Nonmonotonic Variations of the Conductance with Electron Density in ∼70-nm-Wide Inversion Layers

Abstract

The conductance of metal-oxide-silicon field-effect transistors with ~ 70-nm-wide inversion layers exhibits nonmonotonic variations with electron density below 15 K. The variations are largest at low electron concentrations and are the result of variations of the activation energy E A . When E A is largest the current is found to be limited by spatial barriers which contain tunneling channels at discrete energies, as in the model of Azbel.PACS numbers: 73.40.Qv, 71.55.Jv Several groups 1 " 4 have observed nonmonotonic conductance variations with electron concentration in ultranarrow Si inversion and accumulation layers. These variations, seen at cryogenic temperatures, are the result of the quasi onedimensional (Q-1D) structure of the devices, and are not, therefore, found in wide inversion layers. For devices which are narrow but are more than 100 nm wide, the variations are small and have been interpreted 2 ' 3 in terms of the theories of weak localization and interaction. On the other hand, for devices less than 100 nm wide the variations can be very large, and it has been suggested 1 ' 2 that they may result from statistical variations of resistance associated with strong localization. To investigate these large variations we have studied an inversion layer whose mean width is ~ 70 nm. By measuring the current as a function of both the temperature T and voltage drop along the inversion layer V Dy we find that the current at low electron density is limited by tunneling through spatial barriers.Our device is a metal-oxide-silicon field-effect transistor (MOSFET) on a (100) Si surface with a gate that is a narrow aluminum wire. When a gate voltage V G is applied, the electric field confines the electrons to a narrow potential well directly under the gate (see Fig. 1). The narrow gate is created by first reactive-ion etching a 50-nm step down into the 100-nm-thick gate oxide using photoresist as the mask, and then evaporating Al into the step at a glancing angle to the surface. Residual A1 is removed by a liquid etch. The resulting gate is 70 nm wide and 55 nm high with a ~ 20% variation in width. Computer simulations suggest that the inversion layer has about the same width as the gate. As sketched in Fig. 1, wide gates overlap the n + regions so that electrical contact to the narrow inversion layer is made through ~l-mm-wide inversion layers, Electrical continuity of the gate is con-firmed by measuring the resistance between the two wide parts of the gate that overlap the narrow one and are separated by 7 Mm. Conventional (wide) devices were prepared simultaneously on the same wafer over an oxide which was also reactive-ion etched. These wide devices are found to have a fairly high mobility (8000 cm 2 / V-s at 4.2 K).For our narrow devices, increasing V G , which is proportional to the electron concentration, causes the conductance to increase almost linearly at T £ 15 K. This is the same behavior seen at all temperatures in wide MOSFETs. However, as the temperature is reduced below ~15 K the conductance near t...

Coulomb-blockade oscillations in disordered quantum wires

“…39 In very short channels (0.5 μιη long and l //m wide) Fowler et a/. 45 have found well-isolated, temperatureindependent (below 100 mK) conductance peaks, which they attributed to resonant tunneling.…”

Single Charge Tunneling

“…The effect has been seen in electron and hole gases in Si (9,11,14] and in the electron gas in GaAs [10,12,13]. In contrast, previous work by Fowler et al [60] and by Kwasnick et al [61] on narrow inversion and accumulation layers in Si has produced sharp but aperiodic conductance peaks. How are these observations to be reconciled?…”

“…relates the absorptive part x"(w) of the dynamical susceptibility (59) to the Fourier transform (61) ofthe equilibrium phase-phase correlation function. The fl.uctuation-dissipation theorem may be proven in the framewerk of linear response theory which becomes exact if a linear system is treated as is the case here.…”

“…13a). The random conductance fl.uctuations seen previously (60,61] are thought instead tobe due to variable range hopping between a large nurober of localized states, distributed randomly along the length of the channel (Fig. 13b) (62]- [64].…”

“…From the equivalent circuit of our system (shown in Fig. 9 for the specific case of the three-junction arrays) one can get that at Co ~ C the energy € of resulting charge configuration is (61) where N is the number of the junctions in one array. It can be viewed as the binding energy of the exciton.…”