Negative resistance in p-n junctions under avalanche breakdown conditions, part II

The small-signal impedance of the space-charge region of p-n junctions under avalanche breakdown conditions is calculated using reasonably realistic dependences of electron and hole ionization rates and drift velocities upon electric field. Two structures are analyzed: one is p⁺νn⁺structure which has a fairly uniform distribution of avalanche multiplication, and the other is a singly diffused junction which is a hybrid of an abrupt and a linear graded junction. Both structures show negative resistance when the transit time of carriers becomes appreciable. A computer program was evolved which requires, as input, the impurity profile and field dependences of ionization rates and drift velocities. The program first calculates the dc field and electron and hole currents and then solves the ac small-signal problem. Both the ac small-signal impedance and theQof the diode are calculated.     

Natural mode of oscillation in a p-n avalanche diode

Misawa's small-signal equations for an avalanche diode are used to derive a natural mode of oscillation in a symmetrically graded p-n junction. Computer simulations were used to verify the theory.     

State-Space Analysis of General IMPATT Diode Small-Signal Lumped Models

The development of a lumped model for small-signal carrier-field interactions in an IMPATT diode results in a set of state equations. Using state-space analysis techniques, the equations are solved for the small-signal impedance of a general IMPATT diode as a function of dc bias current and frequency. Read, p-n, and p-i-n diodes are studied using realistic values for saturation carrier velocities and carrier-ionization rates. Curves indicating the influence of diode physical properties on the small-signal impedance are presented. By combining state equations describing the behavior of the external microwave circuit with the diode state equations, the small-signal oscillation frequency and threshold dc bias current of a coaxial IMPATT oscillator are determined.     

Dependency of the highest harmonic oscillation frequency on junction diameter of IMPATT diodes

The effect of series resistance and junction capacitance on the high-frequency limit of IMPATT diode operation is studied with a Read-type small-signal theory, and is confirmed experimentally. Oscillation frequencies from 30 to 400 GHz have been measured with Si p⁺-n-n⁺abrupt junction diodes with a depletion layer width of 0.2 µm. The highest oscillation frequency increases as the junction diameter is decreased, owing to reduced junction capacitance and increased bias-current density. The highest oscillation frequency observed is 423 GHz, which is obtained in the fifth harmonic mode with a diode of 16-µm junction diameter. Fundamental oscillation frequency is found to depend strongly on dc bias-current density, and to be close to the avalanche frequency of the small-signal theory.     

Small-signal analysis of the Read avalanche diode

A small-signal analysis is made on the Read-type avalanche transit time diode in which both holes and electrons and differing ionization rates for holes and electrons are considered in a silicon diode. The avalanche region is assumed to be an unsymmetric abrupt junction in which the ionization coefficients vary with the distance through their exponential dependence on the field in the avalanche region. Solutions for the ionization integral are given in the dc case. The time-varying terms are introduced as small-signal perturbations on the dc case and solutions for the ionization integral are again obtained and expressed as a Fourier series. The coefficients of the series appear in the expressions for the admittance. This approach provides simple analytical solutions for the Read diode admittance. Also, direct evaluation of the Fourier coefficients is given in terms of the diode's breakdown voltage and other known parameters. An equivalent circuit for the Read diode is developed. Over a substantial frequency but for small transit angles of the drift region, it consists of a frequency independent negative conductance, inductance, and capacitance. The diode's spreading resistance is in series with these parallel elements. The circuit agrees with the measurements of Josenhans and Misawa. On the basis of the small-signal avalanche analysis the ultimate oscillator efficiency is estimated to be about 26 percent.     

A mathematical technique for an exact small-signal field analysis of multiple-stream interaction in a finite longitudinal magnetic field

A mathematical technique for solving Maxwell's equations and the Lorentz force equation with no approximations except the small-signal approximation is presented. A finite dc magnetic field parallel to the dc velocity of the charges is included. Polarization variables are used, and the boundary conditions include ac surface charge density and surface current density. The advantages of the method are that both fast waves and slow waves are included without a quasi-static approximation, and only the determinantal equation requires computer solution. The partial differential equations are solved directly and need not be solved by computer.     

The effect of small-signal AC voltages on C–V characterization and parameter extraction of SiO2 thin films

The effect of different small-signal ac voltage amplitudes on C–V curves characterized by thin SiO₂ based p-type MOS capacitor with aluminum gate is reported. When the small-signal ac voltage is comparable to the gate bias, the thickness of SiO₂ thin films extracted from the accumulation capacitance is found to be independent of small-signal ac voltage amplitudes, but the flat band voltage shift and interface state density associated with the variation of depletion layer capacitance are dependent on small-signal ac voltage amplitudes. They all increase with the small-signal ac voltage amplitudes. The experimental results reveal that the optimum small-signal ac voltage should be less than 100 mV. The mechanisms involving the depletion layer changes with small-signal ac voltages in SiO₂ thin films are also discussed in this paper.     

Numerical and theoretical analysis of the crosstalk in linear optical amplifiers

The dynamic characteristics, including the crosstalk and relaxation oscillation, of linear optical amplifiers (LOAs) are investigated by small-signal analysis under an averaging carrier density approximation and compared with the results of numerical simulation. The good agreement between the numerical simulation and the small-signal analysis indicated the averaging carrier density is an appropriate approximation for analyzing LOAs. Theoretical analyzes also show that the dynamic properties of the vertical laser fields dominate the dynamic performance of LOAs. Based on the small-signal analysis, a concise equation for the crosstalk under high bit rate was derived, which can be applied to measure the differential gain of LOAs.     

An efficient numerical method for the small-signal AC analysis of MOS capacitors

A numerical method for the small-signal ac analysis of MOS capacitors is presented. The equations describing device operation, which comprise a boundary value problem, are formulated as an initial value problem and are solved by a shooting method. This results in a numerically stable and efficient algorithm for their solution. The recognized ill-conditioning of the boundary value problem, manifesting itself in numerical instabilities in the conductance-voltage characteristics of MOS capacitors is addressed. Calculated small-signal ac admittance as a function of gate bias for homogeneously doped and ion-implanted devices is shown. The high- "and low-frequency" positional dependence of convection and displacement current densities is determined.     

A quasi-one-dimensional analysis of small-signal current gains in lateral transistors

A small-signal analysis of lateral p-n-p transistors has been made using a quasi-one-dimensional model. This model consists of a lateral p-n-p intrinsic transistor section and a vertical p-n-n⁺-p parasitic transistor section. The effect of the retarding electric field of the n⁺subdiffused layer is incorporated explicitly into the model. Besides, the field-dependent nonunity emitter efficiency of lateral transistors has also been taken into account. From the solutions of continuity equations in the base regions, closed-form expressions for small-signal current gains are obtained in terms of an ac field factor which is defined by the geometry and doping profile of the device. Frequency dependence of current gains evaluated from this analysis compares favorably with the results from an earlier two-dimensional analysis. The simplicity of the model and its reasonably good accuracy are expected to be helpful in the modeling of lateral transistors used in linear integrated circuits.     

Low Frequency Characterization of PWM Converters

Low frequency components of states or outputs in pulse-width modulation (PWM) dc and ac converters can be characterized by differential equations called describing state-space equations. These equations are derived by inspection of converter topology and use of switching functions and duty ratios. Their steady-state and small-signal dynamic solutions show how energy-storage elements in a converter/load system shape the frequency response of conversion functions established by the switches.     

TOM3 capacitance model: linking large- and small-signal MESFETmodels in SPICE

Improved accuracy in the modeled gate capacitance of GaAs metal-semiconductor field-effect transistors (MESFET's) is obtained in SPICE using conservation of charge in an implanted layer. The gate junction creates a natural partition between mobile and fixed channel charges. Relating the gate charge to the channel current creates gate capacitances dependent upon the channel current derivatives linking the small-signal model to the large-signal equations. Results are illustrated using a depletion-mode MESFET     

Generalized small-signal analysis of avalanche transit-time diodes

The one-dimensional small-signal analysis of avalanche transit-time diodes with distributed multiplication is reduced to the concept of two layers in cascade, each having a constant ionization rate. The interface is located in the distinguished neutral plane of equal direct electron and hole currents. In this configuration the small-signal problem is characterized by two parameters : namely the location of the neutral plane in the depletion layer and a quantity combining the ionization-rate field dependence and the total direct current density. Normalized admittance diagrams and small-signal growth rates are given which show the relative importance of the low-transit-angle mode where the frequency is smaller than the avalanche resonance frequency and the π mode extending almost to 2π for large current densities. Through a transformation the results are applicable to Read type, abrupt and uniform junctions of Si, Ge, and GaAs avalanche diodes.     

Direct Modulation Characteristics of Composite Resonator Vertical-Cavity Lasers

We report the small-signal modulation characteristics of a monolithic dual resonator vertical cavity surface emitting laser. The modulation response is described by a system of rate equations with two independent carrier populations and a single longitudinal optical mode. The independent optical overlaps and differential gains of the two active regions can each be adjusted to maximize the output response. We show that under certain conditions, the composite resonator may achieve a higher bandwidth than a single cavity laser with the same photon density. We find the relaxation oscillation frequency to depend mainly on the total photon density and not the individual currents in the two cavities. With appropriate current injection, the composite resonator laser achieves a maximum -3-dB bandwidth of 12.5 GHz and a maximum modulation current efficiency factor of approximately 5GHz/ma^1/2      

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.     

Analysis of device parameters for pnp-type AlGaAs/GaAs HBTsincluding high-injection using new direct parameter extraction

Device parameters of the small-signal T equivalent circuit for pnp-type AlGaAs/GaAs heterojunction bipolar transistors (HBTs) are obtained using a new direct parameter extraction technique. These parameters are analyzed not only under the low-current conditions but also under high-current conditions so as to understand the RF-performance fall-off after base pushout occurs. In this analysis, the intrinsic and extrinsic small-signal parameters which affect RF performance are directly determined using several steps without numerical optimization in order to properly analyze device parameters. The T equivalent circuit model determined by the method shows excellent agreement with the mean errors of 3.5-6.9% under both low-and high-current conditions. The analysis showed that the intrinsic transit time, which is the sum of the base transit time (τ_b) and the collector depletion layer transit time (τ_c), small-signal emitter resistance (r_e), small-signal base resistance (r_b) and collector-base capacitance (C_BC) all increase under high-current conditions. In addition, we found that the intrinsic transit time is the dominant parameter for the fall-off of the cut-off frequency (f_t) under high-current conditions, and there is little effect of r_b and C_BC in the fall-off of the maximum oscillation frequency (f_max) under high-current conditions. Judging from these results, device parameters are successfully obtained under a wide current range by a new parameter extraction technique and circuit modeling for HBTs under a wide current range can be achieved using the small-signal T-equivalent circuit     

A simplified field analysis of a distributed IMPATT diode usingmultiple uniform layer approximation

A small-signal field analysis of a distributed IMPATT diode is presented. The active region of the diode is assumed to consist of a uniform avalanche layer and avalanche-free drift layers. The propagation constant and field distributions are obtained without numerical solution of differential equations. The effects of losses caused by the presence of inactive layers are included in the analysis. Numerical examples of GaAs double-Read distributed IMPATT diodes are given which show the dependence of the amplification characteristics on the thicknesses of the avalanche and drift layers     

Perturbation solution of self-pulsing in semiconductor lasers witha saturable absorber

We solve the three-component rate equations for semiconductor lasers with a saturable absorber or for multi-section semiconductor lasers by using a singular perturbation method. The effects of nonlinear gain and spontaneous emission are included in the rate equations. By transforming the rate equations to the generalized coordinates, we eliminate the most rapidly varying term adiabatically for the fast saturable absorber. Then, we solve the two-component nonlinear equations to obtain analytic expressions for parametric dependence of self-pulsing amplitude and self-pulsing frequency. the self-pulsing frequency shifts from the small-signal oscillation frequency to the lower-frequency side as we increase the self-pulsing amplitude. The square of the self-pulsing frequency does not linearly depend on the injection current, in agreement with experimental observations. We also derive an optimum saturable absorber recovery time for the shortest optical pulse generation     

Conservation principles for plasmas and relativistic electron beams

Many useful conservation theorems are derived for relativistic electron beams and anisotropic plasmas. All these theorems are valid for confined-flow and irrotational-flow devices, and cold, collisionless plasmas. All the theorems are derived in a similar way, and a generalization of this method, using linear operators, is given. Among the power theorems discussed are: Tonks' theorem, the instantaneous and sinusoidal small-signal theorems, the energy theorem, a large-disturbance theorem, the Manley-Rowe formulas, an ac power theorem, and a cross-correlation theorem. Contributions to power and energy from surface waves are included. Allowing for relativistic flow and writing all equations in the laboratory frame does not significantly complicate the theorems, and in fact clarifies them somewhat. Many simple applications are discussed, although not in detail. Among these are: small-signal energy, power, and passivity; energy velocity in electron beam and plasma wave-guides; and a conservation theorem for multiple electron beams and electron beam-plasma interactions.     

A critical analysis of Z-source converters considering the effects of internal resistances

Nowadays Z-source networks are the most promising power converter networks that cover almost all electric power conversion (dc–dc, dc–ac, ac–dc and ac–ac) applications. However, the controller design is critical for Z-source converter (ZSC) due to the presence right-half-plane zero (RHPZ) in the control-to-capacitor-voltage transfer function. This RHPZ exhibits non-minimum phase undershoot in the capacitor voltage and also in the dc-link voltage waveforms. A perfect small-signal model is required to predict locations of the RHP zero and its dynamics. This paper contributes towards the small-signal analysis of ZSC under continuous conduction mode considering the parasitic resistance of the inductor, equivalent series resistance of the capacitor, internal resistances of active switch and forward voltage drop of the diode. The maximum allowable value of shoot-through duty ratio (STDR) and voltage gain for different values of the internal resistance and load resistance are discussed in this paper. The accuracy of the developed small-signal average model is compared with detailed circuit model in MATLAB/SIMULINK. Finally, the steady-state simulation results of ZSC are validated with hardware results.