Modeling silicon emitters for VLSI transistors

The accuracy and reliability of predictions from numerical simulations of advanced bipolar transistors for VLSI applications depend on model input parameters. These parameters include the variations with doping and carrier concentrations in both n-type and p-type silicon of (1) the valance and conduction band edges, (2) the effective intrinsic carrier concentrations, (3) the minority carrier mobilities, and (4) the minority carrier lifetimes. This paper reviews recent advances in device physics for modeling the emitters of bipolar transistors with submicrometer dimensions and high concentrations of dopant ions and carriers.     

A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon

A theoretical model that describes the dependence of carrier lifetime on doping density, which is based on the equilibrium solubility of a single defect in nondegenerately doped silicon, is developed. The model predictions are consistent with the longest measured hole and electron lifetimes reported for n-type and p-type silicon, and hence imply a possibly “fundamental” (unavoidable) defect in silicon. The defect is acceptor-type and is more soluble in n-type than in p-type silicon, which suggests a longer fundamental limit for electron lifetime than for hole lifetime at a given nondegenerate doping density. The prevalent, minimum density of the defect, which defines these limits, occurs at the processing temperature below which the defect is virtually immobile in the silicon lattice. The analysis reveals that this temperature is in the range 300–400°C, and thus emphasizes, when related also to common non-fundamental defects, the significance of low-temperature processing in the fabrication of silicon devices requiring long or well-controlled carrier lifetimes.     

Quadratic recombination in silicon and its influence on the bulk lifetime

The coefficient of nonradiative excitonic recombination by the Auger mechanism involving deep-level centers in n-Si was determined by comparing the theoretical dependence of the effective bulk lifetime on the doping level with the experimental dependence. It is shown that this mechanism controls the bulk lifetime in silicon at doping levels on the order of or above 10¹⁶ cm^?3. This mechanism is more pronounced at shorter bulk lifetimes τ _v0 and low doping levels. The dependences of the bipolar diffusion length in n-Si on the doping level (using the parameter τ _v0) were calculated.     

Effective recombination levels in n- and p-type silicon irradiated by 4·5 MeV electrons

The effective recombination levels created at room temperature by 4·5 MeV electron irradiation are deduced from the variations in lifetime vs carrier injection rate, electron fluence, and temperature. This paper aims to compare the properties of the created recombination energy levels and defect centers in N- and P-type silicon single crystals. The characteristics of the samples used extend over a wide range of resistivities, doping impurities and crystal growth techniques. A pulsed neodymium laser has been employed to carry out these studies, and the carrier lifetime has been measured by the photoconductivity-decay method. Information on the specific centers is deduced from the comparison of the present macroscopic results on energy levels and annealing studies with the known properties of microscopic defects.From the results obtained, several types of recombination centers are simultaneously created in N- and P-type silicon, and crystal impurities other than oxygen and dopants may play a big part in the constitution of such centers. In the P-type silicon case, 3 types of recombination centers are clearly operative: (1) centers with a ～E_v+0·20 eV energy level, which could be divacancies, and which would cease to act as recombination centers by trapping irradiation induced interstitial carbon atoms, (2) centers with a ～E_v+0·24 eV level which may involve aluminium interstitial atoms, and finally (3) centers with a ～E_v+0·27 eV level, which are K centres. These recombination centers are more or less active, depending on the initial characteristics of the sample. In the N-type silicon case, only two groups of effective recombination levels, ～E_c?0·17 and E_v+0·3 eV, appear in the irradiated materials. However, the effects of centers possibly linked to the presence of contaminants, such as carbon and aluminium, must be added to the known effects of the divacancy, doping atom-vacancy and oxygen-vacancy complexes to explain the carrier lifetime degradation and recovery.     

A study of efficiency in low resistivity silicon solar cells

A general device analysis program has been utilized to study the efficiency of silicon solar cells. The analysis is applied to specific geometries of both n⁺-p and n⁺-p-p⁺ solar cells and involves a numerical solution of the basic transport and continuity equations. This approach allows solutions free of typical limiting assumptions involved in solving the device equations apart from those relating to lifetime, mobility variations and diffused region profiles. The analysis includes available empirical information of diffusion length, mobility, and lifetime as a function of doping as well as a Gaussian profile for the diffused region. Results are presented which illustrate the limitations of efficiency as a function of doping. It was found that the maximum efficiencies for both types of cell converge at lower resistivities to around 16% with AMO radiation and a single layer absorbing SiO antireflecting film. It was also found that the minority carrier lifetime, both in the n⁺ surface and p-type bulkk regions, presents serious limitations to conversion efficiency particularly in the low resistivity cells.     

The effect of thermal and radiation defects on the recombination properties of the base region of diffused silicon p-n structures

The effect of thermal and radiation defects on the minority-charge-carrier recombination in the base region of a diffused silicon p-n structures with doping levels of 10¹⁴–10¹⁸ cm⁻³ was studied. The parameters of thermal defects responsible for the change of the carrier lifetime in Si following its thermal treatment during the production of p-n structures are determined. The effective minority-charge-carrier trapping is observed in heavily-doped structures at T ⩽ 100 K. The dependence of the coefficient of the radiation-induced change in the carrier lifetime on the base-region doping level was found. Using this data and the results obtained by the capacitance spectroscopy technique the analysis of recombination properties of defects has been done. At carrier concentrations n₀, p₀ ⪢ 10¹⁶ cm⁻³ the coefficient of the radiation-induced change in the carrier lifetime (K_τ) is shown to be determined by the introduction of the E-center in n-Si and the defect level E_c − 0.27 eV in p-Si. At a low excitation level in heavily-doped p-n structures a significant decrease in K_τ is observed at T = 78 K as compared to the value at 300 K.     

Characterization of <Emphasis Type="Italic">n</Emphasis>-Type and <Emphasis Type="Italic">p</Emphasis>-Type Long-Wave InAs/InAsSb Superlattices

The influence of dopant concentration on both in-plane mobility and minority carrier lifetime in long-wave infrared InAs/InAsSb superlattices (SLs) was investigated. Unintentially doped (n-type) and various concentrations of Be-doped (p-type) SLs were characterized using variable-field Hall and photoconductive decay techniques. Minority carrier lifetimes in p-type InAs/InAsSb SLs are observed to decrease with increasing carrier concentration, with the longest lifetime at 77 K determined to be 437 ns, corresponding to a measured carrier concentration of p ₀ = 4.1 × 10¹⁵ cm^?3. Variable-field Hall technique enabled the extraction of in-plane hole, electron, and surface electron transport properties as a function of temperature. In-plane hole mobility is not observed to change with doping level and increases with reducing temperature, reaching a maximum at the lowest temperature measured of 30 K. An activation energy of the Be-dopant is determined to be 3.5 meV from Arrhenius analysis of hole concentration. Minority carrier electrons populations are suppressed at the highest Be-doping levels, but mobility and concentration values are resolved in lower-doped samples. An average surface electron conductivity of 3.54 × 10^?4 S at 30 K is determined from the analysis of p-type samples. Effects of passivation treatments on surface conductivity will be presented.     

Recombination level selection criteria for lifetime reduction in integrated circuits

In the past, lifetime control in integrated circuits has been done on an empirical basis. This paper introduces selection criteria for recombination centers which are to be used for reducing minority carrier lifetime in integrated circuits. It is shown that the recombination level should have a large lifetime ratio (τ_SC/τ_LL) in order to obtain minority carrier lifetime reduction with minimal increase in the leakage current, and should possess large capture cross section values in order to minimize compensation effects. Using these criteria, preferred locations for the recombination center have been defined for both p and n type silicon, and the trade-off between reduction of lifetime and increase in leakage current has been shown to degrade with increase in resistivity and ambient temperature. These criteria have also allowed a quantitative comparison between various lifetime control techniques for the first time, and platinum doping has been identified as the most favorable lifetime control process at the present time.     

Mechanisms of recombination of nonequilibrium charge carriers in epitaxial Cd<Subscript>x</Subscript>Hg<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Te (<Emphasis Type="Italic">x</Emphasis> = 0.20–0.23) layers

The experimental temperature dependences of the photosensitivity and the data on the lifetime of nonequilibrium charge carriers in epitaxial Cd_xHg_1?x Te layers with x = 0.20–0.23 were used to show that, in the region of intrinsic and extrinsic conductivity in n-type films grown by molecular beam epitaxy, CHCC Auger recombination is the prevailing recombination mechanism. At the same time, in p-type films grown by liquid-or vapor-phase epitaxy, it is observed that, in the region of extrinsic conductivity, CHLH Auger recombination competes with Shockley-Read recombination. The n-type films grown by molecular beam epitaxy contain a much lower concentration of recombination centers than the p-type films grown by liquid-or gasphase epitaxy.     

Effect of trap location and trap-assisted Auger recombination onsilicon solar cell performance

Model calculations were performed to investigate and quantify the effect of trap location and trap-assisted Auger recombination on silicon solar cell performance. Trap location has a significant influence on the lifetime behavior as a function of doping and injected carrier concentration in silicon. It Is shown in this paper that for a high quality silicon (τ=10 ms at 200 ohm-cm, no intentional doping), high resistivity (⩾200 ohm-cm) is optimum for high efficiency one sun solar cells if the lifetime limiting trap is located near midgap. However, if the trap is shallow (E_t-E_v⩽0.2 eV), the optimum resistivity shifts to about 0.2 ohm-cm. For a low quality silicon material or technology (10 μs at 200 ohm-cm, prior to intentional doping) the optimum base resistivity for one sun solar cells is found to be ~0.2 ohm-cm, regardless of the trap location. It is shown that the presence of a shallow trap can significantly degrade the performance of a concentrator cell fabricated on high-resistivity high-lifetime silicon material because of an undesirable injection level dependence in the carrier lifetime. The effect of trap assisted Auger recombination on the cell performance has also been modelled in this paper. It is found that the trap-assisted Auger recombination does not influence the one sun cell performance appreciably, but can degrade the concentrator cell performance if the trap-assisted Auger recombination coefficient value exceeds 2×10^-14 cm³/s. Therefore, it is necessary to know the starting lifetime as well as trap location in order to specify base resistivity in order to predict or achieve the best cell performance for a given one sun or concentrator cell design     

Classification of macroscopic defects contained in p-type EFG ribbon silicon

Recombination behavior of the grown-in defects contained in p-type ribbon silicon has been examined. Minority carrier lifetime at various defect sites was measured as a function of temperature by the electron beam induced current (EBIC) method. Based on the lifetime vs temperature characteristics, we classify the defects into three macroscopic (> 20 μm scale) categories: (i) plastically deformed single crystal region; (ii) dislocation arrays with associated impurity atmosphere; and (iii) crystallographic structural line boundaries including twins and grain boundaries. The recombination processes described by category (ii) include a set of shallow electron donor traps near the dislocation core with apparent activation energies E_c − E_t = 0.066−0.087eV. The recombination lifetime of category (iii) can be described by Shockley-Read-Hall statistics with a recombination level located at the lower half of the band gap. Under the measurement condition, the activation energies of the acceptor-like center in category (iii) were found to be E_t − E_v = 0.086−0.114 eV. The recombination properties of category (i) and (ii) defects are consistent with the presence of compensating donor states in the p-type ribbon. Thus, it is believed that these types of defects are primarily responsible for the observed minority carrier lifetime dependence on the photoexcitation level in the EFG ribbon silicon.     

Modeling of Thermoelectric Properties of Magnesium Silicide (Mg2Si)

Thermoelectric (TE) materials based on alloys of magnesium (Mg) and silicon (Si) possess favorable properties such as high electrical conductivity and low thermal conductivity. Additionally, their abundance in nature and lack of toxicity make them even more attractive. To better understand the electronic transport and thermal characteristics of bulk magnesium silicide (Mg₂Si), we solve the multiband Boltzmann transport equation within the relaxation-time approximation to calculate the TE properties of n-type and p-type Mg₂Si. The dominant scattering mechanisms due to acoustic phonons and ionized impurities were accounted for in the calculations. The Debye model was used to calculate the lattice thermal conductivity. A unique set of semiempirical material parameters was obtained for both n-type and p-type materials through simulation testing. The model was optimized to fit different sets of experimental data from recently reported literature. The model shows consistent agreement with experimental characteristics for both n-type and p-type Mg₂Si versus temperature and doping concentration. A systematic study of the effect of dopant concentration on the electrical and thermal conductivity of Mg₂Si was also performed. The model predicts a maximum dimensionless figure of merit of about 0.8 when the doping concentration is increased to approximately 10²⁰?cm^?C3 for both n-type and p-type devices.     

Iodine Doping of CdTe and CdMgTe for Photovoltaic Applications

Iodine-doped CdTe and Cd_1?x Mg _x Te layers were grown by molecular beam epitaxy. Secondary ion mass spectrometry characterization was used to measure dopant concentration, while Hall measurement was used for determining carrier concentration. Photoluminescence intensity and time-resolved photoluminescence techniques were used for optical characterization. Maximum n-type carrier concentrations of 7.4 × 10¹⁸ cm^?3 for CdTe and 3 × 10¹⁷ cm^?3 for Cd_0.65Mg_0.35Te were achieved. Studies suggest that electrically active doping with iodine is limited with dopant concentration much above these values. Dopant activation of about 80% was observed in most of the CdTe samples. The estimated activation energy is about 6 meV for CdTe and the value for Cd_0.65Mg_0.35Te is about 58 meV. Iodine-doped samples exhibit long lifetimes with no evidence of photoluminescence degradation with doping as high as 2 × 10¹⁸ cm^?3, while indium shows substantial non-radiative recombination at carrier concentrations above 5 × 10¹⁶ cm^?3. Iodine was shown to be thermally stable in CdTe at temperatures up to 600°C. Results suggest iodine may be a preferred n-type dopant compared to indium in achieving heavily doped n-type CdTe.     

Theory and experiment for silicon Schottky barrier diodes at high current density

Metal-silicon Schottky barrier diodes exhibit n values which theoretically vary as a function of doping and applied voltage. The expected variation depends on which theoretical model is used to describe the current transport.Titanium n-type silicon barriers were prepared. At a doping level of 3 × 10¹⁵ cm^?3 the barrier height and n-value measured at 100 mV were 0.485±0.005 V and 1.02±0.01 whereas for a doping level of 2 × 10¹⁴ cm^?3 the corresponding values were 0.500±0.005 V and 1.18±0.05.The experimental variation of the diode n value as a function of semiconductor band bending showed good agreement with the thermionic-diffusion model of Crowell and Beguwala: n values increased rapidly as the band bending β → 2, and n values were highest at a given β for diodes with the lowest doping concentration. Similar results were obtained by measurements on magnesium and aluminium barriers on n-type silicon.An analysis of the results has shown that the variation of the diode saturation current I_s follows the predictions of the thermionic-diffusion theory, although there were some anomalies at high current densities. The anomalies did not result from variation of the width of the undepleted region of the epitaxial silicon layer or from diode self-heating effects.     

Charge-carrier lifetime in Hg1−x CdxTe (x=0.22) structures grown by molecular-beam epitaxy

Measurements of the charge carrier lifetime in epitaxial structures based on narrow-gap Hg_1−x Cd_xTe (x=0.22), grown by molecular-beam epitaxy with pulsed excitation using radiation at different wavelengths, are reported. It is shown that in p-type epitaxial films the lifetime is determined by the Auger recombination mechanism at temperatures corresponding to the impurity conductivity, and for n-type epitaxial films recombination via local centers is characteristic. Fiz. Tekh. Poluprovodn. 31, 774–776 (July 1997)     

Carrier recombination and lifetime in highly doped silicon

The predominance of phonon-assisted band-band Auger recombination in highly doped silicon is demonstrated by showing that no recombination mechanism involving common (unavoidable) defects in silicon can yield carrier lifetimes that are consistent with the measured lifetimes, which exhibit an inverse-quadratic doping-density dependence, and/or with their temperature dependence. Both trap-assisted-Auger and Shockley-Read-Hall recombination mechanisms are considered, and dependences of the defect density on the doping density, which are implied by theory and experiment, are accounted for.     

The influence of auger recombination on the forward characteristic of semiconductor power rectifiers at high current densities

It has previously been shown that the recombination of carriers in silicon and germanium at high carrier concentrations is dominated by Auger recombination (impact recombination). Carrier concentrations of 10¹⁸ cm^?3 and higher may occur in high-current devices such as power rectifiers and thyristors. The present paper analyzes the influences of the Auger recombination on the forward characteristic of pin and psn rectifiers at high current densities. It is an extension of the theory developed by Herlet, Spenke et al. for such devices, and does not take into account the concentration dependence of the carrier mobilities. It shows that the Auger recombination is important for the understanding of the current-voltage characteristic at high forward current densities.     

Recombination in cadmium mercury telluride photodetectors

Cadmium mercury telluride is of considerable importance as a material for the detection of IR radiation. Carrier lifetime has been studied intensively as it is the principal factor controlling detector performance. Bulk lifetime is dominated by Auger processes in the narrow bandgap material sensitive between 8 and 14 μm, while it is dominated by radiative recombination in the wider bandgap material sensitive below 5 μm. Auger processes have been studied by observing the photoconductive decay as a function of temperature. This has led to an experimental determination of the overlap integral as 0.3. A fresh calculation of radiative lifetime by the van Roosbroek-Shockley method has led to an analytic expression that agrees well with observed lifetime. Recombination at discontinuities (contacts, surfaces and flaws introduced in processing) are of importance in the photoconductive detectors. Surface recombination velocity can be reduced to low values (less than 200 cm s⁻¹) in n-type material by obtaining an accumulated surface. The rate limiting processes are then transitions between filled surface states and holes. No such accumulation appears to occur at the contacts or lines of damage introduced in processing. As a result there is considerable recombination at these features. When lifetime is controlled by transit time effects it is called sweepout. In sweepout the dependence of ambipolar mobility on majority carrier concentration leads to novel effects. Auger lifetime is reduced in low carrier concentration samples by optical injection of carriers by the background. This effect has often been ascribed to Shockley-Read recombination. These results are being used in modelling of detector performance that reproduces most of the features seen in practical detectors.     

Dopant diffusion studies and free carrier lifetimes during rapid thermal processing of semiconductors

Rapid thermal processing of semiconductors involves significant photonic and subsequent thermal excitation. In the past, photonic excitation during rapid thermal annealing had been speculated to lead to significant enhancement of dopant diffusion or activation. In this work we present some experimental results indicating the absence of any such enhancement at high temperatures (1000–1050°C) which most often are employed during the metal-oxide–semiconductor device processing. The implanted dopant (boron, arsenic or phosphorus) movement in silicon during different rapid thermal annealing conditions was studied using secondary ion mass spectroscopy (SIMS) technique. To understand the effect of point defects in controlling the diffusion process, the concentrations of charged and neutral point defects were calculated as a function of carrier concentration using previously published defect-carrier relations. The dependence of free carrier concentration on lattice perturbation parameters such as impurities and temperature was formulated and used in calculating carrier lifetimes (τ) in silicon. We qualitatively analyze two competing reactions, (i) the phonon release at the defect sites and (ii) the Auger electron process due to many electron interactions, to explain the apparent absence of any enhanced dopant diffusion. In our analyses, we obtain a highest free carrier lifetime of about 442 ns in the case of low dose (1e13/cm²) implanted sample during the transient stage (700°C) of the dopant activation cycle. The corresponding smallest (17 fs) free carrier lifetime was obtained for the high dose implanted sample (dopants already activated) at 1000°C, the steady state part of an extended anneal cycle. Based on the detailed free carrier lifetime analyses, we suggest that any enhanced dopant activation or diffusion, at the best, may occur only at very low temperatures in the samples implanted with low doses of dopant atoms.     

Hall mobility in dielectrically isolated single-crystal silicon films defined by electrochemical etching

The majority-carrier Hall mobility has been measured in thin, single-crystal silicon films defined by electrochemical etching. Both n-type and p-type films with dopant concentrations of about 10¹⁵ cm^?3 were studied. The mobilities observed in p-type thin films and in epitaxial control samples were almost identical while the mobilities measured in n-type films were markedly less than those in epitaxial control samples. This apparent anomaly is attributed to the presence of an n-type surface-charge layer with lower carrier mobility near the bottom of the thin films, although it may possibly be related to voids formed in the n-type films. Measurements on very thin samples indicated that an t-type surface layer is left on the top surface of p-type films immediately after electrochemical etching.