Ultrashallow heavily constrained quantum wells: The cradle for fully electrically controlled and microwave coupled quantum bits

Ge/SiGe heterostructure quantum well structures based on Ge two-dimensional hole gas have become one of the most promising research directions for preparing spin quantum bits due to their low disorder and high mobility. In this study, high-quality virtual substrates were epitaxially grown on 8-in silicon substrates using reduced pressure chemical vapor deposition. The surface roughness of the samples was optimized by adjusting key parameters such as the thickness of the reverse gradient buffer layer and ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ buffer layer. Based on the strain modulation of dislocation dynamics, high-quality strained quantum wells with a density of stress accumulation points (DSAP) of $0.301/\mu {\mathrm{m}}^2$ and surface RMS roughness less than 3 nm were achieved. Ultimately, an ultrashallow heavily constrained and undoped quantum well with a well depth of 15 nm, in-plane compressive strain of ${\varepsilon }_{\parallel }=-1.19\%$, and a mobility of $3.382\times {10}^5{\mathrm{cm}}^2/\mathrm{Vs}$ was obtained. A novel characterization method for quantum wells was proposed based on the defined DSAP. The ultrashallow quantum well depth and higher compressive strain enable the quantum well to maintain a high effective $g$ factor (up to 8.3), becoming the cradle for fully electrically controlled and microwave coupled quantum bits.

Figure 1

(a) Unstrained QW. (b) Standard strained. (c) Heavily strained.

Figure 2

Structural characterization of a Ge/SiGe heterostructure. (a) Ge/SiGe layer schematics (include Ge-rich pulse and TDs). (b) TEM of the Ge/SiGe heterostructure. (A Partial diagram of threading dislocation can be found in the Appendix, Fig. 11.) (c) HAADF of Ge/SiGe heterostructure (d) Heavily and standard Ge QWs with Ge (blue) and Si (green) concentration profiles by TEM/EDX line. (e) HAADF EDX mapping of Ge (blue), Si (yellow), and O (green) distribution.

Figure 3

HRXRD analysis of the Ge/SiGe heterostructure. (a), (b) Rocking curves of (004), (113) and (224). (c)–(e) RSM with sample A, sample B, and sample C.

Figure 4

The relaxation rate, in-plane strain, parallel mismatch, and vertical mismatch of sample A, sample B, and sample C.

Figure 5

GPA analysis of sample C about (a) germanium quantum wells and (b) Ge-rich pulses.

Figure 6

(a) $10\times 10\mu \mathrm{m}$ and $50\times 50\mu \mathrm{m}$ AFM of sample A, sample B, and sample C. (b) 2D Fourier transform of the AFM.

Figure 7

(a) The microscope of the sample etched to below the Ge-rich pulse. The microscope of the sample etched to the Ge QWs with sample A, sample B, and sample C.

Figure 8

(a) SEM image of the sample after etching under a Ge-rich pulse. (b) AFM etching below the Ge-rich pulse. (c) Cross section SEM images of samples etched to quantum wells. (d) SEM images of samples etched to quantum wells. (e)–(g) AFM images of sample A, sample B, and sample C etched to quantum wells.

Figure 9

(a)–(c) DSAP images of sample A, sample B, and sample C. (d) The strain, DSAP, and Rq of the three samples.

Figure 10

Electrical and magnetotransport measurements of Hall-bar shaped HFET. (a) Four-terminal lock-in measurement circuit. The yellow area is the lock-in amplifier, the green area is the source and drain terminal, and the blue area is the top gate. (b) Transfer characteristic curve, ${\mathrm{V}}_{sd}=20\mu \mathrm{V}, f=230$ Hz. (c) Mobility $\mu$ vs carrier density ${\mathrm{p}}_{2\text{DHG}}$. Black filled dots are data points. The blue curve is the fitting curve at low density. ${\beta }_{\mathrm{low}}=3.03\pm 0.03$. The red curve is the fitting curve at high density. ${\beta }_{\mathrm{high}}=1.27\pm 0.013$. The confidence levels of the two curves are both more than 0.999. (d) Longitudinal conductivity ${\sigma }_{xx}$ vs carrier density ${\mathrm{p}}_{2\text{DHG}}$. Black filled dots are data points. The red curve is fitted by ${\sigma }_{xx}\propto {({\mathrm{p}}_{2\text{DHG}}-{\mathrm{p}}_p)}^p$, p=2. The confidence level is 0.999. (e) Quantum Hall effect curve at ${\mathrm{p}}_{2\text{DHG}}=(4.466\pm 0.087)\times {10}^{11}{\mathrm{cm}}^{-2}$. The Landau level integer filling factors ($\nu =2\sim 6$) and minimum of suspected fractional indication are labeled by blue numbers. (f) Temperature dependence of the Shubnikov-de Haas oscillations $\mathrm{\Delta }\rho$ in the range $\mathrm{T}=250–650$ mK after background subtraction.

Figure 11

Due to the combined effect of the Ge-rich pulse and the reverse gradient buffer layer beneath it, dislocations are effectively screened below the Ge-rich pulse. At this TEM magnification, no obvious threading dislocations can be found extending above the Ge-rich pulse.