Patent ID: 8501026

Claim:
A method for determining a minimum tension compensation stress (σ 0 ) with which is provided a membrane having a thickness of less than or equal to one micrometer, secured to a frame, having, in the absence of an external stress, a desired deflection (desired h) equal to k times its thickness (e) with k comprised between about 0.05% and 20% of its thickness wherein: a) dimensions for the membrane, including a length b, a width a and its thickness e, a material so as to have a Young modulus E and a Poisson coefficient ν, a residual stress σ residual which may be zero, and the desired deflection, are selected; b) a weight of the membrane is calculated, expressed by ρge with ρ being the density of material of the membrane and g the acceleration of gravity; c) the weight is applied in the following formula (1), by assimilating it to a pressure which is uniformly exerted on the membrane, P = E 1 - v ⁢ e 3 ⁢ h a 4 ⁡ [ 1 12 ⁢ ⁢ β ⁡ ( 1 + v ) + C ⁢ ⁢ h 2 e 2 ] + C * ⁢ σ residual ⁢ eh a 2 ( 1 ) h being a calculated deflection of the membrane, β, C and C* being coefficients relating to form factors of the membrane, depending on the following quantities: length, width, thickness of the membrane, its Poisson coefficient, its Young modulus, density of the material of the membrane and residual stress; d) the coefficients β, C and C* are calculated by injecting into a suitable mechanics software package, the quantities on which they depend; e) the calculated deflection h of the membrane is inferred from formula (1); f) the calculated deflection is compared with the desired deflection; g) if this calculated deflection is greater than the desired deflection, and if the residual stress is zero, a residual tensile stress is imposed to the membrane, while if the residual stress is non-zero, it is increased so that the calculated deflection is less than or equal to the desired deflection; h) when the calculated deflection is less than or equal to the desired deflection, the minimum tension compensation stress of the membrane secured to the frame in the absence of an external stress is calculated, this minimum tension compensation stress being expressed by equation (2): σ 0 = - E ( 1 - v ) ⁢ e 2 C * ⁢ a 2 ⁡ [ 1 12 ⁢ ⁢ β ⁡ ( 1 + v ) + C ⁡ ( k ) 2 ] + ρ ⁢ ⁢ ga 2 C * ⁢ ke . ( 2 )