Electron and hole ionization rates in epitaxial silicon at high electric fields

Ionization rates for electrons and holes are extracted from photomultiplication measurements on silicon p⁺n mesa diodes for electric fields of 2·0 × 10⁵?7·7 × 10⁵ V/cm at temperatures of 22, 50, 100 and 150°C. These results are particularly pertinent to the analysis of high-frequency (～ 100 GHz) silicon IMPATT diodes.The rates obtained here are in reasonable agreement with previously published data of van Overstraeten and DeMan, although slightly larger in magnitude. Calculated curves of breakdown voltage vs background doping level are presented using the room temperature ionization rates. Also a comparison is made to previously reported rates. The new rates provide a closer agreement between predicted and measured breakdown voltages for breakdown voltages less than 70 V.     

Electron transport properties in GaAs at high electric fields

Electron distribution function, drift velocity, mean energy, valley population fractions and diffusion coefficient were calculated at high, up to 100 kV/cm, electric fields. Calculations were carried out by the Monte Carlo method. The three-valley model of GaAs conduction band was used. The obtained results were compared with the experimental data.     

Avalanche ionization rates measured in silicon and germanium at low electric fields

Ionization rates in semiconductors can be measured at low values of electric field using a new method involving a field-effect transistor (FET) structure which offers greater sensitivity than reverse biased p-n junction diode methods. Carriers of only one polarity cause ionization in the FET and no correction is required for ionization caused by carriers of the opposite polarity. Since secondary carriers resulting from ionization are attracted to a different terminal (gate or substrate) than that used to collect the primary carriers (drain), very small ionization currents can be detected. Values of electron ionization rate αnand hole ionization rate αpas low as 10^-3cm^-1have been obtained for silicon. The approximate relationshipalpha = alpha_{infin}e^{-b/E}is observed and the values of α at high fields correspond to those obtained conventionally. Values of αpfrom 0.04^-1to 0.4 cm^-1have been obtained for germanium. Analytical determination of electric field was provided by a solution of Poisson's equation for the field-effect structure. Difficulty in accurately determining the FET channel doping introduces a ± 30 percent uncertainty in electric field values. The method is applicable to any semiconductor material where junction, MOS, or Schottky barrier techniques can be used to construct field-effect transistors.     

Electron velocity in n GaAs at high electric fields

The velocity of electrons in n GaAs has been measured for electric fields in the range 20?55 kV/cm by the time-of-flight technique. The velocity was found to decrease slowly wlth increasing electric field, and is 8.09×106 cm/s at 55 kV/cm.     

Noise in silicon and FET's at high electric fields

The noise temperature of n-type silicon was measured on an epitaxial layer up to a field strength of 10 KV/cm from 1 to 20 MHz at 77°K. The result was applied to obtain an approximate form for the drain noise of an FET in the high electric field. We found that the noise increases in proportion to the product of the drain current and voltage in high electric fields. The noise of the FET was also measured and the experimental data show reasonable agreement with the theoretical expressions.     

Electron drift velocity in n-GaAs at high electric fields

Measurements have been made on the drift velocity of electrons in n-GaAs by the time-of-flight technique. The method of determining the $\text{ν}\text{E}$ characteristics from the transit time across the non-uniform field depletion region of the sample is described. Velocity/field curves are presented in the field range 20 to 113 kV/cm at various temperatures from 130 to 400°K. All curves show the velocity to decrease slowly as the field is increased and velocity saturation is approached at the highest field values used. The characteristics match up well with the generally accepted experimental curves at the lower fields, and a simple theory is described which predicts well the saturation velocity.     

Electron transient response and impact-ionized plasma instability in GaAs at very high electric fields

Dynamic behavior of electrons in GaAs under impact ionization conditions is studied by the Monte Carlo technique. The relaxation time of impact ionization generation rate is estimated. The linear stage of instability caused by the generation rate lagging the electric field is investigated. The nonlinear regime of this instability is numerically simulated. The electric field and plasma density oscillations with a frequency of the order of 50–1000 GHz are obtained.     

Electron transport properties of quantized silicon carbide inversion layers

Electron transport properties in SiC quantized inversion layers have been studied by means of a Monte Carlo procedure. It has been observed that the contribution of polar-optical phonon scattering produces a significant influence of the effective-electric field on the high longitudinal field transport regime, this being the main difference of SiC with respect to standard Si inversion layers. The energy- and momentum-relaxation times have been calculated and the results suggest that electron velocity overshoot effects are less important than in Si metal-oxide semiconductor field effect transistors. The electron mobility is not very different from their silicon counterparts, but the saturation velocity is higher.     

Electron transport in unipolar heterostructure transistors with quantum dots in strong electric fields

A model for the explaining specific features of the electron transport in strong electric fields in the quantum-dot unipolar heterostructure transistor (AlGaAs/GaAs/InAs/GaAs/InAs) is presented. It is shown that the two-step shape of the output current-voltage characteristic I _D (V _D ) and the anomalous dependence of the drain current I _D on the gate voltage V _G are caused by the ionization of quantum dots in the strong electric field at the drain gate edge. The ionization of quantum dots sets in at the drain voltage V _D that exceeds the V_D1 value, at which the I _D (V _D ) dependence is saturated (the first step of the I-V characteristic). With the subsequent increase in V _D , i.e., for V _D >V_D1, the I _D (V _D ) dependence has a second abrupt rise due to the ionization of quantum dots, and then, for V _D =V_D2>V_D1, the current I _D is saturated for the second time (the second step in the current-voltage characteristic). It is suggested to use this phenomenon for the determining the population of quantum dots with electrons. The model presented also describes the twice-repeated variation in the sign of transconductance g _m =dI _D /dV _G as a function of V _G .     

Electron velocity overshoot at room and liquid nitrogentemperatures in silicon inversion layers

Effective electron velocities in silicon MOSFETs exceeding the bulk saturation values of 10⁷ cm/s at room temperature and 1.3×10⁷ cm/s at liquid-nitrogen temperature are inferred. This conclusion suggests that electron velocity overshoot occurs over a large portion of the device channel length. To infer this phenomenon, submicrometer-channel-length Si MOSFETs with lightly doped inversion layers were fabricated. These devices have low field mobility of 450 cm²/V-s and showed only slight short-channel effects. Effective carrier velocities are calculated from the saturated transconductance g_m at V_DS=1.5 V after correction for parasitic resistances of source and drain     

Electron transport in semiconductors under a strong high frequency electric field

We propose an analytical approach to study the electron transport in semiconductors when a strong high frequency (HF) electric field is applied together with a weak direct current (DC) electric field. We derive a set of dynamic equations, from which the amplitude and phase of each harmonic component of the electron drift velocity and the electron temperature can be obtained. Our calculation shows that the DC conductivity in an n-GaAs sample decreases dramatically with increase of the first and second harmonic applied electric fields and definitely becomes negative.     

Impact ionization in thin silicon diodes

We study the breakdown behavior of thin, abrupt silicon pin-diodes, using a low-power optical technique which can directly measure the avalanche multiplication factors even in the presence of large tunneling currents. Our measurements agree with a simple model for nonlocal avalanche generation, and we use this model to extend the breakdown predictions to a broad class of doped diodes similar to those found in the base-collector region of bipolar devices. Based on this analysis, we make quantitative estimates for the BV/sub CEO/ breakdown of modern Si and SiGe high-speed bipolar transistors.     

Transient space-charge phenomena in semiconductors at high electric fields

The transient response of trap-free semiconductors subjected to a voltage step function and unipolar injection of charge is analyzed for the case that the velocity of the carriers is a non-linear function of the electric field. The method of characteristics is used to evaluate current, density and field profiles as functions of time. Numerical results are presented for the case of n-Si. These results show that there is a sharp bunching of charge accompanying the cusp. This bunching of charge is shown to be a consequence of the decreased differential mobility at high fields.These results are compared with the previously published results for a constant mobility case. A simple model is used to derive exactly the results for a saturated-velocity transient. It is shown that the numerical results for the actual case of non-linear velocity fit well between the results for these two limiting behaviors for the velocity-field curve.Effects of a finite rise-time in the voltage pulse are also studied. It is shown that a significant rise time can considerably reduce the sharpness of the current cusp.     

Electron and hole mobility in silicon at large operatingtemperatures. I. Bulk mobility

In this paper, an experimental investigation on high-temperature carrier mobility in bulk silicon is carried out with the aim of improving our qualitative and quantitative understanding of carrier transport under ESD events. Circular van der Pauw patterns, suitable for resistivity and Hall measurements, were designed and manufactured using both the n and p layers made available by the BCD-3 smart-power technology. The previous measurements were carried out using a special measurement setup that allows operating temperatures in excess of 400°C to be reached within the polar expansions of a commercial magnet. A novel extraction methodology that allows for the determination of the Hall factor and drift mobility against impurity concentration and lattice temperature has been developed. Also, a compact mobility model suitable for implementation in device simulators is worked out and implemented in the DESSIS© code. Comparisons with the mobility models by G. Masetti et al. (1983) and D.B.M. Klaassen (1992) are shown in the temperature range between 25 and 400°C     

Transient behavior of impact ionization in silicon

A transient solution of the ionization coefficient for electrons (α) in silicon has been obtained for various electric field strengths. The results show that α takes a longer time to come to its steady-state value for lower electric field strengths. The time the transient lasts is of the order of 10^-13s.     

Anomalous relaxation of photoconductivity in silicon at high excitation levels

Anomalous relaxation of excess carries at high injection levels is observed in silicon samples upon their excitation with a pulse of light from a laser diode (1060 nm/500 mW). Microwave conductivity measurements and conventional photoconductivity-relaxation measurements were employed in these experiments. Unusual behavior takes place at the initial stage of the photoconductivity’s relaxation after the end of a pulse of light. To explain the anomalous-relaxation effect, we suggest a simplified model that involves excitons at high excitation levels.     

Carrier transport in porous silicon

Carrier transport in porous silicon layers has been studied by the time-of-flight method in the strong injection mode at temperatures T=290–350 K and electric field strengths F=(1.5–7)×10⁴ V cm^?1. The electron and hole drift mobilities μ_e≈2×10^?3 cm² V^?1 s^?1 and μ_h≈6×10^?4 cm² V^?1 s^?1 were obtained at T=292 K and F=4×10⁴ V cm^?1. An exponential temperature dependence of drift mobility with activation energy of ～0.38 and ～0.41 eV for, respectively, electrons and holes was established. It is shown that the type of time dependences of the photocurrent associated with carrier drift and the superlinear dependence of the transit time on the reciprocal of the voltage applied to a sample allow use of the concept of space-charge-limited currents under the conditions of anomalous dispersive transport. The experimental data are accounted for in terms of the model of transport controlled by carrier trapping into localized states with energy distribution near the conduction and valence band edges described by an exponential function with a characteristic energy of ～0.03 eV.     

Electron beams in axially-symmetric crossed fields

M-type traveling-wave tubes use electron beams that drift in crossed electric and magnetic fields. One such tube, the axiotron described by Warnecke and Doehler in 1950, used a hollow beam drifting parallel to the tube axis in a radial electric field crossed by an azimuthal magnetic field. The addition of an axial magnetic field to the azimuthal one adds another degree of complication and flexibility to the beam equations, yet maintains their symmetry about the tube axis. It gives, in effect, a helical magnetic field crossed by a radial electric field. This report examines the behavior of hollow electron beams drifting in laminar flow through fields of the latter configuration. It defines a stability index for electron paths, and four fairly general types of beam. It determines the stability index and the distribution of space charge obtainable in each type as functions of the amplitudes and directions of the fields and drift velocities. In general, the density tends to be greatest at the inner beam radius, but it is possible to approach uniform density in stable beams. This report does not consider beam launching nor the "gun" problem; nor does it consider over-all beam instabilities such as scalloping.     

Space charge limited current in an insulator at high fields

It is shown that the correct high field current/voltage characteristic in space charge limited single-injection solid state diodes is obtained at sufficient high fields.     

Electron transport in silicon carbide natural superlattices under the Wannier-Stark quantization conditions: Basic issues and application prospects

Hot-electron transport in silicon carbide natural superlattices was investigated. Almost all of the theoretically predicted effects related to the Wannier-Stark localization, such as Bloch oscillations, Stark-phonon resonances, miniband-state localization, and resonance tunneling between the minibands, were observed for the first time. In n ⁺-n ^?-n ⁺ structures optimized for the measurements at microwave frequencies, the formation of the mobile electric domain was observed in the electric-field range corresponding to the Bloch oscillation conditions; thus, the onset of the microwave oscillations in the 6H-SiC natural superlattice can be stated with a high degree of confidence.