A simulation of the substrate stress induced by a nitride film is shown below. This example can be found in the examples/exam8 directory under the name. A <111> substrate is considered with mask edges aligned along the <110> directions. The nitride film is 0.02 microns thick. The intrinsic stress in the nitride is assumed to be 1.4E10 dynes/cm2, as reported in Irene [1]. The input deck for the simulation begins as follows.
# # nitride on silicon example foreach SEP ( 10 5 4 2.5 ) line x loc=( - SEP ) tag=l line x loc=-2 spac=0.3 line x loc= 0 spac=0.1 tag=m line x loc= 2 spac=0.3 line x loc= ( SEP ) tag=r line y loc=0 spac=0.1 tag=si line y loc=2 spac=0.3 line y loc=5 tag=b region silicon xlo=l xhi=r ylo=si yhi=b bound expos xlo=l xhi=r ylo=si yhi=si initial ori=111Quite a large piece of substrate is analyzed, starting with a space 10 microns by 5 microns. The foreach loop chooses four different widths to examine the effect of different stripe separations. The structure being simulated has reflecting boundary conditions (no perpendicular displacement) on the left and right sides. Those boundary conditions correspond to a single instance of a repeating pattern of nitride stripes. When the stripes are widely separated, there is little interference between the stress field of one stripe and the next, and the results are found to be independent of the stripe separation. At smaller separations, the patterns begin to overlap. This example will show the stress pattern for widely separated stripes and the modifications that occur as the stripes are brought closer together.
The backside of the wafer also has a reflecting boundary condition. Although that approximation is not quite physical, the nitride film primarily exerts a horizontal force on the substrate, the assumption does not seriously affect the result. This can be verified by using different backside thicknesses; 2 microns or 100 microns gives identical results. The exposed surface is the only surface with free displacements. The spacing around the film edge is 0.1 microns. This could be reduced for more accuracy, at the cost of more cpu time.
deposit nitride thick=0.02 div=2 etch nitride left p1.x = 0The nitride is deposited directly on silicon and patterned.
material intrin.sig = 1.4e10 nitrideThe initial nitride stress is specified in dynes/cm2.
stress temp1=1000 temp2=1000This calculates the stress distribution arising from the nitride initial stress. Stress arising from thermal expansion mismatch would be included by specifying a different temp2. Be warned that large thermal steps often bring into play many more complicated phenomena than the simple thermal expansion mismatch analyzed in SUPREM-IV.GS. For instance breakdown of film adhesion or structural change may occur, but are not taken into account in the program.
The principal slip system in silicon is in the <110> direction on 111 planes. This corresponds to the sxy shear force in the plane of the simulation. The value 3.0E7 is considered by Hu[2] to be the critical shear stress for slip in silicon. Dislocations found in regions where the shear stress is larger than that value will move under the stress field of the nitride film. Therefore when analyzing stress in the substrate, a principal concern is the extent of the sxy equal to 3.0E7 contour.
plot.2 bound x.mi=-2 x.ma=2 y.ma=4 cl=f select z=Sxy contour val=-3e7The contours of sxy equal to 3.0E7 in the silicon are shown in Figure 1. The contour is a double lobe because the shear stress is related to the polar components of stress through sxy = ( srr - sqq) sin 2q + srq cos 2q srr sin 2q. The function sin 2q is at a maximum around 45 degrees from the vertical, and is zero at q = 90. Both srr and cos 2q change sign moving from left to right, so that the sign of sxy is the same throughout. This means that a dislocation which is being driven under the mask by the stress field will continue to move in that direction after passing the mask edge. However as it passes through the center, the decrease in shear stress may leave it stranded under the mask edge. Figure 1 shows that the area of influence of the nitride film is many times greater than its thickness, about 2 microns horizontally, and 1.5 microns vertically.
The largest lobe corresponds to the 10 microns stripe. The result for the 5 microns stripe lies so closely on top that it cannot be distinguished. Thus either can be a reasonable approximation for infinitely separated stripes. The 4 microns and 2.5 microns lobes are somewhat smaller. This shows that the shear stress fields from neighboring stripes tend to cancel each other in their overlap areas, reducing the influence of the nitride film somewhat.