The inductance matrix of a multiconductor transmission line inmultiple magnetic media

A simple relationship between the inductance matrix and the auxiliary capacitance matrix is given. For a multiconductor transmission line consisting of N_c conducting cylinders in inhomogeneous media consisting of N_d homogeneous regions with permeabilities μ_i and permittivities ϵ _i, the inductance matrix [L] for the line is obtained by solving the magnetostatic problem of N_c conductors in N_d regions with permeabilities μ _i. The capacitance matrix [C] for the line is obtained by solving the electrostatic problem of N_c conductors in N_d regions with permittivities ϵ _i. It is shown that [L]=μ₀ϵ₀[C^'] ^-1, where [C^'] is the capacitance matrix of an auxiliary electrostatic problem of N_c conductors in N_d regions with relative permittivities set equal to the reciprocals of the relative permeabilities of the magnetostatic problem, i.e. ϵ^' _i/ϵ₀=μ₀/μ_i     

Modular Representations of Polynomials: Hyperdense Coding and Fast Matrix Multiplication

A certain modular representation of multilinear polynomials is considered. The modulo 6 representation of polynomial f is just any polynomial f + 6g. The 1-a-strong representation of f modulo 6 is polynomial f + 2g + 3h, where no two of g, f, and h have common monomials. Using this representation, some surprising applications are described: it is shown that n homogeneous linear polynomials x ₁,x ₂,...,x _n can be linearly transformed to n ^o(1) linear polynomials, such that from these linear polynomials one can get back the 1-a-strong representations of the original ones, also with linear transformations. Probabilistic Memory Cells (PMCs) are also defined here, and it is shown that one can encode n bits into n PMCs, transform n PMCs to n ^o(1) PMCs (we call this Hyperdense Coding), and one can transform back these n ^o(1) PMCs to n PMCs, and from these how one can get back the original bits, while from the hyperdense form one could have got back only n ^o(1) bits. A method is given for converting n times n matrices to n ^o(1) times n ^o(1) matrices and from these tiny matrices one can retrieve 1-a-strong representations of the original ones, also with linear transformations. Applying PMCs to this case will return the original matrix, and not only the representation.     

On the Fundamental Tradeoff of Spatial Diversity and Spatial Multiplexing of MISO/SIMO Links with Imperfect CSIT

In this paper, we analyze the role of CSIT on the fundamental performance tradeoff for a MISO/SIMO link. Defining CSIT quality order as alpha = - log sigma² _Deltah / log SNR, we showed that using rate adaptation, one can achieve an average diversity order of d ^macr(alpha, r macr) = (1 + alpha - r macr)n where n is the number of transmit or receive antennas, r macr is the average multiplexing gain and alpha is the CSIT quality. We also showed that this diversity order is optimal for r macr isin [0.1 - alpha] and alpha < 1. The relationship suggests that imperfect CSIT can also provide additional diversity order and interpret the CSIT quality order as the maximum achievable spatial multiplexing gain with n diversity order.     

On the Statistics of the Sum of Squared Complex Gaussian Random Variables

In this letter, we derive new results for the statistics of the complex random variable z=^DeltaSigma_n=1 ^N x _n ²=z ₁+jz _Q = re ^jphi where {x _n} is a set of mutually independent complex-valued Gaussian random variables with arbitrary means and equal variances. Each random variable x _n is assumed to have independent real and imaginary components with equal variance for all n. Expressions are derived for the joint probability density function (pdf) of (z ₁,z _Q), for the joint pdf of (r,phi) and also for the marginal pdf of the modulus r. An useful Fourier series expansion for the pdf of the phase phi is also derived. As an application of the results, a theoretical performance analysis of the well-known nondata-aided Viterbi and Viterbi feedforward carrier phase estimator operating with BPSK signals is presented. In particular, the expressions for the exact pdf, variance, and equivocation probability of the carrier phase estimates are derived.     

Three space-economical algorithms for calculatingminimum-redundancy prefix codes

The minimum-redundancy prefix code problem is to determine, for a given list W=[ω₁,..., ω_n] of n positive symbol weights, a list L=[l₁,...,l_n] of n corresponding integer codeword lengths such that Σ_i=1 ⁿ 2^-li⩽1 and Σ_i=1ⁿ ω_il_i is minimized. Let us consider the case where W is already sorted. In this case, the output list L can be represented by a list M=[m₁,..., m_H], where m_l, for l=1,...,H, denotes the multiplicity of the codeword length l in L and H is the length of the greatest codeword. Fortunately, H is proved to be O(min(log(1/p₁),n)), where p₁ is the smallest symbol probability, given by ω₁/Σ _i=1ⁿ ω_i. We present the Fast LazyHuff (F-LazyHuff), the Economical LazyHuff (E-LazyHuff), and the Best LazyHuff (B-LazyHuff) algorithms. F-LazyHuff runs in O(n) time but requires O(min(H², n)) additional space. On the other hand, E-LazyHuff runs in O(n+nlog(n/H)) time, requiring only O(H) additional space. Finally, B-LazyHuff asymptotically overcomes, the previous algorithms, requiring only O(n) time and O(H) additional space. Moreover, our three algorithms have the advantage of not writing over the input buffer during code calculation, a feature that is very useful in some applications     

Experimental studies of switching in metal semi-insulating n-p silicon devices

The switching properties of silicon structures comprising a p⁺-n junction and a metal electrode separated from the n-section of the p⁺-n junction by a semi-insulating (leaky) layer are presented. Two basic types of structure were studied: devices with relatively light doped n-sections, and those with relatively heavily doped sections.

The switching voltage of the first group was found to be proportional to the product of the doping density, N_d and the square of the width of the n-section, and to be only very weakly temperature-dependent. The capacitance-voltage relationship of the device in the high-impedance mode was found to be of the form C⁻¹ ∞ V^1/2, and these measurements established that switching occurred just as the depletion region of the n-section under the gate electrode reached through to the p⁺-n junction. It was thus established that these devices were operating in the punch-through mode.

In the second group of devices, the doping density of the n-section was increased by diffusing an n-well into the section. The switching properties were found to be quite different from the punch-through devices. The switching voltage was found to be independent of the width of the n-section and proportional to N_d^−3/4. Capacitance measurements also showed that the depletion region in the n-section under the oxide at switching, varied with the doping concentration, and was substantially less than the width of the n-layer. It was thus concluded that switching in these devices was of the avalanche-mode type.     

Schottky barrier height of a new ohmic contact NiSi2 to n-type 6H-SiC

We present a new ohmic contact material NiSi₂ to n-type 6H-SiC with a low specific contact resistance. NiSi₂ films are prepared by annealing the Ni and Si films separately deposited on (0 0 0 1)-oriented 6H-SiC substrates with carrier concentrations (n) ranging from 5.8×10¹⁶ to 2.5×10¹⁹ cm⁻³. The deposited films are annealed at 900 °C for 10 min in a flow of Ar gas containing 5 vol.% H₂ gas. The specific contact resistance of NiSi₂ contact exponentially decreases with increasing carrier concentrations of substrates. NiSi₂ contacts formed on the substrates with n=2.5×10¹⁹ cm⁻³ show a relatively low specific contact resistance with 3.6×10⁻⁶ Ω cm². Schottky barrier height of NiSi₂ to n-type 6H-SiC is estimated to be 0.40±0.02 eV using a theoretical relationship for the carrier concentration dependence of the specific contact resistance.     

Leakage currents of np silicon diodes with different amounts of dislocations

Leakage currents in n⁺p silicon planar-diodes appeared to be related to the presence of dislocations, revealed by an X-ray topographic technique, in and near the n⁺ regions. Electrical measurements revealed a dominant bulk recombination—generation level, 0·055 eV. below the middle of the energy gap, and with τ_p0/τ_n0 >1. This latter fact indicates a donor type defect. Surface recombination-generation currents were minimized by using a MOS type guard ring.     

Thermal noise of a silicon double-injection plasma diode

Measurements of the thermal noise of a silicon p⁺−π−n⁺ diode operating in the Lampert-insulating regime agree within 6 per cent with the prediction S_i = 4kT Re(Y). The noise measurements were performed in the cube-law regime with d.c.-currents from 100 μA to 4mA at room temperature.     

Theoretical analysis of word-level switching activity in thepresence of glitching and correlation

This paper presents a novel analytical approach to compute the switching activity in digital circuits at the word level in the presence of glitching and correlation. The proposed approach makes use of signal statistics such as mean, variance, and autocorrelation. It is shown that the switching activity α_f at the output node f of any arbitrary circuit in the presence of glitching and correlation is computed as α_f=Σ_i=1^S-1α(f _i,i+1)=Σ_i=1^{S- 1}p(f_i+1)(1-p(f_i))(1-ρ(f_i,i+1 )) (1) where ρ(f_i,i+1)=ρ(f_i,i+1)=(E[f_i(Sn)f _i+1(Sn)]- p(f_i)p(f_i+1))/(√(p(f _i)-p(f_i)²)(p(f_i+1)- p(f_i+1²))) (2). S number of time slots in a cycle; ρ(f_i,+1) time-slot autocorrelation coefficient; E[x]=expected value of x; p_x=probability of the signal x being “one”. The switching activity analysis of a signal at the word level is computed by summing the activities of all the individual bits constituting the signal. It is also shown that if the correlation coefficient of the higher order bits of a normally distributed signal x is ρ(x_c), then the bit P₀ where the correlation begins and the correlation coefficient is related hy ρ(x_c)=erfc{(2(P₀-1)-1)/(√2σ_x )} where erfc(x)=complementary error function; σ_x=variance of x. The proposed approach can estimate the switching activity in less than a second which is orders of magnitude faster than simulation-based approaches. Simulation results show that the errors using the proposed approach are about 6.1% on an average and that the approach is well suited even for highly correlated speech and music signals     

The physics and fabrication of in situ back-gated (311)A hole gas heterojunctions

This paper reports the fabrication of an in situ back-gated hole gas on the (311)A surface of GaAs. The hole density can be varied from fully depleted to p_s = 2.1 × 10¹¹ cm⁻² with mobilities of up to μ = 1.1 × 10⁶ cm²V⁻¹ s⁻¹. It is seen that for carrier densities down to p_s = 4 × 10¹⁰ cm⁻² the mobility in the [ ] direction is greater than that in the [ ] direction. Using a combination of front- and back-gates we are able to keep the carrier density constant and deform the hole gas wavefunction such that the holes are pushed up against or moved further away from the heterointerface. Thus we are able to separately investigate the various scattering mechanisms that determine the mobility, and compare the experimental data with theoretical calculations based on the shape of the wavefunction.     

Known-Plaintext Attack to Two Cryptosystems Based on the BB Equation

Recently, Rama Murthy and Swamy proposed a symmetric cryptosystem based on the Brahmagupta-Bhaskara (BB) equation. The BB equation is the quadratic Diophantine equation nx ² + k = y ², where k is an integer and n is a positive integer such that radic(n) is irrational. For the particular case k=1, the equation is called the Pell equation. The proposed cryptosystem was modified later by the same authors in order to avoid the cryptanalysis given by Youssef. Below, a known-plaintext attack to both cryptosystems is presented.     

Wide-sense and strict-sense nonblocking operation of multicastmulti-log2 n switching networks

Multicast connections are used in broad-band switching networks as well as in parallel processing. We consider wide-sense and strict-sense nonblocking conditions for multi-log₂ N switching networks with multicast connections. We prove that such networks are wide-sense nonblocking if they are designed by vertically stacking at least t · 2^n-t-1 + 2 ^n-2t-1 planes of a log₂ N networks together, where 1 ⩽ t ⩽ [n/2] and t defines the size of a blocking window K = 2^t. For t = [n/2] and n even, and for [n/2] ⩽ t ⩽ n the number of planes must be at least t · 2^n-t-1 + 1 and 2^t + (n - t - 1) · 2^n-t-1 - 2^2t-n-1 + 1, respectively. In the case of strict-sense nonblocking switching networks, the number of planes is at least N/2. The results obtained in this paper show that in many cases number of planes in wide-sense nonblocking switching networks is less than those for t = [n/2] considered by Tscha and Lee (see ibid., vol.47, p.1425-31, Sept. 1999). The number of planes given in the paper is the minimum number of planes needed for wide-sense nonblocking operation provided that Algorithm 1 is used for setting up connections. The minimum number of planes for such operation in general is still open issue     

Nitrogen vacancy scattering in GaN grown by metal–organic vapor phase epitaxy

Electron mobility limited by nitrogen vacancy scattering was taken into account to evaluate the quality of n-type GaN grown by metal–organic vapor phase epitaxy. Two assumptions were made for this potential for the nitrogen vacancy (1) it acts in a short range, and (2) does not diverge at the vacancy core. According to the above assumptions, a general expression to describe the scattering potential U(r)=−U₀exp[−(r/β)ⁿ], (n=1,2,…,∞) was constructed, where β is the potential well width. The mobilities for n=1,2, and ∞ were calculated based on this equation, corresponding to the simple exponential, Gaussian and square well scattering potentials, respectively. In the limiting case of kβ1 (where k is the wave vector), all of the mobilities calculated for n=1,2, and ∞ showed a same result but different prefactor. Such difference was discussed in terms of the potential tail and was found that all of the calculated mobilities have T^−1/2 temperature and β⁻⁶ well width dependences. A mobility taking account of a spatially complicate scattering potential was studied and the same temperature dependence was also found. A best fit between the calculated results and experimental data was obtained by taking account of the nitrogen vacancy scattering.     

Lateral tunneling transistors fabricated by plane-dependent Si-doping in nonplanar epitaxy on GaAs (311)A and (411)A substrates

We have demonstrated the lateral tunneling transistors on GaAs (311)A and (411)A patterned substrates by using the plane-dependent Si-doping technique. Lateral p⁺-n⁺ tunneling junctions are formed by growing heavily Si-doped layers on patterned substrates. Current—voltage curves for both transistors show gate-controlled negative differential resistance characteristics. Furthermore, the peak current density of the lateral tunneling diodes fabricated on the (311)A patterned substrates increases as buffer layer thickness is increased, and a typical peak current density of 58 A/cm² for p = 6 × 10¹⁹ cm⁻³ and n = 7 × 10¹⁸ cm⁻³ is obtained when the buffer layer thickness is 1.2 μm. This study shows that plane-dependent Si-doping in non-planar epitaxy is a promising technique for fabricating tunneling transistors.     

Ultraviolet emission from OH and ArD in microcavity plasma devices

Intense emission in the ultraviolet (250-400 nm) from OH (A²Sigma⁺) and the rare gas-deuteride excimer ArD has been observed from mixtures of H₂O vapour or D₂ in Ar and excited in microcavity plasma devices. Peak wavelength-integrated intensities are measured for H₂O and D₂ concentrations of ~0.16% and 0.5-1%, respectively. Spectral simulations indicate the OH (A²Sigma⁺, v' = 0) rotational temperature to be 440 plusmn 20 K for 600 Torr Ar/0.3 Torr H₂O mixtures excited in a 45 nL microcavity.     

FIR perfect signal reconstruction from multiple convolutions:minimum deconvolver orders

Given p co-prime finite impulse response (FIR) filters h_i ∈R(m_h), it well known that there exist q _i∈R(m_q) such that Σ_ih_i*q_i=δ. Importantly, this enables signal recovery from its convolutions with p⩾2 co-prime FIR filters by FIR filtering. We show that such q_i exist almost surely if and only if m_q⩾[(m_h-1)/(p-1)], where [x] is the smallest integer greater than or equal to x. The results also provide conditions for full rank of certain key matrices arising in the blind multichannel deconvolution problem     

Metal-germanium Schottky barriers

A systematic study has been made of the electrical characteristics of Schottky barriers fabricated by evaporating various metal films on n-type chemically cleaned germanium substrates. The diodes, with the exception of Al---Ge contacts, exhibit near-ideal electrical characteristics and age only slightly towards lower barrier height values. Al---Ge contacts exhibit very pronounced ageing towards higher barrier height values, due to formation of an extra aluminium oxide interfacial layer. Because of this, the barrier height values of aged Al---Ge contacts derived from I-V and C-V characteristics differ significantly. The dependence of the barrier height, (φ_b) on the metal work function, φ_m, for different metal-germanium contacts shows that surface states play an important role in the formation of the barrier. The density of germanium surface states is estimated to be D_s = 2 × 10¹³ eV⁻¹ cm⁻².     

Conditions at a p-n junction in the presence of collected current

An abrupt p-n junction, such as occurs at the collector junction of an n-p-n transistor, is considered. The ratio of n- to p-region conductivity is taken to be very high, so that the transition region is restricted almost entirely to the p-region. The electron density distribution n within the transition region is investigated as a function of the applied reverse bias V_c, and of the minority carrier electron current density J which is injected into the transition region from the neutral p-region. It is shown that significant departures occur from the conventional solutions in which the presence of current is neglected. In particular, the electron density n_c at the plane of injection and the transition region thickness w_t, used as collector boundary conditions in the analysis of transistor operation, are shown to be current-dependent.

Two cases are considered. In Case I, applicable to transistors with an epitaxial layer in the base region below the collector, the electron velocity is assumed much less than the limiting drift velocity. For low injection level, where the minority carrier density n is everywhere less than the equilibrium majority carrier density p_p, the transition region is essentially a depletion region and the injected electrons move in an electric field determined uniquely by the applied voltage. It is shown that n_c ∝ J and w_t ∝ V_c^1/2. For high injection level, when n p_p, the transition region is essentially an accumulation region, and conditions of space-charge-limited current flow are established for which n_c ∝ J^2/3 and . The low-level injection results are primarily of interest as analytical extensions of the classical treatment. The high-level injection results are also relevant to the treatment of the dielectric diode.

In Case II, applicable to most alloy and diffused-base transistors, the electron velocity is assumed equal to the limiting drift velocity throughout the transition region. Mobile carrier depletion at low injection again gives way to accumulation at high injection. The functional relationships remain as for Case I at low injection, but become at high injection.

Semi-quantitative and detailed quantitative treatments are developed, and normalized graphs of the minority carrier density as a function of distance within the transition region are given for various junction voltages and injected currents.     

Rise time of silicon p-n-p photodiodes

Exact analytical expressions are derived for the short circuit photodiode currents excited by light pulses, under the assumption that the drift carrier velocity linearly depends on the electric field in the depletion layer. Reflection from the back surface of the photodiode is taken into account. Using the obtained expressions it is possible to establish a connection between the rise time t_rise and the product W_eff of the absorption coefficient (λ) and effective depletion layer width W_eff(W) at various ratios of the diode thickness and the effective depletion layer width. The influence of the RC-constant (where C is the photodiode effective capacity and R is the sum of the diode series and loading resistances) on the rise time is also analyzed.

One of the most important conclusions is that generally the rise time is larger for p-n-n⁺ photodiode configurations than for n-p-p⁺ configurations at the same substrate resistivity.