# Deposition Rate of Chemical Vapor Deposition

Chemical Vapor Deposition (CVD) is the process used to deposit thin film of solid material in various applications like fabrications of novel powder, fiber, preforms of ceramic composites, coatings for corrosion and wear resistance, and synthetic diamond. It is the most widely used technique in IC microfabrication for the oxide and nitride layers of the wafers. CVD process grows the film by chemically combining the material to an organic reactant and transports the chemical precursor to the target surface, which is energized either through heat, ion, or photon. The energy in the target drives the chemical reaction between the surface and the precursor to break the chemical precursor and incorporate the material to the growing film on the surface. (see Reaction Mechanisms of Chemical Vapor Deposition)

Reaction-Rate Limited Deposition

The two factors which affect the rate of film growth or the flux of the material in a CVD process are gas diffusion and surface process. As defined by Fick’s Law, the material’s flux to the substrate is a function of gas diffusion coefficient, concentration gradient of the layer, length of the surface for that will be deposited, and Reynold’s number – a dimensionless gas constant. Mathematically, the flux of the material is

Fl = D Δc/2L 3√(Re           Equation 1

Since Reynold’s number is directly proportional to gas velocity, film growth rate is, therefore, also dependent on the square root of gas velocity. Moreover, gas velocity and gas flow rate is proportional to each other in a fixed volume reaction chamber.  Thus, film growth rate can be expressed as a function of gas flow rate, which is outlined in figure 1. The plot manifests the square root dependence of growth rate on flow rate as the former logarithmically increases with the latter.

However, there is a point where the growth rate saturates and becomes independent of the flow rate, which means no matter how much the flow rate is increased it cannot anymore affect the film growth rate. Once this happens, reaction rate takes over the control on deposition as demonstrated in the reaction-rate limited regime or the Arrhenius plot in figure 2 where growth rate is exponentially dependent on temperature. For a thermally driven surface reaction, the film growth rate can be mathematically modeled by:

R = Roe-Ea ⁄ kT            Equation 2

where,

Ro is the frequency factor

Ea is the activation energy in electron Volt (eV), which is presumed to be approximately equal to the slope of the Arrhenius plot in Figure 2

T is temperature in Kelvin (K) Figure 1. Film growth rate as a function of gas flow rate (photo courtesy of book title here) Figure 2. Film growth rate as a function of temperature (photo courtesy of book title here) Figure 3. Vertical and Horizontal Wafer Stacking (photo courtesy of book title here)

In a practical application, reaction-rate limited allows low pressure chemical vapor deposition (LPCVD) to stack the wafers vertically with very minimal spacing in between since the rate of reactant transport holds lesser importance (see Figure 3).  The diffusivity, D, of the reactants in a LPCVD reactor of ~1 Torr is magnified to 1000 times than its value at atmospheric pressure, which increases the arrival rate of the reactants to the substrate to one order of its current magnitude. Thus, the rate limiting step dominates the surface reaction control.

Mass-Transport Limited Deposition

On the other half of figure 2, excessive increase in temperature banishes the effect of reaction rate on the growth rate. At this regime, reaction rate cannot exceed anymore the rate at which the reactant gases are transported on the surface, no matter how high the temperature is. For this phase of rate-limiting reaction, which is known as the mass-transport limited deposition, growth rate is approximately equal to the square root of gas velocity.

Aside from the derived flux equation from Fick’s law (equation 1), the flux of the material, without considering its diffusion through the layer, can also be expressed as

Fl = h(CG-CS)          Equation 3

where,

h is the mass transfer coefficient

CG is the reactant concentration at bulk of gas and

CS is the reactant concentration at substrate surface.

Moreover, the mass transport on a motionless layer in a CVD process is deduced to proceed by diffusion. Mathematically, this assumption is

Fl = D ( (CG-CS) / δ)          Equation 4

Equating equations 3 and 4, yields to

h (CG-CS) = D ( (CG-CS) / δ)

h = D / δ          Equation 5

For mass-transfer limited deposition D = 1. Thus, growth rate in this regime is

R = h = 1/δ = √U          Equation 6

Unlike in the reaction-rate limited regime where temperature owns the main control on growth rate, temperature is less important in mass-transport limited since its level does not limit the deposition rate. Applications for mass-transport limited like the atmospheric pressure chemical vapor deposition (APCVD) operate with the wafers stacked horizontally such that the flux of the reactant species is equally distributed to every corner of the wafer as well as of the other wafers.

Flow Stability

Uniform deposition requires stability of the flow in a CVD reaction chamber, which greatly depends on its laminar development before reaching the susceptor. As predicted by Schlichting, the flow entrance length for a full velocity profile is given by the equation

IF = 0.04HRe          Equation 7

where,

H is height of the flow channel

Re is Reynold’s number

However, the thermal entrance length for a fully developed radial profile is seven times longer than its velocity entrance length.

IF = 0.28HRe          Equation 8

The characteristic of the flow of the gaseous reactants in a CVD process can be measured through a dimensionless gas constant known as Knudsen number (Kn). Knudsen number is defined as the ratio of the average distance that a molecule travels before colliding with another molecule or the molecular mean free path (λ) to the flow field length (L), which, in wafer fabrication’s case, is the size of the device structure. Knudsen number classifies the gas flow as:

• continuum if Kn<0.01
• slip if Kn is in between 0.01 and 0.1
• transition if 0.1<Kn<10
• free molecular for Kn>10

The reactant flow on the substrate usually falls on the transition or free molecular classification. As for the λ, the typical λ in a CVD process ranges from 0.1 microns to >100 microns at 100 Torr. But since the trend for the integrated circuits is to shrink up to the nanometer range, the λ may not be enough to attain uniform thickness over the whole process. For the industry to overcome this challenge on uniformity, the dominance of the molecular flow must be maintained by operating on very low pressure chemical vapor deposition (VLPCVD).

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