Epitaxy of strained, nuclear-spin free $^{76}$Ge quantum wells from solid source materials

Abstract

Germanium quantum well heterostructures have rapidly emerged as a leading platform for solid-state quantum information processing; however, material quality limits scalability, and higher structural quality, higher purity, as well as zero nuclear spin, are required. Here, we address these problems by employing the heaviest of Ge isotopes, by evaporating high-purity $^{76}$Ge radiation detector material, as utilized in fundamental neutrino particle physics experiments, to fabricate $^{76}$Ge/$^{28}$Si$^{76}$Ge quantum wells for quantum applications and explore the respective challenges. Specifically, we demonstrate improved results on strain-relaxed virtual Si$_{0.2}$Ge$_{0.8}$ substrates, forward graded from Si, with a dislocation density below 3.7$\cdot$10$^{5}$ cm$^{-2}$, explore nuclear spin-free solid-source molecular beam epitaxy, and demonstrate first quantum transport in $^{76}$Ge quantum wells. We demonstrate a record-level quantum well interface width of 0.3 nm by X-ray reflectivity, and quantitatively compare it to atom probe tomography and scanning transmission electron microscopy. The grown layer reveals nuclear-spin-bearing impurity concentrations below 10$^{19}$ cm$^{-3}$ and chemical impurity levels below 10$^{18}$ cm$^{-3}$, except for residual carbon attributed to the graphite crucible of the Ge source, which may reach up to 10$^{19}$ cm$^{-3}$. Low-temperature magneto-transport measurements yield electron mobilities of 6.1$\cdot$10$^4$ cm$^2$V$^{-1}$s$^{-1}$ at 15 mK with a carrier density of 2.2$\cdot$10$^{11}$ cm$^{-2}$, indicating that residual carbon is the dominant scattering mechanism.

Figures (7)

• Figure 1: CVD grown virtual substrate properties with (a) a cross-section schematic of the layer stack with the Si substrate, the backstessor and the graded Buffer. (b) An AFM image scanned $\approx$ 45° to [1 1 0 ] of the epi-ready and cleaned surface with an $\sigma_{rms} =$ 0.15 nm. (c) A SECCO etched sample micrograph from the center of a 12" SRB with TDs marked white and a closeup on a TD. On a etched 500 x 500 µm$^2$ area the TD are counted resulting in a TDD = 3.7$\cdot10^{5}~cm^{-2}$.
• Figure 2: AFM based morphology analyses of strained Ge layer grown on Si$_{0.3}$Ge$_{0.7}$ SRB as a function of layer thickness and temperature. Thereby facet analyses shows $\{$1 0 5$\}$, $\{$1 1 3$\}$ and $\{$3 15 23$\}$ facets which are indexed accordingly.
• Figure 3: Structural characterization of a nuclear-spin-free Ge/SiGe heterostructure. (a) Cross-sectional STEM image of the heterostructure, and the according growth temperature profile during the MBE process with the possible to change the Si-cap appearance by changing the growth temperature in (b). (c) APT mass spectrometry data showing the distribution of relevant isotopic masses along the heterostructure. In (b) a reciprocal space map (RSM) in (2 2 4) reflection is displayed as $Q_{\perp}$ vs. Q$_{\parallel}$. The strained Ge QW is located along the Ge CTR cut. The calculated lattice parameters are shown.
• Figure 4: (a) Rendered model from 3D APT data where each point denotes the estimated position of an ionized atom detected. (b) represents isosurfaces with the BIF at the bottom and TIF at the top. Ge concentrations for the isosurface are BIF at Ge: 87.6% and TIF at Ge: 87.7%. This isosurface spans a 30 x 30$~nm^2$ area, which represents the lateral size of a quantum dot, and the corresponding $\sigma_{RMS}$ values are BIF: 0.154 nm and TIF: 0.154 nm. (c) STEM image with a closeup of the Ge QW and marked TIF and BIF and a simulated ideal interface SIF. (d) Comparison of interface sharpness for the TIF and BIF at 4$\tau$, derived from STEM, XRR, and APT analyses, presented as a length versus normalized value plot. The lighter (less opaque) lines indicate the corresponding sigmoid function fits. (e) XRR measurement data and the corresponding calculated fit displayed in an intensity vs. 2$\theta$ plot ($\sigma_{RMS}$ values for BIF: 0.106 nm, TIF: 0.147 nm). (f) Low-temperature magneto-transport measurement on a Ge/SiGe 2DEG at 15 mK and zero back-gate voltage. With image insert of the Hall bar geometry on the top left and the Hall slope plot at the top right.
• Figure 5: (a) Si-cap surfaces grown under different growth temperatures shown in close up STEM images of the Si-cap for an amorphous cap grown at 25 °C and a crystalline, partially oxidized Si-cap grown at 90 °C. I, I$_a$ and I$_b$ show the different Si-cap appearances in a closed up STEM image an II the underlying top barrier. (b) 2$\cdot$2 µm$^2$ AFM images with the according growth Temperature. At 240 °C a 3D representation of the surface morphology is shown. The according $\sigma_{RMS}$ for each AFM meausrement are shown in the table in (c).