Investigation of the transition from tunneling to impact ionization multiplication in silicon p-n junctions

White noise spectra of diodes breaking down between 1·5 and 5 V have been used to investigate the details of the transition from tunneling to avalanche breakdown in silicon p-n junctions. It is found that the transition and carrier multiplication in these junctions is dominated by the influence of the threshold energies for ionization. Because this influence is not explicitly taken into account in the existing theories of carrier multiplication and noise, they are not applicable to low breakdown voltage diodes. Consequently, a multiplication onset model and alternate schemes for calculating the DC multiplication and noise in low breakdown voltage diodes are developed.Analysis of the noise data indicates that the threshold energies for ionization depend slightly on junction widths and, for the diodes employed in this study, range between 1·66–1·9 eV for electrons and 1·79–2·04 eV for holes. The minimum distance between ionizing collisions is found to range from 190 to 240 A for electrons and 200 to 250 A for holes.Application of the threshold energies for ionization to the multiplication onset model permits evaluation of the doping densities on both sides of the step junctions. From it, it is determined that the solubility of aluminum in silicon is N_A = 9·5 ± 0·5 × 10¹⁸ cm^?3.     

The Effect of Temperature on the Ionization Coefficient in Silicon†

The avalanche breakdown of p-n junction diodes across their space charge regions is known to be analogous to the Townsend mechanism for gases. Electric charge carriers, which gain sufficient energy from the field, are able to produce secondary electron-hole pairs. Both the holes and the electrons can themselves have ionizing collisions and thus the process leads to an avalanche. An important factor, controlling the breakdown, is the ionization coefficient a, defined as the number of electron-hole pairs produced by a carrier moving unit distance in the direction of the field.

This paper presents the results of nn investigation into the effect of lattice temperature on the ionization coefficient. This has been achieved by observing the breakdown voltage of a range of silicon diodes with either step or linear graded junctions, and applying simple and well-known relationships between ionization coefficient and breakdown voltage.

Measurements have been made over the temperature range 77 to 400°K, and for field strengths from 4 to 9 × 10⁵ volts/cm. Results show the ionization to become more efficient with decrease in temperature over this range of field strength. Temperature is found to have a greater effect at the lower field strength. This is shown to be consistent with modern theory.     

Avalanche breakdown characteristics of a diffused P-N junction

A one-dimensional analysis is presented on the avalanche breakdown characteristics of a diffused p-n junction diode. By numerically integrating the carrier ionization rate in a junction space-charge layer, avalanche breakdown voltage is calculated for diffused diodes of silicon and germanium; this voltage is graphically illustrated throughout a range of parameters applicable to most practical situations. In addition, for calculating the maximum cutoff frequency of varactor diodes, junction capacity is similarly illustrated assuming the device is biased to avalanche breakdown. From these illustrations, and from an accompanying nomograph which relates the physical constants of a junction to its impurity atom gradient, the above parameters can be readily established without additional calculations. Further, examples are also presented to demonstrate the reduction of breakdown voltage resulting from a rapid increase of conductivity within the space-charge layer of a diffused p-n junction; this situation approximates many epitaxial and double diffused structures.     

雪崩光电探测器的击穿效应模型分析

基于CMOS工艺制备了空穴触发的Si基雪崩探测器(APD),基于不同工作温度下器件的击穿特性,建立空穴触发的雪崩器件的击穿效应模型。根据雪崩击穿模型和击穿电压测试结果,拟合曲线得到击穿电场与温度的关系参数(dE/dT),器件在250～320 K区间内,击穿电压与温度是正温度系数,器件发生雪崩击穿为主,dV/dT=23.3 mV/K,其值是由倍增区宽度以及载流子碰撞电离系数决定的。在50～140 K工作温度下,击穿电压是负温度系数,器件发生隧道击穿,dV/dT=-58.2 mV/K,其值主要受雪崩区电场的空间延伸和峰值电场两方面因素的影响。     

Hopping conduction in heavily doped bulk n-type SiC

The electronic properties of heavily doped n-type 4H, 6H, and 15R SiC have been studied with temperature dependent Hall effect, resistivity measurements, and thermal admittance spectroscopy experiments. Hopping conduction was observed in the resistivity experiments for samples with electron concentrations of 10¹⁷ cm⁻³ or higher. Both band and hopping conduction were observed in all three polytypes in resistivity and Hall effect experiments. The hopping conduction activation energy ε₃ obtained from the resistivity measurements varied from 0.003 to 0.013 eV. The ε₃ value obtained from thermal admittance spectroscopy measurements were slightly lower. The nitrogen ionization levels were observed by thermal admittance spectroscopy only in those samples where hopping conduction was not detected by this experiment. Free carrier activation energy E_a for nitrogen was difficult to determine from temperature dependent Hall effect measurements because of the effects of hopping conduction. A new feature in the apparent carrier concentration vs inverse temperature data in the hopping regime was observed.     

Temperature Coefficient of the Breakdown Voltage of Silicon p-n Junctions†

The temperature coefficient of the breakdown voltage of silicon abrupt and linearly graded junctions is calculated by considering the temperature dependence of the effective ionization coefficient. It is found that the temperature coefficient increases with the breakdown voltage of the junction, and a saturated effect is predicted. Comparison with experimental measurements at room temperature shows a, semi-quantitative agreement.     

Thermal breakdown in silicon p-n junction devices

Current constriction in a p-n junction under a thermal mode of breakdown is analyzed and expressions for terminal voltage and radius of constriction are derived for silicon devices. The values predicted by this model are of the same order as those observed for transistors under second breakdown; it is proposed that second breakdown in transistors is a thermal mode of breakdown which inevitably follows if energy dissipated in the avalanche mode of breakdown is large enough to increase the temperature of some portion of the junction to the intrinsic or turnover temperature of the junction.     

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.     

Reversible breakdown voltage collapse in silicon gate-controlled diodes

A reversible breakdown voltage collapse is recorded in the high voltage range of the junction breakdown voltage vs gate voltage characteristic of silicon gate-controlled diodes, which is explained in terms of a spatial switching of the avalanche breakdown within the device structure. The collapse gate voltage is oxide-thickness dependent and is accurately predictable as the avalanche breakdown voltage of the deeply depleted MOS capacitor within the gate-controlled diode structure.The minimum oxide thickness required for approaching the bulk-determined breakdown voltage in field-plated planar diodes and transistors is found to range from 0.01 to 5.00 μm for substrate impurity concentration from 10¹⁷ to 5 × 10¹⁴ cm^?3, according to a design plot provided in the paper.     

Edge current induced failure of semiconductor PN junction during operation in the breakdown region of electrical characteristic

Typical blocking I-V characteristics are shown and analyzed for PN junctions exhibiting a breakdown region above 1000 V from commercial diodes and power MOSFETs. The leakage reverse current of PN junctions from commercial silicon devices available at this time has a flowing component at the semiconductor-passivant material interface around the junction edge.Part of the plotted experimental current-voltage characteristic fits to linear variation and deviation from this variation at higher applied voltage is attributed to non-controlled current flow in the interfacial layer, between the silicon and passivating material from the junction periphery. The thin interfacial layer including atomic layers both from the semiconductor and passivating dielectric material with fixed charges has imperfections resulted from the junction passivation process. For controlled-avalanche PN junctions no deviation from linear voltage dependence of the reverse current is possible until breakdown region practically at right knee appears. For other PN junctions deviation of the reverse current from linear variation results in a breakdown region with round knee and still with visible voltage dependence at current increase. Such soft breakdown region caused by the phenomena in the interfacial layer is exhibited at lower applied reverse voltage than the expected one for breakdown caused by charge carrier avalanche multiplication at the junction. Operation even for short in the soft breakdown region can lead to PN junction failure and for this reason, a maximum working permissible reverse voltage is specified in device data sheet with a value under the breakdown region. Junction failure consists in significantly lower reverse voltage than the initial one or even electrical short-circuit caused by a spot of material degradation in the interfacial layer from the junction periphery. Operation of the controlled-avalanche diode in the breakdown region is possible only for single pulse of short duration and at junction temperature not higher than 175 °C. Above 150-175 °C even for controlled-avalanche diodes deviation from linear variation of the reverse current has been observed and soft breakdown region can appear before the expected avalanche breakdown. Device failure after operation in the breakdown region, caused by spot of material degradation at the junction periphery has occurred in such conditions. For high voltage commercial power MOSFETs operation in the avalanche breakdown region is limited to 150 °C.     

Tunneling currents in In0.53Ga0.47As homojunction diodes and design of InGaAs/InP hetero-structure avalanche photodiodes

Tunneling currents in InGaAs homojunctions were studied from measurements of temperature dependence of breakdown voltage, current-voltage characteristics, tunneling effective mass, and noise spectrum. Zener emission dominates the reverse current prior to avalanche breakdown in the carrier concentration region of >10¹⁵ cm^?3 and restricts the avalanche gain in InGaAs homojunctions. An InGaAs/InP hetero-structure having a p-n junction in the InP layer was studied to reduce dark currents caused by Zener emission. A design chart to aid in the realization of a high performance APD is discussed.     

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.     

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.     

Device processing and characterisation of high temperature silicon carbide Schottky diodes

High temperature silicon carbide diodes with nickel silicide Schottky contacts were fabricated by deposition of titanium-nickel metal film on 4H-SiC epitaxial wafer followed by annealing at 550 °C in vacuum. Room temperature boron implantation have been used to form single zone junction termination extension. 4H-SiC epitaxial structures designed to have theoretical parallel-plain breakdown voltages of 1900 and 3600 V have been used for this research. The diodes revealed soft recoverable avalanche breakdown at voltages of 1450 and 3400 V, respectively, which are about 80% and 95% of theoretical values. I-V characteristics of fabricated 4H-SiC Schottky diodes have been measured at temperatures from room temperature up to 400 °C. The diodes revealed unchangeable barrier heights and ideality factors as well as positive coefficients of breakdown voltage.     

Analytical solutions for avalanche-breakdown voltages of single-diffused gaussian junctions

Closed-form solutions of the potential difference between the 2 edges of the depletion layer of a single diffused Gaussian p-n junction are obtained by integrating Poisson's equation and equating the magnitudes of the positive and negative charges in the depletion layer. By using the closed form solution of the static Poisson's equation and Fulop's average ionization coefficient, the ionization integral in the depletion layer is computed, which yields the correct values of avalanche breakdown voltage, depletion layer thickness at breakdown, and the peak electric field as a function of junction depth. Newton's method is used for rapid convergence. A flowchart to perform the calculations with a programmable hand-held calculator, such as the TI-59, is shown.     

Impact ionization wave breakdown of drift step recovery diodes

High frequency IMPATT oscillations followed under certain conditions by reversible impact ionization wave breakdown of the p ⁺-n-n ⁺ diode structure have been experimentally observed for the first time in a drift step recovery diode operating in the avalanche breakdown mode after a fast voltage restoration of the p-n junction.     

Thermal instability in very small p-n junctions

Thermally induced second breakdown is studied in very small 6- to 10-volt silicon diodes having uniform breakdown. The formation of a small high-current density region is observed optically at the onset of thermal breakdown. Incremental resistance measurements can be used to determine nondestructively the threshold current for thermal breakdown. The threshold temperature for thermal breakdown is measured using the avalanche voltage temperature coefficient. The voltage drop associated with thermal breakdown is shown to be due to a sudden change in active area of the junction rather than to melting of the crystal.     

Analysis of temperature dependence of linearity for SiGe HBTs in the avalanche region using Volterra series

In this paper, linearity characteristic of silicon germanium (SiGe) heterojunction bipolar transistors (HBTs) at different temperatures in the avalanche regime is investigated by the Volterra approach incorporating with a physics-based breakdown network for the first time. Third-order intermodulation distortion (IMD₃) decreases with increasing temperature in the impact ionization region due to lower nonlinear contributions from individual nonlinearity according to the Volterra analysis results. Calculated gain, output power, and efficiency of SiGe HBTs are in good agreement with measurement results in the avalanche region. This analysis with respect to temperature can benefit the reliability study of linearity for SiGe HBTs in the avalanche regime.     

The anomalous avalanche breakdown

Normally, the breakdown voltage of a p-n junction decreases with increasing doping density. But there are also cases in which the breakdown voltage increases with increasing doping density, e.g., for InSb in the doping range from 10¹³cm^-3to 2 × 10¹⁴cm^-3. The reason for the anomalous behavior is the saturation of the ionization coefficient with increasing electric field strength. The anomalous behavior can only be observed if the tunnel breakdown requires a higher field strength as the one required for saturation of the ionization coefficient. This paper presents a rather simple theory yielding analytical solutions for the normal and anomalous avalanche breakdown. Treated is the influence of the doping profile upon the breakdown voltage in plane junctions and the influence of the radius of curvature for cylindrical one-sided abrupt junctions. The influence of the temperature upon the breakdown voltage and the multiplication factor as function of voltage is calculated for one-sided abrupt plane junctions. Finally, the temperature and doping range for the anomalous avalanche breakdown and the transition region is plotted for the semiconductors InSb, InAs, CdHgTe, PbSnTe, Ge, Si, GaAs, and GaP.     

Surface breakdown in silicon planar junctions—A computer-aided experimental determination of the critical field

Surface breakdown in silicon planar junctions is analysed with emphasis on the evaluation of the critical field (i.e., the maximum electric field within the depletion region at breakdown). This parameter is determined by a computer-aided experimental procedure consisting in relaxation field calculations with boundary conditions governed by junction breakdown voltage (at given gate voltage) as measured on specially processed gate-controlled diodes. The idealization (infinite doping) of the highly doped side of the junction, encountered in previous works, has been eliminated. Values of the critical field determined are in the range of 1 × 10⁶ V/cm (1·0 × 10⁶ V/cm for 1·0 μm gate-oxide and 1·4 × 10⁶ V/cm for 0·3 μm gate-oxide). These values are substantially higher than those estimated by other authors (5–6 × 10⁵ V/cm) and are consistent with independent experimental findings on avalanche (hot-carrier) injection in silicon diodes.