^{1}, Ji-Song Lim

^{1}, Toshinori Numata

^{1,a)}, Toshikazu Nishida

^{1}and Scott E. Thompson

^{1,b)}

### Abstract

Strain altered electron gate tunnelingcurrent is measured for germanium(Ge) metal–oxide–semiconductor devices with gate dielectric. Uniaxial mechanical stress is applied using four-point wafer bending along [100] and [110] directions to extract both dilation and shear deformation potential constants of Ge. Least-squares fit to the experimental data results in and of and , respectively, which agree with theoretical calculations. The dominant mechanism for the strain altered electron gate tunnelingcurrent is a strain-induced change in the conduction band offset between Ge and . Tensile stress reduces the offset and increases the gate tunnelingcurrent for Ge while the opposite occurs for Si.

The authors would like to thank the Applied Materials Foundation, Advanced Micro Devices (AMD), Cypress Semiconductor, IBM, Intel Foundation, Semiconductor Research Corporation (SRC), Texas Instruments, Taiwan Semiconductor Manufacturing Co. (TSMC), Multidisciplinary University Research Initiative (MURI), and the National Science Foundation (NSF) under Grant No. ECS-0524316 for funding this research.

I. INTRODUCTION

II. STRESS ALTERED ELECTRON GATE TUNNELINGCURRENT

A. Energy level shift and splitting

B. Deformation potential

III. EXPERIMENTAL SETUP AND RESULTS

A. Measurement procedure

B. Results

IV. EXTRACTION OF CONDUCTION BAND DEFORMATION POTENTIALS

V. CONCLUSION

### Key Topics

- Germanium
- 37.0
- Tunneling
- 25.0
- Conduction bands
- 19.0
- Elemental semiconductors
- 16.0
- Effective mass
- 11.0

## Figures

(Color online) Conduction-band constant energy ellipsoids are centered at the point and the major axis of eight half ellipsoids are along or [111] direction. Out-of-plane effective mass and are defined along [001] direction (Refs. 14 and 23). Note half of the ellipsoids belong to the (110) plane while the rest of ellipsoids belong to the plane.

(Color online) Conduction-band constant energy ellipsoids are centered at the point and the major axis of eight half ellipsoids are along or [111] direction. Out-of-plane effective mass and are defined along [001] direction (Refs. 14 and 23). Note half of the ellipsoids belong to the (110) plane while the rest of ellipsoids belong to the plane.

(a) Schematic band diagram for direct electron tunneling from the inversion layer in the Ge MOS device. Conduction band offset between and Ge is from Ref. 23. (b) Stress along [100] raises energy level resulting from hydrostatic strain-induced energy level shift . (c) Stress along [110] causes shear strain-induced energy level splitting between the (110) plane valley and . The energy level is raised while the energy level is lowered. Note is an additive for .

(a) Schematic band diagram for direct electron tunneling from the inversion layer in the Ge MOS device. Conduction band offset between and Ge is from Ref. 23. (b) Stress along [100] raises energy level resulting from hydrostatic strain-induced energy level shift . (c) Stress along [110] causes shear strain-induced energy level splitting between the (110) plane valley and . The energy level is raised while the energy level is lowered. Note is an additive for .

[100] tensile stress-altered gate tunneling current for the Ge MOS device under different gate biases. Current is increased due to reduced barrier height resulting from . The inset represents the schematic band diagram of the subband in inversion with no stress and tensile stress along [100].

[100] tensile stress-altered gate tunneling current for the Ge MOS device under different gate biases. Current is increased due to reduced barrier height resulting from . The inset represents the schematic band diagram of the subband in inversion with no stress and tensile stress along [100].

[110] tensile stress-altered gate tunneling current of the Ge MOS device under different gate biases. Current is increased due to reduced barrier height of electrons in the energy level. The inset shows the schematic band diagram with strain-induced subband splitting between the and subbands.

[110] tensile stress-altered gate tunneling current of the Ge MOS device under different gate biases. Current is increased due to reduced barrier height of electrons in the energy level. The inset shows the schematic band diagram with strain-induced subband splitting between the and subbands.

[110] tensile stress-altered electron gate tunneling current of Ge and Si devices at the inversion charge of , where 1.2 and 0.6 V gate biases are applied for Si and Ge MOS devices, respectively, (see Ref. 30). Si data are from Ref. 28 (measured from -MOSFETs with poly gate and dielectric). Note that the strain-altered current is increased in Ge while decreased in Si due to the different position of the conduction band minimum ( for Si and for Ge) (Ref. 14).

[110] tensile stress-altered electron gate tunneling current of Ge and Si devices at the inversion charge of , where 1.2 and 0.6 V gate biases are applied for Si and Ge MOS devices, respectively, (see Ref. 30). Si data are from Ref. 28 (measured from -MOSFETs with poly gate and dielectric). Note that the strain-altered current is increased in Ge while decreased in Si due to the different position of the conduction band minimum ( for Si and for Ge) (Ref. 14).

Schematic band diagrams for [110] tensile stress effects on electron gate tunneling in (a) Si and (b) Ge devices, respectively. A decrease in the tunneling current for the Si device is induced by (1) barrier height enhancement of mostly populated and (2) electron repopulation into subbands, which has a higher out-of-plane effective mass , while only the barrier height lowering of contributes to an increase of the tunneling current of the Ge MOS device.

Schematic band diagrams for [110] tensile stress effects on electron gate tunneling in (a) Si and (b) Ge devices, respectively. A decrease in the tunneling current for the Si device is induced by (1) barrier height enhancement of mostly populated and (2) electron repopulation into subbands, which has a higher out-of-plane effective mass , while only the barrier height lowering of contributes to an increase of the tunneling current of the Ge MOS device.

Change in slopes vs gate voltage with confidence error bars for tensile stress along [100]. Best fits ( and ) for the entire data set occur for and 1.4 eV. Maximum deviations ( and ) from the data occur for and 1.5 eV.

Change in slopes vs gate voltage with confidence error bars for tensile stress along [100]. Best fits ( and ) for the entire data set occur for and 1.4 eV. Maximum deviations ( and ) from the data occur for and 1.5 eV.

Change in slopes vs gate voltage with confidence error bars for tensile stress along [110]. Best fits (, , and ④) for the entire data set occur for to and to 16.8 eV. Maximum deviations ( and ) from the data set occur for and and and 16.0 eV, respectively.

Change in slopes vs gate voltage with confidence error bars for tensile stress along [110]. Best fits (, , and ④) for the entire data set occur for to and to 16.8 eV. Maximum deviations ( and ) from the data set occur for and and and 16.0 eV, respectively.

## Tables

Dilation and shear deformation potentials extracted from gate tunneling current of the Ge MOS device under tensile stress along [100] and [110]. Comparison is made with previous theoretical and experimental results (Refs. 12, 13, 15, 31, and 32). All quantities are in electron-volts.

Dilation and shear deformation potentials extracted from gate tunneling current of the Ge MOS device under tensile stress along [100] and [110]. Comparison is made with previous theoretical and experimental results (Refs. 12, 13, 15, 31, and 32). All quantities are in electron-volts.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content