Radiation and convection cooling of the substrate

Qr is the energy loss per second by a surface at temperature Ts to its surroundings at temperature Tm, the emissivity of the substrate being e, the view factor F being the fraction of the emitted radiation which is absorbed by the cool surroundings, and a being the Stefan-Boltzmann radiation constant (5.67 x 10 8Jm 2s XK 4). In the present case, the emissivity will have a value of about 0.2-0.3 for the metallic substrates, but nearly unity for the non-metals. The view factor can be assumed to have a value of unity in the normal situation where the hot substrate is enclosed in a cooled container. 

There will also be heat loss from the substrate due to convection currents caused by the temperature differential in the surrounding gas phase, but this will usually be less than the radiation loss, because of the low value of the heat transfer coefficient, h, of gases. The heat loss by this mechanism, Qc, can be calculated, approximately, by using the Richardson-Coulson equation 

There are therefore two ways in which lasers may be used to bring about photon-assisted film formation. If the laser emits radiation in the near-ultraviolet or above, photochemical decomposition occurs in the gas phase and some unabsorbed radiation arrives at the substrate, but this latter should be a minor effect in the thin film formation. This procedure is referred to as photolysis. Alternatively, if the laser emits radiation in the infra-red, and the photons are only feebly absorbed to raise the rotational energy levels of the gaseous 

Because of the possibility of focusing laser beams, thin films can be produced at precisely defined locations. Using a microscope train of lenses to focus a laser beam makes possible the production of microregions suitable for application in computer chip production. The photolytic process produces islands of product nuclei, which act as preferential nucleation sites for further deposition, and thus to some unevenness in the product film. This is because the substrate is relatively cool, and therefore the surface mobility of the deposited atoms is low. In pyrolytic decomposition, the region over which deposition occurs depends on the thermal conductivity of the substrate, being wider the lower the thermal conductivity. For example, the surface area of a deposit of silicon on silicon is narrower than the deposition of silicon on silica, or on a surface-oxidized silicon sample, using the same beam geometry. 

The energy densities of laser beams which are conventionally used in the production of thin films is about 103 — 104Jcm 2s, and a typical substrate in the semiconductor industry is a material having a low thermal conductivity, and therefore the radiation which is absorbed by the substrate is retained near to the surface. Table 2.8 shows the relevant physical properties of some typical substrate materials, which can be used in the solution of Fourier s equation given above as a first approximation to the real situation. 

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