Question

450 μm 350 μm

Design a mask opening (shown as ?? in the above figure) to fabricate the given structure in Si.

Etching is performed in TMAH at 20% concentration and 90 degree celsius

Following etching rates are given:

Etching rate in (100) direction is 0.6 um/min

Etching rate in (111) direction is 0.027

Answer 1

Description	TMAH (1)	TMAH (2)	TMAH (3)
Etching solution	Tetra Methyl Ammonium Hydroxide (25%) water, 90oC	Tetra Methyl Ammonium Hydroxide (25%) water with 0.1% surfactants, 60oC	Tetra Methyl Ammonium Hydroxide (25%) 60oC
R(100)	55µm/hr	7.2 µm/hr	7.8 µm/hr
R(111)	1.4 µm/	hr 0.6 µm/hr	0.6 µm/hr
Masking layer S	SiO2 (10-4 R(100)), Si3N4	SiO2 , Si3N4	SiO2 , Si3N4
R(100) (P++ - Si):R(100)	1:40

19. _{AB } v_A (vertical etching velocity of materal A)

v_B (vertical etching velocity of materal B)

• In anisotropic alkaline etchants, the {111} planes, which have the highest atom-packing density, are nonetching compared to the other planes.

• The angle between {100} and {110} planes is 45 .

100. [110] 1 1²   0²   0²   1²   1²   0²   cos

cos                  ¹₂                  45

• The angle between {100} and {111} planes is 54.74 .

100. [111] 1 1²   0²   0²   1²   1²   1²   cos

cos                  ¹₃                 54.74

- The {111} and {110} planes can intersect each at 35.26 , 90 , or 144.74 .

[100]-oriented silicon

-        Provided that a mask opening is accurately aligned with the primary orientation flat, only {111} planes will be introduced as sidewalls from the very beginning of the etch. During etching, truncated pyramids or truncated V-groove depend but not widen. The edges in these structures are <110> directions, the sidewalls are {111} planes, and the bottom is a (100) plane parallel with the wafer surface.

After prolonged etching, the {111} family of planes is exposed down to their common intersection, and the (100) bottom plane disappears, creating a pyramidal pit (square mask) or a V-groove (rectangular mask)

• The width of the rectangular or square cavity bottom plane, W₀, aligned with the <110> directions, is completely defined by the etch depth, z, the mask

opening, W_m, and the above-calculated sidewall slope:

W₀     W_m     2z cot 54.74

W₀     W_m   2 z

• The etch stop at the {111} sidewalls’ intersection occurs when the depth is ~0.7 times the mask opening. If the oxide opening is wide enough, W_m > 849 m (for a typical 6-in wafer with thickness t_Si = z = 600 m), the {111} planes do not intersect within the wafer.

A groove etched in [110] wafers has the appearance of a complex polygon delineated by six {111} planes, four vertical and two slanted (Inset 4.4).

Inset 4.4 Etched structures are delineated by four vertical {111} planes and two slanted {111} planes. The vertical {111} planes intersect at an angle of 70.5 .

111. [110] 0 3 2 cos90
112. [110] 0 3 2 cos90
113. [110] 0 3 2 cos90
114. [110] 0 3 2 cos90

111. [110] 2 3 2 cos35.26

111. [110] 2 3 2 cos35.26

111. [110]   2 3 2 cos144.74   180   35.26

111. [110]   2 3 2 cos144.74   180   35.26