The current understanding of epitaxial CVD silicon doping in the light of modelling and theory development (III). The law of epitaxial layer doping and its limitation

Various doping mechanisms discussed in recent literature are applied to the theoretical concept derived in the previously published Part II of the paper, whereby a variety of hypothetical laws of dopant incorporation is revealed. Those laws cannot be distinguished from each other by doping experiments, but are testable, at least in principle. When substituting three doping-process-relevant empirical constants, all of them might be changed into that single empirical, but theory-aided model equation, which enables apitaxial layer doping to be described as a result of intended variations of the main process parameters: partial pressure of the dopant source, layer growth rate, total pressure, and deposition temperature.     

The current understanding of epitaxial CVD silicon layer doping in the light of modeling and theory development (VII)

Extension and maximum concentration of autodoping profile are discussed for both lateral and vertical autodoping phenomena and, additionally, bearing in mind the typical course of autodoping profile as obtainable by spreading resistance technique, on the background of previously published theoretical concepts of dopant incorporation. It is shown that the “improved” (three-step mechanism) as well as the “consequent” dopant incorporation concepts (two-step mechanism) are suited for theoretically explaining autodoping phenomena. If no additional supposition will be stated, however, it is a consequence of the former that the concentration maximum in the profile of vertical autodoping equals the buried-layer surface dopant concentration in agreement with non-steady state layer doping behaviour after dopant source flow has been immediately interrupted. In the contrary the latter conception simply identifies lateral and vertical autodoping effect since autodoping above as well as beyond buried layer is controlled in the same way by parasitie dopant partial pressure in the gas.     

The current understanding of epitaxial CVD silicon layer doping in the light of modeling and theory development (VIII)

Lateral autodoping along the susceptor in downstream gas direction is described to be the result of a parasitic dopant partial pressure in the gas. Parasitic dopant species are distributed from buried layer surface into the gas during the predeposition period of the epitaxy process. They are diluted as well as gathered by the gas stream along the susceptor. The parasitic dopant pressure profile along the susceptor that exists when layer deposition begins, has been modelled by deriving an exponential expression taking into account a tilted flat susceptor having constant temperature, an increase of gas temperature along the susceptor, total gas throughput, total pressure, buried layer doping level, and the ratio of buried layer area per wafer to the susceptor area related to a wafer.     

The current understanding of epitaxial CVD silicon layer doping in the light of modelling and theory development (IV). The problem of more-than-one kind of dopant species

In Part IV of the present treatise epitaxial silicon layer doping governed by the ratelimiting action of more than one kind of dopant species in the gas is investigated on the theoretical basis which has been derived in the previously published parts. It is shown that both the general reaction scheme of forward and backward reaction steps and the general differential equation statement of counterbalancing the fluxes of those reaction steps and the dopant incorporation flux are suitable for solving the problem under consideration. Only two of the four incorporation-limiting reaction mechanisms, being discussed in the more recent literature, fulfill the requirements needed to agree with experimental findings on the one hand and with the limiting case situation of equilibrium incorporation on the other. Arsenic has been selected as the demonstrating dopant element.     

The current understanding of epitaxial CVD silicon doping in the light of modelling and theory development (II). Theoretical foundations and incorporation equations

Theoretical foundations selected from related fields of science (thermodynamic and chemical equilibria, kinetics of surface-catalized reactions, open systems and steady-state equilibria, solid-state physics of semiconductors) are applied to epitaxial silicon layer doping to reveal the doping process mechanism. In this way it is shown how the empirically based relationships between the controlling parameters of the process and the doping effect (c.f. part I) can be explained by theory. In the course followed, the historical evolution is neglected in favour of the logical interconnection between the empirical and theoretical foundations.     

The current understanding of epitaxial CVD silicon layer doping in the light of modeling and theory development (IX).Verification of the Multi-wafer Autodoping Model

The multi-wafer problem of lateral autodoping has been investigated in a rectangular, horizontally arranged epitaxy reactor by arranging on the top-side As-diffused source wafers and smaller high-resistivity, p-type sensor wafers which were for indicating lateral autodoping dose after a short-lasting intrinsic layer deposition. Wafers were evaluated by sheet resistance measurements, IR-determination of layer thickness and spreading resistance profiling. A linear increase of lateral autodoping dose along the susceptor has been proved and a linearly increasing parasitic dopant partial pressure deduced. These findings give evidence for the validity of the multi-wafer model of lateral autodoping previously developed by the authors.     

The current understanding of epitaxial silicon doping in the light of modelling and theory development (VI) autodoping as a special mode of dopant incorporation

A consequent application of dopant incorporation theory to epitaxial silicon layer growth above buried layer regions explains the formation of an exponentially decaying dopant profile not only above that buried layer but also beyond of it. Taking into account desorption of dopants only and and neglecting readsorption of dopants on buried layer regions allows one to describe both vertical redistribution autodoping and lateral autodoping by the well known exponential expression that originally has been derived by Reif et al. in order to describe intended non-steady state doping behaviour and later applied to lateral autodoping by Wong and Reif. Doping incorporation theory also explains the formation of a near-equilibrium surface coverage with adsorbed dopants outside of buried layer during a preepitaxial baking process. Different dopant sources contributing to autodoping are characterized by different time constants. In this connection the adsorbed layer model derived by Tabe and Nakamura could be related to the action of two different dopant sources of autodoping where one of the two is characterized by a time constant being nearly infinite in number.     

Temperature dependence of doping element incorporation with the chemical vapour deposition of epitaxial silicon (V). Incorporation of arsenic

Based on the knowledge previously obtained with regard to the incorporation of phosphorus as an equilibrium-determined process, theoretical values of the enthalpies of the different possible incorporation equilibria are calculated for the incorporation of arsenic into the growing silicon epitaxial layer. The sublimation enthalpies of elemental arsenic, the formation enthalpy of arsine and the enthalpy of solubility enter into the equation. The results compared to the present experimental data of other authors are discussed.     

Doping of epitaxial CVD silicon with arsenic or phosphorus (II). Non-steady state conditions

Theoretical expressions are developed suggesting how the non-steady state dopant incorporation is influenced by the parameters of the layer deposition process. Expressions for the transient doping profile are dealt with taking into account two different mechanisms of the overall rate controlling step. The one is based on the assumption made by Reif and Dutton that the adsorption step, which is followed by a solution equilibrium, is the rate controlling step, the other is based on the idea that the dopant incorporation reaction and its backreaction, following after the adsorption of dopant particles, are controlling the overall incorporation.     

Doping of epitaxial CVD silicon with arsenic or phosphorus (i). Steady state conditions

A modified theoretical model of dopant incorporation is discussed, while comparing it with the Reif-Dutton model. In contrast to the Reif-Dutton model, which has been based on the adsorption step of dopant substances, the modified model is related to the real dopant incorporation step and its backreaction as the rate controlling factors. By that a thermodynamical decomposition equilibrium of the dopant source material may be established without being influenced by the dopant incorporation. Each component of the decomposition equilibrium acts as a source for making dopant atoms available for incorporation. Equivalent to the Reif-Dutton model the modified model describes the growth rate influence of the layer on the incorporation of dopants and additionally enables the temperature dependence, total pressure dependence and the specific features of dopant incorporation at high concentrations to be explained.     

On the adsorption- and equilibrium-referred interpretation of the doping element incorporation during the growth of CVD epitaxial silicon

For investigating the partial steps of CVD-silicon doping: gas transport, adsorption-desorption, incorporation, a solution reflecting the kinetic influence of the layer growth in a satisfactory way, is obtained only if specific forward and backward reactions of the incorporation step are taken into account. Regardless of assuming a thermodynamical decomposition equilibrium for the doping source material and the incorporation equilibria for each of the individual components of the decomposition equilibrium, these components are not interchangeable in representing the total incorporation flow of dopants. The incorporation process is dominated by that component which exhibits the largest relative equilibrium partial pressure.     

Suppression of epitaxial silicon layer doping with boron in the presence of hydrogen chloride

The present paper informs about thermodynamic calculations of the B Cl H system, carried out irrespective of data, already published by other authors. It further deals with recent experimental results on silicon doping with boron in the presence of hydrogen chloride, the layer growth rate being varied. Finally the possibility of quantitatively interpreting the suppressing influence of hydrogen chloride on the doping of silicon with boron is discussed.     

Temperature dependence of doping element incorporation with the chemical vapour deposition of epitaxial silicon (IV). Incorporation of phosphorus in the Si-H-Cl-lP system

The lower temperature dependence of the phosphorus incorporation with the use of phosphine together with chlorosilanes (ΔH = −13 to −15 kcal/ mole) instead of silane (ΔH = −43 kcal/mole) is explained by introducing a special incorporation equilibrium of phosphine bound to the silicon surface. The source materials phosphorus trichloride and phosphorus pentachloride may be incorporated with this equilibrium.     

Dependence of doping element incorporation on temperature in the chemical vapour deposition of epitaxial silicon (III). Empirical incorporation characteristic of the Si-P-H system

The shape of the empirical incorporation characteristic of phosphorus in epitaxial silicon, deposited from silane-phosphine-hydrogen mixtures, shows two branches with different incorporation dependences on temperature (incorporation enthalpies). In the lower phosphorus-concentration range (N < 10¹⁸) the experimentally determined value of incorporation enthalpy can be explained as a complex quantity, including the enthalpies of the two phosphorus hydrides PH₃ and PH₂, the latter of which is formed by the partial decomposition of phosphine (PH₃) at deposition temperatures. — In the upper phosphorus-concentration range (N > 10¹⁸) the incorporation equilibrium of the dimeric phosphorus molecules, formed by the nearly complete decomposition of phosphine, is reflected in the incorporation enthalpy of the empirical incorporation characteristic.     

On chemical kinetics of silicon deposition from silane (IV). In-situ phosphorus doping of LPCVD poly silicon in the temperature range 900–950 K

Highly in-situ phosphorus-doped LPCVD poly silicon deposition from mixtures consisting of silane and phosphine has been investigated for limited conditions regarding temperature, silane input, phosphine-silane ratio and total pressure. Agreeing with the deposition of undoped poly silicon, growth rate linearly decays along the axis of the wafer cage applied for in-situ doped poly silicon. In consequence layer growth should be controlled by a chemical reaction of 0.5^th order. In contrast to undoped poly silicon the slope of axial growth rate decay increases with the distance between wafers increased. This behaviour is a proof for a homogneous chemical reaction mechanism. The silicon forming reaction is characterized by an activation energy of about 25 kcal/mole for PH₃/SiH₄ = 0.003.     

The mercury pressure dependence of arsenic doping in HgCdTe, grown by organometallic epitaxy (direct alloy growth process)

The effect of Hg partial pressure on arsenic doping of HgCdTe is studied. It is found that control of Hg partial pressure is very important in obtaining reproducible doping, and use of high Hg pressure is the key to obtain heavily doped layers. Typically, a factor of 4 increase in the partial pressure of Hg is found to increase the acceptor concentration by about this same magnitude. In addition, arsine doping results in almost uncompensated layers, even though high concentration of Hg vacancies are present. A mechanism is proposed by which As is incorporated as a Cd-As complex, so that it substitutes preferentially on Te sites.     

Morphology of SiC epitaxial layers grown by temperature gradient zone melting (II). The dependence of the structural properties of the epitaxial layers on the growth conditions

In the present paper the relationships between the structural perfection of the layer, represented by the Tb average integral concentration (which is a criterion for the second phase quantity), the rocking curve half-width (a criterion for the general structural perfection of the layer) and the layer growth conditions, represented by the quantity, which is the most important characteristic of the growth process, namely the supersaturation are discussed. The considered model allows to conclude, that a optimal value of the supersaturation exists, at which the structural perfection is maximal.     

On chemical kinetics of silicon deposition from silane (III). LPCVD poly silicon formation in the temperature range 900–950 K

LPCVD poly Silicon deposition form silane has been investigated for limited conditions regarding temperature, silane input and pumping speed. It has been found that layer growth is controlled by a chemical reaction of 0.5^th-order in consequence of which growth rate linearly decays along the axis of an open isothermal reactor tube. The slope of that decay is determined not only by the reaction rate constant but also by linear gas velocity within the tube and that part of total substrate surface area that is effectively exposed to silane at each wafer position. In conseqence growth rate decay is the steeper not only the higher temperature will be chosen but also the slower gas velocity is adjusted and the smaller wafers are separated to each other. The kind of how axial layer growth rate distribution is effected by changing wafer spacing is a proof for the heterogeneous reaction mechanism. The silicon forming reaction is characterised by an activation energy of about 52 kcal/mole.     

Low-temperature growth of epitaxial (1 0 0) silicon based on silane and disilane in a 300 mm UHV/CVD cold-wall reactor

Epitaxial (1 0 0) silicon layers were grown at temperatures ranging from 500 to 800 °C in a commercial cold-wall type UHV/CVD reactor at pressures less than 7×10⁻⁵ Torr. The substrates were 300 mm SIMOX SOI wafers and spectroscopic ellipsometry was used to assess growth rates and deposition uniformities. High-resolution atomic force microscopy (AFM) was employed to verify the atomic terrace configuration that resulted from epitaxial step-flow growth. Deposition from disilane exhibited a nearly perfect reaction limit for low temperatures and high precursor flow rates (partial pressures) with measured activation energies of ≈2.0 eV, while a linear dependence of growth rate on precursor gas flow was found for the massflow-controlled regime. A similar behavior was observed in the case of silane with substantially reduced deposition rates in the massflow-limited regime and nearly a factor of 2 reduced growth rates deep in the reaction limited regime. High growth rates of up to 50 μm/h and non-uniformities as low as 1σ=1.45% were obtained in the massflow-limited deposition regime. Silicon layers as thin as 0.6 nm (4.5 atomic layers ) were deposited continuously as determined using a unique wet chemical etching technique as well as cross-sectional high-resolution transmission electron microscopy (HRTEM). In contrast, epitaxial silicon deposited in RPCVD at 10 Torr using disilane within the same temperature range showed imperfect reaction limitation. While activation energies similar to that of UHV/CVD were found, no partial pressure limitation could be observed. Furthermore, layers deposited using disilane in RPCVD exhibited a large number of defects that appeared to form randomly during growth. We attribute this effect to gas phase reactions that create precursor fragments and radicals—an effect that is negligible in UHV/CVD.