Of course, I am talking about a semiconductor-dielectric junction. The penetration depends on which way the polarization points. Note that the dielectric is a wide bandgap material.
Dear Burc Misirlioglu ,
When both materials are brought into intimate contact, they will exchange thermal energy and charges till they reach to balance. While the metal can inject electrons or holes into the insulator through thermionic emission, the insulator is assumed initially free from free charges. Electron injection into insulators is a known phenomena. The injection process is controlled by the energy difference between the the conduction band edges of the two contacted materials.
Then-type semicondcutor can inject electrons the conduction band of the insulators. https://journals.aps.org/pr/abstract/10.1103/PhysRev.125.126
Best wishes
There is a potential energy barrier at the interface between a semiconductor and a wide band gap dielectric which the free carrier incident at the semiconductor/dielectric interface will encounter. According to the rules of quantum mechanics, the electron will penetrate into the dielectric, however, the amplitude of its wave-function will exponentially attenuate; which means that the carrier density will sharply decrease with distance from the interface. The electron/hole density attenuation will be larger for larger barrier and larger effective mass. For example, the carrier density will, roughly, attenuate by a factor of 1/e for each 0.16 nm into the dielectric, if the band offset at the interface is 2 eV and the effective mass is equal to 0.16 m.
Dear Prof. Kar,
Thank you very much for your answer. The problem then turns into a case of electron penetrating a barrier. If we solve the problem from a classical point of view, i. e., solving the Maxwell eqn. in the semiconductor and the polar dielectric where the boundary conditions for potential are defined at the interface, charge distributions defined via the Maxwell-Boltzmann limit, how would one interpret the existence of an electron density inside the dielectric (near the interface with a penetration of a few nm's) if the polarization is pointing away from the interface (meaning positive pole is near the interface). The electron density inside the dielectric rapidly decays to zero after a few nm's.
Dielectrics have lots of bulk defects/ traps (though it is unintended). Again dielectric-semiconductor interface also have lots of interface traps which can eventually reduce the barrier height for carriers (though dielectric generally have wide bandgap). These defects help carrier penetration and result in considerable gate leakage.
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