Injected charge density

Clearly, the optimal injection condition is for electrons and holes to be in balance, but this does not necessarily guarantee that b- I. For example, when both contacts are injection limited and the injected charge densities arc small, the prob-... 

A not-trivial ratchet effect can be observed when the injected charge density is voltage-independent, EL/R = Ep eV/2. Symmetry considerations require an asymmetric U (x) for a non-vanishing ratchet current in this case. Also an electron interaction must be present. Indeed, for free particles the reflection coefficient R(E) is independent of the electron propagation direction [14] and hence I(V) = —/(—V). 

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 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). 

We now calculate the J-V characteristics of an organic diode using the equations of the previous section. The values of the constant of integration C as a function of P 0) for different values of l are shown in Fig. 3.11(a) and for different values of J in Fig. 3.11(b). The constant C decreases rapidly as the injected charge density increases for all values of J and l. As 4>b tends to zero, P(0) tends to infinity and the constant C becomes zero. We have already mentioned that now the J-V characteristics of an organic Schottky... 

FIG. 3.12. The effect of current density on the constant of integration C at injected charge density P(0) = 1018 cm-3. Since voltage increases with J, C increases with applied voltage also. The values of the other parameters are the same as given in Fig. 3.11 [44]. 

At low frequencies, that is, for frequencies for which the wavelength of light is much larger than the largest dimension of the circuit, the current is the same everywhere in the circuit. In this case, the displacement current inside the material must be matched by an identical current in the external circuit used to maintain the potential difference across the sample. Thus one can observe the drift motion of the electrons inside the sample by monitoring the current induced in the external circuit. In our example, llie current is qv /L, or the product of the injected charge density with its average drift velocity normalized to the sample thickness. 

We note that the typical dependence results of the voltage dependent charge density, which contrasts with the ohmic conduction where the bulk carrier density is independent of the applied voltage. The thickness dependence in L results of the L dependence of the injected charge density, as opposed to the ohmic carriers density, which is independent of the thickness. 

We consider a current density je inside a medium due to an extra ( injected ) charge density Pe. The two quantities fulfill the continuity equation... 

The above procedure ensures a low density of injected charge carriers at the crystal surface and only about 3 ms elapse (due to the spreading of the solution over the crystal surface) before the current reading is obtained 68>. When charge... 

Several authors have observed that log J versus log V plots are straight lines. This result is consistent with the conventional power law (3.42). It is not clear how this result is modified for non-zero Schottky barriers. The J-V characteristics in our theory depend on the value of the constant of integration C. The Schottky barriers 4>b define P 0), and C depends on P 0), where P(0) is the injected charge carrier density at the contact. 

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