Schottky barrier calculated

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) ... 

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... 

Above equation shows that for infinitely large P(0), C becomes zero. C decreases with increase in Hb and Z and increases with J (or applied voltage). The effect of temperature comes through Z = Tc/T. Numerical calculations show that as Z increases, C decreases. At low temperatures Z is larger and C becomes smaller. The effect of C becomes more pronounced at higher temperatures. The value of P(0) is determined by the Schottky barrier injected charge density at the contact remains constant at its thermal equilibrium value [45, see p. 258] when a current flows through the sample. If cpB = 0, the injected hole density P(0) = 1020 oo and C = 0, (3.46) reduces to Eq. (3.42) (for a = 1) discussed earlier. As mentioned earlier as C increases to > 0, the J-V characteristics deviate considerably from Eq. (3.42). 

Fig. 3.15. J-V characteristics of Schottky diodes with b- For a non-zero Schottky barrier curves B deviate from curves A as applied voltages increases. Curves B become straight lines at higher voltages where C is large. These straight lines correspond to Ohm s law as predicted by Eq. (3.49). The values of the parameters in these calculations are the same as given in Fig. 3.11 [44],...

Fig. 3.17. J-V characteristics of the ITO/PEDOT PSS/MEH-PPV/Au diode at 240 K. The thickness of the active layer is 120 nm. The symbols represent die experimental data. The dash-dot line represents the ohmic region due to thermally generated and background carriers. The dashed line represents die calculated values using the conventional equation (3.42) with a zero Schottky barrier, while die dotted curve represents the calculated values using Eq. (3.46) with a Schottky barrier = 0.1 eV. At lower voltages below die point D, the plot of Eqs. (3.46) and (3.42) are practically identical. The values of die parameters used in this representation are N0 = 1019 cm-3, Tc = 400 K, e = 3, e0 = 8.85x 1(T14 F/cm, fi = 7x 1(T5 cm2/Vs, iVv = 2x 1019 cm-3 and Hh = 4.5 x 1018 cm-3 [44],...

It is of interest to examine the case when both effects are taken into account, i.e. the injection barrier is not zero and also pt p. Such cases can arise in practice only if H, is small. To a non-zero Schottky barrier the value of P(0) is reduced. Since p is always smaller than P(0), a value of p is also reduced. In general this results in pt > p and the power law remains valid and Ohm s law is approached at high voltages. The numerically calculated values of the J-V curves for such a case are shown in Fig. 3.18. 

The measured electron current in PCBM injected through Au electrode is shown in Fig. 3.35. Calculated SCL hole current in OC1C10-PPV is shown by circles in Fig. 3.35 for a thickness of L = 170 nm. Even with the high Schottky barrier of 1.4 eV (the barrier determined from the measured current is 0.76 eV) with A1 cathode for PCBM is not sufficient to suppress the electron current in PCBM below the hole current in OCiCio-PPV. With the large injection barrier the electron current is injection limited. This work shows that it is not possible to make hole only devices using OCiCio-PPV PCBM bulk heterostructures. 

The charge carrier transport model of the CoFe/MgO/CoFe nanostructure taking into account the Schottky barrier and interface charge was developed. TMR and 1-V characteristics were calculated on the basis of experimental data and modeled for different parameters of the nanostructure. Estimates of TMR are realized through the variation of height of the effective barrier for spin-up and spin-down electrons. Growth of TMR is 0.18, 0.40 and 0.55 when the energy difference between barriers is 0.02 eV, 0.05 eV and 0.10 eV, respectively. 

TMR [5] is calculated on the basis of the difference of height of the effective barrier 8q> for spin-up and spin-down electrons, e.g. the magnetic molecular field V Estimates of 5

ideal structure FeCo/MgO/FeCo [6]. It leads to dcp 0.45 eV. In real structures containing intermediate silicon layer and the Schottky barrier the difference between barriers is reduced to 0.02-0.1 eV. 

Fig. 30. Variation in the position of the maxima or minima in the ER spectra of Fig. 29 (o) and variation calculated from the extended theory discussed in the text assuming a classical Schottky barrier ( x).

These promising values leave room for performance loss due to deviation from the ideal behavior. The main contribution in the performance loss comes fi om neglecting the contact resistance, which arises between the metallic contacts and the carbon nanotube and is caused by k-vector mismatch and/or Schottky-barriers. In the following we model this resistance as linear, i.e. ohmic resistance and calculate the performance dependence on the contact resistance. The extrinsic transconductance can be calculated from the intrinsic transconductance g and the extrinsic output conductance gds and is given by ... 

The Schottky barrier height can be calculated if the thermionic emission model is regarded as valid ... 

A second example of some calculated C- V data is shown in Fig. 29 for high fiequency measurements for hypothetical a-Si H Schottky barriers (Cohen and Lang, 1982). Here the four curves displayed are based on (1) the FE density of states of Fig. 4, (2) the two g(E) curves displayed in Fig. 20, and... 

The value Ncy is calculated for a variety of applied bias and measurement frequencies. The correct value of the number density in deep depletion for this hypothetical Schottky-barrier sample is 7 X 10 cm (assumed barrier hei t of 0.7 eV exponential prefactor is 10 ... 

Fig. 38. Typical set of measured TSCAP spectra for one n-type doped (60 ppm PHj) a-Si H Schottky-barrier sample under 2 V reverse bias. The data were obtained in a manner analogous to that described for the calculated discrete-level TSCAP data in Fig. 35. Other parameters are described in the text.

However, experimental ]V curves often deviate from the ideal /scl- In these cases, the measured current /inj is injection limited caused by a nonohmic contact or poor surface morphology. When the MO interface is nonohmic, carrier injection can be described by the Richardson-Schottky model of thermionic emission the carriers are injected into organic solid only when they acquire sufficient thermal energy to overcome the Schottky barrier ((()), which is related to the organic ionization potential (/p), the electron affinity (AJ, the metal work function (O, ), and the vacuum level shift (A) [34,35]. Thus, the carrier injection efficiency (rj) can be calculated by the following equation ... 

Schottky barrier if > E, a layer of the semiconductor next to the surface is inverted in type, and there is then a p-n junction within the material. Let us estimate RA with these limitations for a Schottky barrier photovoltaic detector operating at T=77 K we obtain RA <470ohm-cm from (4.29). This estimate represents the upper limit of RA achievable with a Schottky barrier. We should keep this result in mind for comparison later with the RA values calculated for p-n junction photovoltaic detectors. 

Figure 17.6 Numerical calculation of energy band bending across a metal/silicon nanowire Schottky barrier, a system that bears similarity to surface charging due to chemisorption. The calculation is for a nanowire of n-type doping density at lO cm and diameter equal to...

Several important areas have been omitted. One area is defects in solids. Calculations in impurities, vacancies, interstitials, line defects, and plane defects have been performed using similar methods. Another area is interfaces. Applications are being made to the metal-semiconductor interfaces (Schottky barriers), semiconductor-semiconductor interfaces (heterojunctions), and superlattices. The study of molecules and clusters is a third area. Also, since the method can be used to calculate electron-phonon couplings, phenomena such as resistivity, superconductivity, ultrasonic attentuation, and so forth, can now be studied using these ab initio methods. Results from research in all these areas have been impressive and very encouraging. 

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