An analogue method for the analysis of current carrying semiconductor systems

In an earlier Internal Technical Memorandum (1) and in subsequent work(2), it has been demonstrated that a particular kind of resistance network, in which non-linear elements are associated with each mesh point, can be made to represent an exact analogue to a non-degenerate semiconductor system in the equilibrium or quasi-equilibrium state. The term !exact' in this context implies that the difference equation which governs the potential distribution in the network becomes identical, for the limit of vanishing mesh interval, with the differential equation for the electrostatic potential within the semiconductor system, i.e. the Shockley-Poisson equation. From this type of analogue network information concerning the variation of maximum field intensity and of junction capacitance with applied bias voltages can be obtained for one, two and three dimensional configurations of p and n type regions of arbitrary geometry and impurity concentration profiles. One limitation to the applicability of the analogue technique arises from the restriction to quasi-equilibrium conditions. This restriction precludes the investigation of situations in which current flow contributions to the carrier concentration pattern become significant - for example, in the case of strongly forward biassed p-n junctions, and of p-i-n junctions and transistors operating at high injection levels. In the present paper, the problems involved in an extension of the basic analogue method to the treatment of non-equilibrium situations are examined, and means for their solution are discussed. A review of the methods previously described and an illustration of the nature of their limitations is given in Section 2. This is followed, in Sections 3 to 7, by a detailed treatment of the case of a current carrying semiconductor system in one dimension which leads to a theoretically possible realization in terms of resistancenetwork/ analogue computer techniques, which is, however, too complex to. be considered practical. Section 8 discusses means for the simplification of the proposed schemes and leads to the description of a relatively simple system in which a significant reduction in equipment complexity has been made possible by the adoption of an operating mode based upon an iterative process of successive approximations. The extension of the technique to three dimensions is outlined in Section 9

C.V.D. annual report: January, 1967 research project ru27-1 : analogue study of semiconductor device structures

The e::tension of the resistance network analogue method to the study of a M.O.S.T. structure is described. By means of an iterative technique, data regarding channel current, field distribution, surface charge and position of pinch-off point as function of gate and drain voltagen can be obtained which do not involve the usual 'gradual' channel approximation Results for a particular device geometry are presented. A discussion of a digital computer approach to the solution of semiconductor device current flow problems is included, together with preliminary results

C.V.D. annual report: November 1965 research project RU27-1 :an analogue method for the determination of potential distributions in semiconductor systems

A general method for the solution of the nonlinear Shockley-Poisson differential equation which governs the potential distribution in non-degenerate semiconductor systems is described which can be applied to the evaluation of depletion layer widths, carrier densities and capacitance bias relationships of p-n junction structures. The method is based upon the use of a particular type of resistance network analogue and results obtained for several one and two dimensional configurations are discussed

New Hybrid Protected Lands Layer for Vermont Conservation Design Analysis (February 2019)

This shapefile (.shp) is a hybrid of the March 2017 Edition of the Vermont Center for Geographic Information\u27s (VCGI) Vermont Protected Lands Database (VPLD), the Vermont Land Trust\u27s February 2019 Protected Lands database, and The Nature Conservancy\u27s Secured Areas (SA 2018+) database. The VLT and SA 2018+ datasets were used as the scaffolding for the hybrid protected lands layer, with some VCGI VPLD polygons retained if they contained unique contributions. These datasets were combined by C.D. Loeb because each input dataset was missing some protected lands polygons in the state of Vermont. Additionally, the VCGI VPLD dataset contained many overlapping polygons, making it unusable for the area calculations of interest to our study on the overlap between formally protected lands and Vermont Conservation Design landscape-level targets (see publication reference). This hybrid protected lands layer creates a more complete snapshot of Vermont’s protected lands for our study’s purposes than any other known, publicly available dataset as of February 2019, and also corrects for all improperly overlapping polygons. However, we know that this hybrid product still does not capture all of Vermont\u27s protected lands. Specifically, some Upper Valley Land Trust-protected parcels are missing from this hybrid protected lands layer, and there are probably other protected parcels that could not be captured by the input datasets. Thus, our hybrid product will likely underrepresent actual protections. This layer was created to intersect with Vermont Conservation Design targets for input into the software Tableau. Its purpose was to perform cross tabulations to compare Vermont Conservation Design targets with protected lands in Vermont to-date, and to calculate acreages of protected lands that are also design targets by primary protecting agency. All parcel attributes and delineations in the hybrid output are only as good as the parent datasets. In areas where parcels were digitized differently between parent datasets, “slivers” may have been generated by merging them. Our study objectives originally included an analysis of the GAP Status of protected lands in Vermont (reflected in this layer\u27s metadata); however, some serious errors were detected in parent datasets with regards to GAP Status, so GAP Status was discarded as an analysis object. Please note author-identified GAP Status issues if using this dataset. Please see the shapefile\u27s metadata for detailed creation steps. The user implies knowledge of the limitations of this dataset. This dataset should not be used to ascertain boundaries or legal acreages for any parcels. Note: This version of the hybrid protected lands layer does not have county boundaries embedded in it nor waterbodies excluded from it, since it was created to capture all formally protected lands in the state of Vermont to the best of the authors’ abilities. Prior to use in our analysis, this layer was modified to exclude waterbodies and to introduce county boundaries. To obtain the same hybrid protected lands layer with county boundaries embedded in it and waterbodies excluded from it, please contact C. D. Loeb at [email protected]

Detection of Gravitational Waves from the Coalescence of Population-III Remnants with Advanced LIGO

The comoving mass density of massive black hole (MBH) remnants from pre-galactic star formation could have been similar in magnitude to the mass-density of supermassive black holes (SMBHs) in the present-day universe. We show that the fraction of MBHs that coalesce during the assembly of SMBHs can be extracted from the rate of ring-down gravitational waves that are detectable by Advanced LIGO. Based on the SMBH formation history inferred from the evolution of the quasar luminosity function, we show that an observed event rate of 1 per year will constrain the SMBH mass fraction that was contributed by MBHs coalescence down to a level of ~10^-6 for 20 solar mass MBH remnants (or ~10^-4 for 260 solar mass remnants).Comment: 4 pages, 2 figures. Submitted to ApJ Letter