Small-signal impedance of avalanching junctions with unequal electron and hole ionization rates and drift velocities

A small-signal analysis of an avalanching semiconductor junction is presented for unequal electron and hole ionization rates and saturated drift velocities. The model consists of a thin ionization layer in a thicker depletion layer. The ionization rates are assumed independent of distance in the ionization layer and zero elsewhere. This analysis is an improvement of Read's, and is sufficiently realistic to predict most of the small-signal characteristics shown by the computer analysis of Misawa. The linearized differential equations describing the ionization layer are solved with the ionization rates perturbed by the ac electric field. The ac junction impedance is calculated from the solutions of the differential equations. Although the small-signal analysis does not predict the conversion efficiency of an avalanche diode oscillator, it does predict the threshold conditions for oscillation. It may also help predict the conditions for maximum efficiency through knowledge of the input power and the Q of the diode at the onset of oscillation.     

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.     

Field and carrier current density profiles in linearly graded silicon avalanche diodes

A detailed study for the d.c. field and carrier current density profiles of linearly graded double drift avalanche diodes is presented taking into account the effect of impurity and mobile charge density and the realistic field dependance of the ionization rates and drift velocities for the charge carriers. The study involves finding the location and magnitude of the electric field maximum by an iterative method. A small shift in the position of the electric field maximum towards the p-side of the metallurgical junction is observed which increases with increasing current density and decreasing doping gradient. The maximum field and the depletion layer width change sharply with doping gradient but very slightly with d.c. current density. Over a larger fraction of the depletion layer, hole current density exceeds electron current density and hole dominance increases with decreasing doping gradient. The avalanche centre where J_p = J_n is found to be always on the n-side of the junction.     

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.     

Properties of the transient of avalanche transistor switching atextreme current densities

Avalanche transistor switching at extreme currents is studied under conditions in which the charge of the excess carriers drastically rebuilds the collector field domain, causing fast switching and a low residual voltage across the switched-on device. The dynamic numerical model includes carrier diffusion and considers different dependencies of the velocities and ionization rates for the electrons and holes in the electric field. These dependences determine the principal difference in the switching process between n⁺-p-n₀-n⁺ and p⁺-n-p₀ -p⁺ structures. Reasonably good agreement is found between the simulated and measured temporal dependences of the collector current and voltage drop across the device for a particular type of avalanche transistor. Certain differences in the switching delay can partly be attributed to limitations in the one-dimensional (1-D) approach. It is now certain that collector domain reconstruction defines the transient in a n⁺-p-n₀-n⁺ transistor at high currents, but is not very pronounced in a p⁺ -n-p₀-p⁺ transistor. Some nontrivial features of the device operation are found, depending on the semiconductor structure. In particular, it is shown that the thickness of the low-doped collector region affects mainly the switching delay, and does not significantly effect the current rise time     

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.     

Hg0.56 Cd0.44 Te 1.6- to 2.5-μm avalanchephotodiode and noise study far from resonant impact ionization

An investigation was made on the avalanche multiplication and impact ionization processes in p-n^--n⁺ junctions formed in Hg_0.56Cd_0.44Te solid solutions. Photocurrent multiplication was determined at 300 K in planar p-n^- -n⁺ structures characterized by a breakdown voltage of 30 V. The experimental results were used to calculate the electron, α, and hole, β, ionization coefficients. It was found that α is greater than β because Δ, the spin-orbit splitting energy, is higher than the bandgap energy. These experimental results were in satisfactory agreement with multiplication noise measurements using separate electron and hole injection     

Avalanche Multiplication in InAlAs

A systematic study of avalanche multiplication on a series of In _0.52Al_0.48As p⁺-i-n⁺ and n ⁺-i-p⁺ diodes with nominal intrinsic region thicknesses ranging from 0.1 to 2.5 mum has been used to deduce effective ionization coefficients between 220 and 980 kVmiddotcm^-1. The electron and hole ionization coefficient ratio varies from 32.6 to 1.2 with increasing field. Tunneling begins to dominate the bulk current prior to avalanche breakdown in the 0.1-mum-thick structure, imposing an upper limit to the operating field. While the local model can accurately predict the breakdown in the diodes, multiplication is overestimated at low fields. The effects of ionization dead space, which becomes more significant as the intrinsic region thickness reduces, can be corrected for by using a simple correction technique     

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.     

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.     

The p-n junction quantum well APD: A new solid-state photodetector for lightwave communications systems and on-chip detector applications

A novel variation on the doped quantum well avalanche photodiode is presented that provides comparable signal-to-noise performance at more realizable material doping requirements. The device consists of repeated unit cells formed from a p-n Al0.48In0.52As junction immediately followed by near-intrinsic Ga0.47In0.53As and Al0.48In0.52As layers. As in the doped quantum well device, the asymmetric unit cell selectively heats the electron distribution much more than the hole distribution prior to injection into the narrow-gap Ga0.47In0.53As layer in which impact ionization readily occurs. The effects of various device parameters, such as the junction doping, Ga0.47In0.53As and intrinsic Al0.48In0.52As layer widths as well as the overall bias on the electron and hole ionization rates, is analyzed using an ensemble Monte Carlo method. From the determination of the ionization rates and the ionization probabilities per stage, P and Q, an optimal device design can be obtained that provides high gain at low multiplication noise. In addition, a structure that operates at less than 5 V bias is presented that can provide moderate gain at very low noise. It is expected that the device designs presented herein can serve either as high-gain low-noise detectors for lightwave communications systems or as moderate-gain low-noise detectors for on-chip application.     

Low avalanche noise characteristics in thin InP p+-i-n+ diodes with electron initiated multiplication

We have performed electron initiated avalanche noise measurements on a range of homojunction InP p⁺-i-n⁺ diodes with “i” region widths, w ranging from 2.40 to 0.24 μm. In contrast to McIntyre's noise model a significant reduction in the excess noise factor is observed with decreasing w at a constant multiplication in spite of α, the electron ionization coefficient being less than β, the hole ionization coefficient. In the w=0.24 μm structure an effective β/α ratio of approximately 0.4 is deduced from the excess noise factor even when electrons initiate multiplication, suggesting that hole initiated multiplication is not always necessary for the lowest avalanche noise in InP-based avalanche photodiodes     

Triggering phenomena in avalanche diodes

The operation of a small area p-n junction diode above the breakdown voltage is analyzed. A new formulation in terms of ionization probability is used to derive the rate of turn-on of current in such structures. Two differential equations are given which may be used to compute the probability that a carrier swept into or generated within the space-charge region triggers avalanche breakdown. For a 27-V n⁺-p diode biased 1 V above breakdown, this probability is close to 0.5 for an electron entering from the p side, or 0.1 for a hole entering from n side. Experimental measurements are in good agreement with the theoretical predictions.     

On the time dependency of the avalanche process in semiconductors

An equation is derived for the time dependent current in the avalanche region of a uniform diode, for the case of one charged carrier of either electron or hole is injected, for unequal ionization rates and drift velocities of electrons and holes. The appearing time-constant differs from earlier results, derived on the basis of the well known intrinsic response time. The noise characteristics of the current are established for a Poissonian injection of an electron or hole. The factor which describes the influence of the statistics of the multiplication for low frequencies, is also found to differ from previous published results. At high current multiplication factors the present study is in agreement with previous work.     

Avalanche-initiated space-charge oscillations

Physical mechanisms are proposed for avalanche oscillations in n⁺-n-n⁺semiconductor structures. A linearized analysis is proposed for these mechanisms, the results of which agree well with the results of a large-signal computer simulation. The oscillation mechanism is dependent upon a large excess electron concentration that is present at high current levels in the n region of an n⁺-n-n⁺structure. This electron concentration causes a net negative space charge in the n region, which in turn causes the electric field to be nonuniform, peaking at the anode n⁺contact. At sufficiently high current densities, an avalanche zone will form at the anode contact. The resultant carrier generation in this zone creates a hole domain of density sufficient to quench the avalanche. This hole domain then travels across the n region under the influence of the field. The positive space charge of the hole domain depresses the field sufficiently to prevent avalanche from recurring at the anode until the domain has extracted at the cathode. The field variation during this cycle causes transit-time terminal voltage oscillations. It is shown how, under proper conditions, a steady-state plasma region may be established over a substantial portion of the device length. This plasma region will cause the device to exhibit a negative differential resistance, and will also support relaxation oscillations at a frequency comparable to the reciprocal of its extraction time.     

Excess Avalanche Noise in In0.52Al0.48As

Avalanche multiplication and excess noise arising from both electron and hole injection have been measured on a series of In_0.52Al_0.48As p⁺-i-n⁺ and n ⁺-i-p⁺ diodes with nominal avalanche region widths between 0.1 and 2.5 mum. With pure electron injection, low excess noise was measured at values corresponding to effective k=beta/alpha between 0.15 and 0.25 for all widths. Enabled ionization coefficients were deduced using a non-local ionization model utilizing recurrence equation techniques covering an electric field range from approximately 200 kV/cm to 1 MV/cm     

Intrinsic response time measurements in uniform and nonuniform field avalanche regions in GaAs

Experimental determination of the intrinsic avalanche response time τ1in GaAs microwave diodes shows good agreement with theoretical predictions for structures having uniform electric fields in the avalanche region as opposed to those with nonuniform profiles. Measurements are presented for a high-power GaAs double-drift Read diode, a single drift X-band Read diode and a 35-GHz Lo-Hi-Lo bathtub structure to demonstrate the agreement. The agreement of these results with calculations that neglect high field diffusion indicates that high field diffusivity is not very important in GaAs avalanche regions as narrow as 2000 Å. The value of τ1, for the high-power double-drift diode obtained from high-frequency noise measurements, was found to be in agreement with the value obtained for the same diode by Adlerstein et al., where τ1was obtained from microwave admittance data. Experiments indicate that observed variations in the value of τ1due to changes in the junction temperature are consistent with variations due to the temperature dependence of the scattering limited velocities. It is further concluded that consistent discrepancies found between theory and experiment for structures having nonuniform fields in the avalanche region are the result of nonlocal effects in GaAs.     

A Monte Carlo investigation of multiplication noise in thin p+-i-n+ GaAs avalanche photodiodes

A Monte Carlo (MC) model has been used to estimate the excess noise factor in thin p⁺-i-n⁺ GaAs avalanche photodiodes (APD's). Multiplication initiated both by pure electron and hole injection is studied for different lengths of multiplication region and for a range of electric fields. In each ease a reduction in excess noise factor is observed as the multiplication length decreases, in good agreement with recent experimental measurements. This low noise behavior results from the higher operating electric field needed in short devices, which causes the probability distribution function for both electron and hole ionization path lengths to change from the conventionally assumed exponential shape and to exhibit a strong dead space effect. In turn this reduces the probability of higher order ionization events and narrows the probability distribution for multiplication. In addition, our simulations suggest that fur a given overall multiplication, electron initiated multiplication in short devices has inherently reduced noise, despite the higher feedback from hole ionization, compared to long devices     

Efficiency limitation by transverse instability in Si IMPATT diodes

Measurements of large-signal impedance, ac voltage and dc voltage V0versus dc current I0on Si p-n-n⁺IMPATT diodes in pulse operation (80 ns) suggest that the efficiency of Si IMPATT diodes is limited by instability effects causing a splitup into regions with different current densities. The effect is explained by considering the I0-V0curves at constant ac voltage. These can be S-shaped owing to impact ionization in the drift region.     

A GaAs avalanche diode analysis and an approximate indirect measurement of hole saturation velocity

GaAs avalanche diodes are observed to operate at frequencies considerably lower than those of Si or Ge diodes with similar doping profiles and dc characteristics. This observed behavior and the analysis shown in this paper enable us to evaluate an approximate hole saturation velocity in GaAs. Small signal impedances and Q's of GaAs avalanche diodes with breakdown voltages of 17, 36, and 58 are calculated based on the approximated hole saturation velocity of2 times 10^{6}cm/s. The model assumes an abrupt p⁺-n junction, e.g., zinc diffusion on n-type material, and a realistic electric field in the space-charge region.