3.5.2 Extraction of the Spatial Distribution of Interface Traps in MOSFETs



next up previous contents
Next: Symmetrical Case: Up: 3.5 Hot-Carrier Degradation Analysis Previous: 3.5.1 Charge-Pumping Characteristics of

3.5.2 Extraction of the Spatial Distribution of Interface Traps in MOSFETs

 

A detailed study of the extraction of the spatial distribution of interface traps in MOSFETs by means of charge pumping is presented. Both problems, MOSFET before and after a nonuniform stress are considered. The analysis is based on the rigorous two-dimensional transient model of the charge-pumping experiment, which has been introduced in the preceding section. The accuracy of the extraction procedures is analyzed. A systematic error is found in some charge-pumping methods, which occurs due to the variation of trap emission times during the course of experiments. The present techniques are improved to account for this effect. A charge-pumping method is discussed, which does not suffer from this error.

Hot-carriers in devices produce interface (and bulk) traps, trapped charge in the oxide and additional oxide traps, which could change the device characteristics. How the characteristics of an MOSFET is degraded depends on the amount, location and the nature of the damage. It is quite difficult to extract the parameters of the damaged region from the device static characteristics like the threshold voltage, the transconductance and the drain current, although these quantities are often used as a monitor for the degradation. In fact, the inverse approach is the only way to extract some information from these quantities: for assumed distributions of interface states and fixed surface charge the changes in device static characteristics are modeled by simulation. Comparisons of the simulation results with experimental data provide information on the ``quality'' of the assumed spatial distributions, nature of traps and amount of charge (see references cited in Section 3.5).

 

Experimental methods for the extraction of the amount and the spatial distribution of interface traps and fixed oxide charge which are generated in nonuniform hot-carrier stress are based on:

1)
the drain-bulk gated-diode generation current at reverse bias [444],
2)
the drain-bulk gated-diode recombination current at forward bias [16][15],
3)
the gated-diode tunneling current (at low temperature [4], in restricted way; see discussion in Section 4.1) and
4)
charge-pumping techniques [287].

By the gated-diode generation-recombination current only the contribution of the mid-gap levels can be measured (around ), since these traps give the dominant contribution to the leakage current. Moreover, the amount of the extracted traps depends directly on the corresponding capture cross-sections and , because of . The capture cross-sections are, however, not known accurately, particularly for the spatially localized mid-gap traps generated under nonuniform stress. Unlike the gated-diode leakage methods, in the large-signal charge-pumping techniques the extracted trap density is only weakly dependent on the error in determining the capture cross-sections due to a logarithmic dependence of the active energy interval in the band gap on and .

Charge-pumping techniques have been extensively used to extract the spatial distribution of interface traps [423][398][374][288][287][272][78][34][9] and fixed oxide charge [480][288][78][75][74] along the oxide/semiconductor interface in MOS devices before and after electrical stress. The procedures used to calculate the charge distributions from the experimental data are based on analytical expressions which, however, rely on some approximations:

According to my knowledge, no confirmation has been given for the validity of the charge-pumping-based extraction methods proposed in the literature. The accuracy of the obtained distributions and in the channel and within the junctions is still unknown, because there is no method to measure these distributions directly.

In this study, a rigorous two-dimensional transient model of the charge-pumping experiment is used to evaluate the validity of the extraction procedures. Our approach is described in Figure 3.29. For assumed distributions of interface traps and fixed oxide charge the result of some charge-pumping measurement (e.g. versus source and drain junction reverse bias ) is calculated numerically. The calculated is further used instead of the experimental data. Comparing the obtained trap and charge distributions with the assumed distributions, we are able to evaluate and improve the present experimental techniques. Here we benefit from the ability of the numerical model to provide an exact solution to the problem for an assumed physical model of interface traps, physical parameters and dopant distribution in the device. This model accounts for all parasitic transient effects in the charge-pumping experiment, as well as for all restrictions in the analytical approaches noted above.

 

Before discussing the extraction methods, remember the definitions for the charge-pumping threshold and flat-band voltage; those referred to the total filling of traps. The charge-pumping flat-band potential is defined as the gate-bulk bias at which the surface hole concentration equals to some critical concentration sufficient to refill all interface traps during the gate-pulse bottom level . By introducing , where is the hole capture time constant , one obtains

 

It is expected that , which results in the total filling of almost all traps with holes during . Analogously, the charge-pumping threshold voltage is defined as the gate-bulk bias at which the surface electron concentration equals to some critical value sufficient to refill all traps during the gate-pulse top level . It follows that

 

and depend on the characteristic time intervals and . A comparison between and and the conventional device threshold and flat-band voltages is given in Section 3.3, where one-dimensional analytical model of the MOS structure is employed. Both, and can differ from and significantly. Therefore, and should not be applied for the extraction of spatial trap distributions.

 

We focus only on the interface states and neglect fixed oxide charge in the following. The mostly applied charge-pumping technique to measure consists of applying gate-bulk trapezoidal pulses with all parameters , , , , and fixed, while the drain/source-bulk reverse bias is varied in the experiment. The technique is known as method II from [374]. This technique will be analyzed henceforward. With the reverse bias the current changes due to two effects (in -channel devices):

(1)
The edges of the area available for the hole capture during the low gate-pulse level at the source side and the drain side move with the reverse bias . This is the desired effect used to scan the interface. The edges and are defined by the local .
(2)
The charge-pumping threshold voltage and the charge-pumping flat-band potential (in the junctions) vary with the reverse bias; Figure 3.30. The threshold voltage and the flat-band potential which determine the emission times, vary with as well. Consequently, the emission times for electrons and holes and therefore, the electron and hole emission levels and change with at each position at the interface. This effect has been neglected previously in literature. However, due to the effect, the charge-pumping current changes with not only due to and , but also because of the contribution of the whole channel to changes with . In order to describe the effect rigorously, care must be taken of the fact that the emission times are an explicit function of both, the spatial coordinate and the reverse bias: .

The relations and may be obtained numerically [423][398][374][9] as also done in this study, assuming that the doping profile is known. An analytical model for the width of the depletion region in the lateral direction has been employed too [272][271]. This approach is too rough to be applied in practice, because of the strong two-dimensional distributions in the doping, potential and carrier concentration around the drain/bulk junction close to the interface. In our study, we analyze the accuracy of the extracted trap distributions with respect to variations in . The latter concentration is not known accurately in measurements, since it depends on the capture cross-sections of the stress-induced traps.





next up previous contents
Next: Symmetrical Case: Up: 3.5 Hot-Carrier Degradation Analysis Previous: 3.5.1 Charge-Pumping Characteristics of



Martin Stiftinger
Sat Oct 15 22:05:10 MET 1994