Technical Note
On the mobility extraction for HMOSFETs

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Abstract

Self-consistent Schroedinger–Poisson calculations have been employed to investigate theoretically the mobility extraction for hetero-MOSFETs or HMOSFETs with a thin gate oxide. In this particular case, the contribution of the cap layer to the gate capacitance is crucial. It is shown that there is a considerable error in the effective mobility when extracted with the common constant capacitance approximation and that application of the split-CV method is essential.

Introduction

Hetero-MOSFETs (HMOSFETs) [1], [2] owe their superior performance to a mobility increase in an epitaxial Si1−xGex layer underneath the gate which can be divided into a buffer layer, a channel and a cap layer (see Fig. 1). Ideally, the carriers are confined in the strained heterochannel (see Fig. 2) whose Ge content is higher for p-MOSFETs and lower for n-MOSFETs than the Ge content in the unstrained cap and buffer layers.

In the linear region and for small drain voltages, HMOSFET operation is based on the drain current equation used for conventional MOSFETs [3]:Isd=QiμeffW(Vsd−RsdIsd)Lwhere Isd, Qi, Vsd, Rsd, μeff, L, W are the drain current, the inversion charge per unit area, the drain voltage, the source and drain series resistance, the effective mobility, the effective channel length, and the effective channel width, respectively.

However, mobility extraction for HMOSFETs is not as straightforward as for conventional MOSFETs as the gate capacitance may vary as a result of the population of the Si cap. In this paper, the error resulting from the application of the constant capacitance approximation is studied theoretically for HMOSFETs with a thin gate oxide.

Section snippets

Mobility extraction for HMOS devices

The constant capacitance method is the preferred mobility extraction method of many researchers because the mobility can be extracted from simple drain current measurements. Approximating the capacitance associated with the inversion charge C by the series capacitance of the dielectric and the Si cap per unit area, the effective mobility μeff can be expressed as a function of the channel sheet resistance rch and the gate drive, i.e. the difference between the gate voltage and the threshold

Limits of the constant capacitance approximation

The error in the mobility extraction for a typical p-channel HMOSFET with a thin gate oxide is examined when the constant capacitance approximation is applied. A 1D Schroedinger–Poisson solver [5] is used to calculate the hole density shown in Fig. 3. It takes account of QM effects and includes the strain dependence of the light and heavy hole masses. The band offset [6] in the valence band of the SiGe channel is described by (see Fig. 2):ΔEv=−0.74x(eV)where x is the Ge fraction.

The effective

Conclusion

In this paper, the mobility extraction for typical hetero-p-MOSFETs with a thin gate oxide has been investigated theoretically. The effective mobility extracted with the constant capacitance approximation has been shown to produce a considerable error. Split-CV methods are therefore recommended for HMOSFETs.

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