| Fowler-nordheim Equation |
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The Current Density flowing through a thin oxide layer due to Fowler-Nordheim Tunneling is a function of the Electric Field across the oxide. The electric field is the voltage divided by the distance. This article describes how quickly current increases with voltage. V t E I A J J K K For the Fowler-Nordheim tunneling current density : J The point is that the current increases with the voltage squared multiplied by an exponential increase with inverse voltage. While the second factor, E2, obviously increases rapidly with voltage, the third factor, the exponential, deserves another sentence. For people who are not familiar with exponentials of negative inverses, the following sentences are helpful. Assume, temporarily, that ''K''2 is normalized to be 1. The factor e-1/E increases with E. If E is near zero, the exponent is large, and exp(-large) is near zero. If E is large, 1/E is small, and almost zero: exp(0) = 1 Therefore, exp(-1/E) gets larger as E gets larger, since one is greater than zero. CONCLUSION Terminology note : A variable that is squared makes a parabolic curve. J increases by two voltage-related factors that are multiplied : (exponentially with voltage) x (squared with voltage) The curve of the Fowler Nordheim current versus voltage increase faster than a parabola. EXTERNAL LINK |
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