Metal-semiconductor interface equivalent circuit according to ideal theory neglecting the effects of surface states. Figure 2. Ideal Schottky barrier theory extended to semiconductor surfaces predicts that the contact potential of a semiconductor scales with the work function of the semiconductor, which in turn depends on how the semiconductor is doped. However, in Meyerhof 20 W. Meyerhof , Contact potential difference in silicon crystal rectifiers , Phys. This discrepancy between ideal Schottky barrier theory and experimental reality was explained by Bardeen, 21 J.
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Bardeen , Surface states and rectification at a metal semi-conductor contact , Phys. The crux of his argument is that the presence of surface states requires a reformulation of the electrostatic conservation of charge equation, i. Bardeen's article is foundational to IGS modeling since it is the first application of surface states to rationalize non-ideal electronic behavior in a semiconductor device. In , ideal heterojunction theory neglecting interface states was formulated by Anderson 22 R.
In essence, ideal heterojunction theory is based on invoking appropriate electrostatic expressions for conservation of charge, i. Semiconductor heterojunction interface equivalent circuit according to ideal theory neglecting the effects of interface states. Figure 3. Bardeen's surface state proposal for describing the electronic behavior of a real metal-semiconductor interface is agnostic as to whether surface states are extrinsic, e.
However, in , Heine 23 V.
Review—Practical Challenges Hindering the Development of Solid State Li Ion Batteries
Heine , Theory of surface states , Phys. His proposal ushered in the birth of metal-induced gap states MIGS theory and is therefore of key significance to this IGS modeling review. Prior to overviewing MIGS development subsequent to Heine's proposal, it is necessary to mention another landmark paper from in order to conform to the chronological ordering employed in this historical synopsis. Cowley and Sze 24 A. Cowley and S. Sze , Surface states and barrier height of metal-semiconductor systems , J. Notably, a very thin interfacial insulator layer with a thickness on the order of atomic dimensions is postulated in order to separate the metal from the semiconductor.
The physical nature of this thin interfacial insulator is rather obscure. It is often ascribed to the presence of a native oxide. Equilibrium energy band diagram according to non-ideal Schottky barrier theory as proposed by Cowley and Sze. Adapted with permission from Cowley and Sze.
As an aside, from an IGS modeling perspective, inclusion of a thin interfacial layer is essential to account for conservation of charge, i. Q M is a sheet of charge positioned at the metal-interfacial layer interface while Q SS is a sheet of charge located at the interfacial layer-semiconductor interface. Collectively, Q M and a portion of Q SS constitute an electric dipole with a charge separation distance on the order of atomic dimensions, i. From electrostatic and energy band considerations, Cowley and Sze 24 A.
Dynamics at Solid State Surfaces and Interfaces : Uwe Bovensiepen :
The origin and meaning of [ 2. Some historical highlights of this work are as follows. Louie , J. Chelikowsky , and M. Cohen , Ionicity and the theory of Schottky barriers , Phys. B 15 , Tejedor , F. Flores , and E.
kamishiro-hajime.info/voice/camera/espion-pour-portable.php Louis , The metal-semiconductor interface: Si and zincblende junctions , J. C 10 , In , Tejedor and Flores 27 C. Tejedor and F. Flores , A simple approach to heterojunctions , J. C 11 , In , Tersoff refined charge neutrality level and semiconductor dipole considerations, applying them to both MS 28 J.
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Tersoff , Schottky barriers and the continuum of gap states , Phys. Tersoff , Theory of semiconductor heterojunctions; the role of quantum dipoles , Phys. B 30 , Additionally, Tersoff 28 J. Tersoff , The theory of Schottky barriers: controversy or consensus? It is hard to overemphasize the importance of this relationship in IGS modeling, as will be evident in the remainder of this review article. In , Robertson 34 J. Robertson , Band offsets of wide-band-gap oxides and implications for future electronic devices , J.
B 18 , This article is notable for its clear exposition of MIGS theory, its formulation of heterojunction band offset in terms of charge neutrality levels, and its recognition that MIGS theory can be applied to insulators, as well as semiconductors. In a later article, Peacock and Robertson 35 P. Peacock and J. Robertson , Band offsets and Schottky barrier heights of high dielectric constant oxides , J. Recognition of this is an important step towards being able to account for interface states in the construction of an energy band diagram.
In , Wager 36 J. Wager , Transparent electronics: Schottky barrier and heterojunction considerations , Thin Solid Films , This perspective facilitated construction of energy band diagrams for non-ideal theory situations in which surface state effects are taken into consideration. These ideas were then extended and refined by Wager and co-workers 37—39 J.
Spies , R. Schafer , J. Wager , P. Hersh , H. Platt , D.
Keszler , G. Schneider , R. Kykyneshi , J. Tate , X.
Liu , A. Compaan , and W. Shafarman , Pin double-heterojunction thin-film solar cell p-layer assessment , Solar Energy Mater. Solar Cells 93 , Wager and J. Robertson , Metal-induced gap states modeling of metal-Ge contacts with and without a silicon nitride ultrathin interfacial layer , J. Wager , K. Hoshino , E. Sundholm , R. Presley , R. Ravichandran , C. Knutson , D.