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

The early reionization with the primordial magnetic fields

The early reionization of the intergalactic medium, which is favored from the WMAP temperature-polarization cross-correlations, contests the validity of the standard scenario of structure formation in the cold dark matter cosmogony. It is difficult to achieve early enough star formation without rather extreme assumptions such as very high escape fraction of ionizing photons from proto-galaxies or a top-heavy initial mass function. Here we propose an alternative scenario that is additional fluctuations on small scales induced by primordial magnetic fields trigger the early structure formation. We found that ionizing photons from Population III stars formed in dark haloes can easily reionize the universe by $z \simeq 15$ if the strength of primordial magnetic fields is larger than $0.6 \times 10^{-9}$Gauss.Comment: 8 pages, 5 figures. accepted for publication in MNRA

The Mutual Interaction Between Population III Stars and Self-Annihilating Dark Matter

We use cosmological simulations of high-redshift minihalos to investigate the effect of dark matter annihilation (DMA) on the collapse of primordial gas. We numerically investigate the evolution of the gas as it assembles in a Population III stellar disk. We find that when DMA effects are neglected, the disk undergoes multiple fragmentation events beginning at ~ 500 yr after the appearance of the first protostar. On the other hand, DMA heating and ionization of the gas speeds the initial collapse of gas to protostellar densities and also affects the stability of the developing disk against fragmentation, depending on the DM distribution. We compare the evolution when we model the DM density with an analytical DM profile which remains centrally peaked, and when we simulate the DM profile using N-body particles (the 'live' DM halo). When utilizing the analytical DM profile, DMA suppresses disk fragmentation for ~ 3500 yr after the first protostar forms, in agreement with earlier work. However, when using a 'live' DM halo, the central DM density peak is gradually flattened due to the mutual interaction between the DM and the rotating gaseous disk, reducing the effects of DMA on the gas, and enabling secondary protostars of mass ~ 1 M_sol to be formed within ~ 900 yr. These simulations demonstrate that DMA is ineffective in suppressing gas collapse and subsequent fragmentation, rendering the formation of long-lived dark stars unlikely. However, DMA effects may still be significant in the early collapse and disk formation phase of primordial gas evolution.Comment: 17 pages, 11 figures, to appear in MNRA

Time domain and frequency domain measurement techniques

The principles underlying two distinct approaches to the measurement of electrical network characteristics over a wide frequency range are outlined, together with brief descriptions of currently available test systems which cover the range 0.1 - 4GHZ. The two techniques are assessed in terms of their ultimate capabilities with regard to accuracy, speed of measurement and costs

Constraints on the Proper Motion of the Andromeda Galaxy Based on the Survival of Its Satellite M33

A major uncertainty in the dynamical history of the local group of galaxies originates from the unknown transverse speed of the Andromeda galaxy (M31) relative to the Milky Way. We show that the recent VLBA measurement of the proper motion of Andromeda's satellite, M33, severely constrains the possible values of M31's proper motion. The condition that M33's stellar disk will not be tidally disrupted by either M31 or the Milky Way over the past 10 billion years, favors a proper motion amplitude of 100+-20km/s for M31 with the quadrant of a negative velocity component along Right Ascension and a positive component along Declination strongly ruled-out. This inference can be tested by future astrometric measurements with SIM, GAIA, or the SKA. Our results imply that the dark halos of Andromeda and the Milky Way will pass through each other within the next 5-10 billion years.Comment: Accepted for publication in Ap

Identifying the Environment and Redshift of GRB Afterglows from the Time-Dependence of Their Absorption Spectra

The discovery of Gamma-Ray Burst (GRB) afterglows revealed a new class of variable sources at optical and radio wavelengths. At present, the environment and precise redshift of the detected afterglows are still unknown. We show that if a GRB source resides in a compact (<100pc) gas-rich environment, the afterglow spectrum will show time-dependent absorption features due to the gradual ionization of the surrounding medium by the afterglow radiation. Detection of this time-dependence can be used to constrain the size and density of the surrounding gaseous system. For example, the MgII absorption line detected in GRB970508 should have weakened considerably during the first month if the absorption occurred in a gas cloud of size <100pc around the source. The time-dependent HI or metal absorption features provide a precise determination of the GRB redshift.Comment: 13 pages, 4 figures, submitted to ApJ

Calibrating the Galaxy Halo - Black Hole Relation Based on the Clustering of Quasars

The observed number counts of quasars may be explained either by long-lived activity within rare massive hosts, or by short-lived activity within smaller, more common hosts. It has been argued that quasar lifetimes may therefore be inferred from their clustering length, which determines the typical mass of the quasar host. Here we point out that the relationship between the mass of the black-hole and the circular velocity of its host dark-matter halo is more fundamental to the determination of the clustering length. In particular, the clustering length observed in the 2dF quasar redshift survey is consistent with the galactic halo - black-hole relation observed in local galaxies, provided that quasars shine at ~10-100% of their Eddington luminosity. The slow evolution of the clustering length with redshift inferred in the 2dF quasar survey favors a black-hole mass whose redshift-independent scaling is with halo circular velocity, rather than halo mass. These results are independent from observations of the number counts of bright quasars which may be used to determine the quasar lifetime and its dependence on redshift. We show that if quasar activity results from galaxy mergers, then the number counts of quasars imply an episodic quasar lifetime that is set by the dynamical time of the host galaxy rather than by the Salpeter time. Our results imply that as the redshift increases, the central black-holes comprise a larger fraction of their host galaxy mass and the quasar lifetime gets shorter.Comment: 10 pages, 5 figures. Submitted to Ap