Effective Mobility

Traditionally, the hole mobility has been considered to be the most important parameter, especially for long-channel devices. In particular, comparison with the silicon universal mobility curve is useful means of gauging the performance benefits of the new technology over silicon. Additionally, when the effective mobility is plotted against the effective field, valuable insight is gained into the dominant scattering mechanisms in the device, which is useful in highlighting areas in which further improvements in design and processing can be made.

The effective mobility is plotted against vertical field in Figure 6.19 for a selection of 10µm x 10µm pMOSFETs at room temperature, 77 K and 4 K. The effective field was calculated using the relation:

Figure 6.19: Effective hole mobility at room temperature, 77 K and 4 K for 10 µm x 10 µm germanium pMOSFETs. Data also includes hole mobility values for (100)-silicon [Yang et al., 2003] and for uniaxial strained silicon with SiGe source/drain regions ([Ghani et al., 2003]).

ε_{ef f} = Qbulk+ηQinv κGe²0

(6.2) There is some question about the value ofη. Takagi et al. [1994] showed that a value of 1/3 is valid for holes at both room temperature and 77 K for silicon MOSFETs. This was the value ofη such that the effective mobility could be described by a single universal curve. However, at present, the universal behaviour of germanium MOSFETs has not yet been explored. A universal law in germanium MOSFETs could be potentially be quite complicated due to the vast combination of gate stacks to choose from, and the possibility that they might not all behave in the same way. Consequently, to the best of the author’s knowledge, all of the published literature on the effective mobility of germanium MOSFETs is based on the assumption that they behave in the same way as silicon MOSFETs and assume the same value for the parameterη. In this work, a value of 1/3 was assumed for the value ofη for all temperatures. Perhaps, this assumption is not so unrealistic, given that the germanium pMOSFETs used in this work are passivated with Si/SiO₂, and so is likely to be as close to resembling a standard Si MOSFET as is

possible for a Ge device.

The Ge pMOSFETs exhibit a maximum room temperature hole mobility of ap- proximately 230 cm2_V−1_s−1_{. The silicon universal curve is shown by means of compar-}

ison. The germanium devices maintain a hole mobility enhancement of 2.5 times that of the universal curve, even at fields of 1 MVcm−1_{, typically where the devices would}

be operated. Figure 6.19 also indicates that there is a spread in mobility with the worst device having a peak mobility of 150 cm2_V−1_s−1 _{at room temperature. Nonetheless,}

even the worst device in this case exhibits a hole mobility enhancement of two times that of the silicon universal curve at an effective field of 1 MVcm−1 _{at room temperature.}

These devices represent some of the highest reported mobilities in germanium MOS- FETs with high-κ dielectrics at vertical fields where sub-micron devices would typically be operated.

Figure 6.19 also shows the effective hole mobility for (110)-oriented silicon sub- strates [Yang et al., 2003] and also for uniaxially strained silicon pMOSFETs with SiGe source/drain regions [Ghani et al., 2003]. The germanium pMOSFETs exhibit a signifi- cant enhancement (nearly two times) in hole mobility over the strained-Si pMOSFETs, whilst the improvement in mobility over the (110)-oriented silicon pMOSFETs is much more modest. This is particularly encouraging since neither of these devices employed high-κ gate dielectric. It is envisaged that further mobility enhancements can still be made in germanium pMOSFETs through strain and changing the crystal orientation. Additionally, it is also possible that a reduction of the gate dielectric thickness might also be expected to bring out a further increase in the hole mobility due to reduced charge trapping in the thinner oxide, providing that this does not result in any signifi- cant increase in gate leakage [Ragnarsson et al., 2006].

Figure 6.19 also shows the effective hole mobility of Ge pMOSFETs at both 77 K and 4 K. The effective hole mobility can be increased by approximately a factor 2 at moderate to high vertical fields when operated at 77 K, with a peak mobility of around

Figure 6.20: Effective hole mobility vs effective field for a 10 µm x 10 µm germanium pMOSFET as a function of temperature.

480cm2_V−1_s−1_{. This increase in hole mobility is almost entirely due to the reduction}

of phonon scattering in the channel. However, no significant increases in hole mobility were observed when cooling from 77 K to 4 K. This can be interpreted that below 77 K, phonon scattering is not the limiting factor to the effective hole mobility. Rather, that the hole mobility is limited by Coulomb scattering at low vertical fields and surface roughness scattering at high vertical fields. This is further illustrated by Figure 6.20, which shows the effective hole mobility as a function of vertical field measured on the same transistor over a range of temperatures. At low vertical fields, the hole mobility is found to exhibit a steeper roll-off with decreasing temperature. The Coulomb scattering results from the high substrate doping of these transistors, including halo implants, and is found to become increasingly important with decreasing temperature due to the reduction of the hole carrier energy. In addition, it is also possible that additional Coulomb scattering could result from the increased occupancy of acceptor-like defects at the Ge/HfO2

interface as the temperature is decreased (see Section 6.3.5). At high vertical fields, the hole mobility increases until 77 K, below which, the mobility is almost temperature- independent, indicating that the mobility in this temperature regime is limited entirely

by surface scattering. In this regime, the hole mobility is nearly proportional to ε−_eff1, which is the same dependence as reported in silicon [Takagi et al., 1994].