Planar, buried, ion-exchanged glass waveguides: Diffusion characteristics

A detailed theoretical and experimental study of Ag+-Na+ exchange in soda-lime silicate glasses in a molten bath containing a mixture of NaNO3and Ag+ is presented. With no applied field, concentration profilesC(x, t)(and therefore, the index profiles for low concentrations) are given by complementary error function. The estimated value for the self-diffusion coefficientDof Ag+ is 0.133 μm²/min for low concentrations and it monotonically increases with the surface concentration C0until it saturates at about 0.3 μm²/min forC_{0} geq 10^{-3}MF. However, square root dependence of diffusion depth with time seems to be independent of the C0. Presence of an external fieldEcauses the effective depth of diffusion to increase. In fact, for largeEfields, the profile can accurately be described byC/C_{0} = frac{1}{2} erfc(x' - r)wherer = mu Et/sqrt{2Dt}where μ is the ionic mobility of Ag⁺in glass. We define a new diffusion depthWas the distance from the surface to the1/econcentration point, and for large fields,Wvaries linearly withEandt. Experimental results yielded a value of 15.55 μm²/Vmin forμ. As before, square root dependence ofWwithtand the linear variation ofWversus C0forC_{0} leq 10^{-3}MF, withWsaturating forC_{0} > 10^{-3}MF, were observed in the case of field assisted diffusion. A two-step process, where a surface waveguide formed in the first step with eitherEequal to zero or some finite value, is modified by performing a second diffusion in pure sodium nitrate to produce a buried, symmetrical fiber-like profile. This process is also studied in detail.     

A treatment of diffusion errors affecting junction depth

An error treatment of the diffusion variables of time t, temperature T, and starting resistivity ρ, has been made in regard to their effects upon junction depth. An analytical equation has been derived for engineering usage in determining the per cent error in junction depthx: Per cent error in junction depth =100 sqrt{frac{bar{Δt^{2}}{2t}} +frac{bar{QΔT}^{2}}{2RT^{2}}+bar{frac{sqrt{pi DT}}{microq p^{2}N_{s}x}. Delta rho exp (x^{2}/4Dt)}}A sample calculation using the above equation is presented along with a method of estimating errors in junction depth due to heating and cooling in the diffusion cycle.     

An upper bound to the capacity of the band-limited Gaussian autoregressive channel with noiseless feedback

Upper bounds to the capacity of band-limited Gaussianmth-order autoregressive channels with feedback and average energy constraintEare derived. These are the only known hounds on one- and two-way autoregressive channels of order greater than one. They are the tightest known for the first-order case. In this case letalpha_1be the regression coefficient,sigma^2the innovation variance,Nthe number of channel iterations per source symbol, ande = E/N; then the first-order capacityC^1is bounded by begin{equation} C^1 leq begin{cases} frac{1}{2} ln [frac{e}{sigma^2}(1+ mid alpha_1 mid ) ^ 2 +1], & frac{e}{sigma^2} leq frac{1}{1- alpha_1^2} \ frac{1}{2} ln [frac{e}{sigma^2} + frac{2mid alpha_1 mid}{sqrt{1-alpha_1^2}} sqrt{frac{e}{simga^2}} + frac{1}{1-alpha_1^2}], & text{elsewhere}.\ end{cases} end{equation} This is equal to capacity without feedback for very low and very highe/sigma^2and is less than twice this one-way capacity everywhere.     

An upper bound for codes for the noisy two-access binary adder channel (Corresp.)

Using earlier methods a combinatorial upper bound is derived for|C|. cdot |D|, where(C,D)is adelta-decodable code pair for the noisy two-access binary adder channel. Asymptotically, this bound reduces toR_{1}=R_{2} leq frac{3}{2} + elog_{2} e - (frac{1}{2} + e) log_{2} (1 + 2e)= frac{1}{2} - e + H(frac{1}{2} - e) - frac{1}{2}H(2e),wheree = lfloor (delta - 1)/2 rfloor /n, n rightarrow inftyandR_{1}resp.R_{2}is the rate of the codeCresp.D.     

Concentration-dependent diffusion of boron and phosphorus in silicon

A calculation is made of the tail of the impurity concentration profile resulting from concentration-dependent diffusion from a constant surface concentration into a semi-infinite medium. The calculation predicts that if the concentration dependence at low impurity concentrations is negligible, the low concentration portion of the doping profile should still take the familiar form,C = C'_{s} erfc (x/2 D_{i^{frac{1}{2}}}t^{frac{1}{2}}). Diis the commonly known diffusion coefficient at low impurity concentrations, whileC'_{s}is the "apparent" surface concentration.C'_{s}depends on the actual surface concentration and also depends on how the diffusion coefficient varies with impurity concentration at high concentrations. It is a constant for a given diffusion system but could be orders of magnitude higher than the actual surface concentration. Empirical data have been obtained for boron and phosphorus diffusions in silicon and found to be in good agreement with this prediction.     

Linear feedback rate bounds for regressive channels (Corresp.)

This article presents new tighter upper bounds on the rate of Gaussian autoregressive channels with linear feedback. The separation between the upper and lower bounds is small. We havefrac{1}{2} ln left( 1 + rho left( 1+ sum_{k=1}^{m} alpha_{k} x^{- k} right)^{2} right) leq C_{L} leq frac{1}{2} ln left( 1+ rho left( 1+ sum_{k = 1}^{m} alpha_{k} / sqrt{1 + rho} right)^{2} right), mbox{all rho}, whererho = P/N_{0}W, alpha_{l}, cdots, alpha_{m}are regression coefficients,Pis power,Wis bandwidth,N_{0}is the one-sided innovation spectrum, andxis a root of the polynomial(X^{2} - 1)x^{2m} - rho left( x^{m} + sum^{m}_{k=1} alpha_{k} x^{m - k} right)^{2} = 0.It is conjectured that the lower bound is the feedback capacity.     

Temperature dependence of MOSFET characteristics in weak inversion

A knowledge of the MOSFET operating in weak inversion is important for circuits with low leakage specifications. This paper discusses the effect of temperature on the MOSFET in weak inversion. The reciprocal slopenof the log IDSversus VGSrelationship between source-drain current IDSand gate bias VGSmay be given byfrac{1}{(n - 1 - gamma)^{2}} = frac{2Cmin{ox}max{2}}{qepsilon_{s}N_{B}} [frac{3}{4} frac{E_{g^{0}}{q} - (frac{3}{2}alpha + frac{k}{q})T]withalpha equiv (k/q)(38.2 - ln N_{B} + (3/2) ln T)and γ ≡C_{ss}/C_{ox}, where Coxis the oxide capacitance per unit area, Cssthe surface states capacitance per unit area,qthe electronic charge, εsthe permittivity of silicon, NBthe bulk doping concentration,kthe Boltzmann's constant,Tthe absolute temperature, andE_{g0}the extrapolated value of the energy gap of lightly doped silicon atT = 0K. This theoretical formula was in good agreement with experimental results in a temperature range of interest.     

Thermionic current in a parallel-plane diode

An approximate formula is developed for the current of a parallel-plane diode including the effects of initial velocities of emission. For an oxide-coated cathode (T = 1000°K) the approximate result is:J = 2.33 times 10^{-6} frac{V^{3/2}}{x^{2}} cdot[1 + frac{11.4(J_{s}x^{2})^{1/4}}{V^{3/4}} + frac{3.22(J_{s}x^{2})^{1/8}}{V^{3/2}}]where,J, Js, andxare in suitable units such that Jx²andJ_{s}x^{2}are in amperes and V in volts. A comparison is made between this result, Child's 3/2 power solution, and the Epstein-Fry-Langmuir solution. The result given above being an explicit solution of the current is particularly advantageous over prior approximate solutions.     

Two-dimensional dynamic analysis of short-channel thin-film MOS transistors using a minicomputer

A computer program is described for simulating two-dimensional thin-film MOS transistors on a minicomputer. Data are presented showing the variation of internal carrier density with time until a steady-state condition is reached. These data show the formation of a drain-induced back channel whose conduction properties depend on the back-channel length and carrier mobility. For channel length below 2.0 µm, the two-dimensional steady-state drain current is shown to fit the expressionI_{D}/W = frac{micro_{0}C_{0}}{L[1+(micro_{0}/upsilon_{s} V_{D}{L})^{2}]^{1/2}}(V_{G} - V_{T} - V_{D/2})V{D}for values of drain voltage below a specific saturation value (V_{DM}); andI_{D}/W = frac{10^{-8)(V_{G} - V_{T})^{1/2}}{(T_{ox})^{1/2}L}.(V_{D} - V_{DM}) + I_{DM}for drain voltages above the saturation value.     

Bounds for truncation error in sampling expansions of band-limited signals

Forf(t)a real-valued signal band-limited to- pi r leq omega leq pi r (0 < r < 1)and represented by its Fourier integral, upper bounds are established for the magnitude of the truncation error whenf(t)is approximated at a generic timetby an appropriate selection ofN_{1} + N_{2} + 1terms from its Shannon sampling series expansion, the latter expansion being associated with the full band[-pi, pi]and thus involving samples offtaken at the integer points. Results are presented for two cases: 1) the Fourier transformF(omega)is such that|F(omega)|^{2}is integrable on[-pi, pi r](finite energy case), and 2)|F(omega)|is integrable on[-pi r, pi r]. In case 1) it is shown that the truncation error magnitude is bounded above byg(r, t) cdot sqrt{E} cdot left( frac{1}{N_{1}} + frac{1}{N_{2}} right)whereEdenotes the signal energy andgis independent ofN_{1}, N_{2}and the particular band-limited signal being approximated. Correspondingly, in case 2) the error is bounded above byh(r, t) cdot M cdot left( frac{1}{N_{1}} + frac{1}{N_{2}} right)whereMis the maximum signal amplitude andhis independent ofN_{1}, N_{2}and the signal. These estimates possess the same asymptotic behavior as those exhibited earlier by Yao and Thomas [2], but are derived here using only real variable methods in conjunction with the signal representation. In case 1), the estimate obtained represents a sharpening of the Yao-Thomas bound for values ofrdose to unity.     

Hybrid low autocorrelation sequences (Corresp.)

Skew-symmetric sequences of(2n + 1)terms,a_0,a_1,cdots,a_{2n}, are described for which the "merit factor" begin{equation} F_h = frac{biggl[sum_{i=0}^{2n} mid a_i mid biggr] ^2}{ 2 sum_{k=1}^{2n} biggl[ sum_{i=0}^{2n-k} text{sign} (a_i) cdot a_{i+k} biggl] ^2} end{equation} is unusually high.     

Huffman codes and self-information

In this paper the connection between the self-information of a source letter from a finite alphabet and its code-word length in a Huffman code is investigated. Consider the set of all independent finite alphabet sources which contain a source letter a of probabilityp. The maximum over this set of the length of a Huffman codeword for a is determined. This maximum remains constant aspvaries between the reciprocal values of two consecutive Fibonacci numbers. For the smallpthis maximum is approximately equal toleft[ log_{2} frac{1+ sqrt{5}}{2} right]^{-1} approx 1.44times the self-information.     

A simple analysis of the stable field profile in the supercritical TEA

An analytical investigation supported by numerical calculations has been performed of the stable field profile in a supercritical diffusion-stabilized n-GaAs transferred electron amplifier (TEA) with ohmic contacts. In the numerical analysis, the field profile is determined by solving the steady-state continuity and Poisson equations. The diffusion-induced short-circuit stability is checked by performing time-domain computer simulations under constant voltage conditions. The analytical analysis based on simplifying assumptions gives the following results in good agreement with the numerical results. 1) A minimum doping level required for stability exists, which is inversely proportional to the field-independent diffusion coefficient assumed in the simple analysis. 2) The dc current is bias independent and below the threshold value, and the current drop ratio increases slowly and almost linearly with the doping level. 3) The domain width normalized to the diode lengthLvaries almost linearly with(V_{B}/V_{T}-1)^{frac{1}{2}}/(n_{0}L)^{frac{1}{2}}where VBis the bias voltage VTis the threshold voltage, and no is the doping level. 4) The peak domain field varies almost linearly with (V_{B}/V_{T}-1)^{frac{1}{2}} (n_{0}L)^{frac{1}{2}}. Those results contribute to the understanding of the highn_{0}L-product switch and the stability of the supercritical TEA.     

Local Construction of Near-Optimal Power Spanners for Wireless Ad Hoc Networks

We present a local distributed algorithm that, given a wireless ad hoc network modeled as a unit disk graph U in the plane, constructs a planar power spanner of U whose degree is bounded by k and whose stretch factor is bounded by 1 + (2sin{frac{pi}{k}})^{p}, where k geq 10 is an integer parameter and p in [2, 5] is the power exponent constant. For the same degree bound k, the stretch factor of our algorithm significantly improves the previous best bounds by Song et al. We show that this bound is near-optimal by proving that the slightly smaller stretch factor of 1 + (2sin{frac{pi}{k + 1}})^{p} is unattainable for the same degree bound k. In contrast to previous algorithms for the problem, the presented algorithm is local. As a consequence, the algorithm is highly scalable and robust. Finally, while the algorithm is efficient and easy to implement in practice, it relies on deep insights on the geometry of unit disk graphs and novel techniques that are of independent interest.     

4C6--Concentration and temperature dependences of spin-lattice relaxation times in ruby at helium temperatures: Relaxation in a zero magnetic field

The relaxation times T1for the grouud state levels in ruby were measured in the temperature range 4.2 to 1.6°K for the various concentrations of theCr^{3+}ionsffrom 0.05 to 0.7 percent. The dependenceT_{1}(f)of the formT_{1}^{-1}(f) = T_{1}^{-1}(0) + T_{1}^{-1}(I)f ^{n}withn simeq 2has been obtained for the different transitions. The measurements of relaxation times forpm frac{1}{2} leftrightarrow pm frac{3}{2}transition at zero magnetic field were especially aimed at establishing a form of dependenceT_{1}(f)because of the absence of the cross relaxation effects in this case. The normal temperature dependenceT_{1} propto T_{1}^{-1}has been obtained at all concentrations in comparison with anomalous dependences observed at high concentrations by some researchers.     

Multiplication noise in uniform avalanche diodes

A general expression is derived from which the spectral density of the noise generated in a uniformly multiplying p-n junction can be calculated for any distribution of injected carriers. The analysis is limited to the white noise part of the noise spectrum only, and to diodes having large potential drops across the multiplying region of the depletion layer. It is shown for the special case in whichbeta = kalpha, wherekis a constant and α and β are the ionization coefficients of electrons and holes, respectively, that the noise spectral density is given by2eI_{in}M^{3}[1 + (frac{1 - k}{k})(frac{M - 1}{M})^{2}]where M is the current multiplication factor and Iinthe injected current, if the only carriers injected into the depletion layer are holes, and by2eI_{in}M^{3}[1 - (1 - k)(frac{M - 1}{M})^{2}]if the only injected carriers are electrons. An expression is also derived for the noise power which will be delivered to an external load for the limitM rightarrow infin.     

A bound on lightweight sequences with application to definite decoding (Corresp.)

It is shown that the numberMof binary-valuedn-tuples having fractional weightdeltaor less,0 < delta leq frac{1}{3}, such that no twon-tuples agree in anyLconsecutive positions, is bounded by2^{2LH(delta)+1}. A set ofn-tuples is constructed to show that this bound is not likely to be improved upon by any significant factor. This bound is used to show that the ratiod_{DD}/n_{DD}of definite-decoding minimum distance to definite-decoding constraint length is lower bounded byH^{-l}[frac{1}{6} cdot (1 - R)/ (1+R)]asn_{DD}grows without bound.     

Design consideration for a germanium P-N-P-N switching device with three contacts and a "Sandwich" structure

The current Ioffthrough a germanium p-n-p-n switch in the OFF state is described as a simple function of the control current Itin its third contact. The device is of a so-called "sandwich" structure, the third contact being the outer edge of the middleplayer. The voltages considered are sufficiently small so that avalanche multiplication can be neglected. It is derived that:I_{off} = frac{1}{2}{(a+ I_{t} - sqrt{(a+ I_{t})^{2} - 4(b-cI_{t})}}a, bandcare device parameters determined by the physical and geometrical structure. The conditions for switching into the ON state are given and the temperature dependence of the parameters is predicted. The experimental results are found to be in good agreement with the design theory.     

The inhibition of negative resistance dipole waves and domains in n-GaAs

Expressions describing the growth and propagation of infinitesimal space-charge waves in the presence of a differential negative resistance are derived, and conditions for the inhibition of dipole waves and domains inn-GaAs of resistivity greater than 10Ω-cm at 300°K are obtained. Thermoelectric effects are estimated and found to be small for carrier densities much less than 10¹⁵cm^-3. Taking the negative differential resistivity to be larger than the ohmic resistivity by a factor of 10²leads to 1) condition for inhibition of dipole waves:nl^{2} lsim 10^{9}cm^-12) condition for inhibition of stable domains:nl lsim 10^{12}cm^-2whenn= electron density andl= specimen length. The relevance of these results to explaining the phenomena observed in amplifying crystals is pointed out. It is suggested that the condition for amplification is(frac{10^{9}}{n})^{1/2} lsim l lsim frac{10^{12}}{n}.     

An estimate of the variation of a band-limited process

Upper and lower bounds are established for the mean-square variation of a stationary processX(t)whose power spectrum is bounded byomega_{c}, in terms of its average powerP_{0}and the average powerP_{1}of its derivative. It is shown thatleft( frac{2}{pi} right)^{2} P_{1} tau^{2} leq E {|X(t+tau )-X(t)|^{2}} leq P_{1} tau^{2} leq omega_{c}^{2}P_{0}tau^{2}where the upper bounds are valid for anytauand the lower bound fortau < pi / omega_{c}. These estimates are applied to the mean-square variation of the envelope of a quasi-monochromatic process.