Optical characterization of heavily doped silicon

Out of a variety of optical techniques used to characterize heavily doped semiconductors photoluminescence and Raman spectroscopy will be discussed as tools to study heavy doping effects. Photoluminescence spectroscopy is sensitive to electronic transitions between the conduction and valence band whereas electronic Raman scattering probes transitions within either band. Parameters relevant to device physics such as the band gap shrinkage due to heavy doping are extracted from these measurements. It is further shown that both techniques are applicable to the characterization of thin heavily doped implanted or epitaxial layers.     

Bandgap narrowing in moderately to heavily doped silicon

A model of bandgap reduction in silicon through the stored electrostatic energy of majority-minority carrier pairs is developed and compared with experimental results in the doping range from 3 × 10¹⁷to 1.5 × 10²⁰/cm³at room temperature. An analytic expression for the bandgap reduction in nondegenerate material is obtaineddeltaepsilon _{g} = 3q^{2}/(16pi epsilon) cdot (q^{2}n/epsilonkT)^1/2having a square-root dependence on the majority carrier concentration. At room temperature this becomesdeltaepsilon _{g} = 22.5 (n/10^{18})^{1/2}meV. In degenerate material, the bandgap reduction is independent of temperature, following the relationshipdelta epsilon _{g} = 162 (n/10^{20})^{1/6}meV. The experimental data at room temperature are in excellent agreement with this theory. Plots of bandgap narrowing as a function of doping level are presented for a number of temperatures.     

Measurement of hole mobility in heavily doped n-type silicon

Accurate measurements of the mobility (and diffusion coefficient) of minority-carrier holes in Si:P with doping in the 10¹⁹cm^-3range have been done. The technique employed the measurement of diffusion length by means of lateral bipolar transistors of varied base widths, and the measurement of minority-carrier lifetime on the same wafers from the time decay of luminescence radiation after excitation with a short laser pulse. Minority-carrier hole mobility is found to be about a factor of two higher than the mobility of holes as majority carriers in p-type Si of identical doping levels.     

Modelling of minority-carrier transport in heavily doped silicon emitters

The transport and recombination of minority carriers in heavily doped emitters plays a crucial role in the performance of silicon bipolar transistors and solar cells. In the past, only order-of-magnitude prediction of the value of the current injected into a heavily doped emitter was possible. The limitations to a more accurate modelling stemmed from: (1) the incomplete understanding of the physics of minority carriers in heavily doped semiconductors; (2) the lack of precise measurements of the relevant material parameters; (3) the difficulties encountered with the modelling of transport and recombination in non-homogeneously doped regions, and (4) problems with the characterization of “real” emitters of bipolar devices. This paper reviews recent experimental and theoretical efforts that addressed some of these issues, with the goal of being able to achieve accurate modelling of the current injected into an arbitrary heavily doped region in a silicon device.     

Electrical trimming of heavily doped polycrystalline silicon resistors

The newly discovered phenomenon of resistance decrease in heavily doped polycrystalline silicon resistors by conduction of high current densiy has been investigated experimentally. Threshold values exist for the impurity concentration and for the applied current density for the occurrence of this phenomenon. Decreased resistance is stable as far as current higher than the threshold value is not applied thereafter. Applications to D/A converters and operational amplifiers are described. Electrical trimming of resistors in the circuits with accuracy of ±0.01 percent is easily attained.     

Optical silicon lifetime measurements in heavily doped diffused regions

Monochromatic visible light at various wavelengths was used to generate photocurrent in a silicon n+-p diffused diode. A numerical model which includes electric field, heavy doping band gap reduction and doping level mobility dependence was used with fitting techniques to determine the carrier lifetime in the n+-region at each wavelength.     

Measurement of the minority-carrier transport parameters in heavily doped silicon

A new method for simultaneous measurement of bandgap narrowing and diffusion length in a heavily doped n⁺substrate is proposed. The method uses planar test pattern at the front side of the substrate to determine the hole minority-carrier current injected from a p-type emitter and diodes at the rear side to measure diffusion lengths. The method can be generalized such that the minority-carrier diffusion constant can be estimated and the use of extrapolated literature data can be avoided. Results of measured values of bandgap narrowing and diffusion length versus impurity concentration are given for n-type material.     

Infrared luminescence from silicon nanostructures heavily doped with boron

Intense highly polarized radiation from silicon nanostructures heavily doped with boron to 5 × 10²¹ cm⁻³ is studied as a function of temperature, forward current, and an additional lateral electric field. The features of the radiation intensity and degree of polarization suggest that an important role in the formation of the luminescence spectra is played by the ordered system of B⁺-B⁻ dipoles, formed as a result of the reconstruction of shallow boron acceptors as centers with negative correlation energy. The results obtained are interpreted within a proposed model based on two-electron adiabatic potentials, according to which radiation results from donor-acceptor recombination via boron dipole center states, involving shallow phosphorus donors.     

Measurement of steady-state minority-carrier transport parameters in heavily doped n-type silicon

The relevant hole transport and recombination parameters in heavily doped n-type silicon under steady state are the hole diffusion length and the product of the hole diffusion coefficient times the hole equilibrium concentration. These parameters have measured in phosphorus-doped silicon grown by epitaxy throughout nearly two orders of magnitude of doping level. Both parameters are found to be strong functions of donor concentration. The equilibrium hole concentration can be deduced from the measurements. A rigid shrinkage of the forbidden gap appears as the dominant heavy doping mechanism in phosphorus-doped silicon.     

Redistribution of phosphorus implanted into silicon doped heavily with boron

The special features of redistribution of phosphorus implanted into silicon wafers with a high concentration of boron (N _B=2.5×10²⁰ cm^?3) were studied. It is shown that, in silicon initially doped heavily with boron, the broadening of concentration profiles of phosphorus as a result of postimplantation annealing for 1 h in the temperature range of 900–1150°C is significantly less than in the case of lightly doped silicon. The results are interpreted in terms of the impurity-impurity interaction with the formation of stationary boron-phosphorus pairs. The binding energy of boron-phosphorus complexes in silicon was estimated at 0.6–0.8 eV.     

The spectral response and efficiency of heavily doped emitters in silicon photovoltaic devices

An analytical model of the spectral response and efficiency of an emitter is developed. The model is valid for an emitter of any thickness or any doping concentration and profiles. Explicit expression for the spectral response and efficiency of the emitter are derived. They take into account the space dependent mobility μ_p, band gap narrowing ΔE_g, lifetime and electric field. The expression reduces to simpler forms for quasi-transparent and transparent emitters. It is found that unlike a dark emitter, the effect of electric field on the behavior of the illuminated emitter is not negligible. The effect of change in ΔE_g and μ_p models on the spectral response and efficiency of the emitter is discussed. An increase in ΔE_g degrades the performance of the emitter. An increase in μ_p at high doping also degrades the behavior but only if the surface recombination velocity S_p is large. If S_p is very small, an increase of μ_p improves the spectral response and the efficiency of the emitter. The results calculated theoretically are in good agreement with the experimental results of Ref. [25] both for thin and thick emitters except for λ ≤ 0.4 μm and λ > 1.0μm. This discrepancy is attributed to the uncertainties in the experimental values of α at these wavelengths. It is shown that the value of μ_p at high dopings can be determined from the spectral response measurements provided that the value of S_p can be determined accurately from other independent measurements.     

Comparison of theoretical and empirical lifetimes for minority carriers in heavily doped silicon

The minority carriers determine essential electrical characteristics of bipolar devices and bipolar-like parasitic paths in field effect devices. The electrical behavior of such devices is frequently described by detailed device models. Compared to the other input parameters for detailed device models, the minority carrier lifetimes due to traps or defects as functions of doping density have great uncertainty. Detailed device models, which include the contributions of both Auger recombination and Shockley-Read-Hall processes to this lifetime, give correct values for the d.c. common emitter gain of npn transistors with shallow, heavily doped emitters. However, those models which include commonly used empirical expressions for the above lifetime do not predict correct values for the gain. The physical significance of these device modeling results involves competition between trapping of carriers and Auger recombination when donor densities lie within the decade of 10¹⁹ cm^?3. An example of the foregoing competition is given by applying detailed device models to an npn transistor with an emitter surface concentration of 2.3 × 10²⁰ cm^?3 and with an emitter-base junction depth of 1.1 μm. A major finding in this paper is that the commonly used empirical expressions for the lifetime due to defects may not give correct results when included in detailed models of shallow, heavily doped silicon emitters.     

Evidence of bandgap-narrowing in the space-charge layer of heavily doped silicon diodes

The gradient voltage has been measured for seven heavily doped, graded-junction silicon diodes at 300 K. Experimental values up to nearly 0.5 V lower than conventional theoretical predictions have been observed. The lowering is attributed to bandgap-narrowing in the space-charge region. This narrowing is expected to be much larger than in neutral material of the same doping density because of the absence of free-carrier screening.     

A simple method of calculating the minority-carrier current in heavily doped silicon

It is shown that the calculation of the one-dimensional minority-carrier current density in heavily doped silicon can be described by two coupled differential equations of the first order. These equations are derived with a minimum of assumptions and approximations and without the explicit use of an electric field. The relevant input parameters to these equations are the product of the equilibrium hole density with the diffusion coefficient and the product of the equilibrium hole density with the reciprocal value of the lifetime. These equations can very easily be solved numerically and the solution gives the minority-carrier density and the current density as a function of space coordinate. It is shown that values of the band gap narrowing cannot be derived from current measurements alone.     

Simulation of low-temperature arsenic diffusion from a heavily doped silicon layer

Low-temperature (500–800°C) diffusion of As from a heavily doped Si layer was simulated on the basis of a dual pair mechanism. The anomalously high diffusion rate is attributed to excess self-interstitials accumulated in the layer during the preceding high-temperature diffusion stage. The shift of the concentration profile in the region of intermediate values of concentrations is caused by the presence of a maximum in the concentration dependence of the diffusivity. This shift is attributed to the considerable role that negatively charged self-interstitials play in the arsenic diffusion process (f _I ^? ≈0.4).     

Nitrogen doped silicon films heavily boron implanted for MOS structures: Simulation and characterization

In this work we study the boron diffusion and its activation into recrystallized nitrogen doped silicon thin films (NIDOS) and we also discuss the influence of the chemical interaction between boron and nitrogen in NIDOS films. These films are deposited by low pressure chemical vapor (LPCVD) for the development of a P⁺ polysilicon gate for MOS structures. The reduction of boron diffusion with increasing nitrogen content is observed by SIMS profiles. SUPREM IV software is used in order to estimate the boron diffusion coefficients in NIDOS films. FTIR analyses show the appearance of a B–N complex whose density strongly depends on the annealing treatment in terms of temperature and duration. It is deduced through resistivity measurements and SEM observation that the formation of B–N complexes tends to degrade the electrical properties of polysilicon thin layers through the decrease of both electrically active boron and polycrystalline grains growth.