Low-frequency noise in permeable base transistors

The predominant noise is1/fnoise and consists of two parts: a) Noise varying asImin{C}max{2}, generated mostly with conducting channel and predominating for normal values of the collector voltage VCE. b) Noise at low VCEand practically independent of VCE; it is generated chiefly in the space charge region around the base grating and gives collector1/fnoise atV_{CE} = 0. The turnover frequency of the first noise source lies at about 20 MHz forV_{CE} = 0.30V,V_{BE} = 0.20V. At sufficiently high frequencies the PBT shows thermal noise of the output conductanceg_{c0}at zero bias. Generation-recombination noise is observed at large VBEand low VCEand comes mostly from the space charge region around the base grating.     

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 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|.     

Measurement of avalanche multiplication of injected holds in germanium p-n-p diffused-base transistors

A three-terminal dc measurement is made of avalanche multiplication of holes injected from the emitter into the collector junction of diffused-base germanium p-n-p transistors. The method is applicable to asymmetric thin-base transistors at currents at which dc base current is independent of base width when emitter to base voltage (VEB) is held constant. Injected collector current and VEBare measured at constant emitter current as a function of collector to base voltage (V). VEBis measured to take base narrowing into account. Collector reverse current is balanced out. The advantages of this method over two-terminal measurements are that surface, space-charge recombination and internal field emission currents are balanced out and no a priori assumption of the form of the multiplication factorM(V)is needed. For collector barriers which are nearly stepn^{+}pjunctions with the p-type resistivity in the neighborhood of 1 ohm-cm, the multiplication data, which cover the range1.05 siml M siml 2.0, fit the Miller equationM^{-1} = 1 - (V/V_{B})^{n} n = 3.2 pm 0.2in agreement with Miller's two-terminal measurements using alloy and grown-junction Ge transistors. The parameters VBfrom extrapolation of the present data agree within experimental error of five per cent with the collector diode breakdowns BVCBOmeasured by Miller. However, in the present measurements on diffused-base transistors, appreciable surface current multiplication occurs with the result that BVCBOmeasured at 1 ma is approximately 18 per cent less than VB. The absence of microplasma noise in the multiplied injected hole current indicates that multiplication occurs uniformly in the collector barrier under the emitter at least toM = 2.     

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.     

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.     

Charge analysis of transistor operation including delay effects

The charge control concept of transistor operation is extended to include delay effects in an accurate, yet tractable, way. Defining the transit time τtas the ratio of the excess base charge to the collector current, the transform of the transit time τt(s) is approximated bytau_{t}(1 + Stau_{D}), where τDis the delay time. For a one-dimensional, homogeneous-base transistor,tau_{D} = tau_{t}/6. The results of this technique are in good agreement with exact calculations.     

Source code error bound in the excess rate region

The problem of encoding a discrete memoryless source with respect to a single-letter fidelity criterion, using a block code of lengthnand rateR, is considered. The probability of error,p_{n}(R,D), is defined to be the minimum probability, over all such codes, that the source will generate a sequence which cannot be encoded with distortionDor less. For sufficiently largeR, thatp_{n}(R,D)decreases doubly exponentially with blocklength,nis shown. It is known thatp_{n}(R,D) = 0for some finiten, denoted byn_{0}(R,D). An upper bound ton_{0}(R,D)is also presented and numerically evaluated. The results derived hold independently of the source statistics. It is shown that a theorem of Omura and Shohara for symmetric sources is a special case of the results herein. Additionally, a useful characterization ofR ast (D)for row-balanced distortion matrices is obtained.     

Effect of interfacial oxide thickness on 1/f noise in polysilicon emitter BJTs

The role of the interfacial oxide (IFO) between the polysilicon and monosilicon emitter regions on the noise behavior of n-p-n poly-emitter bipolar transistors was investigated through 1/f noise measurements. Bipolar junction transistors with different IFO thickness, and emitter geometry were utilized. Measurements with variable external base bias resistance (R/sub S/) were used to investigate the relative contribution of each individual noise source from the base current (S/sub IB/), the collector current (S/sub IC/) and, the internal emitter and base series resistances (S/sub Vr/). When the voltage noise power spectral densities S/sub VC/ and S/sub VB/ were measured across resistances in series with the collector and base, respectively, using a relatively large R/sub S/ (/spl sim/1 M/spl Omega/), S/sub IB/ was found to have the dominant noise contribution at lower bias currents. On the other hand, when the voltage noise power spectral densities S/sub VC/ and S/sub VE/ were measured across resistances in series with the collector and emitter, respectively, in a different experimental setup with a low R/sub S/ value, S/sub Vr/ was found to have the dominant noise contribution at higher bias currents. IFO was found to increase S/sub IB/, S/sub IC/, and S/sub Vr/. S/sub IB/ was modeled as a combination of tunneling and diffusion fluctuations of the minority carriers in the emitter; whereas S/sub IC/ was modeled as a combination of number and diffusion fluctuations of the minority carriers in the base. S/sub Vr/ was attributed to the internal emitter resistance noise originating from the fluctuation in the majority carrier flow through the IFO.     

InGaAs/InP double-heterostructure bipolar transistors with near-ideal β versus ICcharacteristic

InGaAs/InP double-heterostructure bipolar transistors (DHBT's) with current gain β ∼ 630 have been realized using gas-source molecular beam epitaxy (GSMBE). These devices exhibit near-ideal β versus ICcharacteristic (i.e., β independent of IC) with a small-signal gainh_{fe} sim 180atI_{C} sim 2nA. In comparison, we findbeta sim I_{C}^{0.5}for a high-quality AlGaAs/GaAs HBT grown by OMCVD. The higher emitter injection efficiency at low collector current levels found in the InGaAs/InP DHBT is due to at least a factor 100 smaller surface recombination current.     

Performance of anM-ary orthogonal communication system using stationary stochastic signals

This paper considers the performance of a communication system which transmits forTseconds the real part of a sample function of one ofMstationary complex Gaussian processes whose spectral densities are all frequency translations of the functionS_{xi (f). At the receiver white Gaussian noise of one-sided densityN_{0}is added. The center frequencies of the processes are assumed to be sufficiently separated that theMcovariance functions are orthogonal overT. Exponently tight bounds are obtained for the error probability of the maximum likelihood receiver. It is shown that the error probability approaches zero exponentially withTfor all ratesR = (ln M)/Tup toC= int_{-infty}^{infty} [S_{xi (f)/N_{0}] df - int_{- infty}^{infty} ln [1 + S_{xi}(f)/N_{0}] dfwhich is shown to be the channel capacity. Similar results are obtained for the case of stochastic signals with specular components.     

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.     

Equipartition laws of thermal noise

Classically, the thermal noise in electricalRCcircuits andLCRseries circuits is governed by the equipartition lawfrac{1}{2}overline{CV^{2}} = frac{1}{2}kT, whereV(t)is the noise voltage developed acrossC. When quantum effects are taken into account, the equipartition law no longer holds forRCcircuits, although an equipartition law can be deemed for the measured mean square noise voltage under certain conditions. InLCRseries circuits the equipartition lawfrac{1}{2}overline{CV^{2}} = frac{1}{2}kT, changes intofrac{1}{2}overline{CV^{2}} = frac{1}{2}bar{E}(f_{0})for high-Qtuned circuits, wherebar{E}(f_{0})is the average energy of a harmonic oscillator tuned at the tuning frequency of the tuned circuit.     

1/f noise in n-channel silicon-gate MOS transistors

It is found that equivalent gate noise power for l/f noise in n-channel silicon-gate MOS transistors at near zero drain voltage at room temperature is empirically described by two noise terms, which vary asK_{1}(q/C_{ox}) (V_{G} -V_{T})/f and K_{2}(q/C_{ox})^{2}/f, where V_{G}is gate voltage, VTis threshold Voltage, and Coxis gate-oxide capacitance per unit area. Unification of carrier-density fluctuation (McWhorter's model)and mobility fluctuation (Hooge's model) can account for the experimental data. The comparison between the theory and experiment shows that the carrier fluctuation term K2is proportional to oxide-trap density at Fermi-level. The mobility fluctuation term K1is correlated to K2, being proportional toradic K_{2}. The origin of this correlation is yet to be clarified.     

Recursive probability density estimation for weakly dependent stationary processes

Recursive estimation of the univariate probability density functionf(x)for stationary processes{X_{j}}is considered. Quadratic-mean convergence and asymptotic normality for density estimatorsf_{n}(x)are established for strong mixing and for asymptotically uncorrelated processes{X_{j}}. Recent results for nonrecursive density estimators are extended to the recursive case.     

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.     

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.     

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.     

Some equivalences between Shannon entropy and Kolmogorov complexity

It is known that the expected codeword lengthL_{UD}of the best uniquely decodable (UD) code satisfiesH(X)leqL_{UD}. LetXbe a random variable which can take on n values. Then it is shown that the average codeword lengthL_{1:1}for the best one-to-one (not necessarily uniquely decodable) code forXis shorter than the average codeword lengthL_{UD}for the best uniquely decodable code by no more than(log_{2} log_{2} n)+ 3. LetYbe a random variable taking on a finite or countable number of values and having entropyH. Then it is proved thatL_{1:1}geq H-log_{2}(H + 1)-log_{2}log_{2}(H + 1 )-cdots -6. Some relations are established among the Kolmogorov, Chaitin, and extension complexities. Finally it is shown that, for all computable probability distributions, the universal prefix codes associated with the conditional Chaitin complexity have expected codeword length within a constant of the Shannon entropy.