3.2 Charge Pumping (CP)

The CP effect was reported in 1969 for the first time [109]. One milestone in the development of this technique was the investigation and explanation of the method in 1984 [110]. The CP technique is a reliable and precise method for the measurement of defects at the substrate/oxide interface of a MOSFET. Thus, it is often used for the characterization of HCD, which is typically associated with an increase of such defects. The corresponding experimental setup is illustrated in Figure 3.4 and the schematic measurement procedure in Figure 3.5. The gate is pulsed by a generator between accumulation, in case of an nMOSFET defined by the low level of the gate voltage () smaller than the flatband voltage (), and inversion, defined by the high level of the gate voltage () higher than . The source to substrate and drain to substrate diodes are slightly reverse biased. Simultaneously, the bulk current (), which consists of leakage currents of the reverse biased diodes and the , is measured.

The occurrence of can be explained by the recombination of majority carriers with minority carriers. A schematic illustration of the gate pulse and the corresponding is shown in Figure 3.5. When the pulse level is in the inversion phase (pulse level at ), a thin layer in the substrate near the interface (channel) is depleted of the majority carriers and populated by minority carriers. This leads to a trapping of some of them by existing interface defects. As soon as the pulse drives the MOSFET into accumulation (pulse level at ), the minority carriers leave the channel and the majority carriers flood it. Simultaneously, some of the interface defects with energies close to the valence band or conduction band can emit their trapped charges by thermal emission before the accumulation phase is reached due to the finite rising and falling slopes. These minority carriers are pushed into the substrate while switching to the accumulation phase without any contribution to because the overall amount of positive and negative charges is not changed throughout this process. By contrast, all other trapped minority carriers recombine with the majority carriers in accumulation, which gives rise to a net flow of charge into the substrate. This can be measured as and is directly proportional to the pulse frequency and the mean interface-state density. In the accumulation phase, some of the majority carriers are trapped by interface defects. Driving the MOSFET back into inversion results in a similar process as described for the transition from inversion to accumulation but with opposite carrier types.

As a consequence of the thermal emission of carriers during the rising and falling edge of the pulse, only interface defects within a particular energy range around midgap, which is smaller than the entire silicon bandgap, can be measured in . The energy boundaries in the lower and upper half of the bandgap, defining the active energy interval, are given by [111]

with

/	boundary in the lower / upper half of the bandgap
	intrinsic Fermi level
/	pulse rise / fall time
	pulse amplitude
	thermal drift velocity
/	capture cross section for holes / electrons
	intrinsic carrier concentration.

For the calculation of , it has to be considered that dependent on the chosen and only a particular fraction of the channel is probed during a gate pulse as shown in Figure 3.6 with two pulses (a) and (b) [112]. Due to the lateral doping profile along the channel (regions near source and drain are typically lightly doped) the local and differ along the channel. The requirement for driving one particular lateral position from accumulation to inversion is met if    and    at this position. Pulse (a) meets this requirement only for the lightly doped regions near the source and the drain but not for the central region because   . Summing up the length of the regions, which contribute to for pulse (a) results in the effective length . By contrast, pulse (b) meets the requirement for a broader lateral range, including the central region of the channel, resulting in an effective length . In this regard, the effective area, which corresponds to the fraction of the channel probed during the gate pulse, can be calculated according to

with

	active channel area
	effective channel length
	gate width.

Finally, the charge pumping current can be written as [110, 112]

with

	pulse frequency
	electron charge
	gate width
/	boundary in the lower / upper half of the bandgap
	interface-state density.

The measurable depends on the active energy interval, which is affected by experimental parameters like and of the pulse, the as well as . This allows for an energetic profiling by modification of the experimental parameters. Moreover, due to the fact that and depend on the lateral position in the MOSFET, the spatial distribution of interface defects can also be analyzed. As a result, different CP techniques have been proposed [112].

For example, the constant amplitude CP technique uses a variable and constant , and as shown in Figure 3.7. is swept through a broad voltage range from    to   . This leads to an () which shows first an increasing behavior with increasing as long as   . Then the charge pumping current reaches its maximum when both    and    are fulfilled. Finally decreases with further increase of when only    is satisfied. In this technique, the active energy interval remains constant but in fact, different channel areas contribute to , depending on and as shown in Figure 3.6 schematically. Although it seems quite advantageous to distinguish between contributions of central interface defects and defects in the lightly doped regions based on the () shape, such a characterization technique remains qualitative because the particular effective channel area () contributing to at each is unknown.

By contrast, remains at a fixed value for the whole measurement satisfying    while is swept through a broad voltage range. As a consequence, is a function of only, which leads to a probing of the channel from outside to inside in a symmetrical way if is swept from    to   . In order to distinguish between local and energetic information, the active energy interval defined by the energy boundaries given in the Equations 3.5 and 3.6 has to be fixed. This is realized by adapting and after every step as a compensation of the increasing . Pure energetic profiling is enabled if and are fixed at and , respectively, and either or are changed. Furthermore, by variation of the active energy interval can be broadened or narrowed.

Both, energetic and position profiling of defects at the interface, typically realized with standard equipment, has made the CP method a widely used characterization technique. It gives a deep insight into degradation mechanisms associated with an increase of interface defects, typically HCD.