A theory is proposed for the impurity-induced tunnelling current which apparently constitutes the major part of the current observed in As and P doped germanium tunnel diodes. The experimental valley-orbit splittings of various donors in. germanium show-that the short range atomic fields of As and P are many times stronger than that of Sb and, for doping levels above 1019/cm3, can be equally or more effective in scattering than phonons. The possible mechanisms for tunnelling caused by impurity scattering are examined; it is found that owing to a special feature of the germanium band structure, namely, (0, 0, 0) conduction band minimum not too high and associated with a particularly small effective mass, a second order process via the (0, 0, 0) minimum should be the dominant process. A method for treating such a second order process is developed, which gives a clear quasi-classical picture of the tunnelling process: an electron tunnelling from a conduction band minimum, when reaching an optimum depth, is scattered inta (0, 0, 0) states and proceeds thereon to the valence band maximum much as in direct tunnelling. An explicit expression for the current is obtained; the magnitude of the current is estimated and a comparison with a similar phonon-assisted current (see accompanying paper II) is made. It is also shown that despite the anisotropic nature of the conduction band minima, the second order current should be nearly direction-independent.