Substrate-bias-dependent dielectric breakdown in ultrathin-oxide p-metal-oxide-semiconductor field-effect transistors

Substrate-bias-dependent dielectric breakdown in ultrathin-oxide p

-metal-oxide-semiconductor field-effect transistors

Sinclair Chiang, M. F. Lu, S. Huang-Lu, S. C. Chien, and Tahui Wang

Citation: Journal of Applied Physics 98, 024105 (2005); doi: 10.1063/1.1980529 View online: http://dx.doi.org/10.1063/1.1980529

View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/98/2?ver=pdfcov Published by the AIP Publishing

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Department of Electronics Engineering, National Chiao-Tung University, Hsinchu, Taiwan, Republic of China 30077

共Received 10 December 2004; accepted 1 June 2005; published online 21 July 2005兲

An explanation of the breakdown behavior of ultrathin-gate-oxide 共1.6 nm兲 p-metal-oxide-semiconductor field-effect transistors under a reverse substrate bias is presented. A significant degradation in lifetime induced by a positive substrate bias and a decrease in the power-law exponent共n兲 were observed. The quantitative hydrogen-based model 关J. Sune and E. Wu, Digest of Technical Papers, 2001 Symposium on VLSI Technology, Kyoto, Japan, 12–14 June 2001 共unpublished兲, p. 97兴 is used to explain this observation while taking the channel quantization effect into consideration. Using this model, the stress voltage dependence of time-dependent dielectric breakdown in our experiment fits well with simulation results. This indicates that the degradation is due to the channel hole quantization-enhanced dissipation energy of injected electrons at the anode interface. © 2005 American Institute of Physics.关DOI: 10.1063/1.1980529兴

I. INTRODUCTION

Gate oxide breakdown has been considered to be one of the most important issues for aggressive oxide thickness scaling. In ultrathin-gate-oxide devices, high fields applied to oxides result in bulk defect generation, interface state forma-tion, and eventually breakdown. The most widely accepted theories to address the defect generation are the anode hole injection 共AHI兲 model1 and the anode hydrogen release 共AHR兲 model.2

However, neither AHI nor AHR can explain the recent observations of voltage-dependent voltage accel-eration of oxide breakdown for ultrathin oxides. Either the analytical formulation of AHI does not seem to be viable or the contribution of AHI is very small while stressed under low voltage in an ultrathin oxide.3,4 Accordingly, a power-law extrapolation with a quantitative hydrogen-based model for the degradation and breakdown of ultrathin gate oxides is proposed.5,6 It has been shown that this quantitative hydrogen-based model can successfully explain the decou-pled plasma nitridation共DPN兲 pressure dependence of oxide breakdown behavior in ultrathin-oxide p-metal-oxide-semi-conductor field-effect transistors共pMOSFETs兲.7

Although the substrate bias dependence of oxide break-down in pMOSFETs under negative gate bias stress has been discovered,8the additional impact ionization induced by the positive substrate bias共Vb兲 at the substrate bulk, which was

proposed to be the main cause of lifetime degradation in Ref. 8, could not precisely explain the lifetime versus applied gate bias 共Vg兲 characteristics in ultrathin-oxide pMOSFETs. In

this paper, we further discuss the time-dependent dielectric breakdown 共TDDB兲 behavior of ultrathin-oxide pMOSFETs 共p+ _{polysilicon gate and n-type silicon substrate兲 biased in} inversion under various reverse substrate biases. A signifi-cant decrease in the substrate-bias-induced power-law expo-nent will be shown. Finally, a modified quantitative hydrogen-based model with channel quantization effect and its simulation results are used to explain these observations.

II. EXPERIMENT

The p+ _{poly gate pMOSFETs used in this work were} fabricated with a 90-nm standard complementary metal-oxide semiconductor 共CMOS兲 process on an n-type silicon substrate. The gate length is 0.09␮m, the gate width is 10␮m, and the physical oxide thickness is 1.6 nm. The ni-trided gate oxide was grown by a 1.4-nm in situ steam gen-eration 共ISSG兲 followed by UMC’s standard decoupled plasma nitridation共DPN兲 process. All devices were stressed using constant voltage stress 共CVS兲 at 140 °C. The stress gate voltage varies from −2.5 to − 2.9 V for inversion mode TDDB stress 共electron injection is from p+_{polysilicon with} an n-type silicon substrate biased in inversion兲. The stress substrate biases were 0, 4, and 7 V, with the source and drain grounded. The initial breakdown event共a 20% jump in gate current兲 was defined as an oxide breakdown regardless of the soft or hard breakdown. The sample size was about 20–30 samples per stress voltage.

a兲_{Electronic mail: sinclairគ[email protected]}

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III. RESULTS AND DISCUSSION

In order to investigate the role of the substrate bias in time-dependent dielectric breakdown of pMOSFETs under inversion mode stress, we simply stressed the devices under various Vb. The results are shown in Fig. 1. Apparently, a

reverse substrate bias aggravates defect generation and con-sequently decreases the time to breakdown. The stress volt-age dependence of breakdown lifetime is depicted in Fig. 2. The stress gate bias varies from −2.5 to − 2.9 V. We clearly see a decrease of the power-law exponent共n兲 as Vbincreases

when the power-law model was used. This decreases the TDDB lifetime at the operating voltage, which is extrapo-lated from the TDDB lifetime under stress voltage for some applications under a reverse substrate bias.

It was proposed that the degradation of time to break-down 共TBD兲 and the decrease of the power-law exponent might be due to the additional impact ionization at the sub-strate bulk with reverse Vb,8 as illustrated in Fig. 3. In this

mechanism, applying a positive substrate bias increases the potential drop in the depletion region共anode兲 without chang-ing the gate field or direct tunnelchang-ing electron injection from the p+ _{poly gate. The initial electrons are accelerated more} with a larger Vband generate hotter holes that are accelerated

to even higher energies by an increased depletion field as they drift back to the oxide. It is noticeable that a larger impact ionization current, which signifies a higher impact ionization rate and results in larger substrate current 共Ib兲 as

marked in Fig. 3, increases the defect generation in gate ox-ide. However, our work shows that the additional anode hot

hole generation from substrate impact ionization has an op-posite trend with what we have seen in Fig. 2. In Fig. 4, the substrate current was used to monitor the rate of anode hole generation under various substrate biases since each impact ionization results in an additional conduction-band electron, which contributes to the substrate current. In other words, the larger the substrate current measured, the shorter the TDDB lifetime should be, if the model presented in Fig. 3 of Ref. 8 is appropriate for our experiment. However, 1 / Ib, which is

inversely proportional to the rate of anode hole generation and defect generation and hence directly proportional to T_BD, showed a dependence between Vgand TDDB that contradicts

the data, as shown in Fig. 2. The junction leakage current between the drain共or source兲 and bulk has been eliminated by measuring the forward biased n+_{-p junction current with}

Vb= 0, 4, and 7 V. It suggests that the degradation of the power-law exponent cannot be well explained by this con-ventional AHI-based model.

According to the above result, a quantitative hydrogen-based model incorporating channel quantization was pro-posed to explain the phenomenon. The model is based on two processes related to chemical reactions involving protons.5 Firstly, electrons, which are injected from the p+ poly gate in the direct tunneling regime, dissipate energy at the anode Si/ SiO2 interface and release protons 共H+兲 from interface suboxide bonds, as shown in Fig. 5. Secondly, the FIG. 1. Weibull distribution of time to breakdown共TBD兲 on pMOSFETs

with Tox= 1.6 nm. The stress gate bias is −2.9 V with Vb= 0, 4, and 7 V.

FIG. 2. Stress gate bias dependence of TDDB lifetime for devices in which width/ length= 10␮m / 0.09␮m. The symbols are experimental data and the curves are extrapolated by the power-law model.

FIG. 3. Band diagram of a pMOSFET with and without a substrate bias, showing the generation and acceleration of hot holes. The impact ionization electrons contribute to the substrate current. It was recently proved that this phenomenon could not explain our observations in Fig. 2.

FIG. 4. 1 / Ibvs gate bias characteristic curves with Vb= 0, 4, and 7 V. The

inverse of the substrate current shows a slightly weaker Vgdependence at

Vb= 0 V as compared with Vb= 4 and 7 V.

024105-2 Chiang et al. J. Appl. Phys. 98, 024105共2005兲

released protons react with oxygen vacancies 共Si–Si兲, as shown in Fig. 6. The rate of proton release from the inter-face,␰1共V,T兲, is modeled as an electron-energy-assisted pro-ton tunneling through an energy barrier 关Eq. 共1兲 and Fig. 7共a兲兴. The reaction of a proton with Si–Si is also described in quantum-mechanical terms by considering the tunneling of a proton through the potential barrier, which separates the two microscopic configurations before and after the reaction关Fig. 7共b兲兴.5

The description of chemical reactions in terms of po-tential barriers is a common practice in the field of quantum chemistry and is also considered in Refs. 9 and 10.

␰1共VT兲 =

K1

1 + exp关共E_th1+ q␸B− qV兲/E0兴

, 共1兲 ␰2共VT兲 = K2V2exp

冉

冊

where V refers to the electron dissipation energy and the other parameters have the same definitions as in Ref. 5. The total defect generation rate is given by 1 /␰= 1 /␰₁+ 1 /␰₂, and the bottleneck for the whole process is the slowest reaction. A detailed explanation of this quantitative hydrogen-based model is described in Ref. 5.

Taking the channel hole quantization effect into consid-eration, the energy-band diagram and the dissipation energy of valance band tunneling electrons at the anode Si/ SiO2

interface are illustrated in Fig. 8. A larger positive substrate bias results in more serious channel quantization and hence the first hole subband energy at the channel region increases. It was then supposed that the TDDB lifetime degradation under a reverse substrate bias might be due to the higher electron dissipation energy at the anode interface.

The maximum available energy共Emax兲 is defined as the energy of electrons at the oxide/anode interface as measured with respect to either the anode conduction band or the an-ode valence band, depending on the availability of empty states in the silicon substrate valence band.11Under ballistic direct tunneling injection, Emax= Vox+ Eh1 for pMOSFETs

stressed in the inversion mode, where Vox is the oxide volt-age and Eh1is the first subband energy of channel holes共Fig.

8兲, while channel holes are mainly distributed at the first subband at temperatures under 140 ° C.12Figure 9 shows the simulated Eh1vs Vgcharacteristic curve for various substrate

biases. The simulation results are calculated by solving the effective-mass Schrödinger equation共in the oxide and silicon regions兲 and the Poisson equation 共in the polysilicon, oxide, and silicon regions兲 self-consistently 关13,14兴:

冋

册

FIG. 7. Schematics of two processes involved in breakdown共Ref. 1兲. 共a兲 Electron-assisted proton release from suboxide bonds at the interface,␰₁.共b兲 Reaction of hydrogen bridge formation modeled by proton tunneling through an⬃0.2-eV barrier.

FIG. 8. Illustration of band diagram showing the electron dissipation energy at the anode interface with/without a reverse substrate bias. The electrons dissipate more energy when Vb= 4 V.

FIG. 5. Illustration of electron energy dissipation at the anode interface and the release of protons共H+_{兲 from interface suboxide bonds.}

FIG. 6. Illustration of the released protons共H+_{兲 reacting with oxygen}

va-cancies共Si–Si兲. The solid and dashed bonds represent the state before and after the reaction, respectively.

d dz

冋

册

where z is the direction perpendicular to the channel, m_i* is the electron or hole effective mass in the ith valley,␸ijis the

envelope wave function for the jth subband in the ith valley,

V is the potential energy, and NA− and ND+ are the ionized

acceptor and donor concentrations respectively. The potential energy V共z兲 in Eq. 共3兲 is related to the electrostatic potential ␾共z兲 in Eq. 共4兲 as follows:

V共z兲 = − q␾共z兲 + ⌬Ec共z兲, 共5兲

where EC共z兲 is the energy due to the band offset at the

Si/ SiO2interface. The wave function␸共z兲 in Eq. 共3兲 and the electron density n共z兲 in Eq. 共4兲 are related by

n共z兲 = kBT ␲ប2

兺

兺

冋

冉

冊

册

where gi is the ith valley degeneracy and md*_i is the ith

density-of-states effective mass.

The parameters used in simulation are m*共Si兲=0.67m0,

m*共SiO2兲=0.55m0,␾h 共hole barrier height at the SiO2 inter-face兲 =4.25 eV, tox= 1.6 nm, and NB 共substrate doping

con-centration兲 =1⫻1018_cm−3_{. The higher the substrate bias, the} weaker is the Vgdependence of Eh1. This simulation result is

similar to our experimental results, which showed a weaker

Vgdependence of TBDat higher Vb.

Replacing the V value of Eqs. 共1兲 and 共2兲 by V⬃Emax = Vox+ Eh1, the experimental breakdown data fit very well, as

shown in Fig. 10. The other model parameters obtained from the fit are Eth1= 1.8 eV, Eth2= 0.2 eV, E0= 0.07 eV, B = 100 V, and K₁/ K₂= 0.04 V−2_{. These values are the same as} those in Ref. 5. This gives an important piece of support to our model. It implies that the decrease of the power-law exponent under a reverse substrate bias for pMOSFETs

stressed in inversion might be due to the variation of the first hole subband energy, which is related to the electron dissi-pation energy at the anode interface.

IV. CONCLUSION

A significant degradation of TDDB lifetime and a de-crease of the power-law exponent when a reverse substrate bias is applied on ultrathin-oxide pMOSFETs were shown in this paper. We discovered that the conventional model, in which the substrate bias influences only the impact ioniza-tion at the substrate bulk, could not explain this phenom-enon. Accordingly, a quantitative hydrogen-based model in-corporating the channel hole quantization effect is presented to explain this breakdown behavior. Using this model, the simulations results are in agreement with the experiments. The excellent agreement between the model and the experi-mental data suggests that the lifetime degradation under re-verse Vbmight be due to the channel-quantization-enhanced

electron dissipation energy, which is the energy supply of defect generation, at the anode interface.

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with Vb= 0, 4, and 7 V. A stronger Vgdependence of subband energy was

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FIG. 10. Lifetime vs Vg plot of measurement and simulation data with

various Vb. The filled symbols represent the measurement data and the open

symbols represent the simulation data. The lines are the extrapolation curves from the measurement data.

024105-4 Chiang et al. J. Appl. Phys. 98, 024105共2005兲