Dependency of mobility on temperature
The performance of a PLEDs or FET s depends upon the mobility of the charges. Previously it was believed that the mobility of charge particle s in a device depends only on temperature and the field applied, but until recently it was found that mobility also depends up on the charge carrier density. W.F. Pasveer and his team has not only shown a productive result for the impregnable dependency of mobility on temperature, carrier density and electric field but they have also established a theoretical equation for all the three parameters dependency on mobility using an current voltage experimental data analysis on two disordered semiconducting polymers. The excellent accord with the experiment confirms that at room temperature charge carrier density dependency of the mobility was more important than the electric field but at low temperature and high field the field's dependency plays an important role. The experimental analysis done on the two materials (NRS-PPV & OC1C10-PPV) doesn't indicate the need for an assumption of certain spatial energy correlation. They also satisfactorily describe the Gaussian site energy distribution; thence a simple uncorrelated Gaussian disorder model was considered. The models considered for the experimental analysis shows an effective result for an average intrachain and interchain hopping in the conjugate semiconductor polymers. These conclusion and results obtained for the samples are also applicable for the small molecule based materials.
Use of conjugate semiconducting polymers in light emitting diodes and field effect transistors has triggered intensive research into the optoelectronics and electrical transport properties of these materials. The charge carrier transport is one of the important factors for determining the performance of the device. The parameters (temperature, charge density & electric field) dependency on mobility of charge carriers influences the designing, synthesization and execution of the device. In the past, the dependency of the charge carrier density on mobility was overlooked, which induces the hoping distance and width of the density of the states in disordered polymers. The dependency of the charge carrier density on the mobility was explained by testing on hole only diodes and FETs with same polymer as active material, which shows a huge difference in magnitude between the diode and FET.
W.F. Pasveer and his team derived the relation between the mobility and charge carrier density by defining mobility from a numerical solution of master equation and by applying periodic boundary condition & site energy to the equation. The dependency of the mobility on charge carrier density can be seen in the equation below:
µ=i,jWij Pi 1-PjRij/PEV
They considered the hopping as thermally assisted tunnelling process and assume coupling to be a system of acoustic phonons. In the experiment, they also consider only the cubic lattice with lattice constant a and the maximum hopping distance considered was 31/2a.
Mobility of charge carriers is an important factor for determining the performance of the device. The charge transport in a disordered polymer is considered as a hopping process between localized sites, which has been underestimated in the previous literature. The variations obtained in the on-site energies due to disorder are assumed to be Gaussian. Hence a Gaussian disorder models were considered for the analysis purpose. The parameters that affect the mobility of the charge carriers are temperature, charge density and electric field. Recently many simulations (Monte Carlo) and empirical form by Vissenberg and matters has been derived to establish a complete relation between the mobility as a function of temperature, field & charge density, but they failed in one way or the other to give a complete equation. The current voltage experiment of W.F.Pasveer and his team on semiconductor polymers based devices shows an excellent output for describing the mobility of the charge carriers.
"The Mobility As A Function Of Temperature, Charge Carrier Density And Electric Field µ T, P, E= µ T, P f (T, E)."
To determine the current voltage characteristics of the polymer layer of certain thickness, which is sandwich between two electrodes they make use of the above obtained results. They have neglect the complication related to injection because of the carrier at the injecting electrode was very high. The conclusion they came up with for a constant mobility including diffusion was that the diffusion effect causes an increase in current at low voltage only and a change in density of charge & field close to electrode only.
W.F.Pasveer and his team have performed a charge density - voltage experiment on two hole-only devices NRS-PPV and OC1C10-PPV. The various dimensional considerations taken for the samples can be seen in the graph and they have used indium tin oxide & evaporated gold contact as top and bottom electrodes. The experimental and theoretical result can be clearly observed in the graph, the symbols in the graph represent the experimental values and the lines represent the theoretical values of current versus voltage result obtained at various temperatures.
We observed an excellent agreement between the experimental and theoretical results. The huge effect of density dependence of mobility was clearly visible from the graph. W.F.Pasveer assured the experiment by calculating the carrier density and electric field distribution in the hole-type device by considering three different situations: (a) dependency of mobility on temperature, charge carrier density & field (full line); (b) dependency of mobility without electric field (Dashed lines); (c) mobility without dependency of charge carrier density and electric field (dotted lines).
These results shows that for a correct description of charge carrier injection, transport & recombination the effect of both charge carrier density and field are need to be accounted. Though this reading obtained was for low carrier density and high electric field but the effect of high carrier density and low electric field is also need to be considered for the interpretation of time of flight measurements, which was done in the previous work by P.W.M.Blom and M.C.J.M. Vissenberg.
Though they have obtained some positive conclusion for the experiment but there were some consequences for the internal field distribution and density of charge carriers for both signs in the devices like LEDs and FETs. Furthermore larger values of width of the Gaussian energy distribution and typical hopping distance were found. However we also need to replace the hopping problem in a polymer by using an isotropic hopping model on a regular lattice.