Location of 1/f noise sources in BJT's and HBJT's—I. theory

The most general case of1/fnoise in transistors can be described by three independent noise current generators: ibebetween base and emitter, ibcbetween base and collector, and iecbetween emitter and collector. By short-circuiting the base and the collector to ground and comparing the base and collector noise spectraS_{IB}(f)andS_{IC}(f)for the case of zero feedback from the emitter with the base and collector noise spectraS'_{IB}(f)andS'_{IC}(f)for the case of strong feedback from the emitter, one can evaluate the relative strength of the three noise sources. By measuring the current dependence ofS_{IB}(f),S_{IC}(f),S'_{IB}(f), andS'_{IC}(f), one can assign physical processes to the current generators ibc, ibe, and iec. It is the aim of this paper to demonstrate theoretically a simple method for locating1/fnoise sources in BJT's and HBJT's by comparing the base and collector1/fnoise for the cases without and with strong emitter feedback. In later papers we shall demonstrate experimentally how this method is applied to practical situations.     

Direct measurement of the potential spike energy in AlGaAs/GaAs single-heterojunction bipolar transistors

A balanced two-step current transport theory, i.e., thermionic emission followed by Shockley diffusion, is applied to study the emitter-base (EB) potential spike energy in the AlGaAs/GaAs single-heterojunction bipolar transistor. It is found, surprisingly, that when the transistor is operated in the active region theI-Vcharacteristics of the collector current (IC) versus base-emitter applied voltage (VBE) exhibits an ideality factor of 1.237. This non-1kT transfer characteristics is due to the bias-dependent potential spike energy at the emitter-base heterojunction. The reverse I-V characteristics of emitter current (IE) versus base-collector bias (VBC), however, shows the traditional 1kT behavior. The difference between ICand IEat the same applied voltage (V_{BE} = V_{BC}) determines the potential spike energy (ΔE). It turns out that Δ E/q = 0.19(V_{BE} - 0.48)whereqis the unit charge. This indicates that the potential spike appears only when the applied voltageV_{BE} > 0.48V.     

Low-frequency noise in Cr—SiO2—N-Si tunnel diodes

Low-frequency noise of Cr-SiO2-n-Si tunnel diodes with about 30-Å-thick oxides is investigated as function of bias, frequency, and temperature. Measurements of1/fnoise are explained by a theory employing the two step tunneling model of Sah. Electrons from the Si conduction band are trapped by states at the Si-SiO2interface and then tunnel into bound states of the oxide located close to the interface. The oxide states of density N00can be represented by a frequency dependent parallel admittance exhibiting frequency-dependent thermal noise that modulates the dc currentItunneling through the oxide barrier. This generates flicker noise at the device terminals proportional toI^{2}N_{00}and inversely proportional to frequencyfand tunneling areaA. The valueA = 5. 10-3A0, determined by fitting theoretical and experimental curves at low frequency, is only a small fraction of the gate area A0, since tunneling preferentially occurs through the thinnest parts of the oxide. The currentIalso exhibits full shot noise at high frequency and low current. Qualitative agreement between theoretical and measured noise is found over 9 decades. Measurements at low temperature show additional noise of generation-recombination centers at larger frequencies and currents.     

Second breakdown of double epitaxial transistors

This paper deals with the second breakdown of transistors with epitaxial collector, epitaxial base, and diffused emitter. Transistors were fabricated with base width WBin the range of 2 to 18 µ and resistivity in the range of 0.1 to 10 ohm . cm. The optimum values of the resistivity and the thickness of these regions were calculated by computer techniques. The devices were mounted onto a TO-63 header and the base and the emitter leads were bonded onto the device ultrasonically. The electrical characteristics, including the frequency response ftand secondary breakdownS/Bcapability, were tested. For the measurement of second breakdown current IM, forward bias condition was used. It was found that for fixed collector and emitter parameters, IMwas controlled by the product of base resistivity ρBand base width WB. The value of IMwas found to increase withrho_{B}W_{B}. However, for a specified device characteristic, an optimum value ofrho_{B}W_{B}was found to exist. For transistors withV_{CEO} =150volts,f_{t}=20mHz andh_{FE}=20, the optimum value ofrho_{B}W_{B}was found to be 6 × 10^-4ohm . cm².     

Measurement of high-frequency equivalent circuit parameters of junction and surface barrier transistors

Methods are described for the determination of the high-frequency parameters of junction and surface barrier transistors and involve, in addition to the knowledge of the usual low-frequency parameters, measurement of the product of Ccand the extrinsic base resistancer_{b0},r_{b0}itself, and the alpha cutoff frequency fα. A previously described method is used to determine the productr_{b0}C_{c}, but new methods are described for the measurement ofr_{b0}and fα. The measurements are of "bridge" type, involving simple circuit adjustments for a response null at a single frequency. Typical experimental results are given for transistors having fαvalues as high as 85 mc, Ccvalues down to 2.3 pF andr_{b0}ranging from 45 to 400 ohms. The limits quoted for fαand Ccrefer to surface barrier transistors. Comparison with results derived by alternative methods of measurement show good agreement.     

Origin of 1/f noise in bipolar transistors

In planar n-p-n transistors fabricated in IC technology, the dependence of 1/fnoise on the base current density jB, the base width WB, and the emitter area FEwas measured. The power spectrumS_{iB}(f)of the base current fluctuations iBcan be represented by the empirical relationS_{iB} = const. jmin{B}max{gamma} cdot Fmin{E}max{beta} cdot wmin{B}max{-1} cdot f^{-1}where1 leq gamma leq 2and β has been found to be 1.3 or 2. The results of measurements on gate-controlled devices indicate that 1/fnoise cannot be explained by McWhorter's surface model. Therefore, a new model is proposed which assumes resistance fluctuations in the base region as the cause of 1/fnoise in bipolar transistors. The model establishes the relation forS_{iB}(f)as well as the magnitude of the coefficients β and γ.     

Noise in short n+-n--n+GaAs diodes

Noise measurements in a short, near-ballistic, n⁺-n^--n⁺GaAs diode are reported. The device had a linear characteristic below 100 mA. It showed1/fnoise at low frequencies and a white noise close to the thermal noise of the device conductancegat high frequencies. The1/fnoise is most likely mobility fluctuation noise; we evaluated Hooge's parameter α and found a value of 1.95 × 10^-6at room temperature and 0.959 × 10^-6at liquid nitrogen temperature. We also observed a1/fnoise spectrum turning over into1/f^0.5spectrum at 77 K.     

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.     

Geometrical factors in avalanche punchthrough erase

It is known that the surface potential of an IGFET can be raised to high levels by reverse-bias pulsing its source and drain. This high surface potential is contingent upon both punchthrough and avalanche injection of majority carriers into the surface region. Erase of some multilayer charge storage memory cells is accomplished using such an avalanche punchthrough erase (APTE) operation. In this paper the maximum surface potential achievable in this manner is assessed for a variety of geometries. The calculation is based upon a Fourier sine transform solution of Poisson's equation, coupled with the sampling theorem for spatially localized functions. The depletion width is determined self-consistently and is found to vary from a minimum value at mid-channel to a maximum value at the channel ends. It is found that the maximum surface potential is achieved for devices whose junction depth is comparable to or greater than the channel length. Under these conditions the surface potential can be as large as the reverse bias less the punchthrough voltage. To avoid serious short-channel behavior during normal read operations, it is suggested that the conditionNl^{2} > 2V_{D}kisin_{0}/ebe observed, whereN= doping level/cm³,l= half channel length, VD= drain voltage during read, K = dielectric constant of semiconductor, ∈0= permittivity of free space,e= electronic charge. Thus for a 2-µm channel length we recommend a junction depth ≥2 µm, and a doping level ≈6.5 × 10¹⁵/cm³for a memory cell which is to use APTE and a read voltageV_{D} simeq 5V.     

Low-frequency noise figure and its application to the measurement of certain transistor parameters

Low-frequency noise measurements are shown to provide a convenient and reasonably accurate (±10 per cent) means of measuring r'_{b}. Their application to the measurement of the factornin the junction lawp_{e} = p_{n} (e_^{qV/nkT} - 1)is also described, though the values ofnobtained from noise measurements do not check accurately with the values ofndetermined by other methods. Experimental determinations of the variation of low-frequency noise figure with emitter-bias current are also presented for several transistor types. The observed behavior suggests that the principal source of1/fnoise in low-noise transistors may be in the emitter-base transition region instead of on the base surfaces where it is placed in presently accepted noise models.     

Noise figure of UHF transistors as a function of frequency and bias conditions

It is shown that the observed values of the minimum noise figureF_{min}of UHF transistors in common base connection can be explained in terms of the device parameter(1-alpha_{dc}) r_{b'b}/R_{e0}and fαfor frequencies up to 1000 MHz. An interesting collector saturation effect is observed that gives a strong increase in UHF noise figure at high currents. Many features of the dependance ofF_{min}on operating conditions can be explained by this effect. The current dependence ofF_{min}for large values of |VCB| and high currents suggests a distribution in diffusion times through the base region. At intermediate frequencies, the noise figure increases with increasing collector bias |VCB| due to an increase inr_{b'b}, which in turn is caused by the dependence of the base width on |VCB|.     

4C1--Nonlinear effects in an NMR experiment

We have studied multiple-photon transition in a low-field nuclear magnetic resonance (NMR) experiment. It is well known that a saturation of the NMR occurs when using a sufficiently high alternating magnetic field which induces multiple-photons transitions. We show theoretically that these multiphoton transitions are accompanied by an harmonic generation. For an-photon transition, this generation occurs mostly on thenth and (n pm 1)th harmonic. For an irradiating field2H_{1} cos omegat of pulsation ω such thatnomega= gamma H_{0}=omega_{0}where H0is the steady field and θ is the angle between H0and H1the amplitudesSmin{n}max{n}andSmin{n}max{n+1}of these components are given bySmin{n}max{n} = f_{n}(theta) (H_{1})^{n},Smin{n}max{n+1} = cos theta f_{n}(theta) (H_{1})^{n+1}. We have verified these equations in a low-field NMR experiment (H_{0} = 0.7Gs/s), polarizing first a flowing liquid in a high magnetic field. The liquid then flows in a modified Bloch spectrometer. The receiving coil is still perpendicular to the steady field but it is possible to adjust the angle θ between the axis of the emission coils (H1field) and the steady-field H0. Using a synchronous detection at the output of the receiving coil on the pulsation(n - 1) omega, nomega, or(n + 1) omega, we have directly detected multiphoton transistions. The above equations have been verified forn = 2ton = 5. There are slight discrepancies at high excitation which may be explained taking into account a large saturation.     

Magnitude and dispersion of Kleinman forbidden nonlinear optical coefficients

Starting with a perturbation expansion for the Kleinman forbidden nonlinear optical coefficientd_{ijk^{F}}and for Miller'sDelta_{ijk^{F}}, and making several approximations, we arrive at a simple result for the ratio of forbidden to allowed mixing nonlinearities (omega_{1} + omega_{2} = omega_{3}), namelyDelta_{ijk^{F}}/Delta_{ijk^{A}} propto (omega_{3}^{2} + 2omega_{1}omega_{2}). For second-harmonic generation (SHG) this can be expressed asDelta_{ijk^{F}}/Delta_{ijk^{A}} simeq (omega/chi)(partialchi/partialomega), which clearly shows the close connection betweenDelta_{ijk^{F}}and the linear dispersion. These expressions are shown to give good agreement with literature experimental values, as well as for our measurements on TeO2for various input frequencies ω1and ω2(i.e.,omega_{3} = 1.88, 2.33, 2.82, 3.50, and 3.76 eV).     

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.     

Pulsed discharge initiated chemical lasers -- Part II: HF laser emission from NF3and N2F4systems

A transverse, multiple-arc pulsed discharge has produced laser emission in NF3and N2F4mixed with H2, CH4, C2H6, HCl, HBr, and natural gas.P_{10}, P_{21}, P_{32}, and P43HF transitions were observed. The peak powers measured ranged from ∼8.5 to 25 kW with typical pulsewidths ofsim0.3 mus.     

The photoionization cross sections of the Rg*2[3Σ+u] excimer states for Ne*2, Ar*2, and Kr*2

Based on the recently determined Rydberg series of the³Sigma+_{u}excimer states of Ne*2, Ar*2and Kr*2, the photoionization cross sections of these molecules are calculated using a single-channel quantum defect method. These cross sections are found to differ considerably from those of the asymptotic metastable atomic Rg*(ns^{3}P_{2}) states, but are in good agreement with recently reported experiments at isolated wavelengths. The implications of these results for VUV and XUV lasers are discussed.     

A laser augmented reaction: SF6+ SiH4→S*2+ SiF4+ HF + H2· retention of isotopic selectivity during detonation

A single unfocused pulse of a free running CO2laser, area ∼ 8 cm², initiates an explosive reaction between SF6and SiH4. This occurs at a minimum energy of 4 J [full width at half maximum (FWHM)sim 1.5 /mus] of which about one half is absorbed in an 8 cm long cell; total pressure 12 torr; 0.65 <p(SiH4)/p(SF6) < 1.8. The spectral and temporal distributions of the emitted chemiluminescence depend sensitively on the fuel to oxidizer ratio, and on the pulse energy; we investigated the range 4 → 20 J. The principal emission is due to S2(B^{3}Sigma-_{u} rightarrow X^{3}Sigma-_{g}). Transitionsupsilon' (0-4) rightarrow upsilon" (2-15)were recorded. In the³Sigma-_{u}state, vibrational temperatures range from 3000-13000 K. The luminosity peaks sharply at (SiH4)/(SF6) = 1.0 ± 0.05. On each side of the maximum of the emission versus composition curve [at (SiH4)/(SF6) ≈ 0.95 and 1.22, for a 12 J pulse] the residual SF6(0.2-0.5 percent of initial amount) is enriched in³⁴SF6; the observed fractionation factors at these two compositions are 8 ± 2. The separation between the two sharply peaked optimum compositions appears to increase with increasing pulse energy. Preliminary results with other fuels suggest that the concurrent absorption of CO2laser radiation by the fuel, as well as a highly exothermic reaction, are pre-requisite for fine tuning of composition, injected power, and total pressure for optimum isotope fractionation.     

A low-frequency noise analysis using the two-dimensional numerical analysis method

A low-frequency (1/f) noise analysis is presented for a MOSFET. Poisson's equation and current continuity equation are numerically Solved to determine hole and electron concentrations in two dimensions, The Power spectrum of the fluctuation in the drain currentS_{i}_{d}is calculated by using obtained hole and electron concentrations, current distribution, and mobility distribution, based on the number fluctuation (NF) and mobility fluctuation (MF) models. It is found, from the comparison with experiments for n- and p-channel surface mode MOSFET's, that both NF and MF models can explain noise characteristics for surface-mode MOSFET's. In the case of a depletion-mode MOSFET, the MF model shows thatS_{i}_{d}is proportional to drain current id, which is in agreement with the experimental result for a commercial depletion-mode MOSFET. However, the NF model cannot explain theS_{i}_{d} alpha i_{d}characteristic.     

The effect of distributed series resistance on the dark and illuminated current—Voltage characteristics of solar cells

Distributed series resistance effects in solar cells are analyzed and the correctness of representing these by a lumped parameter is discussed for any conditions of bias and illumination. In addition to a general mathematical methodology, analytical expressions are derived to simplify the estimation of series resistance effects on the dark and illuminatedJ-Vcharacteristics of the cell. The equivalent series resistance (rs) in the dark is found to decrease with current densityJfromr_{b} + r_{e}/3at smallJto (r_{e} r_{b})^{1/2}at very highJ, where reand rbare the emitter layer and base region resistances, respectively. For illuminated conditions rsdepends onJas well, being maximum near short-circuit and minimum near open-circuit; however, rsfurther depends on the photogenerated current JL: its short-circuit value increases with JLfromr_{b} + r_{e}/3tor_{b} + r_{e}/2and the open-circuit value decreases with JLfromr_{b} + r_{e}/3to(r_{e}r_{b})^{1/2}. The variability of rsis therefore related to the relative importance of rbandr_{e};r_{b}plays the role of attenuating this variability, a situation not well recognized previously. Previous theoretical and experimental work is critically reviewed throughout this paper.     

Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate

We have measured the low-frequency ("unclamped") electrooptic and piezoelectric coefficients in undoped BaTiO3and SrxBa1-xNb2O6(x = 0.61) crystals using interferometric techniques. The contribution of the piezoelectric effect to the Pockels measurements is discussed. For an applied ac electric field in the range 0.1-200 V/cm, the electrooptic and piezoelectric effects are linear in the magnitude of the applied field and independent of its frequency in the range 10 Hz-100 kHz. The unclamped electrooptic coefficients of poled BaTiO3single crystals arer_{13} = 19.5 pm 1pm/V andr_{33} = 97 pm 7pm/V, and for strontium barium niobate arer_{13} = 47 pm 5pm/V andr_{33} = 235 pm 21pm/V, all measured at a wavelength of 514.5 nm and atT = 23degC. For the barium titanate samples the measured Pockels coefficientr_{c} equiv r_{33} - (n_{1}/n_{3})^{3} r_{13} = 79 pm 6pm/V is in good agreement with the valuer_{c} = 76 pm 7pm/V computed from the above values of r13and r33, where n1and n3are the ordinary and extraordinary indexes of refraction, respectively. The measured piezoelectric ] coefficient isd_{23} = +28.7 pm 2pm/V for barium titanate, and isd_{23} = +24.6 pm 2pm/V for strontium barium niobate. We also measured the photorefractive coupling of two optical beams in the crystals, and we show that the dependence of the coupling strength on beam polarization is in fair agreement with the measured values of the Pockels coefficients.