-dot lateral separation as estimated from grazing incidence small angle x-ray scattering (GISAXS) measurement. Moreover, we have observed the anomalous decrease of spectral linewidth with temperature which can also be described as a consequence of the tunnel induced faster inter-dot carrier transfer at higher sub-monolayer coverage. The absence of any wetting layer in SML QD resulted in speeding up of carrier transfer through inter-dot tunneling pathways with tunnel time as low as 350 ps. This is significantly faster than the conventional InAs/GaAs SK QDs with tunnel time of 1328 ps.

Determination of internal quantum efficiency in GaInN-based light-emitting diode under electrical injection: carrier recombination dynamics analysis

We proposed a method to determine the internal quantum efficiency (IQE) of GaInN-based light-emitting diode (LED). For the accurate determination thereof, we carefully reviewed a conventional carrier rate equation and then proposed a set of advanced formulae, which can comprehensively explain the carrier dynamics in a modern GaInN-based LED. Based on our proposed formula, this convenient method to determine the IQE is presented. Next, to identify the proposed carrier rate equations and recombination dynamics, we investigated carrier lifetime. We also discuss the physical origins of IQE degradation in a modern GaInN-based LED such as efficiency droop and green gap.

Modeling and simulation analysis of PIN photodetector

为了优化PIN光电探测器响应特性，首先依据载流子速率方程，并考虑芯片寄生参量和封装寄生参量，建立光电探测器的等效电路模型。然后仿真分析了反偏电压、I区宽度、光敏面、芯片寄生电阻和电容、封装寄生电阻、电容和电感对光电探测器脉冲响应特性和频率响应特性的影响。结果表明：通过增大反偏电压，减小光敏面和寄生参量(芯片寄生电容和电阻，封装寄生电容和电阻)，选取合适的I区宽度，利用引线电感的谐振效应现象，可以抑制脉冲响应波形畸变，提高频率响应带宽。

Modeling Parametric Processes in Few-Mode Semiconductor Optical Amplifiers

Few-mode semiconductor optical amplifiers (FM SOAs) allow more than one transverse modes to propagate inside of the waveguide region. They are useful in optical signal processing of distinct spatial mode signals when applied to spatial division multiplexing in an optical fiber communication. A model for FM SOAs including carrier rate and coupled-mode equations, which govern linear and nonlinear effects, is derived for the first time. The model reveals two distinctions of parametric process in FM SOAs through carrier gratings. First, the carrier gratings with transverse variation patterns provide unique mode selectivity, which only allows efficient interaction between certain modes. This mode selectivity is summarized as a parallelogram rule, a simple method to find the interacting modes and categorize them. Second, degenerate four wave mixing (FWM) via static carrier grating diffraction distinguishes itself from other types of FWMs for the highest wave interaction efficiency. Theoretical analysis and numerical simulation show that optical signal processing based on the degenerate FWM features high power efficiency, broadband operation, phase sensitivity, and mode selectivity. The processing can be done either in the spatial mode domain or in the frequency domain, or by combing them together. These features bestowed by the introduction of spatial degree of freedom, make FM SOAs promising in optical signal processing.

Modeling the effects of interband and intraband transitions on phase and gain stabilities of quantum dot semiconductor optical amplifiers

In this paper, the effects of interband and intraband transitions on the gain and phase stabilities in quantum dot semiconductor optical amplifier (QD-SOA) are investigated both temporally and spectrally employing electrical and optical pumping schemes. For this purpose, the carrier rate equations in different energy states coupled to the traveling wave optical field equation have been numerically solved to derive the dynamical behavior of QD-SOA. Our results show that the gain and phase response can be stabled under optical pumping (OP) scheme because the role of the interband and intraband transitions on the dynamics of QD-SOA is reduced. This behavior leads to high-speed pattern effect-free cross-phase modulation (XPM) in QD-SOA. It is found that optically pumped QD-SOA can have high performance in phase based applications. Moreover, it is shown that under OP scheme although the QD-SOA has lower gain value and slower gain recovery time, the ultrafast cross-gain modulation (XGM) without pattern effect is possible and the phase is recovered within a shorter time compared to EP scheme. The behavior arises from the different capacity of the carrier reservoir for pumping schemes.

Simultaneous determination of effective carrier lifetime and resistivity of Si wafers using the nonlinear nature of photocarrier radiometric signals

A rigorous treatment of the nonlinear behavior of photocarrier radiometric (PCR) signals is presented theoretically and experimentally for the quantitative characterization of semiconductor photocarrier recombination and transport properties. A frequency-domain model based on the carrier rate equation and the classical carrier radiative recombination theory was developed. The derived concise expression reveals different functionalities of the PCR amplitude and phase channels: the phase bears direct quantitative correlation with the carrier effective lifetime, while the amplitude versus the estimated photocarrier density dependence can be used to extract the equilibrium majority carrier density and thus, resistivity. An experimental ‘ripple’ optical excitation mode (small modulation depth compared to the dc level) was introduced to bypass the complicated ‘modulated lifetime’ problem so as to simplify theoretical interpretation and guarantee measurement self-consistency and reliability. Two Si wafers with known resistivity values were tested to validate the method.

Equivalent circuit model of Ge/Si separate absorption charge multiplication avalanche photodiode

The equivalent circuit model of Ge/Si Separate Absorption Charge Multiplication Avalanche Photodiode (SACM-APD) is proposed. Starting from the carrier rate equations in different regions of device and considering the influences of non-uniform electric field, noise, parasitic effect and some other factors, the equivalent circuit model of SACM-APD device is established, in which the steady-state and transient current voltage characteristics can be described exactly. In addition, the proposed Ge/Si SACM APD equivalent circuit model is embedded in PSpice simulator. The important characteristics of Ge/Si SACM APD such as dark current, frequency response, shot noise are simulated, the simulation results show that the simulation with the proposed model are in good agreement with the experimental results.

Modeling Passive Mode-Locking via Saturable Absorption in Graphene Using the Finite-Difference Time-Domain Method

An approach for modeling the dynamic saturable absorption of graphene using the finite-difference time-domain method is presented. In particular, this paper focuses on sub-picosecond pulse formation in a passively mode-locked semiconductor laser. The dynamics and the saturability of the gain and absorption are described by a carrier rate equation. The carrier dynamics are coupled to the electromagnetic field through an effective current density. All parameters of the graphene dynamics are obtained from reported experimental measurements. Using this numerical method, the dependence of output intensity and pulse width on input current density, graphene location, and cavity size is investigated. We find that pulse widths in the range 100–200 fs can be reliably generated with peak output intensities of around 0.15 mW/ $\mu \text{m}^{2}$ . The optimal placement of the graphene layer in the cavity is strongly dependent on the standing wave pattern near the mirror. We found that cavities as small as 30 $\mu \text{m}$ still support stable pulse formation.

Self-consistent electro-opto-thermal model of quantum cascade lasers with coupled electron and phonon interactions far from equilibrium

A self-consistent model of quantum cascade lasers (QCLs) is presented here for the study of the QCL’s behavior in the far from equilibrium conditions. The approach is developed by employing a number of physics-based models such as the carrier and photon rate equations, the energy balance equation, the heat transfer equation and a simplified rate equation for the creation and annihilation of nonequilibrium optical phonons. The temperature dependency of the relevant physical effects such as stimulated gain cross section, longitudinal optical (LO) phonons and hot-phonon generation rates are included in the model. Using the presented model, the static and transient device characteristics are calculated and analyzed for a wide range of heat sink temperatures. Besides the output characteristics, this model also provides a way to study the hot-phonon dynamics in the device, and to explore the electron temperature and thermal roll-over in the QCLs.

Room-Temperature Spin Polariton Diode Laser.

A spin-polarized laser offers inherent control of the output circular polarization. We have investigated the output polarization characteristics of a bulk GaN-based microcavity polariton diode laser at room temperature with electrical injection of spin-polarized electrons via a FeCo/MgO spin injector. Polariton laser operation with a spin-polarized current is characterized by a threshold of ∼69 A/cm^{2} in the light-current characteristics, a significant reduction of the electroluminescence linewidth and blueshift of the emission peak. A degree of output circular polarization of ∼25% is recorded under remanent magnetization. A second threshold, due to conventional photon lasing, is observed at an injection of ∼7.2 kA/cm^{2}. The variation of output circular and linear polarization with spin-polarized injection current has been analyzed with the carrier and exciton rate equations and the Gross-Pitaevskii equations for the condensate and there is good agreement between measured and calculated data.

A novel model on time-resolved photoluminescence measurements of polar InGaN/GaN multi-quantum-well structures

Based on carrier rate equation, a new model is proposed to explain the non-exponential nature of time-resolved photoluminescence (TRPL) decay curves in the polar InGaN/GaN multi-quantum-well structures. From the study of TRPL curves at different temperatures, it is found that both radiative and non-radiative recombination coefficients vary from low temperature to room temperature. The variation of the coefficients is compatible with the carrier density of states distribution as well as the carrier localization process. These results suggest that there is a novel method to calculate the internal quantum efficiency, which is a complement to the traditional one based on temperature dependent photoluminescence measurement.

The method of pulsed x-ray detection with a diode laser

A new class of pulsed X-ray detection methods by sensing carrier changes in a diode laser cavity has been presented and demonstrated. The proof-of-principle experiments on detecting pulsed X-ray temporal profile have been done through the diode laser with a multiple quantum well active layer. The result shows that our method can achieve the aim of detecting the temporal profile of a pulsed X-ray source. We predict that there is a minimum value for the pre-bias current of the diode laser by analyzing the carrier rate equation, which exists near the threshold current of the diode laser chip in experiments. This behaviour generally agrees with the characterizations of theoretical analysis. The relative sensitivity is estimated at about 3.3 × 10-17 C ⋅ cm2. We have analyzed the time scale of about 10 ps response with both rate equation and Monte Carlo methods.

Evaluation of the temperature-dependent internal quantum efficiency and the light-extraction efficiency in a GaN-based blue light-emitting diode by using a rate equation model

The internal quantum efficiency (IQE) and the light extraction efficiency (LEE) of a GaN-based blue light-emitting diode (LED) are evaluated separately in the temperature range between 20 to 80 °C. The theoretical IQE model based on the carrier rate equation of semiconductors is applied to determine the IQE and the LEE separately from a measured external quantum efficiency (EQE) versus current relation for the LED sample. While the peak EQE of the measured sample decreases by 3.2 % as the temperature increases from 20 to 80 °C, it is found that the peak IQE decreases by 4.5 % and the LEE increases by 1.5 %.