Voltage

[As of April, 2011]

Failure modes such as oxide film breakdown, hot carriers, Al corrosion and characteristic degradation due to mobile ions are accelerated by voltage. Of these, the failure mode that appears most dominantly as a result of voltage acceleration is oxide film breakdown. When a constant electric field is continuously applied to the oxide film, breakdown occurs over time, even if the electric field in the oxide film is below the breakdown limit. The voltage acceleration model ^{Note 1} for time dependent dielectric breakdown (TDDB) can be expressed using the following equation, given time to failure T_F and the voltage applied to oxide film V. Case examples have been obtained where the TDDB lifetime for a thick oxide film (film thickness: 5 nm or greater) is dependent on the electric field. In such a case, calculations can be performed by replacing voltage with the electric field.

T_F: Time to failure
V: Voltage applied to oxied film
E: Electric field applied to oxied film
A: Constant
β: Voltage acceleration constant

Therefore, using an example where the lifetime is dependent on the electric field and assuming the time to failure at E₁ and E₂ to be T_F1 and T_F2, respectively, the acceleration rate A_F can be expressed as:

The time-dependent dielectric breakdown of oxide film can be tested by the following:

1. Constant voltage test
2. Step stress test
3. Constant current test

These tests can be summarized as follows:

1. Constant Voltage Test
   A constant voltage stress test applies constant stress to the oxide film to evaluate the breakdown distribution over time.
   In general, the TDDB lifetime distribution varies greatly and depends largely on voltage. Therefore, it can take an extremely long time to obtain results using this method and the failure distribution may not be clear. A step stress test can be performed to cope with this problem.
2. Step Stress Test
   The step stress test applies voltage to the oxide film in increased infixed steps at constant intervals to evaluate where breakdown will occur. The test produces results in a short period of time and the TDDB acceleration equation can be used to find out the overall failure distribution of the oxide film.
3. Constant Current Test
   The constant current test evaluates the failure distribution of the oxide film by applying a constant current as stress, based on the theory ^{Note 2} that the amount of electrical charge that passes through the oxide film until it breaks down will be constant. This test is not commonly used for oxide film lifetime estimations since usage conditions are expressed in terms of voltage or electric field intensity. However, it is generally used for oxide film quality evaluation since standardized data is obtained.
   Figure 1 shows the data for a constant electric field test performed by Toshiba. This data is an example for oxide film used in a Toshiba product. The applied electric field for the oxide film of the product is 3.125 MV/cm and the oxide film lifetime in normal use is 10 years or longer. The results of acceleration tests can be used in this manner to estimate the lifetime of oxide film in the field.

Note 1: Bibliography. E. S. Anolick and Li-Yu Chen; "Application of Stress to Time Dependent Breakdown," 19th Annual Proc. Rel. Phys. (1981)

Note 2: Bibliography. In-Chin Chen, S. E. Hollard, and C. Hu; "Electrical Breakdown in Tunneling Oxides," IEEE Trans. Ed. Vol. 32 (1985)

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