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.     

Calculation of p-type GaAs IMPATT admittance

The unequal ionization rates reported for holes and electrons in GaAs have been used to calculate the small-signal admittance for a complimentary p-type IMPATT diode. For the uniformly doped n and p device structures considered, the p-type structure is found to have significantly increased negative conductance.     

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.     

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.     

Circuit representation of avalanche region of IMPATT diodes for different carrier velocities and ionisation rates of electrons and holes

A parallel resonant circuit representing the small-signal behaviour of the avalanche region of IMPATT diodes is given. The components are calculated in a nonquasistatic manner for different ionisation rates and drift velocities of electrons and holes. With the results, the avalanche frequencies of Si, Ge and GaAs as functions of the avalanche zone width are compared.     

Avalanche induced dispersion in IMPATT diodes

Numerical analysis has been performed on the effect of the carrier dispersion caused by avalanching on the small signal admittance and the transient step response in the avalanche region of an idealized IMPATT diode having a uniform electric field profile. The degree of dispersion, referred to hereafter as Avalanche Induced Dispersion (AID), depends on the relative magnitudes of ionization rates of the two carriers. AID becomes largest when the two ionization rates are equal and decreases with increasing discrepancy between them.It is found that the build-up of an avalanche can be faster if either electrons or holes are strongly ionizing than when both of them ionize equally. Also, the small signal negative conductance is minimum when the dispersion is most pronounced. Since the time delay in the avalanche build-up depends strongly on AID, the upper limit of the high-frequency performance of IMPATT diodes can be estimated from the theoretical value of AID.     

A proposed punch-through microwave negative-resistance diode

A new microwave negative-resistance diode is proposed. The diode is similar to the Read diode insofar as the negative resistance is partially due to the finite transit time of carriers flowing through a depletion region. Unlike the Read diode, however, the carriers are injected into the depletion region by punch through rather than by avalanche. The resulting device is therefore expected to have a considerably better noise performance than the Read diode. The paper first explains qualitatively the punch-through operation of the proposed device and contrasts it with similar structures proposed earlier by Read and by Shockley. The large signal admittance of the punch-through diode is then obtained by using a sharp pulse approximation of the injection process. A device Q of -15 is calculated. Considering the device as a microwave oscillator, it is found that conversion efficiencies of the order of 20 percent should be possible. Estimates of the upper bounds on the microwave power are given. The paper concludes with a detailed account of design considerations for the device. Numerical designing examples for the frequency range of 1 to 5O GHz are given.     

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.     

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.     

Electronic tuning effects in the read microwave avalanche diode

Read's theory of the negative-resistance avalanche diode has been examined in detail for the small-signal case. The space-charge wave approach has been used in the analysis leading directly to a simple equivalent circuit and a general expression for the small-signal impedance which includes the significant design and operating parameters. The theory indicates that strong tuning effects will occur through variation of the dc avalanche current. This has been verified experimentally.     

Temperature dependence of carrier ionization rates and saturated velocities in silicon

The temperature dependencies of the carrier ionization rates and saturated drift velocities in silicon have been extracted from microwave admittance and breakdown voltage data of avalanche diodes. The avalanche voltage and broadband (2–8 GHz) microwave small-signal admittance were measured for junction temperatures in the range 280 to 590 K. An accurate model of the diode was used to calculate the admittance characteristic and voltage for each junction temperature. Subsequently, the values of ionization coefficients and saturated velocities were determined at each temperature by a numerical minimization routine to obtain the best fit between the calculated values and measured data. The resulting ionization rates are well fitted by the temperature dependent model developed by Crowell and Sze from the Baraff ionization-rate theory. The carrier scattering mean free path lengths, average energy loss per collision, and relative ionization cross section are obtained from the best fit agreement between the scattering model and experimental data. The parameter values determined here relevent for use with the above theory are the following:Parameter Holes Electrons ε_r(eV) 0.063 0.063 ε_i(eV) 1.6 1.6 λ_oo(Å) 81.2 77.4 σ 0.391 0.593 The values and temperature dependence of the saturated carrier velocities determined are in good agreement with other published results. At 300 K the low field (E?10⁴ V/cm) saturated velocity for electrons and holes is 10.4 and 7.4×10₆ cm/sec, respectively. The results obtained in this study are of general use for the modeling of effects related to avalanche breakdown and high-field carrier transport in silicon.     

Parametric effects in a microwave Read avalanche diode

The parametric effects in the microwave Read avalanche diode are studied using a simplified one-dimensional model. The signals of frequencies ω1and ω2interact with each via the pumping wave of frequencyomega_{0} = omega_{1} + omega_{2}, through the nonlinearity in avalanche. This paper shows the range in which the microwave Read avalanche diode has the parametric negative resistance, some typical values of the impedance matrix elements of the microwave Read avalanche diode, and shows that the small-signal impedance locus of the microwave Read avalanche diode on Smith chart coincides approximately with Kita's experimental results.     

Computer-Aided Small-Signal Characterization of IMPATT Diodes

This paper is a discussion of IMPATT wafer small-signal characteristics in the frequency range of 2.0-8.0 GHz. These characteristics have been obtained by computer conversion of reflection phase-gain data. The data handling technique which allows establishment of the desired reference plane and the reduction of the admittance data into the desired equivalent circuit is presented. A calibration procedure using reference impedances consistent with the diode geometry is discussed. The validity of the microwave measurement technique and the data handling process is demonstrated by comparison of the values of junction capacitance determined at microwave frequencies with junction capacitance measurements at 30 MHz. Representative plots are given for wafer conductance and susceptance as a function of frequency with current density as a parameter. In addition, typical values obtained for the circuit elements are presented. These data illustrate the capability of determining package inductance, series resistance as a function of bias voltage, and, with the diode in avalanche, the parallel G, L, and C of the wafer admittance. The diode equivalent circuit was studied as a function of current density to compare results with the existing analytical small-signal theories. This procedure permits the separation of the wafer elements from the parasitic elements of the package. Data obtained from these measurements are extremely useful for ascertaining wafer design parameters and assisting in circuit design.     

The effect of injecting contacts on avalanche diode performance

Metal-semiconductor contact injection on the junction side of diffused-mesa avalanche diodes has been found to have a significant effect on the performance of these diodes as oscillators. A minority carrier injection ratio of 6 percent reduces the efficiency of what would be 9 percent efficient diodes to less than 1 percent and increases the FM noise by a factor of 2 as tested in a 6-GHz oscillator circuit. The dependence of the minority carrier injection ratio of the metal-semiconductor barrier upon current density has been measured and quantitatively modeled. Calculated values of diode admittance, including the effects of injection at the contact, are shown to be in agreement with measured values of both small-signal diode admittance versus frequency and large-signal diode admittance versus RF voltage. Germanium avalanche diodes with low-minority carrier injection contacts have demonstrated CW oscillation efficiencies greater than 9 percent at 6 GHz. The realization of low-injection contacts is shown to be a requirement for achievement of high-efficiency avalanche oscillation.     

Large-Signal Silicon and Germanium Avalanche-Diode Characteristics

A technique for measurement of the large-signal single-frequency microwave amplifier admittance of avalanche diodes is described, and results are presented for silicon and germanium avalanche diodes. Single-frequency amplifier operation can provide a unique characterization of diode-admittance variation with RF drive for diodes operated near the optimum transit angle (the case in which all harmonic voltages are negligibly small compared to the fundamental). Such characterization is useful for predicting diode performance for circuits in which the harmonic voltages are not large enough to have an appreciable effect on the diode admittance at the fundamental frequency. A process of matching quadratic forms to the above admittance data which may be used for calculation of diode terminal admittance and power output is discussed. The usefulness of the measurement technique is illustrated by the agreement of the calculated maximum power output with the measured power output in a single-transformer coaxial circuit. The corresponding circuit admittance may be used for circuit-design purposes and for evaluating variations in diode-assembly techniques. The ability to obtain the diode equivalent circuit as a function of incident power allows studies in the design of the associated semiconductor device. For example, one has the capability of obtaining an accurate single-frequency large-signal model near the optimum transit angle, a model which can be studied without building a circuit. With this model it is possible to carry out optimization procedures at considerable savings of time and money.     

Effect of Temperature on Device Admittance of GaAs and Si IMPATT Diodes

The effect of temperature on the small-signal admittance of IMPATT diodes with uniformly doped and high-low doped (Read) structures is investigated experimentafly and theoretically. Small-signal admittance characteristics of X-band Si p+-n-n+, GaAs M-n-n+ (Schottky-uniform), and GaAs M-n+-n-n+ (Schottky-Read) IMPATT diodes are measured at various junction temperatures for different dc current levels. Small-signal analysis is performed on GaAs IMPATT diodes of uniformly doped and high-low doped structures, and the calculated results on temperature dependence of the device admittance are compared with the experimental results. Reasonable agreement is found between theory and experiment. It is shown that GaAs IMPATT diodes are superior to Si diodes in admittance temperature characteristics and that the uniformly doped structure has a small admittance temperature coefficient in magnitude, compared to the high-low doped structure. It is also shown by calculation that the admittance temperature coefficient of a punch-through diode is small in magnitude, compared to that of a non-punch-through diode.     

Large-signal performance of microwave transit-time devices in mixed tunneling and avalanche breakdown

A large-signal model for Read-type diode structures with narrow generation-region widths where mixed tunneling and avalanche exist is given. The generation region is modeled by use of a modified Read equation along with effective ionization rates. The injected current pulse, which is formed in the generation region, is calculated in isolation from the drift region in order that the effects of tunneling current can be clearly shown. The drift region is modeled by use of difference-equation versions of the device equations and is suitably interfaced to the generation region. The large-signal model of the total device is used to calculate the device admittance and efficiency. Large-signal results for GaAs and Si devices are given and the results are discussed and compared.     

Characterization of avalanche diode TRAPATT oscillators

The characteristics of a coaxial avalanche diode oscillator circuit are calculated and compared with experimental results. The circuit admittance, as seen at the diode terminals, is calculated in the frequency domain for "optimally tuned" experimental conditions. The impulse response function of the circuit, as obtained from the transformed admittance, is used to obtain time-evolution solutions of the avalanche diode circuit system. The impulse response is more general than the previously employed differential equation characterization of a lumped element equivalent circuit. The simulation presented of the high-efficiency mode of oscillation allowed no adjustable parameters and is in excellent agreement with experiment. The simulation verifies the original TRAPATT [1] explanation for the high-efficiency mode of oscillation.     

Large-Signal Equivalent Circuits of Avalanche Transit-Time Devices

A large-signal analysis for IMPATT diodes is derived, which allows carrier multiplication by impact ionization to occur at every point in the diode. Therefore, the operating characteristics of IMPATT diodes with a wide range of realistic doping profiles can be investigated. For a given operating frequency, RF voltage, dc bias current, and doping profile, the admittance, power output, efficiency, bias voltage of a diode can be obtained. An equivalent circuit the diode package, microwave circuit mount and diode, is obtained experimentally. Using this circuit, the admittance of the diode is measured by a reflection-type circuit and an oscillator circuit as a function of the RF voltage, dc bias current, and frequency.     

Growth and photoreflectance characterization of GaAs impact ionization avalanche transit time diodes

The organometallic vapor phase epitaxial growth of GaAs double-drift Read impact ionization avalanche transit time diodes where the p-type layers were doped with carbon is described. Ka-band oscillation testing yielded average performance of 3.5 W with 16% efficiency for pulse lengths >1 μs and 10.5 W with 13% efficiency for pulse lengths <1 μs; these RF performances are similar to conventionally grown vapor phase epitaxy IMPATTs where the p-type dopant was zinc. Photoreflectance spectra obtained from diode structures were found to be dominated by the electric field in the avalanche region and hence are sensitive to the amount of charge in the doping spikes that determine the electric field in that region.