On batch homogeneity in horizontal CVD reactors (I). Model of heating the process gas

A model of heating of the process gas during its flow along the heater is given as a supposition for a modelling of the batch homogeneity with layer deposition and gas phase etching processes in horizontal CVD-reactors. An analytical expression is derived for the resulting longitudinal temperature profile T(x) in dependence of gas properties, suszeptor temperature, geometric parameters of the reactor, and gas flow rate.     

A unified treatment of thickness homogeneity problems in CVD (II). Cold-wall reactors

Chemical vapor deposition in susceptor-heated horizontal reactors is included into a simple treatment of reactant depletion and its compensation, given previously. Extending the model of EVERSTEYN et al. (including thermodiffusion), the whole range from diffusion control to reaction control is covered. At diffusion control, the condition for constant deposition rate along large reactor lengths cannot be satisfied by the usual tilting of a plane susceptor out of the direction of the main gas stream. From this point of view, the model statements (at least in the approximation that neglects entrance effects) are less favorable than for vertical epitaxy reactors.     

A unified treatment of thickness homogeneity problems in CVD (I). Hot-wall reactors

The principal possibilities and limitations for improving macroscopic layer thickness homogeneity in the direction of the main gas stream in chemical vapor deposition (CVD) for electronic purposes are discussed. Approximative expressions are given for optimum temperature profiles in surface reaction-controlled deposition of polycrystalline and amorphous layers, as well as for the optimum tilting angle of substrates out of the main gas stream in diffusion-controlled deposition of epitaxial layers.     

Investigations on the HCl gas-phase etching of differently doped and oriented gaas crystals

The influence of the orientation and dopant on the dissolution of GaAs surfaces in H₂–HCl gas mixtures has been investigated. For this purpose the etch rates, temperature regions of different etching behaviour and the corresponding activation energies were determined for temperatures ranging from 540 °C to 945 °C. The etch rate anisotropy is correlated with the three existing temperature regions of different dissolution mechanisms. The orientation-dependent transition temperatures are influenced by the dopant and can be related to the thermodynamic data of the dopant.     

Basic steps and layer homogeneity in CVD [II]

Taking into account reactant depletion, gas diffusion, surface processes, and a fourth basic step that is connected with the influence of surface equilibria, the compensation of depletion is treated for both host material deposition and in-situ doping. So, some aspects can be given for the realization of layer homogeneity in epitaxy, as well as in LPCVD. In conclusion, the terminology of border cases in CVD is discussed.     

Basic steps and layer homogeneity in CVD (I)

As a first basic step in chemical vapor deposition (CVD), reactant depletion within batchtype reactors is treated. By introduction of a depletion resistance into the circuit representation of epitaxy and of LPCVD processes, the joint treatment of problems concerning layer thickness and doping homogeneity becomes more transparent. In the case of compensated depletion, this resistance increases linearly with the distance from the reactor input, and is independent on the kind of reactants if gas diffusion is negligible in the down stream direction. Without compensation it becomes nonlinear in the downstream local coordinate and depends on the resistance of the subsequent basic steps. Aspects of lowering the depletion 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.     

On Some Transition Metal Complexes Having Orientational Properties(II). Copper(II) complexes

Alignment layers containing copper(II) complexes with acrylic acid or polyvinylpyrrolidone show homeotropic orientational properties. This behaviour is supposed to be due to the particular structure of the complex copper(II) ions. We give spectroscopic arguments to support the anchoring of liquid crystal (LC) molecules by coordination to the copper ion within the alignment layer.     

Simplified treatment of transient doping behaviour in CVD (II)

Using circuit representations, the influence of the deposition rate for semiconducting CVD layers on transient behavior of doping concentrations is rechecked for a simple decomposition reaction of the dopant species. The existence of a space-charge region below the surface is taken into account. Simple estimations show that atomically abrupt doping transitions are to be expected, if the storage of foreign atoms in the surface is responsible for transient behaviour, and if their concentration becomes frozen in. In order to explain flatter doping profiles occurring with As and P in Si, molecular storage has to be included in the study. Only some simplified cases with one capacitance, or a sum of capacitances, in the circuit representation are being treated.     

Transport phenomena analysis for boron CVD in a horizontal cold-wall reactor

The transport phenomena in a horizontal cold-walled semicircular reactor are analyzed for the CVD of boron from BCl₃ and H₂. The mixed problem of energy, momentum, and mass conservations is solved by a simple finite difference method. The concentration of the B-reactant on the deposition surface is substituted by the sum of equilibrium mole fractions of the B-containing gas species. The profiles of temperature, velocity, and reactant concentrations in the CVD reactor are illustrated, and the boron deposition rate profile along the substrate is predicted. The effect of the reactant input composition on the deposition rate is calculated, and compared with the experimental data.     

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.     

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.     

Nonstoichiometry in steps on AB crystals (II). Extended treatments

Concentrations of atoms with different numbers of nearest neighbours, and of the kink and non-kink positions between atoms in step fronts, have been calculated by two treatments. The results differ in the general case, but agree in cases with extreme nonstoichiometry as well as in nearly stoichiometric cases. With respect to the relevance of the model calculations, further investigations are necessary on step reconstructions, on the positions of stability limits of AB compounds in terms of step nonstoichiometry, and on the possibility of roughening transitions in connection with step nonstoichiometry. With increasing nonstoichiometry in the steps, neighbouring kink positions, and the corresponding neighbour-kink atoms become increasingly important. In contrast to this, the concentrations of double kink positions become smaller, and they vanish in the extreme cases where the PBC-directed steps consist merely of A, or of B neighbour-kink atoms. These concentrations are negligible in the extended model calculations at sufficiently low temperatures, together with concentrations of triple and further multiple kink positions.     

A method for determination of size-dependent crystal growth kinetics from batch experiments (I). One-experiment estimation

The method developed for determining size-dependent crystal growth kinetics makes use of the assumption that the linear growth rate is a product of a size-dependent factor and a supersaturation-dependent one. The transformed form of the population balance equation, obtained by means of this assumption, is the basis of the evaluation utilizing measurement data from one seeded batch crystallization experiment, namely the size distributions of the seed and product crystals as well as the supersaturation course. The application of the method is illustrated by evaluating an experiment with potash alum crystals.     

On the deposition mechanism of boron in silicon CVD epitaxy

The deposition mechanism of boron doping in CVD silicon epitaxy has been investigated by exposing silicon substrates to B₂H₆ H₂ doping gas mixtures at epitaxy temperatures and examining the effect by dopant profile measuring in an afterwards intrinsically in-situ deposited epitaxial silicon layer. It has been shown that boron is deposited increasing its concentration on the surface linearly with prolonged exposition time and desorbed by purging the surface in pure hydrogen. In the latter case its content decreases linearly proportional to the predeposited concentration. The desorbed boron builds up a secondary doping source which maintains a parasitic boron flow for reincorporation during following layer growth.     

Vibrational Properties of LiGaO2 (II). Theoretical Model Considerations

On the basis of the correlation method and of a simplified version of the extended Keating model with bond-bending forces neglected sphalerite- and chalcopyrite-like modes can be identified in the lattice vibration spectrum of LiGaO₂. In agreement with recently published results for LiInTe₂ it is found that the Li O bond is considerably weaker than the Ga O bond.     

Doping process control in silicon epitaxy (II). Calculation of optimum control

A procedure is developed to obtain desired dopant profile in epitaxial layer growth. Based an the results of system identification, linear-quadratic optimal control theory is used to determine the optimal input PH₃ concentration as a function of time. In the performance index an auxiliary weighting coefficient must be incorporated. It is discussed how to select this weighting coefficient.     

In-situ doping of LPCVD poly silicon (II). Temperature influence

Poly silicon deposition by pyrolysis of silane under low pressure conditions has been investigated with respect to the influence of temperature when simultaneously in-situ doping of the deposited layer takes place. The growth rate of poly silicon is retarded in the presence of phosphine provided that a certain lower PH₃/SiH₄-ratio has been exceeded. It has been shown how that lower ratio depends on temperature. Increasing PH₃/SiH₄-ratio not only slows down layer growth rate but also the apparent activation energy of the layer forming reaction. An empirical equation describing the temperature dependence of that activation energy has been derived. Phosphine adsorption has been discussed as a cause of both layer growth rate and activation energy reduction. Additionally, incorporation of phosphorus during layer growth has been investigated with respect to the total amount and the electrically active concentration, the latter measured after a postdeposition anneal at 1000 °C.     

Temperature distribution in growing semi-transparent crystals (II). Comparison of theory with experiments

Calculated temperature difference between the liquid/solid interface and bulk of the melt was compared with the wide-angle scattering (celluae density) of Al₂O₃ and YAG crystals. Celluae free coloured crystals were grown using higher energy losses from the upper part of the crystal and the melt. Colourless crystals were successfully grown under opposite conditions. The results are in accordance with the calculated temperature differences which are proportional to the actual temperature gradient at the interface.