^{1}, Kain Lu Low

^{1}, Wei Wang

^{1}, Pengfei Guo

^{1}, Lanxiang Wang

^{1}, Genquan Han

^{1,a)}and Yee-Chia Yeo

^{1,a)}

### Abstract

We investigate germanium-tin alloy (Ge 1− x Sn x ) as a material for the design of tunneling field-effect transistor (TFET) operating at low supply voltages. Compared with Ge, Ge 1− x Sn x has a smaller band-gap. The reported band-gap of Ge 0.89Sn0.11 is 0.477 eV, ∼28% smaller than that of Ge. More importantly, Ge 1− x Sn x becomes a direct band-gap material when Sn composition x is higher than 0.11. By employing Ge 1− x Sn x in TFET, direct band-to-band tunneling (BTBT) is realized. Direct BTBT generally has higher tunneling probability than indirect BTBT. The drive current of TFET is boosted due to the direct BTBT and the reduced band-gap of Ge 1− x Sn x . Device simulations show that the drive current and subthreshold swing S characteristics of Ge 1− x Sn x TFETs with x ranging from 0 to 0.2 are improved by increasing the Sn composition x. For Ge 0.8Sn0.2 TFET, sub-60 mV/decade S is achieved at a high current level of ∼8 μA/μm. For x higher than 0.11, Ge 1− x Sn x TFETs show higher on-state current ION compared to Ge TFET at a supply voltage of 0.3 V. Ge 1− x Sn x alloy is a potential candidate for high performance TFET composed of group IV materials.

Research grant from the National Research Foundation (NRF) (Award number NRF-RF2008-09), Singapore is acknowledged.

I. INTRODUCTION

II. EXTRACTION AND CALCULATION OF MATERIAL PARAMETERS

III. SIMULATION METHODOLOGY

IV. ANALYSIS AND DISCUSSION

V. CONCLUSION

### Key Topics

- Germanium
- 101.0
- Elemental semiconductors
- 33.0
- Tunneling
- 31.0
- Band gap
- 22.0
- Effective mass
- 13.0

## Figures

(a) Composition dependence of Ge1− x Sn x band-gap at Γ-valley (EG, Γ) and L-valley (EG , L ) for Ge1− x Sn x alloy. Symbols are experimental data and the lines are obtained from EPM calculations. For Ge1− x Sn x alloys with Sn composition x below 0.11, the conduction band minimum is at L-point, and the alloy is an indirect band-gap material. For x higher than 0.11, Ge1− x Sn x is a direct band-gap material since the conduction band minimum is located at Γ-point. (b) Full band E-k dispersion for Ge and Ge0.89Sn0.11. As Sn composition increases, Ge1− x Sn x alloy transits from indirect to direct band-gap at around x = 0.11. The differences in band-gaps at Γ-point and L-point are highlighted as ΔEG, Γ and ΔEG , L .

(a) Composition dependence of Ge1− x Sn x band-gap at Γ-valley (EG, Γ) and L-valley (EG , L ) for Ge1− x Sn x alloy. Symbols are experimental data and the lines are obtained from EPM calculations. For Ge1− x Sn x alloys with Sn composition x below 0.11, the conduction band minimum is at L-point, and the alloy is an indirect band-gap material. For x higher than 0.11, Ge1− x Sn x is a direct band-gap material since the conduction band minimum is located at Γ-point. (b) Full band E-k dispersion for Ge and Ge0.89Sn0.11. As Sn composition increases, Ge1− x Sn x alloy transits from indirect to direct band-gap at around x = 0.11. The differences in band-gaps at Γ-point and L-point are highlighted as ΔEG, Γ and ΔEG , L .

(a) The DOS electron effective mass in the L-valley ( ) is larger than the one in the Γ-valley ( ) for Ge1− x Sn x alloys with various x. (b) The intrinsic carrier concentration and electron occupation ratio versus Sn composition. For Ge1− x Sn x with x > 0.11, although the conduction band minimum at the Γ-valley is lower than the one at the L-valley, there are more electrons in L-valley than Γ-valley.

(a) The DOS electron effective mass in the L-valley ( ) is larger than the one in the Γ-valley ( ) for Ge1− x Sn x alloys with various x. (b) The intrinsic carrier concentration and electron occupation ratio versus Sn composition. For Ge1− x Sn x with x > 0.11, although the conduction band minimum at the Γ-valley is lower than the one at the L-valley, there are more electrons in L-valley than Γ-valley.

Tunneling reduced masses for Γ-Γ BTBT ( ) and Γ-L BTBT ( ) decrease as Sn composition increases.

Tunneling reduced masses for Γ-Γ BTBT ( ) and Γ-L BTBT ( ) decrease as Sn composition increases.

(a) Schematic showing device structure of DG Ge1− x Sn x TFET. (b) Band diagram near surface along X-axis of Ge0.95Sn0.05 TFET at VGS = VDS = 0.3 V. Since EC , L is lower than EC, Γ, the tunneling distance from EV at the source side to EC , L in the channel dind (denoted by gray arrow) is shorter than that from EV at the source side to EC, Γ in the channel ddir (denoted by black arrow). (c) Band diagram near surface along X-axis of Ge0.86Sn0.14 TFET at VGS = VDS = 0.3 V. Since EC, Γ is lower than EC , L , ddir is shorter than dind .

(a) Schematic showing device structure of DG Ge1− x Sn x TFET. (b) Band diagram near surface along X-axis of Ge0.95Sn0.05 TFET at VGS = VDS = 0.3 V. Since EC , L is lower than EC, Γ, the tunneling distance from EV at the source side to EC , L in the channel dind (denoted by gray arrow) is shorter than that from EV at the source side to EC, Γ in the channel ddir (denoted by black arrow). (c) Band diagram near surface along X-axis of Ge0.86Sn0.14 TFET at VGS = VDS = 0.3 V. Since EC, Γ is lower than EC , L , ddir is shorter than dind .

Spatial distributions of (a) , (b) , and (c) for Ge0.95Sn0.05 TFET at VGS = VDS = 0.3 V. As the double-gate device is symmetrical about a mirror line at Y = 12.5 nm, only the upper half body (0 < Y < 12.5 nm) is shown.

Spatial distributions of (a) , (b) , and (c) for Ge0.95Sn0.05 TFET at VGS = VDS = 0.3 V. As the double-gate device is symmetrical about a mirror line at Y = 12.5 nm, only the upper half body (0 < Y < 12.5 nm) is shown.

Spatial distributions of (a) , (b) , and (c) for Ge0.86Sn0.14 TFET at VGS = VDS = 0.3 V. As the double-gate device is symmetrical about a mirror line at Y = 12.5 nm, only the upper half body (0 < Y < 12.5 nm) is shown. The magnitude of for Ge0.86Sn0.14 TFET is larger than that for Ge0.95Sn0.05 TFET shown in Fig. 5(c) .

Spatial distributions of (a) , (b) , and (c) for Ge0.86Sn0.14 TFET at VGS = VDS = 0.3 V. As the double-gate device is symmetrical about a mirror line at Y = 12.5 nm, only the upper half body (0 < Y < 12.5 nm) is shown. The magnitude of for Ge0.86Sn0.14 TFET is larger than that for Ge0.95Sn0.05 TFET shown in Fig. 5(c) .

(a) Simulated IDS -VGS for Ge0.95Sn0.05 TFET. Vind is lower than Vdir since EG , L is smaller than EG, Γ. As VGS is larger than Vind , BTBT from EV at source side to EC , L occurs. However, at VGS > Vdir , BTBT from EV to EC, Γ dominates the tunneling current. (b) Simulated IDS -VGS for Ge0.86Sn0.14 TFET. Vdir is lower than Vind since EG, Γ is smaller than EG , L . As VGS > Vdir , BTBT occurs from EV at source side to EC, Γ and dominates the drive current once VGS reaches Vdir .

(a) Simulated IDS -VGS for Ge0.95Sn0.05 TFET. Vind is lower than Vdir since EG , L is smaller than EG, Γ. As VGS is larger than Vind , BTBT from EV at source side to EC , L occurs. However, at VGS > Vdir , BTBT from EV to EC, Γ dominates the tunneling current. (b) Simulated IDS -VGS for Ge0.86Sn0.14 TFET. Vdir is lower than Vind since EG, Γ is smaller than EG , L . As VGS > Vdir , BTBT occurs from EV at source side to EC, Γ and dominates the drive current once VGS reaches Vdir .

(a) A set of IDS -VGS curves of Ge1− x Sn x TFETs with x ranging from 0 to 0.2. (b) Point S versus IDS for Ge1− x Sn x TFETs with x from 0 to 0.2. For Ge0.8Sn0.2 TFET, sub-60 mV/decade S is achieved at a high current level of ∼8 μA/μm.

(a) A set of IDS -VGS curves of Ge1− x Sn x TFETs with x ranging from 0 to 0.2. (b) Point S versus IDS for Ge1− x Sn x TFETs with x from 0 to 0.2. For Ge0.8Sn0.2 TFET, sub-60 mV/decade S is achieved at a high current level of ∼8 μA/μm.

IOFF versus ION of Ge1− x Sn x TFETs with x = 0.00, 0.05, 0.08, 0.11, and 0.17 at a supply voltage of 0.3 V. For a given IOFF , VOF F is the value of VGS when IDS equals to the IOFF , ION is extracted at VGS – VOFF = VDS = 0.3 V. IOFF is varied from 10−9 to 10−2 mA/μm. For a fixed IOFF , ION of Ge1− x Sn x TFET is higher than that of Ge TFET.

IOFF versus ION of Ge1− x Sn x TFETs with x = 0.00, 0.05, 0.08, 0.11, and 0.17 at a supply voltage of 0.3 V. For a given IOFF , VOF F is the value of VGS when IDS equals to the IOFF , ION is extracted at VGS – VOFF = VDS = 0.3 V. IOFF is varied from 10−9 to 10−2 mA/μm. For a fixed IOFF , ION of Ge1− x Sn x TFET is higher than that of Ge TFET.

## Tables

Summary of material parameters used in TCAD simulation.

Summary of material parameters used in TCAD simulation.

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