Appendix D: Charge-Pumping Signals in MOSFETs



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Appendix D:

Charge-Pumping Signals in MOSFETs

 

In this appendix we will present the evolution of the total generation-recombination currents and the terminal currents in a small MOSFET during one period of the gate pulse. We consider large-signal charge pumping with the trapezoidal pulses applied on the gate. All results are obtained by using a selfconsistent numerical model. The signals are qualitatively discussed. Signals in MOS capacitors are modeled in one-dimension by an analytical approach in [435][434][233][232] and numerically in [149][87]. Measured signals can be found in [233][232]. Signals in MOSFETs obtained by an one-dimensional numerical approach are presented in [395][145][144] and by an analytical model in [115]. According to my knowledge, this is the first detailed illustration of the complete processes in the time domain, which occur during the charge pumping in a short-channel MOSFET, obtained by a two-dimensional transient approach.

In this appendix we consider two devices which are also used for the calculations presented in Sections 3.5.1 and 3.5.3:

  1. Virgin device: -gate/-channel MOSFET, with gate length ; effective (metallurgical) channel length (junction subdiffusion ); junctions are abrupt (no LDD); oxide thickness ; channel width . Acceptor-like traps are assumed uniformly distributed along the interface and in the energy space (arbitrary); trap density .
  2. Stressed device: the same as the virgin device, but with additional localized acceptor-like (arbitrary) traps; uniformly distributed in the energy space (arbitrary) and gaussian distributed along the interface with a peak density and peak location . Standard deviation is chosen as , giving the full width at half-maximum of which is comparable to the oxide thickness and to the width of the lateral field-peak. To propose the peak-location , we assumed the stress bias at , () and found that the lateral field-peak is located at . The maximum of the damage is chosen to be located away from the field-peak, toward the metallurgical junction, i.e. from the junction. In addition to the field distribution, the spatial distribution of the electron and hole currents injected into the oxide are calculated by MINIMOS [172]. At the stress bias holes are injected in the interval from to , whereas the injection current falls rapidly without this interval. The channel hot-electrons are injected in a broad interval before the pinch-off pointgif which is located at . After the pinch-off in the region toward the drain, electrons are injected into the oxide in a large amount as well, but a significant part of them does not contribute to the gate current (does not arrive at the gate electrode) due to the repulsive oxide field and the scattering in the oxide before approaching the potential maximum. As a conclusion, the position of the stress-generated traps corresponds approximately to the place where a significant injection of both, electrons and holes occurs.
    As a consequence of the chosen position and the standard deviation , almost all stress-generated traps reside within the drain junction, but very close to the metallurgical boundary. This fact has particular consequences on the charge-pumping characteristics.

The calculated signals of the total electron and hole net generation rates in the virgin and the stressed device are presented in Figure D.1, for the falling edge and in Figure D.2, for the rising edge of the gate pulse. Since the top level of the trapezoidal pulses is higher than the channel threshold voltage, the complete interface becomes inverted during the top level. However, only the interface region from to approximately is accumulated during the bottom level, because of a limited penetration into the junctionsgif (see Figure 3.22). As a consequence, some of the stress-generated gaussian distributed traps are not active in charge pumping.

The electron emission at the beginning of the falling edge occurs at first in the steady-state mode, Figure D.1. The emission current is governed directly by moving the Fermi level of electrons at the interface in time; . The traps laying above Fermi level are emitted. For these traps the emission time constant is shorter than the capture time constant which depends on the surface concentration . depends on the slope of the gate bias changes. The maximum of the electron emission current corresponds approximately to the transition from the steady-state to the non-steady-state emission mode. When the gate bias pass the threshold voltage, the surface electron concentration and, consequently, fall rapidlygif. From this moment the electron emission current becomes independent of the gate bias changes and falls to zero obeying a nearly exponential law. The localized gaussian traps

 

are assumed to be of acceptor type and in an amount which is sufficient to increase significantly the local potential (by nearly ). However, these traps are emitted after the uniform traps residing mostly in the channel do, because of a strong fall-off of the local threshold voltage in the junctions (Figure 3.5.1). Similarly, due to the spatially variable flat-band potential the capture of holes occurs later for the traps localized in the junction than for the traps in the channel. The opposite holds for the electron capture at the rising edge of the gate pulse, Figure D.2.

As evident from the calculation, significant emission and capture take place at the rising and falling edges of the gate pulses, namely when the gate bias varies, while these processes nearly vanish during the bottom and top levels. To explain this fact, let us observe that the total generation-recombination currents in MOSFETs are influenced by two effects while changing the gate bias:

The total electron and hole net generation currents are determined by both effects simultaneously.

At the beginning of the falling edge, a step in the generation currents occurs. Note that the complete interface including the junctions is active in the emission at this moment. Since the emission occurs in the steady-state mode and changes suddenly, the emission current exhibits a step from zero to a finite value. At the end of the falling edge, the amplitude of the emission current falls rapidlygif. This decrease is caused by stopping the broadening of the interface area which becomes active in the emission processes while decreasing the gate bias, noted as effect 1. above. An additional effect is that traps in the narrow interface area which has just become active, begin to emit in the steady-state mode. A sharp change in at the end of the falling edge causes a step in the emission current from this area.

Both effects noted above modulate the evolution of the total hole and electron capture currents. While the active localized traps are almost completely filled by electrons at the rising edge, they are only partially filled by holes at the falling edge. During the falling edge the penetration of the accumulation layer into the junction towards the drain causes that more and more localized traps become captured, thus producing a large hole recombination current. When the gate bias approaches the bottom level, the penetration into the junctions stops. Most of the active localized traps have already been filled by holes, as a consequence of the rapidly increasing hole concentration. However, traps around the region where the local charge-pumping flat-band potential equals to the bottom level are not filled. They begin to capture holes at the beginning of the bottom level (). Because the surface hole concentration is constant, the total recombination current falls with an exponential law to zero, as is shown in Figure D.1.

 

The evolution of the total emission and capture currents for electrons and holes in the stressed device may be nearly represented by a superposition of the currents for uniform and localized traps. The charge-pumping current is calculated to be in the virgin device and in an idealized device which only contains the localized traps. The current in the stressed device is which is very close to the sum of the former two currents. In this example the DC component of the bulk current differs from the DC component of the net generation currents of electrons and holes by only about due to the geometric current component and the reverse junction leakage currents. The fact that the total signal is a superposition of the signals from the traps residing in the particular interface and volume regions of the device is a typical peculiarity of the charge-pumping effect. The signals of terminal currents are shown in Figures D.3 and D.4 for the stressed device (both traps) and the virgin device (uniform). The terminal switching currents are two to three orders of magnitude larger than the generation-recombination currents. Since we calculate the charge-pumping current as the DC component of the terminal currents, it is evident that very accurate calculation of the transient terminal currents is indispensible for our approach.

 

In order to better understand the transient processes in the stressed device against those in the virgin device, we calculate the switching currents for an equivalent device which contains high density uniformly distributed traps in the channel. In this device, the traps are removed away from the junctions; thereby, the signals are not influenced by the geometric effects discussed in 1. In addition, the terminal currents in an equivalent device which does not contain any traps are calculated as well. The results are shown in Figures D.5.

At the falling edge when the localized traps begin to emit (from to in Figure D.3) the drain current is smaller in the stressed device than in the virgin device. The sum of the total charge in the inversion layer and the total charge trapped in interface states is nearly equal in both devices, because it depends primarily on the effective gate bias. In the virgin device a larger part of the total charge reside in the channel and a smaller part is trapped in interface states in comparison with the stressed device. As a consequence, the drain current is larger in the virgin than in the stressed device while removing the inversion layer. The effect may be clearly observed in Figure D.5 (upper).

The hole capture on the localized traps increases the bulk current in the stressed device with respect to in the virgin device (from to ). At the beginning of the rising edge, in the stressed device is slightly larger than the current in the virgin device due to the hole emission from the localized traps, as is shown in Figure D.4.

Electron capture processes at the rising edge can be nicely seen in Figure D.4. When electrons start to fill the traps which are not charged by the hole emission, the drain current increases compared with the device without traps. During the formation of the inversion layer the drain current in the device with traps is smaller than in the device without traps because of a smaller inversion-layer charge in the latter device. The net charge transfer which is represented by the area under the gate-current signal in one half period, is nearly equal in both devicesgif.

 

 



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Next: E Analytical Modeling of Up: PhD Thesis Predrag Habas Previous: C Selfconsistent Coupling of



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