Impact Ionization In Silicon Research Articles

Impact ionization in silicon at low charge-carrier energies

Photons absorbed in silicon produce electron–hole pairs, which can cause impact ionization and quantum yield larger than one. Reliable determination of quantum yield at low charge-carrier energies (<4 eV) has been challenging because photon losses due to reflectance and charge-carrier losses due to recombination affect the resulting photocurrent. Here, we present how the measurement of this fundamental characteristic of silicon crystals can be improved in the charge-carrier energy range of 1.6–4 eV by using a predictable quantum efficient detector based on induced junction photodiodes optimized for photon-to-electron conversion efficiency. The measured quantum yield values are compared with the results of theoretical calculations, revealing increased impact-ionization probabilities at 2.25 and 3.23 eV on the top of a smooth background curve calculated by a model based on free charge carriers in the silicon lattice. For the results at the lowest energies, both data and an asymptotic extrapolation model suggest that quantum yield exceeds unity by ∼10−4 at 1.6 eV corresponding to a photon wavelength of 450 nm.

An 82-GHz 14.6-mW Output Power Silicon Impact Ionization Avalanche Transit Time Transmitter With Monolithically Integrated Coplanar Waveguide Patch Antenna

The design, fabrication, and characterization of a 4.08 mm2 monolithic 82-GHz silicon impact ionization avalanche transit time (IMPATT) transmitter are presented. The vertical IMPATT diode was grown by molecular beam epitaxy and followed by the typical circuit fabrication process. The oscillator design is experimentally well verified both by the Kurokawa condition from impedance matching and by Barkhausen’s criteria from the reflection coefficient aspect, respectively. An 82.5-GHz coplanar waveguide (CPW) patch antenna with 50- $\Omega $ input impedance is monolithically integrated to an IMPATT oscillator with similar working frequency. Under the biasing condition of 25 mA (13.41 V), the $H$ -plane radiation pattern of the monolithic IMPATT transmitter was characterized at 82.17 GHz in an E-band anechoic chamber. From link budget calculation, the equivalent isotropically radiated power of the transmitter chip achieved 18.43 dBm (69.66 mW). With the simulated directive gain (7.35 dBi) of CPW patch antenna and measured CPW interconnect loss (0.57 dB), the output power of transmitter achieved 11.65 dBm (14.62 mW) with dc-to-radio frequency efficiency of 4.36%.

Detection of single holes generated by impact ionization in silicon

We propose a method for the observation of the electron-initiated impact ionization process in Si, which is potentially capable of detecting individual impact ionization events. This method detects holes generated by the impact ionization with single charge sensitivity. We demonstrate the method at 8 K by detecting the chain of single holes generated for a constant electron-injection current with the injection-energy threshold close to the Si bandgap energy.We propose a method for the observation of the electron-initiated impact ionization process in Si, which is potentially capable of detecting individual impact ionization events. This method detects holes generated by the impact ionization with single charge sensitivity. We demonstrate the method at 8 K by detecting the chain of single holes generated for a constant electron-injection current with the injection-energy threshold close to the Si bandgap energy.

Compact High-Precision Models for Silicon p-n Step Junction Avalanche-Breakdown Voltages

Advanced silicon impact-ionization models are linked with simple accurate 1-D breakdown-voltage formulas for p-n step junctions. The models are useful for ab initio calculations and improve the accuracy of older models due to a new parameterization based on a numerical simulation. New parameters for effective impact-ionization coefficients are presented for Chynoweth and Fulop formulations. The parameter sets are based on impact-ionization models of Van Overstraeten and De Man and of the Universita di Bologna, including its recent updates. They allow quick computing of silicon p-n junction breakdown voltages from 10 V to 10 kV with maximum deviation from numerical data of ±5%. The new breakdown-voltage models account for the junction temperature and the depletion on both sides of the p-n junction.

On the Limitations of Silicon for I-MOS Integration

This paper discusses the scalability of the supply voltage with the device length in silicon impact ionization MOS (I-MOS) transistors, by presenting results from both experiments and simulations. It is first shown that the supply voltage of silicon I-MOS devices saturates at low device lengths and does not fall under about 4.5 V. Second, it is shown from 2-D simulations and measurements on sub-100-nm devices that the transistor effect is lost also at low device lengths. We then propose an explanation for this phenomenon, based once again on the saturation of the supply voltage. Based on our findings, we conclude that silicon may be an inadequate material for I-MOS devices, and we envision germanium as a more promising replacement.

Measurement and modeling of the electron impact-ionization coefficient in silicon up to very high temperatures

In this paper, an experimental investigation on high-temperature electron impact-ionization in silicon is carried out with the aim of improving the qualitative and quantitative understanding of carrier transport under electrostatic discharge (ESD) conditions. Special test devices were designed and manufactured using Infineon's SPT5 technology, namely: a bipolar junction transistor (BJT), a static-induction transistor (SIT) and a vertical DMOS transistor (VDMOS), all of them with a cylindrical geometry. The measurements were carried out using a customized measurement setup that allows very high operating temperatures to be reached. A novel extraction methodology allowing for the determination of the impact-ionization coefficient against electric field and lattice temperature has been used. The experiments, carried out up to 773 K, confirm a previous theoretical investigation on impact-ionization, and widely extend the validity range of the compact model here proposed for implementation in device simulation tools. This is especially useful to predict the failure threshold of ESD-protection and power devices.

Modelling of the hole-initiated impact ionization current in the framework of hydrodynamic equations

Several research papers have shown the feasibility of the hydrodynamic transport model to investigate impact ionization in semiconductor devices by means of mean-energy-dependent generation rates. However, the analysis has been usually carried out for the case of the electron-initiated impact ionization process and less attention has been paid to the modelling of the generation rate due to impact ionization events initiated by holes. This paper therefore presents an original model for the hole-initiated impact ionization in silicon and validates it by comparing simulation results with substrate currents taken from p-channel transistors manufactured in a 0.35 μm CMOS technology having three different channel lengths. The experimental data are successfully reproduced over a wide range of applied voltages using only one fitting parameter. Since the impact ionization of holes triggers the mechanism responsible for the back-bias enhanced gate current in deep submicron nMOS devices, the model can be exploited in the development of non-volatile memories programmed by secondary electron injection.

Influence of the operating temperature on the design and utilization of 94-GHz pulsed silicon IMPATT diodes

The RF and thermal behavior of 94-GHz P/sup +/PNN/sup +/ double drift flat doping profile silicon impact ionization avalanche transit time (IMPATT) diodes for high-power pulsed operation is investigated by means of time domain electrical oscillator models. It is demonstrated that these diodes have a limited optimum temperature range of operation, associated to specific matching and bias conditions, to achieve a stable and high power operation. This restriction necessitates a thermal control when the oscillator must operate over a wide ambient temperature range. Highly doped, short active zone length diodes appear to have the best potential for high power performance.

Impact ionization in silicon: A microscopic view

A microscopic, single-particle view of impact ionization in silicon is obtained from a modified full-band Monte Carlo simulation. For each ionization event, the balance between the energies supplied by the electric field and lost to the lattice is plotted as a function of time before ionization. It is shown that two separate mechanisms can be identified. The lucky-electron model describes well impact ionization at very low electric fields. At higher fields, a different form of “lucky scattering” becomes the preferred ionization mechanism, where ionizing electrons suffer a sequence of scattering events with a final velocity directed along the electric field. This process is the microscopic equivalent of the energy-transport theories describing the ensemble dynamics at high fields.

Dead space approximation for impact ionization in silicon

We demonstrate the validity of the dead space approximation for impact ionization in silicon. Monte Carlo simulations are used to obtain realistic ionization probabilities, and the corresponding avalanche gain in constant field structures is computed. We show that the hard-threshold dead space model is in good agreement with a more refined model taking into account soft-threshold effects, if an effective threshold energy of 3 eV is adopted for electrons. We also show that hole nonlocal effects do not significantly affect the result.

Monte Carlo Analysis of Hot Electron Transport and Impact Ionization in Silicon

A novel impact ionization model which is consistent with a realistic band structure of Si has been developed. The present model contains only one parameter directly corresponding to the average matrix element for the ionization transition. The ionization probability is calculated at every k-point in the first Brillouin zone and the intrinsic anisotropy of the ionization probability is explicitly taken into account. Employing the Monte Carlo procedure including the present ionization model, the ionization coefficients are calculated and a best-fitting to the experimental ionization coefficients is obtained when the value of the parameter in the ionization model is equal to that extracted from the first-principles calculations.

Quantum yield of electron impact ionization in silicon

p-channel Si-gate metal-oxide-semiconductor transistors of very thin oxides are used for the study of quantum yield of electron impact ionization in silicon. Electrons are injected into silicon from the polysilicon gate by tunneling to give an approximate δ-function energy distribution. This energy distribution is preserved when electrons pass through the oxide by direct tunneling. Using the carrier-separation properties of the induced junction, we are able to experimentally measure the number of generated electron-hole pairs as a function of the incident electron energy, up to 5 eV. Our results are found to be in excellent agreement with recent theoretical calculations of quantum yield. Beyond 5 eV, the interpretations on the experimental data are difficult due to the broadening of the incident electron energy distribution. This broadening effect is caused by strong scattering in the oxide when electrons tunnel by the Fowler–Nordheim (F–N) process. It is observed that the average energy of those electrons tunneled by the Fowler–Nordheim process becomes a function of oxide field, relatively independent of the oxide thickness.

Fundamental limitations on DRAM storage capacitors

The evolution of the silicon dynamic RAM toward higher levels of integration has occurred primarily as a result of decreasing the size of the area in which a single bit is stored. This has been accomplished by reducing the thickness of the storage capacitor insulator, introducing higher dielectric constant materials, and increasing the silicon doping levels. Existing published data are used to explore the consequences and requirements of continuing existing density trends into the 1-4 Mb range. The results indicate that the stored charge density requirement for planar capacitors will be limited by the resultant electric field both in the insulator and silicon. These limitations are imposed by insulator conduction, tunneling, and silicon impact ionization. It is evident that for the projected stored charge density of 30 fc/μm2 for a 4-Mb DRAM, new concepts of cell design or operation must be introduced.

Impact ionization of electrons in silicon (steady state)

Monte Carlo simulations of electron impact ionization in silicon are presented which include the pseudopotential band structure as well as collision broadening and higher order effects in the electron phonon interaction. Conduction in the two lowest conduction bands of silicon is considered. We also present new results for the impact ionization probability and deformation potential constants which are obtained by comparing our theory with a variety of experimental results.

Electron transport and ionization in silicon at high fields

The saturated drift velocity measured for electrons at high fields is inconsistent with Shockley's model for impact ionization in silicon. It is explained in terms of a field-dependent mean free path for high energy phonon creation in the electric field direction, electrons creating a high energy phonon as soon as they have acquired sufficient energy from the field. Assuming that the electron wavepacket travels at the saturated drift velocity without dispersion, it can be shown that the increased scattering rate at high fields must result in a large spread in the carrier energy. If a drifted Maxwellian distribution is assumed, a unique expression can be obtained for the carrier temperature T * which is in good agreement with the measured field dependence of the ionization coefficient. In this model, a cylindrical hot carrier distribution must be assumed with the hot carrier energy in a plane perpendicular to the applied field. Exact calculations of the magneto-resistance of such a distribution can be made verifying that the drift velocity is indeed saturated.

Transition probability of impact ionization in silicon : S. Ahmad and W. S. Khokley, J. Phys. Chem. Solids28 (1967), p. 2499

Transition probability of impact ionization in silicon : S. Ahmad and W. S. Khokley, J. Phys. Chem. Solids28 (1967), p. 2499

Transition probability of impact ionization in silicon

Transition probability of impact ionization in silicon

Transition probability of impact ionization in silicon

Using time dependent perturbation calculation and Bloch functions for the states of electrons and the hole, transition probability per unit time for electron-hole pair generation by impact ionization has been obtained. Further, utilizing the various possibilities in the types of momenta conservation with energy conservation relation, it is shown that there are several thresholds of energy. Three of these are found taking band structure of silicon in (1, 0, 0) direction. The total probability per unit time of pair generation by impact ionization has been estimated for energies lying between the lowest and the next higher threshold of ionization. It is found that the probability of ionization increases with increasing energy of the ionizing electron.

Spectral Shape and Attenuation Length for Hot Electrons in the Presence of Finite Absorption

The space and energy distribution of electrons released into a field-free semiconductor provides a means of studying the interaction of the electrons with the material, as experiments by Bartelink, Moll, and Meyer have shown. In the presence of finite absorption, or large energy losses per collision, the conventional methods of solving the Boltzmann equation governing the distribution function fail to give reliable results. We have found that a considerable amount of information may be obtained from the Boltzmann equation itself without a spherical harmonic expansion by studying its Laplace transform with respect to energy. In particular, we obtain an analytic expression for the exponential attenuation length which reduces to the BMM expression in the limit of small absorption and small energy loss. We obtain expressions for the average energy loss and average spread of the distribution, both of which increase linearly with distance, and for the total intensity of the distribution, which decreases exponentially with the distance through which the electrons must diffuse. This form of variation is independent of the energy distribution of the source of hot electrons. Therefore, if the energy distribution of electrons is measured at two different distances from the same source, the rate at which the average energy, for example, decreases with distance may be determined. This rate, being independent of the source distribution, is a characteristic of the medium, as is the BMM attenuation length. These two quantities together provide sufficient information to determine the mean free path for optical phonon emission and the mean free path for impact ionization. Measuring the energy distribution of the electrons in the medium can be done by measuring the distribution of electrons emitted into the vacuum provided that the angular distribution of the particles is known. This angular distribution may be approximated from knowledge of the Laplace transform. The effect of this analysis on the interpretation of the BMM experiments is to suggest that the mean free path for impact ionization in silicon may be closer to 300 \AA{} than to 200 \AA{}.