3.4 Geometric Current Component and Other Non-Ideal Effects



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Next: 3.4.1 Minority Carriers Remaining Up: 3 Analytical and Numerical Previous: 3.3.2 Emission in the

3.4 Geometric Current Component and Other Non-Ideal Effects

 

In the standard charge-pumping theory which is considered in the preceding section, it is regularly adopted that the free minority and majority carriers behave quasi-statically in MOSFETs. The only transient effects occur due to the generation and recombination through the interface and bulk traps. It has been proposed, already at the time of discovering the charge-pumping effect, that the charge-pumping current can also originates due to a finite time for removing the minority carriers out of the channel during the MOSFET turn-off, in addition to the current due to the transient generation-recombination over the traps [43]. As the time for the removing of the minorities is found to be strongly dependent on the geometry of MOSFETs, this current component is called ``geometric component'' [43]. In the measurements of trap properties, this current represents a parasitic effect. The primary interest was always to suppress it, either by using devices with a sufficiently short channel, by avoiding the application of very steep gate pulses or by biasing the source and drain junctions reversely [154][117]. A detailed study of the geometric component in the charge-pumping current is still missing. Recently, a very sensitive technique has been proposed to measure the geometric component also in the cases when the generation-recombination component largely dominates in the charge-pumping current [98].

In this section we studied the geometric component by means of numerical two-dimensional transient model of MOSFETs. After each transient simulation, the DC component of the net generation rates and the terminal currents is calculated for the periodic-steady-state conditions. Comparing the DC components of these quantities the geometric current component can be easily extracted. Such an approach represents a unique method to clarify the geometric component in detail [169]. We have studied bulk MOSFETs and SOI devices [192][169]. In this work, we focus on the bulk MOSFETs.

The family of the characteristics shown in Figure 3.12 represents the charge-pumping current calculated for several identical MOSFETs, but with different gate length . The devices contain uniformly distributed interface states. Trapezoidal pulses are applied on the gate. The fall time is varied from to , while other parameters of the waveform are kept constant (with exception of ). A dramatical increase in the is obtained for short , particularly in the long-channel devices. Figure 3.13 shows the same family, but calculated assuming a large reverse bias applied on the source and drain junctions with respect to the bulk.

 

Some conclusions follow:

The data shown in Figures 3.12 and 3.13 should be compared with the some of practical judgements in the literature, like those that the response time of minority carriers is less than some in devices [144], or that for devices with the geometric component vanishes if [117]. Note that the relative importance of the geometric component depends on the total number of traps in device.

 

The measured charge-pumping current is the DC component of the bulk current , which consists of the electron and the hole component: . In an ideal theory vanishes and equals to the DC component of the total net recombination rate in device (for -channel MOSFETs). The results shown in Figure 3.12 are splitted into the electron and hole components of and presented in Figure 3.14. It is obtained that

It is important to clarify which kind of devices we consider. The thickness of the substrate is assumed to be only about . This depth is much smaller than the thickness of the substrate in the real bulk MOSFETs (several hundred ) and even smaller than a typical depth of the wells in CMOS technology. The assumed value of is, however, larger than the thickness of the active part of devices. The minority carriers injected into the bulk from the device active area are detected by the bulk contact positioned at in our calculations. These carriers can also be collected by a - junction laying closely under the device, as is employed in the experimental technique in [98]. For devices made directly in the bulk (no wells), the injected electrons have to travel huge distances to arrive at the physical bulk contact. A part of them recombine over the deep traps in the substrate while traveling, which increases the bulk hole current and decreases the bulk electron current. This effect is not interesting for us. We only analyze the processes in the active part of devices and all conclusions given in this study refer to this assumption.

 

In order to find the physical mechanisms responsible for the geometric component, we considered the evolution of the surface carrier concentrations during the turn-off of an MOSFET. Figure 3.15 presents the numerically calculated distributions of electrons and holes in the center of the channel as a function of the distance from the interface at different moments. Due to a significant time for removing the carriers from the inversion layer through the junctions, as a consequence of a very short fall time of applied on the device which has the gate-length of , the minority carrier concentration near the interface is much higher than its quasi-equilibrium value for a given . Moreover, the concentration of the majority carriers is also higher than the quasi-equilibrium value which corresponds to the current gate-bias. In a short time interval (here of about ) high concentrations of both, electrons and holes are presented at the interface simultaneously. We propose three phenomena which could occur as result of a fast switching at the falling edge of the gate pulses:

  1. A very high surface electron concentration can reduce the emission of electrons from the interface traps by keeping the quasi-Fermi level high during the fall time. This effect is able to increase the in a limited amount, since it only cancels the lost of the trapped charge through the emission. Moreover, the traps emit from a very narrow energy range for very short . Accordingly, this effect is expected to be of a minor importance.
  2. A simultaneous presence of the high concentrations of both carrier types can cause an extended recombination over the interface traps and the bulk traps close to the interface. This effect is not limited with the number of the available traps, as the effect 1. The total recombination current is proportional to the free carrier concentrations or (whichever is lower), the duration of the process and the concentration of the trapping sites . The increase of the charge-pumping current due to an enhanced recombination is

     

    All holes recombined by this effect contribute to the charge-pumping current. If the process lasts a long time the recombined current can be large, which could explain a significant increase in the geometric component at short fall times, as proposed in [479][83]. In a limiting case at very short , all charge in the inversion layer can be removed by the recombination with the incoming holes. However, as we concluded in (1), the transient numerical calculations do not show an increased hole recombination, even at very short . Therefore, contrary to the believe in [479][83], this mechanism cannot explain the geometric component observed in experiments. Moreover, there is a negligible recombination over the bulk traps in the active part of devices (as suggested in [494]), as well. The enhanced-recombination effect is small because the surface concentrations are too low in comparison with very short times available for the process. In the example shown in Figure 3.15, the time interval is only (between the steps and ). For the surface concentration we calculate that the increases by about , which is completely negligible in comparison with . In general, when decreases the and increase, but becomes shorter. Even being of a minor importance, the enhanced recombination can be observed in the switching characteristics of long channel MOSFETs at very short fall times, as is demonstrated in Figure 3.16.

  3. The absolute dominant effect in generating the geometric current component is the injection of the minority carriers which remain in the channel, towards the bulk. These carriers are removed fast from the active part of MOSFETs. If the bulk contact lies closely under the device, as in our calculations, the transferred minority carriers arrive at the bulk contact in complete, where they are detected as the minority-carrier component of . There is no recombination in the bulk, since the transfer time is very short. In the following, the process is explained in detail.
    Let us assume quasi-static conditions. In strong inversion, with reducing the total charge in semiconductor decreases and the inversion-layer charge reduces according to the decrease of . The depletion-region charge is nearly constant. Bellow the threshold voltage the drops significantly, while the depletion-region width and the reduce so that the charge conversion is maintained for . If the junctions are not biased, equilibrium holds in the bulk.

     

    In transient conditions, nearly follows its quasi-static value during the falling edge for the gate voltages laying significantly over . Close to the current through the junctions becomes insufficient to maintain the quasi-static conditions in the channel. The is higher than in the quasi-static case, leading to a decrease in the surface potential . The reduction of is smaller that in the quasi-static case. Both, and decrease, since the is reduced. With further reducing under the surface field decreases, but less than in the quasi-static case. The is no longer removed from the channel in a relevant amount. Both, and instantaneously respond to the drop in because of a very small dielectric relaxation time of the majority carriers. Due to an enlarged , both, and are a bit smaller than their quasi-static values. There is no longer equilibrium for the minority carriers in the direction perpendicular to the interface. In the equilibrium the diffusion current component due to the gradient of equals to the drift current component due to . In the transient conditions the drift current is smaller than an enlarged diffusion current and the minorities start to diffuse towards the bulk, driven by the gradient of the minority quasi-Fermi level . To summarize, the minority carriers which have been remained in the channel inject into the bulk by the predominant diffusion and generate in -channel devices. Note that the diffusion is a very fast process; in absence of any electric field the peak of the charge-wave moves by diffusion in time obeying a law , where is the minority carrier mobility. Assuming we estimate a transit time of about . The carriers leave the active part of devices before the hole surface concentration increases significantly, namely before changes the sign and becomes repulsive for the minorities. The process of the generation of the diffusion-wave can be recognized in Figure 3.15. From Figures 3.16 it is obvious that a part of the minority carriers travels towards the bulk before the main part of them does, because the is always a bit larger in the transient conditions than in the quasi-static conditions. This is particularly evident in Figure 3.16 for . The charge injection into the bulk has also been simulated by a transient numerical model in [349].





next up previous contents
Next: 3.4.1 Minority Carriers Remaining Up: 3 Analytical and Numerical Previous: 3.3.2 Emission in the



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