  Conventional Josephson metal-insulator-metal devices are inherently
underdamped and exhibit hysteretic current-voltage response due to a very high
subgap resistance compared to that in the normal state. At the same time,
overdamped junctions with single-valued characteristics are needed for most
superconducting digital applications. The usual way to overcome the hysteretic
behavior is to place an external low-resistance normal-metal shunt in parallel
with each junction. Unfortunately, such solution results in a considerable
complication of the circuitry design and introduces parasitic inductance
through the junction. This paper provides a concise overview of some generic
approaches that have been proposed in order to realize internal shunting in
Josephson heterostructures with a barrier that itself contains the desired
resistive component. The main attention is paid to self-shunted devices with
local weak-link transmission probabilities so strongly disordered in the
interface plane that transmission probabilities are tiny for the main part of
the transition region between two superconducting electrodes, while a small
part of the interface is well transparent. We consider the possibility of
realizing a universal bimodal distribution function and emphasize advantages of
such junctions that can be considered as a new class of self-shunted Josephson
devices promising for practical applications in superconducting electronics
operating at 4.2 K.
