Charge-carrier density

The most simple pentaeene OTFT test structure used in many labs is based on a Si wafer piece covered with a thermal oxide. Here, the heavily doped Si wafer takes the role of the back gate electrode, and the Si02 takes the role of the gate dielectric. A pentacene thin film is deposited as the semiconducting layer. Source and drain electrodes are deposited either on the silicon oxide (bottom contact) or on top of the pentacene film (top contact). 

Pentacene OTFT curves are usually analysed within MOSFET theory [43]. 

For the saturation regime (Fj Fq - Ft) the aeeumulation within the channel is incomplete. This so ealled pinch off arises due to the superposition of the gate and drain potential. The source-drain eurrent ff in the saturation regime reads  

The most important physical parameter of an OTFT beyond the mobility pi is the number of charge carriers (n induced by a given gate voltage (Vq). can be estimated from the measured channel conductivity cr by 

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The energy position Cp of peak p in the lED of an ion with mass m is seen to be dependent on the plasma potential Vpi, the RE period T, and the ion plasma frequency cd, = yje n j m(o). Equation (48) can be used to determine the (net) charge carrier density in the sheath and the time-averaged potential Vpi from measured lEDs. The mean position Xp follows from combining Eq. (47) and Eq. (48) ... 

In silane discharges several ions are observed to be involved in a charge exchange process, and therefore maxima in their ion energy distribution at distinct energies are observed. The charge carrier density and the plasma potential that result from the fit of the lED allow for the quantification of the related parameters sheath thickness and ion flux. This method has been be used to relate the material quality of a-Si H to the ion bombardment [301. 332] see also Section 1.6.2.3. 

The charge carrier density in the sheath increases by a factor of 3 on increasing the excitation frequency from 13.56 to 65 MHz. As a consequence, the... 

The interaction of semiconductor with nanocarbon induces a modification of the intrinsic properties of semiconductor particles (band gap, charge carrier density, lifetime of charge separation, non-radiative paths, etc.) [1] as well as of the surface properties which were discussed in detail in the previous section. 

The work of Mensfoort et al. is a striking test of the importance of charge carrier density effects in space-charge-limited transport studies. For a given applied voltage the space charge concentration is inversely proportional to the device thickness. This explains why in Fig. 9 the deviation from the In cx... 

Where Vs is the potential value at the surface of the electrode. Then plotting the value of 1/Csc versus the applied potential E should yield a straight line whose intercept with the E axis represents the flat band potential, and the slope is used for the calculation of N, the charge carrier density in the semiconductor. A typical example of Mott-Schottky plot is given in Fig. 2 [7] in this graph, the extrapolated values of the fb potential are -1-0.8 V and —0.6 V vs. SCE for p-Si and n-Si respectively. 

On lowering the temperature through Ty, a bandgap Eg = 0.1 eV appears in the FeB-ai(l) conduction band of Fig. 3 at Ep. The Hall coefficient increases as Rh exp(Ty/T), indicating that the charge-carrier density increases exponentially with T" , as in a normal semiconductor, and the Hall mobility increases from about 0.1 to 0.4 cm /Vs on lowering the temperature from Ty = 120 K to 77 K ... 

The mobilities of holes are always less than those of electrons that is fXh < Me- In silicon and germanium, the ratio [ie/[ih is approximately three and two, respectively (see Table 6.2). Since the mobilities change only slightly as compared to the change of the charge carrier densities with temperature, the temperature variation of conductivity for an intrinsic semiconductor is similar to that of charge carrier density. 

Neglecting the variation of the term, which is negligible compared to the variation with temperature in the exponential term, and recalling that the mobilities are less sensitive to temperature than are the charge carrier densities, Eq. (6.30) can be rewritten as... 

Unlike intrinsic semiconductors, in which the conductivity is dominated by the exponential temperature aud band-gap expression of Eq. (6.31), the conductivity of extrinsic semiconductors is governed by competing forces charge carrier density and charge carrier mobility. At low temperatures, the number of charge carriers initially... 

Figure 6.16 Temperature dependence of charge carrier density and conductivity of extrinsic semiconductor Ge doped with 2 ppb As. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission John Wiley Sons, Inc.

In metals, the concentration of mobile electrons is enormously high so that the excess charge is confined to a region very close to the surface, within atomic distances [14, 15]. In semiconductors with substantially less charge carrier density, on the other hand, a region of spatial charge distribution can be found [16, 17]. 

Semiconductor electrodes, which have much lower charge carrier densities (1013—1019 carriers/cm3), typically absorb in the infrared but exhibit much lower absorption by charge carriers than metals of comparable film thickness, and frequently show a transparency window in much of the visible spectrum due to a substantial band-gap energy, before absorbing again in the ultraviolet. For example, Sn02 and ZnO, like many common semiconductor electrode materi-... 

Lastly a note on the chemical surface properties of 0. So far we have carried out only a few preliminary CDA experiments adding 5 vol.-% H2 to the N2. The observed decrease of the polarization and/ hence/ of the charge carrier density at the surface suggests that H2 consumes O , probably by way of oxidation H2 + 2 O" = H20 + O2". Further work will be required to study these reactions in more detail. 

In an attempt to rationalize the measured capacitance values, and especially the low value for the basal plane (ca. 3pF/cm2), these authors first concluded that space charge within the electrode is the dominant contribution (rather than the compact double layer with ca. 15-20 pF/cm2, or the diffuse double layer with >100 pF/cm2). They then applied the theory of semiconductor electrodes to confirm this and obtained a good agreement by assuming for SAPG a charge carrier density of 6 x 1018/cm3 and a dielectric constant of 3 for GC, they obtained 13 pF/cm2 with the same dielectric constant and 1019 carriers per cubic centimeter. 

In chemical terms, it may be proposed that the it electrons of the first graphite layer at the surface are localized at states which are separate from the bands of the bulk. Significant contribution of these states to the double layer capacitance necessitates an overpotential which is beyond the applied potential range (limited by water electrolysis). In terms of semiconductor theory, it may be assumed that the charge carrier density at the first and probably the second graphite layer is much lower than the bulk charge density value of 6 x 1018 carriers per cm3. 

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