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^{1}, M. F. Li

^{1,a)}, H. Y. Yu

^{1}, X. P. Wang

^{1}, Y.-C. Yeo

^{1}, D. S. H. Chan

^{1}and D.-L. Kwong

^{2}

### Abstract

In this letter, we report on a physical model to explain the frequency dependence of dynamic charge trapping in metal-oxide-semiconductor(MOS)transistors with ultrathin gate dielectrics. For transistors operating in a complementary MOS inverter circuit with a given gate voltage amplitude, we observed a reduction of charge trapping when the stress frequency is increased. This can be explained by the traps in the high- dielectric have the property of negative- centers. One trap can capture two electrons sequentially, and the trap energy is reduced as a result of lattice relaxation. Results of calculation using the model show excellent agreement with all experiment data.

This work was supported by a Singapore A-STAR research grant (No. R263-000-267-305). One of the authors (M. F. L.) wishes to thank Professor Peter Yu of U. C. Berkeley for his invaluable comments on the negative- centers.

### Key Topics

- Electrons
- 21.0
- Dielectrics
- 19.0
- Electron capture
- 17.0
- Metal insulator semiconductor structures
- 5.0
- MOSFETs
- 5.0

## Figures

Time evolution of threshold voltage under static and dynamic stresses of different frequencies for (a) -MOSFET, and (b) -MOSFET. The evolution has a power-law dependence on stress time.

Time evolution of threshold voltage under static and dynamic stresses of different frequencies for (a) -MOSFET, and (b) -MOSFET. The evolution has a power-law dependence on stress time.

(a) shift in alternating stress and passivation cycles of period . Symbols are experimental data, lines are from model simulation. (b) Frequency dependence of degradation in -MOSFETs after dynamic stress of , and (c) for -MOSFETs.

(a) shift in alternating stress and passivation cycles of period . Symbols are experimental data, lines are from model simulation. (b) Frequency dependence of degradation in -MOSFETs after dynamic stress of , and (c) for -MOSFETs.

(a) Three possible cases for the relationship between the number of trapped electrons versus stress time in one cycle of the dynamic stress. When increases from (where , and is the stress frequency) to , the number of trapped electrons increases from to . If the relationship between and is linear (curve L), then . Therefore, the number of trapped electrons during the same stressing time would be the same for two frequencies and the accumulative shift would be frequency independent. In order to explain the frequency dependence observed in dynamic charge trapping, must be larger than . This means that the relationship should be described by a concave-up curve. (b) Two-step procedure of capturing two electrons by a negative- trap. is the trap energy capturing one electron and is the number of those traps. is the trap energy capturing two electrons and is the number of those traps. When an additional electron is trapped, energy of the trap is lowered from E1 to E2 due to lattice distortion (Refs. 10 and 12). This energy lowering favors two electrons to occupy on the trap.

(a) Three possible cases for the relationship between the number of trapped electrons versus stress time in one cycle of the dynamic stress. When increases from (where , and is the stress frequency) to , the number of trapped electrons increases from to . If the relationship between and is linear (curve L), then . Therefore, the number of trapped electrons during the same stressing time would be the same for two frequencies and the accumulative shift would be frequency independent. In order to explain the frequency dependence observed in dynamic charge trapping, must be larger than . This means that the relationship should be described by a concave-up curve. (b) Two-step procedure of capturing two electrons by a negative- trap. is the trap energy capturing one electron and is the number of those traps. is the trap energy capturing two electrons and is the number of those traps. When an additional electron is trapped, energy of the trap is lowered from E1 to E2 due to lattice distortion (Refs. 10 and 12). This energy lowering favors two electrons to occupy on the trap.

Calculated time evolutions of using Eqs. (1)–(4) at various frequencies are plotted using lines, showing good agreement with the experimental data (symbols).

Calculated time evolutions of using Eqs. (1)–(4) at various frequencies are plotted using lines, showing good agreement with the experimental data (symbols).

## Tables

Definition of parameters used in the model.

Definition of parameters used in the model.

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