^{1,2,a)}, Chao Jiang

^{3}, Guo-Dong Li

^{3}, Liu-Wan Zhang

^{2}, Tao Yang

^{1}, Xiang-Lin Liu

^{1}, Shao-Yan Yang

^{1}, Qin-Sheng Zhu

^{1,b)}and Zhan-Guo Wang

^{1}

### Abstract

We suggest a new theoretical model to study the anisotropic scattering effect of the elongated quantum dots embedded in the GaAs/InGaAs double hetero-junction quantum well on the two-dimensional electron gas (2DEG). The elongated quantum dot (QD) with geometry which differs from ball-shaped quantum dot having isotropic cross section is assumed to be ellipsoid in the present calculation. The results show that the scattering in the direction parallel to the ellipsoid orientation (having small cross section) is weaker than that in the direction perpendicular to the ellipsoid orientation (having larger cross section) for the elongated QD when the mobile 2DEG is confined within the channel plane.

This work was supported by National Science Foundation of China (Nos. 91233111, 11275228, 61006004, 61076001, 60976008, and 10979507), Special Funds for Major State Basic Research Project (973 program) of China (No. A000091109-05), and the 863 High Technology R&D Program of China (No. 2011AA03A101).

I. INTRODUCTION

II. MODEL DESCRIPTION

III. RESULTS AND DISCUSSION

IV. SUMMARY

### Key Topics

- Quantum dots
- 53.0
- Electron gas
- 23.0
- Anisotropy
- 16.0
- Quantum wells
- 13.0
- Electron scattering
- 9.0

## Figures

(a) Surface SEM image of an uncapped Ga_{0.55}In_{0.45}As dot sample.The surface is tilted by 70° to enhance the height contrast. Reproduced with permission from A. Loffler, J.-P. Reithmaier, and A. Forchel, J. Cryst. Growth. **286**, 6 (2006). Copyright 2012 Elsevier. (b) Schematic diagram of the geometrical shape of dots used in the calculation.

(a) Surface SEM image of an uncapped Ga_{0.55}In_{0.45}As dot sample.The surface is tilted by 70° to enhance the height contrast. Reproduced with permission from A. Loffler, J.-P. Reithmaier, and A. Forchel, J. Cryst. Growth. **286**, 6 (2006). Copyright 2012 Elsevier. (b) Schematic diagram of the geometrical shape of dots used in the calculation.

Schematic diagram of the elastic scattering process. In the x-y plane, β is the angle between the initial wave vector ** k ** and the

**axis, is the scattering angle between**

*x***and**

*k***, is the angle between**

*k′***and**

*q***axis, is polar angle between**

*x***and**

*ρ***, we can get and the angle between**

*q***and**

*ρ***axis equals to**

*x*Schematic diagram of the elastic scattering process. In the x-y plane, β is the angle between the initial wave vector ** k ** and the

**axis, is the scattering angle between**

*x***and**

*k***, is the angle between**

*k′***and**

*q***axis, is polar angle between**

*x***and**

*ρ***, we can get and the angle between**

*q***and**

*ρ***axis equals to**

*x*Calculated is plotted as a function of the 2DEG density n_{2D} for different incidence angle of the initial wave vector ** k **, where = k

_{F}, l = 10 nm, r = 5 nm, h = 1.5 nm, and the position of the dots plane z

_{dot}is located at the well center, i.e., L∕2.

Calculated is plotted as a function of the 2DEG density n_{2D} for different incidence angle of the initial wave vector ** k **, where = k

_{F}, l = 10 nm, r = 5 nm, h = 1.5 nm, and the position of the dots plane z

_{dot}is located at the well center, i.e., L∕2.

Calculated anisotropic mobility is plotted as a function of the 2DEG density n_{2D}. In this calculation, we choose l = 10 nm, r = 5 nm, h = 1.5 nm, and the dots plane position z_{dot} = L∕2, where L is the QW width.

Calculated anisotropic mobility is plotted as a function of the 2DEG density n_{2D}. In this calculation, we choose l = 10 nm, r = 5 nm, h = 1.5 nm, and the dots plane position z_{dot} = L∕2, where L is the QW width.

Calculated anisotropic mobility is plotted as a function of the position of the dots plane z_{dot}. In this calculation, we have chosen l = 10 nm, r = 5 nm, h = 1.5 nm, and the 2DEG density n_{2D} 1 × 10^{12} cm^{−2}.

Calculated anisotropic mobility is plotted as a function of the position of the dots plane z_{dot}. In this calculation, we have chosen l = 10 nm, r = 5 nm, h = 1.5 nm, and the 2DEG density n_{2D} 1 × 10^{12} cm^{−2}.

Anisotropic mobility ratio is plotted as a function of the 2DEG density n_{2D} for different values of the length l and width r of the ellipsoid QDs. In this calculation, we have chosen h = 1.5 nm, and the dots plane position z_{dot} = L∕2, where L is the QW width.

Anisotropic mobility ratio is plotted as a function of the 2DEG density n_{2D} for different values of the length l and width r of the ellipsoid QDs. In this calculation, we have chosen h = 1.5 nm, and the dots plane position z_{dot} = L∕2, where L is the QW width.

## Tables

Parameters used in the theoretical calculation.

Parameters used in the theoretical calculation.

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