Pauli-spin-blockade transport through a silicon double quantum dot

We present measurements of resonant tunneling through discrete energy levels of a silicon double quantum dot formed in a thin silicon-on-insulator layer. In the absence of piezoelectric phonon coupling, spontaneous phonon emission with deformation-potential coupling accounts for inelastic tunneling through the ground states of the two dots. Such transport measurements enable us to observe a Pauli spin blockade due to effective two-electron spin-triplet correlations, evident in a distinct bias-polarity dependence of resonant tunneling through the ground states. The blockade is lifted by the excited-state resonance by virtue of efficient phonon emission between the ground states. Our experiment demonstrates considerable potential for investigating silicon-based spin dynamics and spin-based quantum information processing.

Figure 1

(Color online) (a) Schematic cross section of a Si MOS structure with three lower gates ${\mathrm{LG}}_1$, ${\mathrm{LG}}_2$, and ${\mathrm{LG}}_3$. A bias voltage was applied between the source (S) and the drain (D). Thicknesses of the buried oxide, the gate oxide, and the oxide around the lower gates are 400, 35, and $30\mathrm{nm}$, respectively. The width of the lower gate is $15\mathrm{nm}$ and the gate spacing is $85\mathrm{nm}$. (b) Top-view SEM of the device before fabricating the upper gate UG. The Si wire width is $40\mathrm{nm}$. Two dots L and R are formed between gates ${\mathrm{LG}}_1$ and ${\mathrm{LG}}_2$ (marked by white circles). (c) Current $I$ through the DQD as a function of $V_{{\mathrm{LG}}_1}$ and $V_{{\mathrm{LG}}_2}$. Hexagonal charge domains are outlined by dashed lines, where $(n,m)$ denotes the effective electron numbers in dots L and R.

Figure 2

(Color online) (a) Fine scan of the rectangular region in Fig. 1c at $V_{\mathrm{D}}=1.1\mathrm{mV}$. Solid and dashed gray lines outline the sequential tunneling and cotunneling regions, respectively. (b) Cotunneling current $I$ as a function of $V_{{\mathrm{LG}}_1}$ swept along the arrow $\alpha$ in (a). Each trace is shifted for clarity. (c) Current $I$ through the DQD as a function of the energy offset $\epsilon$. The hatched pattern denotes inelastic tunneling through the DQD. The corresponding energy diagram and localized wave functions at $\epsilon >0$ are shown in the inset. (d) Dependence of phonon-emission rate ${\Gamma }_{\mathrm{ph}}$ on the energy $E$. The calculation was done for the spontaneous phonon emission from the antibonding state to the bonding state at $\epsilon =0$ (corresponding energy diagram and wave functions shown in the inset) for GaAs (dashed line) and Si (solid line) DQDs. We consider Gaussian-shaped dots (radius $R=25\mathrm{nm}$ for GaAs and $12\mathrm{nm}$ for Si) separated by $2R$. Deformation coupling $(\Xi =7\mathrm{eV})$ and piezoelectric coupling $(e_{14}=0.16\mathrm{C}∕{\mathrm{m}}^2)$ for GaAs and isotopic deformation coupling $(\Xi =3.3\mathrm{eV})$ for Si were used (Ref. 23). Data from this work for Si DQDs (◇) and from Ref. 24 for GaAs DQDs (●) are plotted.

Figure 3

(Color) (a) Fine scan of the rectangular region in Fig. 1c at $V_{\mathrm{D}}=-1.1\mathrm{mV}$. (b) Current $I$ through the DQD as a function of $\epsilon$ at various $V_{\mathrm{D}}$. Each trace is shifted for clarity. (c) $I\text{−}{V}_{\mathrm{D}}$ plot traced at the triple point in the linear transport regime. Energy diagram denoting the Pauli spin blockade is plotted in the inset. (d) Energy spacing ${\Delta }_{ST}$ and ${\Delta }_{S{S}^{\prime }}$ as functions of magnetic field $B$ perpendicular to the substrate. Corresponding energy diagrams are shown in the lower right and upper right insets, respectively.