Shockley equation

Hole injection into the / -region similarly results in a positive current flow from to, leading to the Shockley diode equation (eq. 12), with a... 

Shockley diode equation, 22 243, 246 Shockley equation, 74 838-839 Shock synthesis of diamonds, 3 536 Shock treatment... 

The dark and illuminated characteristics of the PCBM PPV solar cells for different concentrations of PCBM are shown in Fig. 5.18. It can be seen that the dark characteristics are not described by Shockley type equation. Forward illuminated I(V) curves are strongly dependent on the applied voltage. Under reverse bias the illuminated current is not so sensitive to the voltage. 

Hegedus et al. [146] also measured the I-V curves of amorphous Si p-i-n solar cells at different temperatures. The curves in the dark and also under illumination are shown in Fig. 5.25. The I-V curves under illumination obey Eq. (5.8) in this case also. The built in voltage calculated from the illuminated curves was satisfactory. Hegedus et al. [146] took small portion of the dark I-V curves which could be represented by an equation of the type (5.5). They then attempted to derive the built in voltage using this dark current as Shockley currents. They obtained very strange results. Hegedus et al. [146] wrote Our results also clearly demonstrate that it is completely inappropriate to analyze J( V) data measured in the dark on a-Si p-i-n devices and then attempt to correlate the results with photovoltaic performance Measurements in the dark are not applicable to understand-... 

According to this equation, the lifetime of excited carriers decreases with increasing majority carrier density and consequently with doping. A similar result is obtained if the recombination process occurs via impurity centers (Shockley-Read equation [20]), which will not be shown here. The recombination rate also influences the stationary density of electrons and holes produced by light excitation. One obtains from Eqs. (6) and (7) ... 

What about the minority carrier injection process depicted in Figure 14 Here, contrasting with the process considered above, the hole injection step itself is usually very fast (see below). Then the current is limited by diffusion/recombination described by the Shockley equation [201] ... 

This is the so-called Shockley-Read equation describing recombination via traps. It also plays an important role in the description of recombination processes via surface states, as discussed in Chapter 2. In the above equation one may also replace n and pt by the relations... 

For the analysis of the mobility and the threshold voltage the saturation regime is used here. An analytical model based on the Shockley equation by Schmechel et al. [13] assumes that the electron and hole mobilities as determined from the linear or saturation regime are also valid in the ambipolar regime. As previously shown for the system under consideration, the mobilities determined from the saturation and ambipolar regime are in excellent agreement [27]. 

According to the IEEE standard test methods for the characterisation of OFETs [26], the Shockley equations for insulated gate field effect transistors (IGFETs) are used to approximate the field-indueed drain eurrent in the organic material between the drain and source contaets. It should be reeom-mended that the following assumptions form the basis of the applieability of the equations ... 

The Shockley equations describe a linear dependence between drain current and permittivity of the gate dielectric. In order to lower the supply voltage of OFETs, silicon nitride was examined because its permittivity Cnitride 8 is almost twice as large as that of silicon dioxide. Moreover, with a roughness of 1-2 nm rms it has the smoothest surface of the chemical vapour deposited dielectrics, which is one essential requirement for the growth of a well-ordered pentacene film. 

Of course these equations do not account for a field- and charge carrier density dependent mobility, which will result into slight deviations in the transistor characteristics. A similar model which is extended by the field dependent mobility was presented by Smits et al. [4]. Furthermore, the transistor subthreshold behaviour is not represented. Nevertheless, the extended Shockley equations are quite useful for a qualitative interpretation of obtained experimental results. 

The hole mobility was calculated using the Shockley equation for linear (Eq. (3a)) and saturation (Eq. (3b)) regimes [26-28] of the OFET correspondingly ... 

For the lower part, at j < 1 O 4 A cm 2, the ideality factor n was 2 and was independent of temperature in the range 300 to 600 K. It was shown by Strelchuk [23] that for this region the current is described in terms of the Sah-Noyce-Shockley model for recombination via a deep level close to the middle of the forbidden gap. According to the model, the pre-exponential factor j0 is determined by the equation ... 

We will now consider the open infinite chain, simulating surface formation. If the ideal hybridization condition Eq.(2.128) is satisfied, dangling orbitals with orbital energies a = as = ap appear at the end of the chain. These are the Shockley surface states, because they are strictly localized on atoms 1 and N, The solution for the general case is found by solving the secular equations for the open chain. Equations (2.123) have to be solved with bonding conditions ... 

One can readily verify that substitution of solution q.(2.156b) into Eq.(2.180) gives Eq.(2.159) for (7n. We will use this approadi to study again the equation for the Shockley surface states, but now in the limit of small coupling between the s and p electrons. The matrix elements of H are now ... 

The change of current with applied voltage is given by the Shockley equation. In a simplified form this is ... 

Furthermore, let gi () denote the piecewise linear approximation of the nonlinear flow versus effort relation of the t-tti diode according to Shockley s equation implemented by the switch model Sw Z),. 

FIGURE 8.22 Plot of the current given by the Shockley equation as a fnnction of the difference of potential across the junction. 

The Shockley equation models the behavior of an ideal diode or p-n junction made by joining two semiconductors differently charged by doping, one positively (p-type semiconductor) and the other negatively ( -type) (see Figure 8.22) ... 

Equation (6.10) can be put into a form familiar to that of the simple Shockley-Read theory, by means of the definition... 

Fig. 10 Definition of the four rates of capture and emission of electrons and holes by a single trap level. These four rate equations are the basis of Shockley-Read-Hall statistics, which defines the occupation probability and the recombination rate via this trap...

Equation (2.36) is the famous Shockley equation which is the ideal diode law [16]. According to Eq. (2.35), we have obtained again the same basic current-voltage dependence as already derived for majority and minority carrier devices with semiconductor-metal junctions (see Eqs. (2.18) and (2.31)). As already mentioned, the physical difference occurs only in the pre-exponential factor / g. The general shape of a complete j-U curve in a linear and semilog plot has already... 

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