Trapped carrier density

Fig. 6 Trapped carrier density profiles calculated from the steady-state continuity equation for open and short circuit conditions. A1l,o = 10 cm- ...

We developed earlier in (39) the relationship between free and trapped carrier density when the system rests at equilibrium. Equation (69) has a different meaning in that it states that equilibrium will be maintained for any time variation during kinetic measurements. Equation (69) is termed the quasistatic approximation and it was introduced to account for the properties of measured time constants in DSC [51 ]. 

There are many ways of increasing tlie equilibrium carrier population of a semiconductor. Most often tliis is done by generating electron-hole pairs as, for instance, in tlie process of absorjition of a photon witli h E. Under reasonable levels of illumination and doping, tlie generation of electron-hole pairs affects primarily the minority carrier density. However, tlie excess population of minority carriers is not stable it gradually disappears tlirough a variety of recombination processes in which an electron in tlie CB fills a hole in a VB. The excess energy E is released as a photon or phonons. The foniier case corresponds to a radiative recombination process, tlie latter to a non-radiative one. The radiative processes only rarely involve direct recombination across tlie gap. Usually, tliis type of process is assisted by shallow defects (impurities). Non-radiative recombination involves a defect-related deep level at which a carrier is trapped first, and a second transition is needed to complete tlie process. 

The excellent agreement between the TSC and P1A results has two implications. First, since the TSC method probes the product of mobility and carrier density, while the P1A probes only the carrier density, there seems to be no dominant influence of temperature on the carrier mobility. This was also found in other conjugated polymers like /ra/ry-polyacetylene [19, 36]. Second, photoconductivity (observed via the thermal release of photoexcited and trapped earners) and photo-induced absorption probe the same charged entity [36, 37J. 

TSDC experiments are customarily analyzed assuming the sample behaves ohmic, i.e., the contacts do not introduce an inhomogeneous distfibution of the electric field or carrier density and a uniform bulk density of carriers extend through the entire sample. Experiments were carried out in such a way as to minimize injection effects. Contact configuration was typical for TSDC experiments. Because the currents through the sample are, in almost aU cases, extremely small, we have used a sensitive DC ammeter (model Ul-15, detection limit <10 A) with a hnear output signal. The simplest way to obtain a record of TSDC is an X-Y recorder that displays I(T) and the temperature. The equipment for the extraction of trap-spectroscopic information may be connected with devices for electronic data processing. The experimental errors in determination are less than 2%. 

Capture and emission processes at a deep center are usually studied by experiments that use either electrical bias or absorbed photons to disturb the free-carrier density. The subsequent thermally or optically induced trapping or emission of carriers is detected as a change in the current or capacitance of a given device, and one is able to deduce the trap parameters from a measurement of these changes. 

Where Ms is the trap state density, N is the doping density, n and E, are the intrinsic carrier density and Fermi level in the grain boundary. Under illumination Fermi level changes to quasi-Fermi level and occupancy of traps also changes. This in turn changes... 

Here, an is the Bohr orbit radius of the isolated center and nc is the critical carrier density at the M-NM transition. Another way of viewing the transition is that of an electronic instability which ensues when the trapping of an electron into a localized level also removes one electron from the Fermi gas of electrons. This must clearly lead to a further reduction in the screening properties (which are themselves directly related to the conduction electron density) and a catastrophic situation then ensures the localization of electrons from the previously metallic electron gas. 

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