3.5.1 Charge-Pumping Characteristics of MOSFETs after Hot-Carrier Stress: A Numerical Study



next up previous contents
Next: 3.5.2 Extraction of the Up: 3.5 Hot-Carrier Degradation Analysis Previous: 3.5 Hot-Carrier Degradation Analysis

3.5.1 Charge-Pumping Characteristics of MOSFETs after Hot-Carrier Stress: A Numerical Study

 

The influence of the localized interface states and fixed oxide charge on changes in the charge-pumping characteristics after stress will be discussed in this section. Typical characteristics, namely the charge-pumping current versus gate bottom level is considered. The changes in can provide a good quantitative estimate of the amount of the generated interface traps. However, only restricted information on the trap location and nature, as well on parameters of the damaged region consisting of oxide trapped charge is accessible [492][380][196][194][187][77][38]. Although the authors are clearly aware of these limitations [196][194], a quantitative study is still missing in literature.

In the first example we consider an -gate/-channel conventional MOSFET stressed at maximum substrate current: , . After analyzing the spatial distributions of the field, Figure 3.23, and the current injected into the oxide [172] by using MINIMOS, we assume that the peak of the damaged region is located at . The damage consists only of acceptor-like interface states (stress at maximum ) which are gaussian distributed along the interface. The chosen standard deviation of is somewhat smaller compared to a realistic two to three times larger value. In fact, we consider a narrow distribution to emphasize an influence of the exact position of the damage. Before the stress, the traps are uniformly distributed along the whole interface in an amount of . These virgin and stressed devices are those introduced in Appendix D. No fixed charge is present in the devices. Figure 3.21 shows the curve calculated numerically for both, the virgin and the stressed device. Apparently, a large shift to the left occurs for the stressed device with respect to the virgin device, in spite of a large amount of acceptor-like traps which should increase the local threshold voltage. To explain this unexpected result we analyzed the spatial distribution of the charge-pumping threshold and flat-band voltage near and within the drain junction, Figure 3.22. A large difference of between in the middle of the channel and at the location of the damage causes the localized traps to be scanned at a lower gate top level than the traps in the channel, resulting in the shift to the left and not to the right, as expected. Even in the channel region close to the metallurgical junction, is remarkably lower than in the middle of the channel; at the metallurgical junction this difference becomes , which corresponds to a density of uniformly distributed trapped charge in our example. An unexpectedly large lowering of in the channel region near the junction (excluding them) is produced by 1) decreasing channel doping and 2) the two-dimensional effects due to the proximity of the junction - charge sharing.

 

A second observation is that the increase of the local charge-pumping threshold voltage due to the interface charge is only at the location of the trap peak density, in spite of a large amount of traps. Three facts deserve attention here:

 

Henceforward, we focus on the latter effect. In order to estimate the amount of the localized interface charge, the local potential shift is a quantity usually subjected to measurements. Typical examples represent the displacement on the voltage axis of the GIDL characteristics [455][278][111][4], the voltage shift in the charge pumping [492][480][196][194][74][39][30] and capacitance measurements [288], as well as different voltage changes connected with terminal currents [490][481]. For a uniformly distributed charge at the oxide/bulk interface, it yields a density of from the measured voltage shift . As a rule this expression is also used for a localized charge, in such a way that the measured voltage shift associated with some position at the interface is converted in the local interface charge density at this position by simply setting . This approach is incorrect and can lead to a large underestimation in the density-peak. A very detailed analytical and numerical study of this problem is presented in Appendix F. Hence, an example is adduced and some conclusions from Appendix F are noted. Let us consider the interface charge with a constant density of in the interval . Figure 3.24 shows the spatial distribution of the local threshold voltage in the area around the localized charge, where , with the normalized charge width being a parameter. The MOS structure consists of -type bulk which is uniformly doped in moderate concentration . The threshold voltage at a particular position is defined in a standard way, as necessary to induce the surface electron concentration of at this position. The variation of the threshold voltage associated with the middle of the trap region lies far behind its extreme value which is connected with the spatially uniform charge , even when the width of the trap region is larger than the oxide thickness (). As opposed to the uniform charge which results in a simple translation on the voltage axis, is not constant, but is affected by several parameters: gate-bulk bias , oxide thickness , charge density , charge width and bulk doping in the general case. An exact calculation can be carried out exclusively by a two-dimensional numerical model, although a fairly accurate theoretical model can be derived assuming the total depletion approximation, as is done in Appendix F. To explain the physical mechanism lying behind small surface potential changes for a localized charge, remember the mechanism taking place when a uniform charge is inserted at the interface; a problem which can be considered in one dimension. Hence we fixed the gate-bulk bias. A negative interface charge reduces the surface field in semiconductor, thereby reducing the total charge in the semiconductor per unit area which corresponds to . The surface potential decreases to a value determined by . Decreasing causes the oxide field to increase, consequently increases, as well. The latter effect partially cancels the initial lowering of . For the localized interface charge the initial decrease in induces a smaller decrease in than that for the uniform charge, because the space-charge region residing remotely from the interface is influenced strongly by the oxide field from the interface region surrounding the localized charge due to the two-dimensional effect. The phenomenon is particularly pronounced when the width of the localized traps is much shorter than the depletion region width; a condition typically fulfilled in total depletion and inversion. When the trap region is supposed to be sufficiently wide to gain control over the whole space-charge region under itself, this two-dimensional effect vanishes and the local surface potential becomes close to that corresponding to the uniform interface charge.

 

When carefully exploring the effect of a spatially inhomogeneous interface charge , two problems can be extracted:

  1. to find the surface-potential perturbation occuring due to . The gate and other terminal biases are assumed constant.
  2. to find the variation in the gate bias necessary to establish the same conditions in the point at the interface with presence of the charge in device, as those conditions holding at with absence of charge. In this problem , and are fixed.
In the typical measurements of the voltage shift we are dealing with the second problem. These two formulations are completely different. In Appendix F we solved theoretically the first problem for the localized uniform charge-sheet, under the restriction of total depletion in the bulk; expressions F.15, F.16 and F.19. The solution to the second problem follows after establishing a connection between both solutions (relationship F.21). For a largely depleted bulk it turns out that . The localized charge becomes ineffective in both, perturbing the surface potential and shifting the gate bias ; Figures 3.24 and F.5. If the bulk is only shallowly depleted, increases, easily approaching the limiting value of . As opposite, attenuates, although increases with respect to its extreme value influenced by the depletion-region width; expression F.22 and Figure F.3. This condition corresponds to e.g. flat-band calculation, presented in Figure F.4.

From the preceding analysis two practical consequences arise: 1) a very localized interface charge can be quite ineffective in perturbing the local potential and 2) if some kind of the distribution which is connected with the damaged region is available from measurements, it is not a trivial task to reconstruct the exact interface charge distribution which produces , even though the doping profile is known in this region. In particular, from the measured an average interface charge density cannot be calculated by , but the width of the damaged region and the width of the bulk depletion region must be accounted for in the calculation, as well. A useful engineering approach has not been developed yet, but the study in Appendix F has laid a solid base to accomplish this task.

Generally we may conclude that an artificial shift, due to doping profile, vicinity of the junction and other two-dimensional effects, is absolutely dominant over the local voltage shift due to charge in the damaged region itself, including the damage located in the channel near the junction. However, in nonuniform hot-carrier stress the damage is never generated in the channel areas remote from the junctions.

 

We continue the discussion on the charge-pumping characteristics. Evidently, changes in the potential depend on the charge density. To examine the influence of the trap density on in a quantitative manner, we vary both, the location and the peak density of the gaussian distributed traps for the same devices as in the first example. The numerically calculated differential charge-pumping curves are shown in Figure 3.25, where the curves for the density of are multiplied by . The family of the characteristics for the density of is less displaced to the left with respect to the virgin device, than the family for , as results from a higher local potential increase induced by the trapped charge. The differences in the voltage shift between the two families are much less than the changes in the shift when varying the location of the peak by only. Note that a distance of nearly represents the resolution of the charge-pumping methods for the extraction of the lateral trap profile. Moreover, in spite of the traps located at also residing in the channel, the displacement of the post-stress curve is only influenced by the density of the induced traps slightly.

 

Similar result come out when analyzing the impact of the nature of the traps on the post-stress . Figure 3.26 presents the result carried out by numerical calculation for the same device, assuming either a donor or acceptor nature of the induced traps. Acceptor-like traps induce a shift to the right, mostly at the rising edge, while donor-like traps induce a shift to the left, mostly at the falling edge of the differential characteristics. As follows from the calculation, a drastic change in the nature of the traps has just the same impact on the characteristics as minor changes in the position of the damage by .

The conclusion that the exact location of the damaged region is more important than the density and nature of the traps induced by stress is consistent with the observations in the literature [196]. It has not been expected, however, that the effect be so strong. It is worth to adduce that, although the shift of the post-stress curves cannot provide reliable information of the nature and density of the induced traps, the derivation of these curves at the upper plateau from the maximum to the abrupt part of the falling edge directly yields the spatial trap distribution (cf. Section 3.5.2).

 

It has been proposed that the back-shift of the edges of the stressed curve after a subsequent hot-electron injection may be used to estimate the amount of fixed positive charge which is trapped in the oxide in the primary stress [380][196][194][30]. Considering -channel devices, after hot-electron-hole stress (EH-stress) and hot-hole stress (H-stress) at a medium and a low gate bias with respect to the drain bias () both, interface trap generation and trapping of holes in the oxide occur. During short subsequent channel-hot-electron injection (E-stress) at a high gate bias (), electrons are efficiently trapped

In spite of several extensive studies which of these two trapping sites are present in a larger amount in stressed devices, this is still a subject of controversy in literature [197][107]. To prove the claim that the back-shift of the characteristics after the E-stress is directly proportional to the positive charge trapped in the oxide, we carried out additional model-experiments including fixed charge in our device. Figure 3.27 shows the calculated characteristics for different locations of the positive charge: 1 - at the same position as interface traps , 2 - left from the interface traps, in the channel and 3 - right from the traps, in the junction. Both, and have a gaussian distribution with . Interface traps reside partially in the channel, but mostly in the junction. The dashed curve is for absence of any fixed charge. It can model the characteristics after neutralization of all trapped holes by E-stress if no electron trapping on neutral sites occurs. Calculations show that the back-shift is affected by the position of the peak of the oxide charge with respect to interface states . However, this fact may be exploited to estimate the relative positions of both damages with respect to each other. Small changes in the deep-tail region (low ) suggest that is generated mostly left from in the region towards the channel. Large differences in the deep-tail region clearly show that is produced right of in the area towards the drain. According to simulation, a fairly parallel shift of the rising edge occurs when the locations of and coincide. In this example, we calculate from the shift of . This value is smaller than the value assumed in the calculations, as a consequence of the local effect studied in Appendix F.

If electrons are trapped on the neutral sites which are generated in the initial stress, fixed oxide charge will be negative after the E-stress. The charge-pumping characteristics for this case are shown in Figure 3.28. From the upper figure we conclude that it seems to be impossible to judge in practice whether the curve is shifted to the pure- curve (dashed line) or to the curve (dotted lines) after the E-stress. Examining the characteristics on the lin-log scale qualitative differences between dashed and dotted lines may be observed in the deep-tail region. If the negative charge resides near the interface states, the differential characteristics with the negative charge (dotted curve 1) and without the negative charge (dashed curve) behave similarly. If the negative charge is displaced from the localized interface states in the region towards the drain, the negative charge is able to lower the local threshold voltage so that the negative differential charge-pumping current occurs. The change in the sign of is a typical indication of the presence of a negative trapped charge in the oxide. This effect can be used to prove the existence of the trapped electrons in a device, but only the presence not the absence can be checked. In the stress at low and very low gate bias the traps are produced in small amount and the hole injection

 

dominates (-channel devices). In these conditions the change in the sign of may be well observed [492], indicating that a large amount of neutral electron traps are generated in the oxide while injecting holes [103]. For the stress at , the situation is much more complicated. This stressing conditions are known to result in a maximal generation of interface states. After the subsequent E-stress the change in sign of may or may not appear, which is dependent on the relative position of the generated interface states and oxide trapped electrons to each other. Both curves, 1 and 2 in Figure 3.28, are calculated assuming a large amount of negative oxide charge, but only the latter exhibits a sign change. Additional experimental work, connected with numerical modeling, is necessary to explore the potentials of this effect to study the degradation at maximum stress.



next up previous contents
Next: 3.5.2 Extraction of the Up: 3.5 Hot-Carrier Degradation Analysis Previous: 3.5 Hot-Carrier Degradation Analysis



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