Hole current density

The boundary conditions are given by specifying the panicle currents at the boundaries. Holes can be injected into the polymer by thermionic emission and tunneling [32]. Holes in the polymer at the contact interface can also fall bach into the metal, a process usually called interlace recombination. Interface recombination is the time-reversed process of thermionic emission. At thermodynamic equilibrium the rates for these two time-reversed processes are the same by detailed balance. Thus, there are three current components to the hole current at a contact thermionic emission, a backflowing interface recombination current that is the time-reversed process of thermionic emission, and tunneling. Specifically, lake the contact at Jt=0 as the hole injecting contact and consider the hole current density at this contact. 

Now think of the n —>p hole current. When the holes from the n-type of medium reach the junction [see Fig. 7.21(c)], they do not see any barrier due to an electrical potential difference, so they simply tumble over the potential drop. Hence, the n —> p hole current density at equilibrium is controlled only by diffusion and is simply proportional19 to the number of holes, nhn, in the rz-type of material ... 

Now, what happens if the potential difference across the junction is lowered by an amount rj (Fig. 7.23) The holes making thep —> n crossing find a smaller barrier to chmb, and hence the p —>n hole current density becomes... 

But the holes crossing from the n- to p-type of material still have no barrier to climb. Hence, then— p hole current density still depends only on the number of holes in the 7 i-type of material and... 

The total current density across the junction is therefore equal to the sum of the electron and hole current densities, just as the total ionic-migration current density in an... 

In equation 17, lp is the hole current density, Gp is the rate of generation of holes, and Rp is the rate of recombination of holes. The hole current density is defined by equation 18... 

The measured photocurrent response is the sum of the charging and transfer components or alternatively the difference between the photogenerated hole current density qg and the recombination current density /rec... 

The three terms on the left-hand side of (16.26) account, respectively, for the diffusion, recombination, and generation of holes under illumination. Without advancing into mathematical details, one obtains the hole current density at the interface between the bulk and the space charge region, i.e., the diffusion current density ydiff, as given by... 

Let the semiconductor pass current in the x-direction only so that a one-dimensional model is being used. Consider any narrow region lying between x and x+Ax. Then electron and hole current densities flow in and out of this region and there is also a recombination current density eUAx (where e E [e ). The illustration fig. 5.1 of the charge conservation condition is drawn with the current directions appropriate for a p-n junction under forward bias. One sees that... 

Further we determine the separate components of the electron and hole current density vectors. It is necessary to eliminate the components of electric field and concentration gradient along the y axis from the expression for the current density along the x-axis. The same is valid in the opposite direction. 

Let us consider separately the electron and the hole current. First, we eliminate the x-component of the hole concentration gradient from the expression for the y-component of the hole current density. In this manner we obtain... 

The equations for hole current density and the corresponding continuity equation are obtained in the equivalent manner. 

J and Jp are the respective electron and hole current densities is the semiconductor permittivity q is the unsigned charge of an electron Np) and are the donor and acceptor concentrations N, is the trap density... 

---