PVD by Evaporation

I. Evaporation Basics

The rate of free evaporation of vapor atoms from a clean surface per unit area in vacuum, Mc, is given by Langmuir's equation:
		Mc=5.85*10^(-2)*P*(M/T)^0.5  	g*cm^(-2)*s^(-1)

Where 	P=vapor pressure of evaporant under saturated vapor conditions at temperature T, torr or mmHg.
	M=molecular weight of evaporant material
	T=absolute temperature, K   

Alternatively, we may write the evaporation rate as
		Ne=3.51*10^22*P*(MT)^(-.5)	molecules*cm^(-2)*s^(-1)

where Ne=rate of evaporation of vapor molecules per unit area in vacuum

(a)Profile of vapor material condensed at different angles. (b) Schematic of a surface element receiving coating from a small-area source

The directionality of the evaporant molecules leaving the source is given by the well-known cosine law :

Small source surface area dA1 emitting a vapor flux M. Then the material passing through a solid angle phi at a direction of angle psi with the normal to the surface dA1 per unit time is:
		dM=(M/PI)*cos(phi)*cos(psi)

Material arrived at a small substrate area dA2 inclined at an angel theta to the vapor stream direction at a distance r from the source is given by:
		dM=M*cos(phi)*cos(theta)*dA2/(PI*r*r)
For a point source,
		dM/dA2=M*cos(phi)/(PI*r*r)


II. Details of Evaporation Processes