Schottky-barrier

The energy barrier of a depletion layer (the potential across a depletion layer I I) is called the Schottky barrier in semiconductor physics. Assuming that all the impurity donors or acceptors are ionized to form a fixed space charge in the depletion layer, we obtain the following approximate equation, Eqn. 5—75, for the thickness of depletion layer, dx, [Memming, 1983]  

Further, the total excess charge Osc in a depletion layer may be given approximately by the product of the impurity concentration N and the layer thickness dx in Eqn. 5-76  

The thickness of depletion and deep depletion layers may be approximated by the effective Debye length, Lo, ff, given in Eqn. 5-70 Ld, is inversely proportional to the square root of the impiuity concentration, In ordinary semiconductors 

ff is in the order of 100 nm. In contrast, the thickness of the accumulation and inversion layers, in which the mobile charge carriers (electrons or holes) are concentrated, is in the order of 5 to 10 nm and is much thinner than the thickness of the depletion layer. 

From Eq. (3), the Galvani potential difference between the semiconductor and the metal, Am, is given by 

Effect of the Redox Potential on the Potential Drop in the Semiconductor at the Semiconductor/Electrolyte Interfaces 

The Galvani potential difference between the semiconductor bulk and the electrolyte bulk, A, is given by Eq. (28) in analogy to Eq. (25) and to Eq. (26)  

As one can easily recognize by comparing Eqs. (26) and (29), the one big difference between the semiconductor/electrolyte and the semiconductor/metal interfaces is the existence of the potential drop in the Helmholtz layer, AVh, even if AVg can be neglected. When one considers the effect of the redox potential on A V,c it is better to use V,edox(ref. scale) rather than V,edox(vac. scale) since only the former values can be obtained directly by experiments. From Eqs. (7) and (9) 

As is the case at a metal/semiconductor interface, when the surface state density is very low and the carrier density of the semiconductor is not too high. 

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The second class of atomic manipulations, the perpendicular processes, involves transfer of an adsorbate atom or molecule from the STM tip to the surface or vice versa. The tip is moved toward the surface until the adsorption potential wells on the tip and the surface coalesce, with the result that the adsorbate, which was previously bound either to the tip or the surface, may now be considered to be bound to both. For successful transfer, one of the adsorbate bonds (either with the tip or with the surface, depending on the desired direction of transfer) must be broken. The fate of the adsorbate depends on the nature of its interaction with the tip and the surface, and the materials of the tip and surface. Directional adatom transfer is possible with the apphcation of suitable junction biases. Also, thermally-activated field evaporation of positive or negative ions over the Schottky barrier formed by lowering the potential energy outside a conductor (either the surface or the tip) by the apphcation of an electric field is possible. FIectromigration, the migration of minority elements (ie, impurities, defects) through the bulk soHd under the influence of current flow, is another process by which an atom may be moved between the surface and the tip of an STM. 

Trigonal selenium is a -type semiconductor with an energy gap of 1.85 eV (104) and a work function of about 6 eV (105), which is the largest value reported for all the elements. Accordingly, a Schottky barrier should be created at the contact of selenium with any metal. This is consistent with the... 

Fig. 9. Schottky barrier band diagrams (a) a rare situation where the metal work function is less than the semiconductor electron work affinity resulting in an ohmic contact (b) normal Schottky barrier with barrier height When the depletion width Wis <10 nm, an ohmic contact forms.

Both ohmic and rectifying behavior are possible, depending on the sign of Unlike the p—n junction the current in a rectifying Schottky barrier... 

Table 7. Schottky Barrier Heights for Metals on Compound Semiconductors...

The degree of surface cleanliness or even ordering can be determined by REELS, especially from the intense VEELS signals. The relative intensity of the surface and bulk plasmon peaks is often more sensitive to surface contamination than AES, especially for elements like Al, which have intense plasmon peaks. Semiconductor surfaces often have surface states due to dangling bonds that are unique to each crystal orientation, which have been used in the case of Si and GaAs to follow in situ the formation of metal contacts and to resolve such issues as Fermi-level pinning and its role in Schottky barrier heights. 

The charge earner depletion width, W, at the recti Tying contact, which forms a Schottky barrier, can be calculated using the following Eq. (99) (47) ... 

Figure 9-22. Energy diagram ol a metal/ scmiconductor/meta Schottky barrier (0... workfunction, x,. electron affinity, /,... ionization potential, . ..bandgap, W... depletion width).

These Schottky energy barriers are measured in the presence of an electric field in the structure which is necessary to be able to collect the photocurrent. The photocurrent thresholds are not the zero electric field Schottky barriers because of the electric field in the polymer and the image chaise potential created when the electron leaves the metal. This effect results in a lowering of the Schottky energy barrier given by [34]... 

Parker [55] studied the IN properties of MEH-PPV sandwiched between various low-and high work-function materials. He proposed a model for such photodiodes, where the charge carriers are transported in a rigid band model. Electrons and holes can tunnel into or leave the polymer when the applied field tilts the polymer bands so that the tunnel barriers can be overcome. It must be noted that a rigid band model is only appropriate for very low intrinsic carrier concentrations in MEH-PPV. Capacitance-voltage measurements for these devices indicated an upper limit for the dark carrier concentration of 1014 cm"3. Further measurements of the built in fields of MEH-PPV sandwiched between metal electrodes are in agreement with the results found by Parker. Electro absorption measurements [56, 57] showed that various metals did not introduce interface states in the single-particle gap of the polymer that pins the Schottky contact. Of course this does not imply that the metal and the polymer do not interact [58, 59] but these interactions do not pin the Schottky barrier. 

M.S. Sze, Physics of Semiconductor Devices, Wiley-lnterscience, New York 1981 B. L. Sliarma (Ed.) Metal-Semiconductor Schottky Barrier Junctions and Their Applications, Plenum Press, New York 1984. 

A polymer layer al a contact can enhance current How by serving as a transport layer. The transport layer could have an increased carrier mobility or a reduced Schottky barrier. For example, consider an electron-only device made from the two-polymer-layer structure in the top panel of Figure 11-13 but using an electron contact on the left with a 0.5 eV injection barrier and a hole contact on the right with a 1.2 cV injection barrier. For this case the electron current is contact limited and thermionic emission is the dominant injection mechanism for a bias less than about 20 V. The electron density near the electron injecting contact is therefore given by... 

Friend et at. studied the influence of electrodes with different work-functions on the performance of PPV photodiodes 143). For ITO/PPV/Mg devices the fully saturated open circuit voltage was 1.2 V and 1.7 V for an ITO/PPV/Ca device. These values for the V c are almost equal to the difference in the work-function of Mg and Ca with respect to 1TO. The open circuit voltage of the ITO/PPV/A1 device observed at 1.2 V, however, is considerably higher than the difference of the work-function between ITO and Al. The Cambridge group references its PPV with a very low dark carrier concentration and consequently the formation of Schottky barriers at the PPV/Al interface is not expected. The mobility of the holes was measured at KT4 cm2 V-1 s l [62] and that for the electrons is expected to be clearly lower. 

An important step toward the understanding and theoretical description of microwave conductivity was made between 1989 and 1993, during the doctoral work of G. Schlichthorl, who used silicon wafers in contact with solutions containing different concentrations of ammonium fluoride.9 The analytical formula obtained for potential-dependent, photoin-duced microwave conductivity (PMC) could explain the experimental results. The still puzzling and controversial observation of dammed-up charge carriers in semiconductor surfaces motivated the collaboration with a researcher (L. Elstner) on silicon devices. A sophisticated computation program was used to calculate microwave conductivity from basic transport equations for a Schottky barrier. The experimental curves could be matched and it was confirmed for silicon interfaces that the analytically derived formulas for potential-dependent microwave conductivity were identical with the numerically derived nonsimplified functions within 10%.10... 

The numerical calculation of the potential-dependent microwave conductivity clearly describes this decay of the microwave signal toward higher potentials (Fig. 13). The simplified analytical calculation describes the phenomenon within 10% accuracy, at least for the case of silicon Schottky barriers, which serve as a good approximation for semiconduc-tor/electrolyte interfaces. The fact that the analytical expression derived for the potential-dependent microwave conductivity describes this phenomenon means that analysis of the mathematical formalism should... 

Badawy,W.A. Photovoltaic and Photoelectrochemical Cells 30 Based on Schottky Barrier Heterojunctions... 

The optical properties of electrodeposited, polycrystalline CdTe have been found to be similar to those of single-crystal CdTe [257]. In 1982, Fulop et al. [258] reported the development of metal junction solar cells of high efficiency using thin film (4 p,m) n-type CdTe as absorber, electrodeposited from a typical acidic aqueous solution on metallic substrate (Cu, steel, Ni) and annealed in air at 300 °C. The cells were constructed using a Schottky barrier rectifying junction at the front surface (vacuum-deposited Au, Ni) and a (electrodeposited) Cd ohmic contact at the back. Passivation of the top surface (treatment with KOH and hydrazine) was seen to improve the photovoltaic properties of the rectifying junction. The best fabricated cell comprised an efficiency of 8.6% (AMI), open-circuit voltage of 0.723 V, short-circuit current of 18.7 mA cm, and a fill factor of 0.64. 

Fig. 12 a and b. Reactions at catalyst loaded particles a) catalyst forming an ohmic contact b) forming a Schottky barrier... 

In this context it should be mentioned that the height of the Schottky barrier depends on the proc iure of metal deposition and also on the pretreatment. Aspnes and Heller have investigated for instance metal-semiconductor contacts produced by depositing Ru, Rh or Pt as 400 A thick films. They found barrier heights for the metal in contact with air, of 0.6 eV for Ru on Ti02, which decreased to zero in the presence of hydrogen. These results are consistent with those of Yamamoto et al. . ... 

This result was interpreted by the formation of a Schottky barrier at the CdS/ Ru02-interface as already discussed in the previous section. The H2-production at CdS/Ru02-suspensions could be considerably increased by addition of sulfite because the latter rved as a sink for sulfur produced via reaction (40)... 

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