Subgap Leakage in $\hbox{Nb/Al}$– $\hbox{AlO}_{\rm x}\hbox{/Nb}$ Josephson Junctions and Run-to-Run Reproducibility: Effects of Oxidation Chamber and Film Stress

Fabrication Process and Properties of Fully-Planarized Deep-Submicron Nb/Al– $\hbox{AlO}_{\rm x}\hbox{/Nb} $ Josephson Junctions for VLSI Circuits

“…This is commonly expressed by the statement that I c R N product at a given temperature is a constant for the given type of JJs. For tunnel junctions the relationship is known as Ambegaokar-Baratoff (AB) formula [33] I c = G N V AB (T) and V AB (T) = g(πV g /4)tanh(V g /4k B T), (11) where V g is the gap voltage (Δ 1 +Δ 2 )/e, Δ 1 (T) and Δ 2 (T) are the superconducting energy gaps in the junction electrodes, and g is a numerical factor of order unity which accounts for deviations from the ideal model [33], such as barrier nonideality, proximity between Nb and Al overlayer in the base electrode, strong coupling effects in Nb, etc.…”

“…We determined V AB at 4.2 K for our junctions and used it to infer the critical current of JJs from their conductance. Also, we experimentally established the relation between the normal state conductance G N at 4.2 K, entering into the AB formula (11), and the JJ conductance G 300 at 300 K. This chain of relationships allows us to use G 300 to characterize the value of I c of the junctions at 4.2 K.…”

“…Hence, a normalized value of I c standard deviation σ Ic = [Var(I c )] 1/2 /E(I c ) can be written as (12) where σ G and σ Vab are the normalized standard deviations of the JJ conductance and the Ambegaokar-Baratoff voltage -I c R N product, -respectively. In turn, the σ Vab is the same as the relative standard deviation of the gap voltage σ Vg in the ensemble of junctions since the variation of the hyperbolic tangent term in (11)…”

“…Achieving very large scale integration (VLSI) with 10 6 JJ/circuit and beyond requires decreasing the scale of all components to deep submicron dimensions. While there have been a number of reports on submicron JJs [4]- [11] with both low and high critical current density, J c , the JJ definition was produced with e-beam lithography in circuits with a small number of JJs on small-size wafers [12]. There are no data and statistics on submicron JJs defined by modern steppers and scanners with 248 nm and 193 nm exposure wavelength, on a very large scale and on large-size wafers.…”

Enhanced Superconductivity Induced by the Hexagonal-Array-Cooling-Shrinkage Effect

“…Based on eq , we can calculate that the cool shrinkage-induced compressive stress of PSs is about 110 ± 40 MPa, which exists in the contact areas of the PSs/Nb hybrid, like a period stress field, as shown in Figure S6. The stress seems small but is high enough to make a difference between the contact and noncontact areas in the PSs/Nb hybrid. , …”