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In order to design and optimize high-sensitivity silicon nanowire-field-effect transistor (SiNW FET) pressure sensors, this paper investigates the effects of channel orientations and the uniaxial stress on the ballistic hole transport properties of a strongly quantized SiNW FET placed near the high stress regions of the pressure sensors. A discrete stress-dependent six-band k.p method is used for subband structure calculation, coupled to a two-dimensional Poisson solver for electrostatics. A semi-classical ballistic FET model is then used to evaluate the ballistic current-voltage characteristics of SiNW FETs with and without strain. Our results presented here indicate that [110] is the optimum orientation for the p-type SiNW FETs and sensors. For the ultra-scaled 2.2 nm square SiNW, due to the limit of strong quantum confinement, the effect of the uniaxial stress on the magnitude of ballistic drive current is too small to be considered, except for the [100] orientation. However, for larger 5 nm square SiNW transistors with various transport orientations, the uniaxial tensile stress obviously alters the ballistic performance, while the uniaxial compressive stress slightly changes the ballistic hole current. Furthermore, the competition of injection velocity and carrier density related to the effective hole masses is found to play a critical role in determining the performance of the nanotransistors.

Based on CMOS-MEMS technology [

In this paper, based on the theory developed by Luttinger and Kohn [

As shown in _{Si}, is assumed to be equal to the wire width, W_{Si}.

In order to investigate the ballistic hole transport properties of SiNW FETs, we have to calculate the valence subband _{n}_{z}_{n,kz} (

The Luttinger parameters we use well reproduce the bulk _{kp}_{strain}_{so}

Based on the effective valley degeneracy and the hole effective masses extracted from the bandstructures, which are calculated by using the 2-D discrete stress-dependent six-band k.p model, the ballistic I–V characteristics of the corresponding p-type SiNW FETs are evaluated by using a top-of-the-barrier ballistic FET model [

In this way, this model treats ballistic transport semiclassically by filling the _{scf}

For the valence band of the ultra-scaled cross section SiNW, the degeneracy between light and heavy holes is lifted by the strong quantum confinement. Because holes mainly occupy the first subband,

To account for the influence of subband nonparabolicity on the effective mass, the following expression for zone-center effective mass _{//} of SiNW is utilized [_{//} is the hole energy measured from the subband edge, _{//} is the hole wave vector, and α is nonparabolicity factor. Both the hole effective masses and nonparabolicity factors, also shown in

In order to explain the origin of the phenomenon, in _{z}^{−1}). Because the more nonparabolicity effect of the same-oriented subbands is in the transport direction, the larger the transport mass will be [_{n=1} = 0.31). Under the stress, the wave function components are found to be sensitive to the tensile stress, which enhances the HH component and results in the band mixing effect among HH, LH, SO bands. However, this band mixing controlled by the tensile stress reduces nonparabolicity effect (^{−1} due to quantum confinement, resulting in lighter effective mass (0.2951), in other word, the quantum confinement effect is partly nullified by the tensile stress. This can be seen from the change of the wave function shape, which reflects a different charge distribution in space. Under the tensile stress, the charge confined at the center of the cross-section relocalizes in the surface of SiNWs, which is similar as the classical case (_{n=1} = 0.31).

In _{z}

Changes in the bandstructure due to quantum mechanical confinement, strain and various transport orientations reflect on the transport characteristics of the strained SiNW with three wire orientations, [100], [110] and [111]. Based on the effective valley degeneracy and the effective masses extracted from the stress-dependent subbands, the top-of-the-barrier ballistic transport model is used to self-consistently calculate the drain current, carrier density and injection velocity of p-type SiNW transistors. Note that for the valence band of SiNWs along the [110] orientation, the band-edge of the second highest band is close to that of the highest band. So the second highest band also contributes to the hole density and current, and the effective valley degeneracy is close to 2. Besides, at the same doping concentration and temperature, the change of _{V}_{fs}_{V}_{DS} by adjusting the gate work function. Thus, the threshold voltage shift will not be seen in the relative performances.

_{DS}= – 0.6 V for 2.2 nm square SiNW FETs with three different channel orientations. The results show that the SiNW FET performance displays a strong orientation dependence. For p-type SiNW FETs, [110] is the optimum orientation that offers the highest drain current, followed by the [111] SiNW, whereas the [100] SiNW has the lowest drain current. On the other hand, the effect of strain on the ballistic drain current of SiNW FETs with the [110] and [111] orientations, except for the [100] orientation, turns out negligible in the case considered, which can be attributed to an only slight variation of the non-parabolic valence structure under the strong quantum confinement. In other word, in this case, the effect of the stress is nullified by quantum confinement.

Because current is the product of the carrier density and the injection velocity, in

This result indicated the competition of injection velocity and carrier density related to hole effective masses plays a critical role in determining the performance of the nanotransistors. Furthermore, the effect of the stress on the injection velocity and the carrier density is also too small to be considered due to the strong quantum confinement.

As discussed above, due to the limit of the strong quantum confinement, the effect of the stress on the ballistic hole transport properties of the ultra-scaled 2.2 nm square SiNWs is almost too small to be considered. To gain further insight into the effect of the stress, we determine to investigate larger cross section SiNWs. _{GS}=V_{DS}= – 0.6 V) of the p-type 5 nm square SiNW FETs with a as a function of the stress. Because the degree of the competition between the stress and quantum confinement is different for different size wires, the 5 nm square SiNW for tensile stresses behaves in a different manner with respect to the 2.2 nm one.

In particular, although the uniaxial compressive stress slightly changes the ballistic hole current, the uniaxial tensile stress obviously alters the ballistic hole current in three different channel orientations. In other word, the effect of tensile stress is more obvious in the 5 nm one due to weaker quantum confinement effect. This clearly indicates that in order to obtain the high-sensitivity NW FET pressure sensors, the tensile stress should be applied.

Meanwhile, in order to enhance the effect of the stress, the size of the SiNW can not be too small or narrow, resulting in the strong quantum effect, which will counteract the stress effect. In addition, it can be seen from

On the other hand, in

In order to design and optimize high-sensitivity SiNW FET sensors, we have provided a detailed examination of the impact of the orientations and the uniaxial stress on the hole subband structure and the relative ballistic transport characteristic of the p-type SiNW transistor by using the stress-dependent k.p method which is discretized with the nine-point finite difference method, and the top-ofthe-barrier ballistic transport model. It shows that SiNW FETs display a strong orientation dependence. We have identified [110] as the optimum orientation for the unstrained SiNW FETs. The dependence of SiNW FET performance on the uniaxial stress was also explored and the results show that there is a clear performance improvement when uniaxial tensile stress is applied along the transport orientation, and [110] is the optimum orientation for the p-type SiNW FET pressure sensors, whereas [100] is the optimum orientation for the very high tensile-strained p-type SiNW FETs. However, the effect of the uniaxial compressive stress on the ballistic drain current of SiNW FETs is small in the case considered, which can be attributed to an only slight variation of the non-parabolic valence structure under a compressive stress. Furthermore, it is observed that quantities related hole effective masses, such as carrier injection velocity and carrier density play key roles in determining the performance of p-type ballistic SiNW transistors.

Project is supported by the National Basic Research Program of China (Grant No. 2006CB300404), and the National High-Tech Research and Development Program of China (Grant No. 2007AA04Z301).

A schematic diagram of the SiNW FET pressure sensor. In this work, the SiNW FETs with various channel orientations i.e., [100], [110], [111] are explored.

Illustration of the ‘top-of–the-barrier’ ballistic FET model. Semiclassical ballistic transport is assumed for the calculation of hole density and current. Filled circles represent states that are filled by the source Fermi level _{fs}_{fd}

The energy dispersion relations for the first subband of the simulated strained and unstrained SiNWs with various channel orientations. T_{Si}=W_{Si}=2.2 nm.

HH component, LH component, and SO component of the wave function of the ground state at _{z}

Percent of the HH, LH, SO components in the first subband of the simulated SiNWs versus wavevector

The I_{DS}–V_{GS} curves for p-type strained and unstrained SiNW FETs with various channel orientations at V_{DS}= – 0.6 V. The oxide thickness is assumed to be 1 nm and the temperature is 300 K.

Injection velocity of the simulated strained and unstrained SiNW FETs with various channel orientations versus gate bias at V_{DS}= – 0.6 V.

Carrier density of the simulated strained and unstrained SiNW FETs with various channel orientations versus gate bias at V_{DS}= – 0.6 V.

ON-current of the p-type 5 nm square SiNW FETs as a function of the stress.

Injection velocity of the p-type 5 nm square SiNW FETs as a function of the stress.

Carrier density of the p-type 5 nm square SiNW FETs as a function of the stress.

Luttinger parameters, deformation potentials, spin-orbit split-off energy used in the calculation.

γ_{1} |
γ_{2} |
γ_{3} |
_{v} |
Δ_{so} (meV) | ||
---|---|---|---|---|---|---|

4.22 | 0.39 | 1.44 | 2.46 | −2.1 | −4.8 | 44 |