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On the origin of the mobility reduction in n- and p-metal–oxide–semiconductor field effect transistors with hafnium-based/metal gate stacks
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10.1063/1.4737781
/content/aip/journal/jap/112/3/10.1063/1.4737781
http://aip.metastore.ingenta.com/content/aip/journal/jap/112/3/10.1063/1.4737781

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the gate stack structure considered in this work and definition of the symbols. The dielectric constant of the various layers is also indicated together with the positions (A, B, C) for the dipoles and the charges. The is equal to the positions and in the configuration A and C, respectively. In the configuration B, the charges and are placed at .

Image of FIG. 2.
FIG. 2.

Simulated effective mobility vs. effective field for a gate stack consisting of a thick layer of HfO2 without IL as obtained from simulations in this work (filled symbols) and in the literature.11,16,43–45 The considered scattering mechanisms are: acoustic and optical phonons in the Si substrate, surface roughness, and soft optical phonons. Parameters for phonons and surface roughness have been calibrated to reproduce the universal curves (dashed line Ref. 42) in SiO2/Si stacks.36,38,39

Image of FIG. 3.
FIG. 3.

Same as in Fig. 2 but considering only our model and the one in Ref. 43. Plot a: mobility vs. inversion density at  = 300 K. Plot b: mobility vs. temperature for  = 2 1011 cm 2.

Image of FIG. 4.
FIG. 4.

Simulated effective mobility vs. effective field taking into account the SOph scattering mechanism for various HK dielectrics without IL. Results for electron (filled symbols) and hole (open symbols) inversion layers are shown, with doping  =  cm 3 and  =  cm 3, respectively. Scattering mechanisms are the same as in Fig. 2. The dotted-dashed line shows the -MOS mobility obtained accounting only for the lowest SOph of the HfO2.

Image of FIG. 5.
FIG. 5.

Open symbols: lowest mode of the full dispersion relationship of the SOph modes in stacks featuring an HfO2 high- layer with  = 5 nm and various values of . The numerical model accounts for the two TO modes in the IL as well as the two TO modes in the high- layer. Closed symbols: lowest mode (originating from the TO1 mode in the HfO2) as obtained from Eq. (6). Similar results have been found over a wide range of values.

Image of FIG. 6.
FIG. 6.

Comparison between the experimental mobility data for nBulk-A (Ref. 4) and the MSMC simulations including SOph (which have essentially no influence on the mobility for these devices (Ref. 17)) and RemQ at the IL/HK interface with cm 2 at 300 K (plot a) and 100 K (plot b). The calibration of the simulator (solid line) on the SiO2 reference device of Ref. 4 (dashed line) is also shown.

Image of FIG. 7.
FIG. 7.

Comparison between simulated electron mobility (filled symbols) accounting for the SOph and RemQ ( cm 2) mechanisms and experimental data (open symbols) for the HfO2 devices with nm and nm in (Ref. 49) ( nm). The dashed line is taken from (Ref. 42) as SiO2 reference.

Image of FIG. 8.
FIG. 8.

Comparison between simulated electron mobility accounting for the SOph mechanism (filled squares), for the SOph and the RemQ ( cm 2) mechanisms (filled circles) and experimental data of Ref. 48 (solid line). HfO2 devices with  = 0.8 nm and  = 3 nm. The calibration of the simulator (open circles) on the SiO2 reference from (Ref. 48) (dashed line) is also shown. The dotted-dashed curve is taken from (Ref. 42) and refers to a channel doping of cm 3.

Image of FIG. 9.
FIG. 9.

Comparison between simulated electron mobility accounting for the SOph mechanism (filled squares), for the SOph and the RemQ ( cm 2) mechanisms (filled circles) and experimental data of Ref. 3 (solid line). The calibration of the simulator (open circles) on the SiO2 reference from (Ref. 3) (dashed line) and the universal mobility curve from (Ref. 42) are also shown.

Image of FIG. 10.
FIG. 10.

Comparison between simulated electron and hole mobility accounting for the SOph mechanism (squares), for the SOph and the RemQ mechanisms (circles) and experimental data (solid line) for undoped 12 nm thick SG-SOI - and -devices with nm (SiO2), nm (HfO2), and metal gate. The curves obtained excluding SOph and RemQ scatterings (triangles) are also shown. The dashed lines are from (Ref. 42) and are taken as SiO2 reference for both - and -MOSFETs.

Image of FIG. 11.
FIG. 11.

Comparison between simulated electron mobility accounting for the RemQ mechanism (filled symbols) and experimental data for undoped nm thick SG-SOI featuring HfSiON (open circles) and for a bulk device featuring HfZrO2 (open triangles). The channel doping of the HfZrO2 bulk devices is cm 3.

Image of FIG. 12.
FIG. 12.

Comparison between simulated and experimental (Ref. 4) electron mobility versus the effective field for nm thick HfO2 devices with nm and nm for K (left plot) and for K (right plot). Simulations have been obtained accounting for SOph and DipQ scattering mechanisms. The concentration of the DipQ centres is cm 2 and is nm (Ref. 27). The experimental SiO2 reference data and its simulation are also shown (dashed and solid lines).

Image of FIG. 13.
FIG. 13.

Simulated electron mobility versus the effective field for the nBulk-A device with  = 1 nm and  = 3 nm of Ref. 4. The curves obtained with or without the RemQ scattering and the experimental data of Ref. 4 are also shown. The concentration of the DipQ or the RemQ centres is cm 2.

Image of FIG. 14.
FIG. 14.

(a) Configurations in the (,) plane of the dipole in the position reproducing the experimental mobility of Ref. 4 in Fig. 13. The configurations giving  = 10 V or  = 1.0 V are also shown. (b) Same as (a) with the dipole in the position . (c) Same as (a) with the dipole in the position .

Image of FIG. 15.
FIG. 15.

Comparison between simulated and experimental (Ref. 4) electron mobility versus the effective field for nm thick HfO2 devices with nm and nm. Simulations have been obtained accounting for SOph and MG/HK-DipQ scattering mechanisms. The concentration of the DipQ centres is cm 2 and is nm (Ref. 54). The experimental SiO2 reference data of Ref. 4 and its simulation are also shown (dashed and solid lines).

Image of FIG. 16.
FIG. 16.

Energy dispersion, versus , for the coupled phonon-plasmon modes calculated by solving numerically Eq. (A1) (filled circles) in a structure with an infinitely thick HfO2 layer on top of the bulk Si with cm 3. The open squares indicate the two values obtained by neglecting the phonon-plasmon coupling (Eq. (3)). The solid lines identify the boundaries of the Landau damping region assuming (). The dotted-dashed lines identify the boundaries of the Landau damping region, obtained as the region where the magnitude of the imaginary part of is larger than . The values of the thermal wave vector at K are also indicated ( nm 1 (Ref. 47)). (a) Inversion density cm 2. (b) Inversion density cm 2.

Tables

Generic image for table
Table I.

Summary of the devices simulated in this work. The experimental data for the bulk devices are taken from literature, whereas the SG-SOI devices have been measured in this work.

Generic image for table
Table II.

List of the parameters allowing to reproduce universal mobility curves of Ref. 42 in SiO2 devices. is the coupling constant for elastic phonons, is the concentration of charges at the SiO2/Si interface, and are parameters describing the surface roughness spectrum.

Generic image for table
Table III.

Summary of the parameters used to simulate the devices in Table I, which have been found calibrating the simulations on the respective SiO2 control devices.

Generic image for table
Table IV.

due to the RemQ density of charges needed to reproduce the experimental data. All the charges are assumed to have the same sign and to be at the IL/HK interface.

Generic image for table
Table V.

Density of charges either in the bulk of the IL () or at the Si/IL interface () necessary to reproduce the mobility of nBulk-A devices with or nm and nm. The produced by such densities of charges have been calculated using: ; .

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/content/aip/journal/jap/112/3/10.1063/1.4737781
2012-08-01
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the origin of the mobility reduction in n- and p-metal–oxide–semiconductor field effect transistors with hafnium-based/metal gate stacks
http://aip.metastore.ingenta.com/content/aip/journal/jap/112/3/10.1063/1.4737781
10.1063/1.4737781
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