MOSFET Time-to-Failure For a MOSFET with the parameters given below, calculate the time-to-failure τ for operation at VDD = 5 V. If the device is to be used in a system that must operate reliably for 10 years, what is the maximum drain-supply voltage that can be used? Device parameters are xox =

Question

MOSFET Time-to-Failure

For a MOSFET with the parameters given below, calculate the time-to-failure [latex] au [/latex] for operation at [latex] V_{DD} = 5 [/latex] V. If the device is to be used in a system that must operate reliably for 10 years, what is the maximum drain-supply voltage that can be used?
Device parameters are [latex] x_{ox} = 20 nm, x_j = 0.2 μm, V_{Dsat} = 1 V, V_T = 0.7 V [/latex], channel length L = 1 μm. Use the failure criteria [latex] \Delta I_D/I_D [/latex] = 10% with [latex] K_1 [/latex] = 10 and m = 3.

Accepted Answer

Using Equation 10.1.16,

[latex] \ell =0.22x_j^{1/2}x_{ox}^{1/3} [/latex] (10.1.16)

[latex] \ell =0.22 x_{ox}^{1/3}x_j^{1/2}=0.124 \ \mu m [/latex]

Then from Equation 10.1.15,

[latex] \xi _m\approx \frac{(V_D-V_{Dsat})}{\ell } \ \ \ \ ext{ for } \ \ \ \ (V_D-V_{Dsat})\gt 1V [/latex] (10.1.15)

[latex] \xi _m\approx \frac{V_D-V_{Dsat}}{\ell }\approx 3.23 imes 10^5 \ V \ cm^{-1} [/latex]

From Equation 10.2.6, and the associated value of [latex] A_i/B_i [/latex],

[latex] I_{sub}\approx \frac{A_i}{B_i} (V_D-V_{Dsat})I_D\exp\left(-\frac{\ell B_i}{V_D-V_{Dsat}} ight) [/latex] (10.2.6)

[latex] \frac{I_{sub}}{I_D} =1.2(V_D-V_{Dsat})\exp\left(-\frac{B}{\xi _m} ight) =0.025 [/latex]

Finally, using Equation 10.4.1,

[latex] au \approx K_1\left(\frac{I_{sub}}{I_D} ight) ^{-m} [/latex] (10.4.1)

[latex] au =K_1\left(\frac{I_{sub}}{I_D} ight) ^{-3}=7.4 [/latex] days

Note that in this problem, L and [latex] V_G [/latex] are not explicitly utilized because [latex] V_{Dsat} [/latex], is specified for the given biasing condition.

For a lifetime of 10 years, [latex] au = 3.15 imes 10^8 [/latex] s. Therefore, we need

[latex] \frac{I_{sub}}{I_D} =3.17 imes10^{-3}\Rightarrow \xi _m\lt 2.4 imes10^5 \ Vcm^{-1} [/latex]

The corresponding value of [latex] V_{DD(max)}\approx 4.22 \ V [/latex]

Question 10.3: MOSFET Time-to-Failure For a MOSFET with the parameters giv...

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