Electronic cooling junctions

'On-chip' cryogenic devices consist of cooling junctions capable of reaching sub-Kelvin temperatures via direct electron cooling. The process focusses on removing the most energetic electrons from a system, thus lowering the average temperature of the electron gas.

Superconductor - Semiconductor - Superconductor (SSmS) junctions are a particular type of cooling junction developed to address a number of flaws inherent to earlier Normal metal - Insulator - Superconductor devices.

Figure 1: An energy-level diagram of a NIS junction with a half-band gap of Δ. A bias voltage, V ≤ Δ/e, is applied across the junction, allowing electrons with an energy greater than E_F to tunnel across the insulator into the superconductor. The device is analogous to a high-pass filter, with each electron carrying an energy (E-eV) out of the semiconductor (reproduced from [1]).

The design of the SSmS junction takes advantages of the Schottky barrier which is created when a superconductor and semiconductor are brought into contact. This energy barrier takes the place of the insulator in an NIS junction. Not only does this simplify the manufacturing process, but given that Schottky barriers are non-physical they are not susceptible to the heat absorbing impurities that would be present in an insulator.

Figure 2: An energy-level diagram of an SSmS junction which incorporates two junctions in contrast to the single junction in an NIS device. This second junction assists in the cooling of the system by enabling cold electrons to replace the hot electrons that are removed from the semiconductor. Aside from assisting cooling, replacing the lost electrons ensures that the device is kept neutral (reproduced from [2]).

The cooling power of a NIS and S-Sm-S junctions arises principally from the current of high energy electrons leaving the semiconductor, each carrying an energy (E-eV) out of the system. This current is given by the equation [3]

$I=\frac{1}{eR_T}\int^{\infty}_{-\infty}{F.g(E)dE}$

with

$F=f(E-eV/2,T_b)-f(E,T_{sm}).$

Here R_T is the tunnelling resistance and F is the combined Fermi-Dirac distribution of a double junction, with T_sm as the semiconductor temperature and the superconductor being at the temperature of the thermal bath, T_b. g(E) describes the density of states within the superconductor into which the electrons tunnel [4], and can be written as

$g(E)&=\,0                    & \forall|E|<\Delta\nonumber\\$

$g(E)&=\frac{|E|}{\sqrt{E^2-\Delta^2}}& \textrm{     otherwise}.$

This current removes energy form the semiconductor at a rate [5]

$P_{cool}=\frac{2}{e^2R_T}\int^{\infty}_{-\infty}(E-eV/2).F.g(E)dE$

with the factors of two accounting for applied voltage being split across the two junctions of the SSmS device.

Refernces

J. Pekola et al., Physics Today 57 (2004)
A. Savin et al., Applied Physics Letters 79 (2001)
F. Giazotto et al., Reviews of Modern Physics 78 (2006)
R. Dynes et al., Physical Review Letters 41 (1978)
L. Luukanen er al., Journal of Low Temperature Physics 120 (2000)