Quantum Mott Transition in a Silicon Quantum Dot

Considering a double-barrier structure formed by a silicon quantum dot covered by natural oxide, we derive simple conditions for the conductance of the dot to become a step-like function of the number of doping atoms inside the dot, with negligible dependence on the actual position of the dopants. The found conditions are feasible in experimentally available structures. The fabrication of Si nanostructures became possible through very recently developed new technologies [1, 2]. One unique preparation technology for individual silicon quantum dots (SQD) has been reported in [2]. They are spherical Si particles with diameters d in the range 5–12 nm covered by a 1–2 nm-thick natural SiO 2 film. Metallic current terminals made from degenerately doped Si are defined lithographically to touch each individual dot from above and from below. To ensure metallic electrodes the donor concentration n should be n ≥ n M ott , where n M ott = 7.3 × 10 17 cm −3. The critical concentration n M ott is defined by the Mott criterion [3], introducing the transition to a metallic type of conductivity in a semiconductor at: a B × (n M ott) 1/3 = 0.27. (1) where a B nm is the Bohr radius of an electron bound to a donor inside the Si crystal, in the case of phosphorus-donors a B = 3 nm [3]. As for the doping of the dot, the situation concerning a Mott transition in that small dots is much less trivial than the one described by Eq. (1). Let us consider dots with diameters d = 10 nm formed from n-doped Si with n = n M ott as an illustrative example. Then each dot contains in average one donor. Note that we will consider degenerately n +-doped electrodes with n ≫ n M ott which ensures metallic conduction up to the borders of the dot. Real fabrication technology [2] provides a wafer with hundreds of SQDs on it with current leads towards each individual SQD. Dots in average have the same value of mean dopant concentration n, which is determined by the parent material of bulk silicon the dots are formed from. However, on the level of each individual