Question 10.3: MOSFET Time-to-Failure For a MOSFET with the parameters giv...
MOSFET Time-to-Failure
For a MOSFET with the parameters given below, calculate the time-to-failure \tau for operation at V_{DD} = 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 x_{ox} = 20 nm, x_j = 0.2 μm, V_{Dsat} = 1 V, V_T = 0.7 V , channel length L = 1 μm. Use the failure criteria \Delta I_D/I_D = 10% with K_1 = 10 and m = 3.
Using Equation 10.1.16,
\ell =0.22x_j^{1/2}x_{ox}^{1/3} (10.1.16)
\ell =0.22 x_{ox}^{1/3}x_j^{1/2}=0.124 \ \mu mThen from Equation 10.1.15,
\xi _m\approx \frac{(V_D-V_{Dsat})}{\ell } \ \ \ \ \text{ for } \ \ \ \ (V_D-V_{Dsat})\gt 1V (10.1.15)
\xi _m\approx \frac{V_D-V_{Dsat}}{\ell }\approx 3.23 \times 10^5 \ V \ cm^{-1}From Equation 10.2.6, and the associated value of A_i/B_i ,
I_{sub}\approx \frac{A_i}{B_i} (V_D-V_{Dsat})I_D\exp\left(-\frac{\ell B_i}{V_D-V_{Dsat}} \right) (10.2.6)
\frac{I_{sub}}{I_D} =1.2(V_D-V_{Dsat})\exp\left(-\frac{B}{\xi _m} \right) =0.025Finally, using Equation 10.4.1,
\tau \approx K_1\left(\frac{I_{sub}}{I_D} \right) ^{-m} (10.4.1)
\tau =K_1\left(\frac{I_{sub}}{I_D} \right) ^{-3}=7.4 days
Note that in this problem, L and V_G are not explicitly utilized because V_{Dsat} , is specified for the given biasing condition.
For a lifetime of 10 years, \tau = 3.15 \times 10^8 s. Therefore, we need
\frac{I_{sub}}{I_D} =3.17\times10^{-3}\Rightarrow \xi _m\lt 2.4\times10^5 \ Vcm^{-1}The corresponding value of V_{DD(max)}\approx 4.22 \ V