Impact ionization resonance and auger recombination in Hg1 - xCdxTe (0.6 ≤ x ≤ 0.7)

The purpose of this paper is the study of the impact ionization and the Auger recombination in Hg1-xCdxTe avalanche photodiodes, with0.6 leq x leq 0.7. Forx sim 0.7it is shown that the spin orbit splitting Δ is lower than the bandgap energy Egso that impact ionization is initiated by holes from the Split-off valence band. Forx sim 0.6, Delta sim E_{g}, the rate of the Auger recombination is maximum, corresponding to a resonant impact ionization and to a maximum ratiok = beta / alphawhere α and β are, respectively, the impact ionization coefficient for electrons and holes.     

Extremely Low Excess Noise in InAs Electron Avalanche Photodiodes

Measurements of the avalanche multiplication noise in InAs p-i-n and n-i-p diodes at room temperature demonstrate unambiguously that the avalanche multiplication process is dominated by impact ionization of electrons. This results in the excess noise factor for electron initiated multiplication asymptotically approaching a maximum value just less than two and becoming virtually gain-independent for higher gains. Measurements for predominantly hole initiated multiplication show corresponding high excess noise factors suggesting the electron to hole ionization coefficient ratios are comparable to those reported for $hbox{Hg}_{1-{x}}hbox{Cd}_{x}hbox{Te}$ electron avalanche photodiodes.      

Determination of germanium ionization coefficients from small-signal IMPATT diode characteristics

Small-signal measurements of germanium IMPATT diode admittance in the frequency range from 2 to 8 GHz were taken for various current densities. These measurements were compared with the small-signal admittances calculated using the model developed by Gummel, Scharfetter, and Blue [1], [2]. Values for the ionization coefficients and saturated velocities for electrons and holes used for the calculations have been chosen to secure reasonable agreement between theory and experiment for the diode avalanche voltage, the frequencies at which the small-signal susceptance and conductance cross zero, and the slope and general shape of the admittance versus frequency curves. The calculated small-signal admittance characteristics of the n⁺-p-p⁺mesa diode investigated are quite sensitive to the saturated hole velocity and the field dependence of the ionization rates. For the operating junction temperature, the velocity which gives the best fit is resolvable to about 5 percent. The best fit velocity is in agreement with published values. However, the ionization coefficients determined give a substantially smaller dependence of ionization rate on electric field than was obtained by Miller [3]. The coefficients obtained can be fitted by Baraff's theoretical model [4] using a low value for r, the normalized ionization cross section, in order to obtain the small dependence on field. The values of the ionization rates determined here,alpha_{p}=2.15 times 10_{5} exp(-7.10 times 10_{5}V.cm^-1/E) cm^-1alpha_{n}=4.90 times 10_{5} exp(-7.90 times 10_{5}V.cm^-1/E) cm^-1are believed to be generally applicable to impact ionization effects in germanium semiconductor devices.     

Effect of band shapes on carrier distribution at high temperature

This paper indicates both experimentally and graphically how the distribution of carriers changes above a critical temperature Tc, which is related to the density of states ρ in the band tails. Thus,kT_{c} = E_{0}, whererho = rho_{0} exp (DeltaE/E_{0}). The emission spectrum shifts with changing excitation (band filling) at lower temperatures (T < T_{c}) and stays at a constant value independent of excitation at higher temperatures (T > T_{c}). Experimental results of photoluminescence studies with GaAs crystals show that the quantity E0, obtained from the dependence of the peak energy upon the degree of excitation is the same as the quantitykT'_{c}, obtained from the dependence of the peak energy upon temperature. This is in agreements with the analysis. For lasing diodes, the threshold will increase steeply with increasing temperature above Tc, if the excited carriers are located mostly in the exponential states of the band tail.E_{0} = (10 sim 20)meV and Tc= (120 sim 250degK) are typical for crystals of heavily compensated GaAs.     

Accelerated testing of time-dependent breakdown of SiO2

Electric-field acceleration factor β is the slope of thelog (t_{BD})versus Eoxcurve, where tBDis the time to breakdown at oxide field Eox. We report that β is not a constant but proportional toEmin{ox}max{-2}. This is the main cause of the wide divergence of β values reported in the literature. The reported oxide thickness dependence of β is believed to be a result of the higher electron trap densities in thicker oxides. Oxide lifetime extrapolation usinglog (t_{BD}), or better,log (Q_{BD})against1/E_{ox}plots is more accurate and has a theoretical basis. Highly accelerated oxide testing appears to be feasible especially for very thin oxides.     

The distribution of gains in uniformly multiplying avalanche photodiodes: Theory

Expressions are derived for the probabilityP_{n,m}that a pulse initiated bynelectrons (or holes) in a uniformly multiplying semiconductor diode will result in a total number of electrons (or holes)m, to give a gainm/n, and for the probabilityQ_{n,m}that the gain will bem/nor greater. It is shown that the distributions are far from Gaussian. The gain distributionP_{1,m}for a single photoelectron, for example, is shown to have a maximum value form = 1for any value of the average gainM=m/n. The derivations are valid for any electric field distribution and assume only that the hole ionization coefficientbeta(E) can be approximated by the relationbeta(E) =kalpha(E), wherealpha(E)is the electron ionization coefficient andkis a constant. A method of determining an effective value ofk, for cases wherebeta=kalphais not a good approximation, is presented. The results can be used to calculate the average gain and the mean square deviation from the average, giving results in agreement with previously published relations [1], [2]. The implications of this theory on the use of avalanche diodes for low-level photodetection are discussed. It is shown that in the near infrared, cooled avalanche photodiodes can compare favorably with the best available photomultiplier when used either in a photon-counting mode, or for the reliable detection of low-level laser pulses.     

Optimum low-level injection efficiency of silicon transistors with shallow arsenic emitters

The influence of As surface concentration CSEon the emitter efficiency βγand the temperature dependence of βγare reported. The theoretical model that is used to explain the variation of βγwith CSEis based upon the difference in the effective energy bandgaps in the emitter and base regionsDeltaE_{g}. Experimental measurements ofDeltaE_{g}versus CSEare presented. Measurements of βγversus CSEshow that the effective emitter doping densityQ_{E}/x_{eb}reaches a maximum value atC_{SE} cong 1.5 times 10^{20}atoms/cm³, corresponding to the threshold above whichDeltaE_{g} > 0. For the case of a constant active base doping/cm²QB, this also corresponds to an optimum in the emitter efficiency βγ. However, it is shown that in typical sequential diffusion processing of transistors, βγincreases monotonically with CSEbecauseQ_{B} = Q_{B}(C_{SE})decreases. In addition, for devices fabricated in this study,Deltabeta_{gamma}/DeltaC_{SE}atC_{SE}=2 times 10^{20}atoms/ cm³for As-diffused emitters (doped oxide) was ≈ 5 times greater than for ion-implanted-diffused As emitters, showing the superiority of implantation in controlling gain. Finally, transistors that were made withC_{SE} siml 1.4 times 10^{20}atoms/cm³(DeltaE_{g} = 0) showed βgamma(85°C)/ βγ(-15°C) ≤ 1.05.     

Robust prediction of band-limited signals from past samples (Corresp.)

For a complex-valued deterministic signal of finite energy band-limited to the normalized frequency band|w| leq piexplicit coefficients{a_{kn}}are found such that for anyTsatisfying0 < T leq 1/2,left| f(t)-sum^{2n}_{k=1}a_{kn}f(t - kT)right| leq E_{f}cdot beta^{n}whereE_{f}is the signal energy andbeta doteq 0.6863. Thus the estimate off(t)in terms of2npast samples taken at a rate equal to or in excess of twice the Nyquist rate converges uniformly at a geometric rate tof(t)on(- infty , infty). The suboptimal coefficients{a_{kn}}have the desirable property of being pure numbers independent of both the particular band-limited signal and of the selected sampling rate1/T. It is also shown that these same coefficients can be used to estimate the value ofx(t)of a wide-sense stationary random process in terms of past samples.     

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.     

The temperature dependence of the DC base and collector currents in silicon bipolar transistors

Detailed measurements have been made of the base and collector-current characteristics of both n-p-n and p-n-p silicon transistors as a function of temperature. The collector current shows ideal behavior over the temperature range -60 to 150°C in thatI_{C} infin exp (eV_{BE}/kT). On the other hand, the base current is nonideal:I_{B} infin exp (eV_{BE}/nkT), wheren > 1.0. The nonideality of IBis the main source of the temperature dependence ofh_{FE} = I_{C}/I_{B}. There is no evidence for bandgap narrowing in the devices we have investigated. The temperature dependence of the collector current is given byI_{C} infin T_{m} exp (-e E_{g0}/kT) exp (eV_{BE}/kT), wherem = 1.4or 1.7 for n-p-n or p-n-p devices, respectively.E_{g0} = 1.19 pm 0.01eV. This result is consistent with the findings of others. The base current is a complicated function of temperature due to the presence of nonideal components.     

Wavelength dependence of multiplication noise in silicon avalanche photodiodes

Theoretical and experimental results on wavelength dependence of multiplication noise in silicon avalanche photodiodes are described. When the photodiode has a p-n⁺-junction and is illuminated from the n⁺-side, multiplication noise increases by decreasing optical wavelength. Effective ionization coefficient ratio keffis equal tokexp (2Kw_{a}) for a uniform junction electric field, wherekis the ratio of ionization coefficients of electrons α and holes β. The multiplication noise depends on the product of optical absorption coefficientKand the avalanche-region width wa. Calculations show that there exists an optimum wafor minimizing multiplication noise at a given wavelength. Theoretical results are shown to agree with results of experiments on diodes with a low-high-low impurity profile. Measured ionization coefficient ratiokvalues are 0.04 and 0.08 at 0.811- and 0.633-µm wavelength, respectively.     

Field dependence of impact ionization coefficients in In/sub 0.53/Ga/sub 0.47/As

Electron and hole ionization coefficients in In/sub 0.53/Ga/sub 0.47/As are deduced from mixed carrier avalanche photomultiplication measurements on a series of p-i-n diode layers, eliminating other effects that can lead to an increase in photocurrent with reverse bias. Low field ionization is observed for electrons but not for holes, resulting in a larger ratio of ionization coefficients, even at moderately high electric fields than previously reported. The measured ionization coefficients are marginally lower than those of GaAs for fields above 250 kVcm/sup -1/, supporting reports of slightly higher avalanche breakdown voltages in In/sub 0.53/Ga/sub 0.47/As than in GaAs p-i-n diodes.     

An Hg0.3Cd0.7Te avalanche photodiode for optical-fiber transmission systems at λ = 1.3 µm

The purpose of this paper is the characterization of Hg0.3Cd0.7Te avalanche photodiodes at γ = 1.3 µm. These devices are manufactured by tile Société Anonyme des Télécommunications. The multiplication noise for these APD's is measured. The value of the ratiok= β/α is deduced from noise measurements, β and α being, respectively, the hole and electron ionization coefficients. It is shown that these HgCdTe APD's are promising candidates for detectors of 1.3-µm optical communication.     

Hole trapping and breakdown in thin SiO2

The field dependence of the hole generation rate, also known as the impact ionization coefficient α, in thin SiO2(< 20 nm) was characterized by measuring the negative flat-band shift due to hole trapping. In thicker oxides,alpha = alpha_{0}e^{-H/E}where H = 78 MV/cm for electric fields ranging from 7 to 14 MV/cm, which covers the field range from the onset of significant Fowler-Nordheim current to instant breakdown. The similar field dependences of α and charge-to-breakdown supports the model that hole generation and trapping leads to oxide wearout. Because of the fact that positive charge generation is observed for oxide voltage well below the SiO2bandgap, we propose that the generated holes arise from transition between band tails in the amorphous SiO2. It is also observed that α decreases rapidly when the applied oxide voltage is very low; thus α is a function of both oxide field and voltage in general. This suggests that ultra-thin oxide with low operating voltages might be a good candidate for high endurance E²PROM devices at very low oxide field.     

A theoretical study of the two-photon ionization of metastable He with linearly and circularly polarized laser light

Generalized cross sectionshat{sigma}_{L}andhat{sigma}_{C}for the two-photon ionization of He from the metastable2^{1}Sstate are calculated for linearly and circularly polarized incident laser light, respectively, in the wavelength range 3725-5100 Å. Significant enhancement of cross sections occurs through real3^{1}Pand4^{1}Pp intermediate states. The ratiohat{sigma}_{C}/hat{sigma}_{L}shows a minima at the wavelengths close to 3743 and 4450 Å.     

Design of single mesh flashlamp driving circuits with resistive losses

The normalized nonlinear equation(dI/dtau) pm [alpha + beta|I|^{1/2}] + intmin{0}max{tau}I dbar{tau}= 1describing current evolution in a single mesh flashlamp driving circuit has been solved using numerical methods for the case of a critically damped pulse (alpha simeq 0.84) and beta = r/Z_{0} neq 0. Normalized current, power, and energy waveforms for values of β in the range0 leq beta leq 0.5are obtained. The energy efficiency ηE, which is numerically equal to the flashlamp dissipated energy di-Vided by the energy stored in the driving circuit, is also shown as a function of β. Increased numerical accuracy has improved the previously used value of α for critical damping and leads to a slightly different form for the curve representing the locus of values (α β) to obtain critically damped pulses in the presence of restrictive losses.     

The integral for multiplication factor M with single or equal ionization coefficients

General expressions for the multiplication factorMare derived for both step and linear graded junctions by integrating the common form for the ionization coefficientalpha(E)= alpha_{infin}exp(-b/E). Equal ionization coefficients are assumed. The results are compared with a commonly used approximation.     

Determination of carrier lifetime in Si by optical modulation

A contactless optical modulation technique for the determination of photogenerated carrier lifetime in silicon is presented. The method is based on the measurement of the optically modulated free-carrier absorption in Si at 10.6 µm. The fractional change in transmitted intensity of a dc below band-gap probe beam (with ħω_{p}<E_{g}) due to a modulated pump beam (with ħω_{p} > E_{g}) is proportional to the excess carrier lifetime. This optical modulation technique, which is relatively simple, contactless, and nondestructive, may have significant potential as a high-resolution high-sensitivity tool for Si wafer screening, crystal growth studies, and process evaluation.     

Linear and nonlinear optical properties of AgGaS2, CuGaS2, and CuInS2, and theory of the wedge technique for the measurement of nonlinear coefficients

The refractive indices of the ternaryA^{I}B^{III}C_{2}^{VI}semiconductors AgGaS2, CuGaS2, and CuInS2have been measured over the entire range of transparency of these crystals. The optical nonlinear coefficients for second-harmonic generation have also been determined. Three-frequency collinear phase matching is analyzed in detail for AgGaS2. The birefringences of CuGaS2and CuInS2are not large enough to permit three-frequency phase matching within the transparent regions. A parametric oscillator threshold calculation for a pump wavelength 0.89 μ, which is within the range of the GaAs injection laser, indicates that AgGaS2is promising for this application. The upconversion efficiency in AgGaS2for sum mixing of the CO2laser (lambda = 10.5 mu) with the xenon ion laser (lambda = 0.597 mu) is also calculated. The result indicates that, depending upon system requirements and the availability of high optical quality material, AgGaS2can be comparable to ZnGeP2for upconversion. In Appendix II, we present a theory of the wedge technique for the measurement of nonlinear coefficients. This theory takes into account losses and assumes a Gaussian beam geometry. Furthermore, a discussion of units in nonlinear optics is given.     

On the avalanche initiation probability of avalanche diodes above the breakdown voltage

In the calculation of the turn-on probabilities per unit time of avalanche diode microplasmas, or of the single-photon detection probabilities of avalanche photodiodes used in the photon-counting mode, it is desirable to know how the avalanche initiation probability varies with voltage above the breakdown voltage. It is shown that the two coupled differential equations derived by Oldham et al. for the probabilities that a self-sustaining avalanche will be initiated in an avalanche diode biased above the breakdown voltage by an injected electron or by an injected hole (avalanche initiation probabilities) can be combined to provide a single integral equation for each of the electron, hole, and electron-hole pair initiation probabilities. These equations can be integrated for the special case in which the electron and hole ionization rates αeand αhare related byalpha_{h} approx kalpha_{e}wherekis a constant. A method of computing an effective value ofkfor other cases in which this approximation is not a good one is presented. The resulting expressions are shown to be consistent with previously published calculations by McIntyre of the breakdown probabilities both for the casek = 1and for the more general casek neq 1.