Monte Carlo Modeling of VLWIR HgCdTe Interdigitated Pixel Response

Increasing very long-wave infrared (VLWIR, λ _c ≈ 15 μm) pixel operability was approached by subdividing each pixel into four interdigitated subpixels. High response is maintained across the pixel, even if one or two interdigitated subpixels are deselected (turned off), because interdigitation provides that the preponderance of minority carriers photogenerated in the pixel are collected by the selected subpixels. Monte Carlo modeling of the photoresponse of the interdigitated subpixel simulates minority-carrier diffusion from carrier creation to recombination. Each carrier generated at an appropriately weighted random location is assigned an exponentially distributed random lifetime τ _i, where 〈τ _i〉 is the bulk minority-carrier lifetime. The minority carrier is allowed to diffuse for a short time dτ, and the fate of the carrier is decided from its present position and the boundary conditions, i.e., whether the carrier is absorbed in a junction, recombined at a surface, reflected from a surface, or recombined in the bulk because it lived for its designated lifetime. If nothing happens, the process is then repeated until one of the boundary conditions is attained. The next step is to go on to the next carrier and repeat the procedure for all the launches of minority carriers. For each minority carrier launched, the original location and boundary condition at fatality are recorded. An example of the results from Monte Carlo modeling is that, for a 20-μm diffusion length, the calculated quantum efficiency (QE) changed from 85% with no subpixels deselected, to 78% with one subpixel deselected, 67% with two subpixels deselected, and 48% with three subpixels deselected. Demonstration of the interdigitated pixel concept and verification of the Monte Carlo modeling utilized λ _c(60 K) ≈ 15 μm HgCdTe pixels in a 96 × 96 array format. The measured collection efficiency for one, two, and three subelements selected, divided by the collection efficiency for all four subelements selected, matched that calculated using Monte Carlo modeling.     

Status of HgCdTe Bicolor and Dual-Band Infrared Focal Arrays at LETI

In this paper we show the latest achievements of HgCdTe-based infrared bispectral focal plane arrays (FPAs) at LETI infrared laboratory. We present and compare the two different pixel architectures that are studied now in our laboratory, named “NPN” and “pseudo-planar”. With these two technologies, a wide range of system applications in dual-band detection can be covered. Advantages of both architectures will be pointed out. We also review performances obtained with these different architectures. The first one has been studied for several years in our laboratory, and we review results obtained on FPAs of size 256 × 256 pixels on a 25 μm pitch, in the MWIR/MWIR (3 μm/5 μm) range. Very high noise equivalent temperature difference (NETD) operability is obtained, at 99.8% for the λ_c = 3 μm band and 98.7% for the λ_c = 5 μm band. The second one has been developed more recently, to address other applications that need temporal coherence as well as spatial coherence. We show detailed performances measured on pseudo-planar type FPAs of size 256 × 256 pixels on a 30 μm pitch, in the MWIR/LWIR (5 μm/9 μm) range. The results are also very promising for these prototypes, with NETD as low as 15 mK for an integration time as short as 1 ms, and good operability. The main manufacturing issues are also presented and discussed for both pixel architectures. Challenging process steps are, firstly, molecular beam epitaxy (MBE) HgCdTe heterostructure growth, on large substrates (cadmium zinc telluride) and heterosubstrates (germanium), and, secondly, detector array fabrication on a nonplanar surface. In particular, trenches or hole etching steps, photolithography and hybridization are crucial to improve uniformity, number of defects and performances. Some results of surface, structural and electrical characterizations are shown to illustrate these issues. On the basis of these results, the short-term and long-term objectives and trends for our research and development are presented, in terms of pixel pitch reduction, wavelengths, and dual-band FPA size.     

Plasma Passivation Etching for HgCdTe

Inductively coupled plasmas (ICP) are the high-density plasmas of choice for the processing of HgCdTe and related compounds. Most dry plasma process works have been performed on HgCdTe for pixel delineation and the p-to-n-type conversion of HgCdTe. We would like to use the advantages of “dry” plasma processing to perform passivation etching of HgCdTe. Plasma processing promises the ability to create small vias, 2 μm or less with excellent uniformity across a wafer, good run-to-run uniformity, and good etch rate control. In this study we developed processes to controllably etch CdTe, the most common passivation material used for photovoltaic-based HgCdTe devices. We created a process based on xenon gas that allows for the slow controllable CdTe etch at only 0.035 μm/min, with smooth morphology and rounded corners to promote further processing.     

Planar <Emphasis Type="Italic">n</Emphasis>-on-<Emphasis Type="Italic">p</Emphasis> HgCdTe FPAs for LWIR and VLWIR Applications

Mainly driven by space applications, mercury cadmium telluride (MCT) focal-plane arrays (FPAs) have been successfully developed for very long wavelengths (λ _CO > 14 μm at 55 K). For this purpose, the standard n-on-p technology based on MCT grown by liquid-phase epitaxy (LPE) and involving vacancy doping has been modified to extrinsic doping by a monovalent acceptor. Due to the planar diode geometry obtained by ion implantation, most of the carrier generation volume is located in the p-type region with a thickness of approximately 8 μm. According to our understanding, the Shockley–Read centers connected with the Hg vacancies are thus significantly reduced. This situation should lead to longer minority-carrier lifetimes and smaller generation rates under equilibrium conditions, therefore yielding lower dark current. We indeed observe a reduction by a factor of approximately 15 by using extrinsic doping. Recent dark current data obtained in the temperature range from 55 K to 85 K on 288 × 384 FPAs with λ _CO(60 K) = 12 μm, either intrinsically or extrinsically doped, corroborate this finding. These data, new results on a 112 × 112 pixel demonstrator array with λ _CO(55 K) = 14.4 μm, and earlier measurements are compared with Tennant’s Rule 07 established for p-on-n technology.     

Status of LWIR HgCdTe-on-Silicon FPA Technology

The use of silicon as an alternative substrate to bulk CdZnTe for epitaxial growth of HgCdTe for infrared detector applications is attractive because of potential cost savings as a result of the large available sizes and the relatively low cost of silicon substrates. However, the potential benefits of silicon as a substrate have been difficult to realize because of the technical challenges of growing low-defect-density HgCdTe on silicon where the lattice mismatch is ∼19%. This is especially true for long-wavelength infrared (LWIR) HgCdTe detectors where the performance can be limited by the high (∼5 × 10⁶ cm⁻²) dislocation density typically found in HgCdTe grown on silicon. The current status of LWIR (9 μm to 11 μm at 78 K) HgCdTe on silicon focal-plane arrays (FPAs) is reviewed. Recent progress is covered including improvements in noise equivalent differential temperature (NEDT) and array operability. NEDT of <25 mK and NEDT operability >99% are highlighted for 640 × 480 pixel, 20-μm-pitch FPAs.     

High-Performance MWIR/LWIR Dual-Band 640 × 480 HgCdTe/Si FPAs

HgCdTe grown on large-area Si substrates allows for larger array formats and potentially reduced focal-plane array (FPA) cost compared with smaller, more expensive CdZnTe substrates. The goal of this work is to evaluate the use of HgCdTe/Si for mid-wavelength/long-wavelength infrared (MWIR/LWIR) dual-band FPAs. A series of MWIR/LWIR dual-band HgCdTe triple-layer n-P-n heterojunction (TLHJ) device structures were grown by molecular-beam epitaxy (MBE) on 100-mm (211)Si substrates. The wafers showed low macrodefect density (<300 cm⁻²) and was processed into 20-μm-unit-cell 640 × 480 detector arrays which were mated to dual-band readout integrated circuits (ROICs) to produce FPAs. The measured 80-K cutoff wavelengths were 5.5 μm for MWIR and 9.4 μm for LWIR, respectively. The FPAs exhibited high pixel operabilities in each band, with noise equivalent differential temperature (NEDT) operabilities of 99.98% for the MWIR band and 99.6% for the LWIR band demonstrated at 84 K.     

Dual-Color InAs/GaSb Superlattice Focal-Plane Array Technology

Within a very few years, InAs/GaSb superlattice technology has proven its suitability for high-performance infrared imaging detector arrays. At the Fraunhofer Institute for Applied Solid State Physics (IAF) and AIM Infrarot-Module GmbH, efforts have been focused on developing mature fabrication technology for dual-color InAs/GaSb superlattice focal-plane arrays for simultaneous, colocated detection at 3 μm to 4 μm and 4 μm to 5 μm in the mid-wavelength infrared atmospheric transmission window. Integrated into a wide-field-of-view missile approach warning system for an airborne platform, a very low number of pixel outages and cluster defects is mandatory for bispectral detector arrays. Process refinements, intense root-cause analysis, and specific test methodologies employed at various stages during the process have proven to be the key for yield enhancements.     

Performance and Modeling of the MWIR HgCdTe Electron Avalanche Photodiode

The operation of the mid-wave infrared (MWIR) HgCdTe cylindrical electron injection avalanche photodiode (e-APD) is described. The measured gain and excess noise factor are related to the collection region fill factor. A two-dimensional diffusion model calculates the time-dependent response and steady-state pixel point spread function for cylindrical diodes, and predicts bandwidths near 1 GHz for small geometries. A 2 μm diameter spot scan system was developed for point spread function and crosstalk measurements at 80 K. An electron diffusion length of 13.4 μm was extracted from spot scan data. Bandwidth data are shown that indicate bandwidths in excess of 300 MHz for small unit cells geometries. Dark current data, at high gain levels, indicate an effective gain normalized dark density count as low as 1000 counts/μs/cm² at an APD gain of 444. A junction doping profile was determined from capacitance–voltage data. Spectral response data shows a gain-independent characteristic.     

l 2–l ∞ Filtering Design for Piecewise Discrete-Time Linear Systems

This paper is concerned with the l ₂–l _∞ filtering problem for a class of piecewise discrete-time linear systems. Attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the l ₂–l _∞ sense. By using the piecewise Lyapunov function, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities (LMIs). It has been shown that the l ₂–l _∞ filtering problem can be solved as an LMI optimization problem. Two numerical examples are presented to demonstrate the validity of the proposed design method.     

Robust l 2–l ∞ Filter for Uncertain Discrete-Time Switched Time-Delay Systems

This paper is concerned with the problem of robust l ₂–l _∞ filter design for a class of uncertain switched time-delay systems based on a switched Lyapunov functional. The parametric uncertainties are assumed to be time varying but norm bounded. The purpose is to design a switched filter such that, for all admissible uncertainties, the resulting filtering error system is robustly stable and satisfies a prescribed l ₂–l _∞ performance level. By introducing some extra matrices, a desired filter can be constructed by solving certain linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the proposed method.     

Quantized <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Filtering for Singular Time-varying Delay Systems with Unreliable Communication Channel

This brief is concerned with the issue of quantized H _∞ filtering for singular time-varying delay systems with an unreliable communication channel. The missing data are described by a binary switching sequence satisfying a conditional probability distribution. The purpose is to design a linear H _∞ filter such that the filtering error system is regular, causal, stochastically stable, and satisfies the prescribed H _∞ performance constraint. First, based on a finite sum inequality, a new delay-dependent stability condition is obtained. Then, the filter parameters are derived by solving a linear matrix inequality (LMI). Finally, numerical examples are given to illustrate that the proposed approach is effective and feasible.     

Modeling of LWIR HgCdTe Auger-Suppressed Infrared Photodiodes under Nonequilibrium Operation

The general approach and effects of nonequilibrium operation of Auger-suppressed HgCdTe infrared photodiodes are well understood. However, the complex relationships of carrier generation and dependencies on nonuniform carrier profiles in the device prevent the development of simplistic analytical device models with acceptable accuracy. In this work, finite element methods are used to obtain self-consistent steady-state solutions of Poisson’s equation and the carrier continuity equations. Experimental current–voltage characteristics between 120 K and 300 K of HgCdTe Auger-suppressed photodiodes with cutoff wavelength of λ _c = 10 μm at 120 K are fitted using our numerical model. Based on this fitting, we study the lifetime in the absorber region, extract the current mechanisms limiting the dark current in these photodiodes, and discuss design and fabrication considerations in order to optimize future HgCdTe Auger-suppressed photodiodes.     

A numerical method for calculation of transients in electric circuits

 The present paper describes a numerical method for calculation of transients in electric circuits,using a step by step approach.For a small interval of time △t=const,for each branch j of circuit one calculates α_j=R_j+L_j/△t+△t/C_j,β_j=R_j+△t/C_j and θ=△t/C_j.After that,for each interval △t the current increments △i_(jk),the currents i_(jk)=i_(jk-1)+△i_(jk)and the capacitor\'s voltage u_(cjk)=u_(cjk-1)+Au_(cjk)are calculated. The values of △i_(jk)are the roots of a system of simultaneous linear equations.The results of numerical calculation of transients by the proposed method do not differ from those obtained by analytical ones.The proposed method can be applied to a large number of problems in electrical engineering.A similar approach can be used for the calculation of transients in non-linear electric circuits and in other engineering disciplines(mechanics,thermodynamics,hydraulics etc.).Several numerical examples show how the pro- posed method can be applied.     

H ∞ Filtering for Systems with Delays and Time-varying Nonlinear Parameters

This paper is concerned with the gain-scheduled H _∞ filtering problem for a class of parameter-varying continuous systems with time delays. The systems under consideration are represented by nonlinear fractional transformation (NFT) which is a generalization of linear fractional transformation (LFT). Attention is focused on the design of a stable filter guaranteeing a prescribed disturbance attenuation level in an H _∞ sense. Sufficient solvability conditions of this problem are obtained based on Lyapunov function approach. A gain-scheduled filter can be constructed in terms of a set of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the applicability of the proposed approach.     

Delay-Range-Dependent L 2–L ∞ Filtering for Stochastic Systems with Time-Varying Interval Delay

This paper focuses on the problem of delay-range-dependent L ₂–L _∞ filter design for stochastic systems with time-varying delay. The time delay varies in an interval. A delay-range-dependent sufficient condition is formulated in terms of linear matrix inequalities (LMIs), which guarantees the existence of a linear filter. The proposed filter ensures that the filtering error system is stochastically asymptotically stable and that its L ₂–L _∞ performance satisfies a prescribed level. The corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. This work is partially supported by the Natural Science Foundation of China (60674055, 60774047), and the Taishan Scholar Programme of Shandong Province.     

A Delay-Dependent Approach to Robust H ∞ Control for Uncertain Stochastic Systems with State and Input Delays

In this paper, the problem of delay-dependent robust H _∞ control for uncertain stochastic systems with state and input delays is investigated. The time delays are assumed to be bounded and time varying and the uncertainties are assumed to be norm bounded. By using the Lyapunov functional method, a new delay-dependent robust H _∞ control scheme is presented in terms of linear matrix inequalities (LMIs). Some numerical examples are given to illustrate the effectiveness of the proposed approach. This work is partially supported by the Natural Science Foundation of China (60674055, 60774047), and the Taishan Scholar Programme of Shandong Province. An erratum to this article can be found at     

Optical trapping of metallic Rayleigh particle by combined beam

Radiation forces and trapping stability of metallic(i.e.gold) Rayleigh particle by combined beam are analyzed,and the combined beam is formed by superimposing two partially coherent off-axis flat-topped beams.The dependences of radiation forces on off-axis distance parameter,correlation length and particle radius are illustrated by numerical examples.The results show that there exist critical values d0,cand σ0,c for the combined beam.For 0相似文献   

Analysis of mechanisms for electron scattering in GaAs/AlxGa1−x As superlattices with doped quantum wells for longitudinal resonant current flow in high electric fields and at low temperatures

Formulas are derived for, and a numerical analysis made of, the dependence of the transverse phase relaxation time on electron energy for resonant current flow through GaAs/Al_xGa_1−x As superlattices with doped quantum wells. The parameters are chosen to be close to those of superlattices used for creating photodiodes for operation at λ⋍10 μm. The analysis is limited to the interactions of electrons with neutral atoms and impurity ions at low temperatures. Resonant current flow is ensured by an electric field that brings the ground state and the first excited state of the “Stark ladder” into resonance with neighboring, weakly interacting quantum wells. Fiz. Tekh. Poluprovodn. 33, 438–444 (April 1999)     

Time-Delay Dependent H∞ Model Reduction for?Uncertain Stochastic Systems: Continuous-Time Case

The problem of robust H _∞ model reduction for uncertain stochastic systems with time delay is investigated in this paper. The attention of this paper is focused on the construction of a reduced-order model for a given stable system. Several sufficient conditions are obtained for ensuring the existence of the reduced-order model by means of linear matrix inequalities and a coupling non-convex rank constraint condition. Under the sufficient conditions, the desired reduced-order model can be constructed, and the error system between the original model and the reduced-order model is asymptotically stable and has a prescribed H _∞ performance. Based on the proposed method, the construction approaches of reduced-order models with special structures, such as the zeroth-order model, the delay-free model, and the no-parameter-uncertainties model, are also developed. Finally, the effectiveness of the proposed model reduction method is illustrated by a numerical simulation example.     

Operation of a semiconductor opening switch at ultrahigh current densities

The operation of a semiconductor opening switch (SOS diode) at cutoff current densities of tens of kA/cm² is studied. In experiments, the maximum reverse current density reached 43 kA/cm² for ∼40 ns. Experimental data on SOS diodes with a p ⁺-p-n-n ⁺ structure and a p-n junction depth from 145 to 180 μm are presented. The dynamics of electron-hole plasma in the diode at pumping and current cutoff stages is studied by numerical simulation methods. It is shown that current cutoff is associated with the formation of an electric field region in a thin (∼45 μm) layer of the structure’s heavily doped p-region, in which the acceptor concentration exceeds 10¹⁶ cm⁻³, and the current cutoff process depends weakly on the p-n junction depth.