Carrier Density Distribution Research Articles

Electro-Thermal Behavior of a Sub-Micrometer Bulk CMOS Device: Modeling of Heat Generation and Prediction of Temperatures

The electro-thermal behavior of a bulk CMOS device is analyzed using the hydrodynamic model equation. The analysis is first applied to an introductory example of a single field-effect-transistor (FET) to indicate the importance of incorporating a non-equilibrium state between charge carriers and phonons in the analytical model. Then, the system of hydrodynamic model equations is described in detail, which takes into account carrier generation/recombination process and non-equilibrium between charge carriers and phonons. A supposed bulk CMOS device has nano-meter dimensions and thus is vulnerable to malfunction due to crosstalk between the constituent FETs. The simulation of electro-thermal transients in the entire CMOS domain is performed focusing on the behavior in a short period after switching of the gate voltage from low to high. The result shows a significant level of crosstalk that may lead to impairment of the switching function of the CMOS. Also shown is the development of a hot spot at the source region of the activated FET in addition to the one at the gate/drain corner. The deliberate omission of sub-continuum mechanisms, particularly the carrier generation/recombination, from the analytical model produced erroneous distributions of charge carrier density and temperature, thus proving the significance of this mechanism in defining heat generation and heat flow in the device.

Noncontact-mode scanning capacitance force microscopy towards quantitative two-dimensional carrier profiling on semiconductor devices

Scanning capacitance force microscopy (SCFM) is a promising tool for investigation of two-dimensional carrier density distribution on semiconducting devices. Its sensitivity is strongly dependent on the Q factor of the mechanical resonance mode of the cantilever. Therefore, measurement in vacuum is more appropriate for increasing the sensitivity. In this letter, the authors describe noncontact-mode (NC) SCFM which is combined with the frequency modulation detection method and its signal characteristics. The authors derived a quasiquantitative calibration curve which correlates to the amplitude signal in NC-SCFM to the dopant density. Using the calibration curve, the authors obtained a quasiquantitative two-dimensional dopant density distribution map on a cross-sectional transistor device.

A Mueller-Matrix Formalism for Modeling Polarization Azimuth and Ellipticity Angle in Semiconductor Optical Amplifiers in a Pump–Probe Scheme

This paper presents a Mueller-matrix approach to simulate the azimuth and ellipticity trajectory of a probe light in a tensile-strained bulk semiconductor optical amplifier (SOA) in a conventional pump-probe scheme. The physical mechanisms for the variations of polarization azimuth and ellipticity angle of the probe originate from the significant nonuniform distributions of carrier density across the active region in the presence of an intense pump light. Due to this carrier-density nonuniformity, the effective refractive indexes experienced by transverse-electric (TE) and transverse-magnetic (TM) modes of the probe are different. This results in a phase shift between TE and TM modes of the probe upon leaving the SOA. Simulations of the carrier distributions along the cavity length at different pump-light levels are demonstrated using multisection rate equations, which take into account the longitudinal nonuniform carrier density. The optical gain is considered via the parabolic band approximation. The influences of the spontaneous recombination and carrier-dependent material loss on the amplifier performance are included. The Mueller-matrix formalism is utilized to predict the variations of azimuth and ellipticity angle, which greatly reduces the complexity of the simulations in comparison with Jones-matrix formalism. The suggested approach is beneficial to experimental investigations due to the fact that during the optical-tuning process, Stokes parameters are virtually measurable on the Poincareacute sphere, and the Stokes vector of the incoming probe can be adjusted by a polarization controller and monitored by a polarization analyzer. Based on these carrier-induced nonlinearities in SOAs, an optical and gate with extinction ratio larger than 14 dB and Q-factor larger than 25 is presented at a bit rate of 2.5 Gb/s

Monte Carlo analysis of terahertz oscillations of photoexcited carriers in GaAsp−i−nstructures

Pulsed terahertz emission from the electron-hole plasma excited by a femtosecond optical pulse in GaAs $p\text{\ensuremath{-}}i\text{\ensuremath{-}}n$ structures is studied by Monte Carlo simulations. The conduction band composed from $\ensuremath{\Gamma}$, $L$, and $X$ valleys, and the valence band composed from heavy, light, and split-off subbands, are considered in the simulations. The Pauli exclusion principle and the intercarrier scattering between electrons and holes are taken into account self-consistently with the time- and position-dependent carrier density and momentum distribution. Good agreement between Monte Carlo results and experimental data is obtained. The simplified hydrodynamic model of the transient dynamics of the photoexcited carriers is suggested. The proposed model accurately reproduces Monte Carlo results when the excitation is considered to be spatially uniform.

Carrier Transport and Optical Properties of InGaN SQW With Embedded AlGaN$delta$-Layer

We investigate the carrier transport and optical properties of a thick InGaN single quantum well (SQW) where an AlGaN delta-layer is embedded. By way of simulation, it is found that the carrier density distribution in the active region is more uniform in such a QW structure, compared to a double QW (DQW) configuration showing a discontinuity in the hole quasi-Fermi level due to the large effective mass of the holes along with the strong piezoelectric field. Through the photoluminescence (PL) measurements, we have shown that the PL peak energy varies depending sensitively on the delta-layer thickness, providing an extra degree of freedom in the wavelength-tuning control. In particular, such a QW structure is highly desired for long-wavelength emission as the wavelength tuning can be achieved with lower indium composition. The embedded delta-layer also increases the wave function overlap between holes and electrons, thereby shortening the PL lifetime. The results of PL measurements are shown to be consistent with the self-consistent numerical results. A possible application of the proposed QW structure is to the design of long-wavelength light-emitting diodes and laser diodes

Threshold Analysis of Vertical-Cavity Surface-Emitting Lasers With Intracavity Contacts

A numerical analysis of vertical-cavity surface-emitting lasers (VCSELs) incorporating intracavity contacts and distributed Bragg reflectors (DBRs) is presented. The model considers polarization dependent reflection at the DBRs, current spreading, and nonuniform carrier density distribution self consistently. Analytic expressions for the current spreading and the corresponding series resistance for VCSELs incorporating intracavity contacts are derived. It is shown that current spreading strongly affects the lateral gain profile, the threshold current density, the transverse mode shape and the transverse mode discrimination through the creation of intracavity optical phase and gain apertures. The series resistance and the depth of the dip in the current density distribution are used as figures-of-merit to provide guidelines for device optimization, as illustrated by means of two examples of long wavelength VCSEL designs

Effect of Index Variation in Active Layer on Transverse Mode for Vertical-Cavity Surface-Emitting Lasers

The distribution of carrier density in an active layer of a vertical-cavity surface-emitting laser (VCSEL) produces a refractive index distribution, affecting the transverse-mode behavior of the VCSEL causing high-order-mode lasing. To achieve high-power fundamental-mode operation, we investigated the reduction in this effect by elongating the cavity. Experimental data show that the high-order mode started lasing immediately above a threshold in a lambda-cavity VCSEL with an active area large than 10 µm in diameter. By introducing a long monolithic cavity, high-order-mode lasing was suppressed. Theoretical results clearly show that such high-order-mode suppression is achieved because the effect of carrier-induced index change in the active layer is reduced by elongating the cavity.

Luminescence mechanisms of green and blue organic light-emitting devices utilizing hole-blocking layers

Optical and electrical measurements on green and blue organic light-emitting devices (OLEDs) with and without hole-blocking layers (HBLs) were performed, and the luminescence mechanisms of green and blue OLEDs utilizing HBLs were investigated by using energy band diagrams and carrier density distributions. The dependence of the electroluminescence efficiencies on the existence of HBLs was described on the basis of a luminescence mechanism. The density distributions of the electrons and the holes in OLEDs under applied electric fields were estimated from the energy band diagrams, taking into account the electronic parameters and the layer thicknesses. The luminescence efficiencies and the color chromaticities were significantly affected by the existence of the HBLs. These analyses can help improve understanding of the luminescence mechanisms at play in and the electroluminescence efficiencies of green and blue OLEDs with HBLs, and the present results provide important information on the optical properties for enhancing the efficiencies of OLEDs operating in the green and the blue regions of the spectra.

Electrical activation phenomena induced by excimer laser annealingin B-implanted silicon

The activation process induced by excimer laser annealing (ELA) has been investigated in 10keV B-implanted samples. It is found that for energy densities inducing melt depths of the order or larger of the implanted region the junction depth is controlled by the melt depth, with activation approaching 100% and box-shaped carrier density distributions with abrupt junction profile. For energy densities inducing a melting shallower than the implanted region, two different activation mechanisms have been identified: the first occurring in the molten region and leading to complete B activation; the second occurring in the region immediately below the molten zone and leading to thermal activation of B, induced by the heat wave propagating into the Si wafer. This last process is characterized by an activation energy of 5eV and is not accompanied by B diffusion. As a consequence, a deep tail of active B is produced, preventing the possibility to form abrupt and ultrashallow junctions. These results suggest that for the formation of ultrashallow junctions it is essential to combine ELA with ultralow energy ion implantation.

Internal behavior of BCD ESD protection devices under TLP and very-fast TLP stress

BCD electrostatic discharge (ESD) protection npn devices with different layout variations are analyzed experimentally and by device simulation. The device internal thermal and free carrier density distributions during the transmission line pulse (TLP) and very-fast transmission line pulse (vf-TLP) stresses are studied by a backside transient interferometric mapping technique. The lateral part of the npn transistor dominates the devices operation. The action of the vertical part of the transistor is influenced by the device layout. Experimentally observed activity of both parts of the npn transistor is well reproduced by the simulation. The devices exhibit an excellent ESD performance at both TLP and vf-TLP stress.

Thermographic imaging of free carrier density in silicon for solar cells

The measurement of free carrier density in silicon is a crucial parameter for the characterisation of silicon solar cell material. Carrier Density Imaging (CDI) is a valuable tool to obtain spatially resolved images of the free carrier density distribution. This article describes the experimental setup of CDI for absorption mode and recently developed emission mode measurements. The theoretical dependence of the absorption and emission of infrared radiation on the free carrier density is discussed. Results of absorption and emission mode measurements are presented and the advantages of the new emission mode are elaborated.

Detailed model and investigation of gain saturation and carrier spatial hole burning for a semiconductor optical amplifier with gain clamping by a vertical laser field

A detailed model for semiconductor linear optical amplifiers (LOAs) with gain clamping by a vertical laser field is presented, which accounts the carrier and photon density distribution in the longitudinal direction as well as the facet reflectivity. The photon iterative method is used in the simulation with output amplified spontaneous emission spectrum in the wide band as iterative variables. The gain saturation behaviors and the noise figure are numerically simulated, and the variation of longitudinal carrier density with the input power is presented which is associated with the on-off state of the vertical lasers. The results show that the LOA can have a gain spectrum clamped in a wide wavelength range and have almost the same value of noise figure as that of conventional semiconductor optical amplifiers (SOAs). Numerical results also show that an LOA can have a noise figure about 2 dB less than that of the SOA gain clamped by a distributed Bragg reflector laser.

Effects of magnetic field on the carrier density distribution of semiconductor power device operated in pulsed power conditions

AbstractTurn‐on characteristics of semiconductor power devices are evaluated under external magnetic field to study the effects of external magnetic field generated in a pulsed power circuit. Two pin diodes that have a basic structure of power devices are connected in parallel and driven by a pulsed voltage source. It was found the magnetic field applied to one diode in the perpendicular direction of current‐flow changed the current balance between the diodes. Besides the on‐resistance of a diode was increased under external magnetic field. The carrier‐density distribution inside of the diodes was measured by using a free carrier absorption method. The data show that the carrier‐density distribution changes from nearly the uniform one to the one‐sided one. It can be concluded that the effects of magnetic‐field have to be considered for the evaluation of switching characteristic in pulsed power operations. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(1): 10–16, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10271

Ferromagnetic phase in II–VI semiconductors controlled by carriers

AbstractOne main interest of carrier‐induced ferromagnetism in diluted magnetic semiconductors, is that it allows an active and sometimes reversible control of the magnetic properties, simply by manipulating the carrier density or carrier distribution using the usual techniques of semiconductor technology. We shall give two examples realised in (Cd,Mn)Te quantum wells: (i) control of the magnitude of the magnetisation by changing the carrier density; (ii) control of the magnetic anisotropy by changing the light‐hole/heavy‐hole splitting by strain and confinement in a quantum well. We will also shortly discuss the peculiarities of the II–VI quantum wells with respect to systems based on other diluted magnetic semiconductors. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of the potential in n-type DBR on threshold in vertical-cavity surface-emitting lasers

In this paper, a simulation software with a direct coupling in quasi-three-di mensions for the gain-waveguide vertical-cavity surface-emitting lasers has b een realized. The electrical field, carrier density, optical-field and temperature distributions in the vertical-cavity surface-emitting lasers are given. The proper threshold characteristics are shown only when the potentia ls in the p-type and n-type DBR layers are studied together.

Photon iterative numerical technique for steady-state simulation of gain-clamped semiconductor optical amplifiers

The photon iterative numerical technique, which chooses the outputs of the amplified spontaneous emission spectrum and lasing mode as iteration variables to solve the rate equations, is proposed and applied to analyse the steady behaviour of conventional semiconductor optical amplifiers (SOAs) and gain-clamped semiconductor optical amplifiers (GCSOAs). Numerical results show that the photon iterative method is a much faster and more efficient algorithm than the conventional approach, which chooses the carrier density distribution of the SOAs as the iterative variable. It is also found that the photon iterative method has almost the same computing efficiency for conventional SOAs and GCSOAs.

Analysis of Transverse-Mode Control in Vertical-Cavity Surface-Emitting Lasers Using a Convex Mirror

We theoretically studied the modal discrimination of vertical-cavity surface-emitting lasers (VCSELs) using a convex mirror and a long spacer. Our model is based on a three-dimentional beam propagation method (BPM). Carrier density distribution in the active layer is calculated by solving the rate equation including transverse carrier diffusion. Results indicate that the side-mode suppression ratio (SMSR) and single fundamental mode output power would be improved by applying a convex mirror with a suitable curvature.

Reduced linewidth re-broadening by suppressing longitudinal spatial hole burning in high-power 1.55-μm continuous-wave distributed-feedback (CW-DFB) laser diodes

For the first time, the impact of longitudinal photon density distribution and longitudinal carrier density distribution on the spectral linewidth re-broadening effect in single-electrode 1.55-μm distributed feedback (DFB) laser diodes (LDs) is investigated experimentally in details. By optimizing the front-to-rear facet power ratio, the nonuniformity of the photon density distribution along the laser cavity is reduced, hence reducing the degree of longitudinal spatial hole burning (SHB). Using this optimized value of front-to-rear facet power ratio, the degree of longitudinal SHB can be further reduced through reduction of the nonuniformity of the longitudinal carrier density distribution by increasing the cavity length. As a result, the local stimulated emission is reduced, hence reducing linewidth re-broadening caused by longitudinal SHB. The outcomes of this analysis is being used fruitfully to design high-power 1.55-μm DFB LDs exhibiting very narrow spectral linewidth of approximately 1.3 MHz at an output power of 175 mW under continuous-wave operation.

Realistic model for the output beam profile of stripe and tapered superluminescent light-emitting diodes.

We present a new model to analyse the spatial characteristics of the output beam of conventional (straight-stripe) and tapered superluminescent light-emitting diodes. The device model includes both spontaneous and stimulated emission processes as well as a nonuniform carrier density distribution to correctly represent current spreading and carrier diffusion effects. Near- and far-field intensity profiles computed with this model are accurately verified over a wide range of injection currents by comparisons with experimental results measured from in-house fabricated devices.

Nonequilibrium Green’s function method for a quantum Hall device in a magnetic field

We have developed a practical approach for the inclusion of magnetic fields in the nonequilibrium Green's function method and we have formulated a general scheme for transport calculations in a multiterminal device with magnetic field. Formulas for the self-energy terms in the presence of magnetic fields have been derived and disorder effects in the potential have been introduced through a model accounting for scattering by impurities. To demonstrate the validity of the model, we have applied it to the quantum Hall effect (QHE), for which a wealth of experimental results and information is readily available. Calculations for a simple structure at zero temperature were first carried out to verify the properties of the solutions over a wide range of conditions. The calculated Green's function results provide the carrier density distribution in the structure, and in order to analyze the QHE results, the resistances ${R}_{\mathrm{xx}}$ and ${R}_{\mathrm{xy}}$ are obtained using B\uttiker's approach. Our results for the integer QHE show a pattern that clearly resembles the edge state picture of transport. To further validate the theoretical model, comparisons have been conducted with experimental results for a realistic quantum Hall device at finite temperature, obtaining good agreement.