• Infrared and Laser Engineering
  • Vol. 51, Issue 3, 20210276 (2022)
Jun Ma
Author Affiliations
  • Beijing Institute of Space Mechanics & Electricity, Beijing 100094, China
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    DOI: 10.3788/IRLA20210276 Cite this Article
    Jun Ma. Coplanarity evaluation model of long linear LWIR detector[J]. Infrared and Laser Engineering, 2022, 51(3): 20210276 Copy Citation Text show less

    Abstract

    Due to the influence of thermal stress and boundary conditions, the long linear long wave infrared(LWIR) detector will deform when it works, which may damage the chip or make the photosensitive surface un-confocal. The coplanarity evaluation of the detector under the condition of thermal-mechanical coupling is one of the important contents of the design of long linear LWIR FPA. The factors that may cause detector deformation were analyzed, and the main factors were identified by finite element model(FEM) simulation. Taking these main factors as variables, the coplanarity evaluation model of long linear LWIR detector which under the condition of thermal-mechanical coupling, was established based on the laminate theory. Error analysis of the coplanarity evaluation model was presented, and the error introduced by the model was acceptable in engineering. The coplanarity evaluation model was used to improve the structure of the focal plane assembly(FPA), and the effectiveness of the improvement was verified by FEM simulation and test. The verification results show that, after the structure is improved, the flatness change of photosensitive surface is reduced from 170 μm to 10 μm, which meets the design requirements of less than 20 μm.
    $\left\{ {σxσyσzτyzτzxτxy} \right\} = \left[ {C11C12C12000C12C11C12000C12C12C11000000C11C122000000C11C122000000C11C122} \right]\left\{ {ε0x+zκxαΔTε0y+zκyαΔTαΔT00γ0xy+zκxy} \right\}$(1)

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    $\left\{ {σxσy} \right\} = C\left\{ {ε0xε0y} \right\} + zC\left\{ {κxκy} \right\} - \alpha \Delta T({C_{11}} + 2{C_{12}})\left\{ {11} \right\}$(2)

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    $\left\{ {FxFy} \right\} = \left[ {wx00wy} \right]\sum\limits_{k = 1}^n {\int_{{h_{k - 1}}}^{{h_k}} {\left\{ {σxσy} \right\}} } {\rm d}{\textit{z}}$(3)

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    $\left\{ {FxFy} \right\} = \left[ {wx00wy} \right]\left( {\sum\limits_{k = 1}^n {({h_k} - {h_{k - 1}}){C_k}\left\{ {ε0xε0y} \right\} + \frac{1}{2}} \sum\limits_{k = 1}^n {({h_k}^2 - {h_{k - 1}}^2){C_k}\left\{ {κxκy} \right\}} - \Delta T\sum\limits_{k = 1}^n {{\alpha _k}({h_k} - {h_{k - 1}}){{({C_{11}} + 2{C_{12}})}_k}\left\{ {11} \right\}} } \right)$(4)

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    $\left\{ {MxMy} \right\} = \left[ {wx00wy} \right]\left( {\frac{1}{2}\sum\limits_{k = 1}^n {({h_k}^2 - {h_{k - 1}}^2){C_k}\left\{ {ε0xε0y} \right\} + \frac{1}{3}} \sum\limits_{k = 1}^n {({h_k}^3 - {h_{k - 1}}^3){C_k}\left\{ {κxκy} \right\}} - \frac{1}{2}\Delta T\sum\limits_{k = 1}^n {{\alpha _k}({h_k}^2 - {h_{k - 1}}^2){{({C_{11}} + 2{C_{12}})}_k}\left\{ {11} \right\}} } \right)$(5)

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    $\left\{ {FxFyMxMy} \right\} = W\left( {{M_r}\left\{ {ε0xε0yκxκy} \right\} - \Delta T {T_r}} \right)$(6)

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    $W = \left[ {wx0000wy0000wx0000wy} \right] $()

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    ${M_r} = \left[ {k=1nCk(hkhk1)12k=1nCk(hk2hk12)12k=1nCk(hk2hk12)13k=1nCk(hk3hk13)} \right] $()

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    ${T_r} = \left\{ {k=1nαk(C11+2C12)k(hkhk1)k=1nαk(C11+2C12)k(hkhk1)12k=1nαk(C11+2C12)k(hk2hk12)12k=1nαk(C11+2C12)k(hk2hk12)} \right\}$()

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    $\left\{ {FM} \right\} = S\left\{ {ΔdΔθ} \right\}$(7)

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    $\left\{ {Fr_xFr_yMr_xMr_y} \right\} = {S_{xy}}\left\{ {Δxsinαx+ΔlcosαxΔysinαy+ΔlcosαyΔθxΔθy} \right\}$(8)

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    $\left\{ {Fr_xFr_yMr_xMr_y} \right\} = {S_{xy}}{Q_{xy}}\left\{ {ε0xε0yκxκy} \right\} + {S_{xy}}{R_{xy}}$(9)

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    ${Q_{xy}} = \left[ {dx2sinαx0000dy2sinαy0000dx20000dy2} \right]$(10)

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    ${R_{xy}} = \left\{ {ΔlcosαxΔlcosαy00} \right\}$()

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    $\left\{ {ε0xε0yκxκy} \right\} = - {\left( {{S_{xy}}{Q_{xy}} - W{M_r}} \right)^{ - 1}}\left( {{S_{xy}}{R_{xy}} + \Delta TW{T_r}} \right)$(11)

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    ${F_s}{\rm{ = sign}}(\frac{1}{{{\kappa _x}}})\left( {\left| {\frac{1}{{{\kappa _x}}}} \right| - \sqrt {{{\left( {\frac{1}{{{\kappa _x}}}} \right)}^2} - {{\left( {\frac{{{d_b}(1 + {\varepsilon _{0x}})}}{2}} \right)}^2}} } \right)$(12)

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    $\left\{ {FxMx} \right\} = {w_x}\left( {{M_{rx}}\left\{ {ε0xκx} \right\} - \Delta T{T_{rx}}} \right)$(13)

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    $ {M_{rx}} = \left[ {Mr_11+Mr_12Mr_13+Mr_14Mr_31+Mr_32Mr_33+Mr_34} \right],\;{T_{rx}} = \left\{ {Tr_1Tr_3} \right\} $()

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    $\left\{ {F1_x+F3_xM1_x+M3_x} \right\} = ({w_{1\_x}} + {w_{3\_x}})\left( {{M_{rx\_1}}\left\{ {ε1_0xκ1_x} \right\} - \Delta T{T_{rx\_1}}} \right)$(14)

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    $\left\{ {F2_xM2_x} \right\} = {w_{2\_x}}\left( {{M_{rx\_2}}\left\{ {ε2_0xκ2_x} \right\} - \Delta T{T_{rx\_2}}} \right)$(15)

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    ${F_{1\_x}} + {F_{2\_x}} + {F_{3\_x}}{\rm{ = }}{F_{r\_x}}$(16)

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    ${M_{1\_x}} + {M_{2\_x}} + {M_{3\_x}}{\rm{ = }}{M_{r\_x}}$(17)

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    $ {\varepsilon _{{\rm{1}}\_0x}}{\rm{ = }}{\varepsilon _{2\_0x}},\;{\kappa _{1\_x}}{\rm{ = }}{\kappa _{2\_x}} $(18,19)

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    ${ε2_0xκ2_x}=((w1_x+w3_x)Mrx_1+w2_xMrx_2SxQx)1×(SxRx+ΔT((w1_x+w3_x)Trx_1+w2_xTrx_2)) $(20)

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    ${Q_x} = \left[ {dx2sinαx00dx2} \right]$()

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    ${R_x} = \left\{ {Δlcosαx0} \right\}$()

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    ${F_{\rm{m}}}{\rm{ = sign}}(\frac{1}{{{\kappa _{2\_x}}}})\left( {\left| {\frac{1}{{{\kappa _{2\_x}}}}} \right| - \sqrt {{{\left( {\frac{1}{{{\kappa _{2\_x}}}}} \right)}^2} - {{\left( {\frac{{{d_{b{\rm{c}}}}(1 + {\varepsilon _{2\_0x}})}}{2}} \right)}^2}} } \right)$(21)

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