PHYSICAL REVIEW B VOLUME 42, NUMBER 9 Coulomb blockade of resonant tunneling 15 SEPTEMBER 1990-II Atanas Groshev Division of Theoretical Physics, University of Sofra, 5 Anton Ivanov Boulevard BG-i126 Sofia, Bulgaria (Received 12 February 1990; revised manuscript received 29 May 1990) Ultrasmall double-barrier semiconductor structures are investigated in terms of the semiclassi- cal sequential theory of resonant tunneling. The quantization of the charge buildup in the quan- tum well is taken into account. A peaked I-V characteristic is obtained, with each peak corre- sponding to an integer number of electrons in the well. A new explanation of the experiment of Reed et al. [Phys. Rev. Lett. 60, 535 (1988)I is proposed. The large value of the charging energy in their experiment E, e'/2C 43 meV makes semiconductor tunneling structures more con- venient for observation of charging effects than the usual ones. As a result of recent advances in lithography and crystal-growth technology, the possibility for an experi- mental investigation of two new phenomena appear. The first phenomenon is Coloumb blockade of single-charge- carrier tunneling in ultrasmall normal or superconducting junctions. ' Modern nanolithography forms the back- ground for experimental investigations of this effect. The second phenomenon is resonant tunneling in double- barrier semiconductor structures. These structures are made with the high technology of molecular-beam epi- taxy. Combining these two techniques one can make a new device — ultrasmall resonance tunneling structure (see Fig. 1). In such structures the effects of charge quantization become noticeable. s Recently Reed et al. investigated electronic transport through a three-dimensionally confined quantum well (see Fig. 1). Their structure consisted of a 500-nm n+-type GaAs layer (Si doped at 2x 10' cm, graded to approx- imately 10'6 cm ' over 20 nm, followed by a 10-nm un- doped GaAs spacer layer), a 4-nm Ale 25Gae75As tunnel barrier, and a 5-nm undoped In„Ga|, As quantum well. Symmetrically about the central plane of the well corre- sponding layers were grown. Electron-beam lithography and reactive ion etching were used to define isolated columns. Reed et al. measured the current-voltage characteristics of large-area mesas (with lateral dimen- sions ~ 2000 nm) and detected two resonance peaks: a ground state at 50 meV and an excited state at 700 meV. CONDUCTION CORK BARRIERS They also measured small-area mesas (quantum-box resonance-tunneling structure) with 100 nm diameter. At low temperature (~ 10 K) they observed additional fine structure emerging superimposed on the excited-state res- onance peak (see the inset of Fig. 2). There are two theories attempting to explain the posi- tion of the fine-structure peaks. Reed et al. made esti- mates for the lateral confinement due to the sidewall de- pletion, supposing harmonic-oscillator radial potential. They obtained the equidistant harmonic-oscillator split- ting of 25 meV which they considered to be consistent with the splitting of the upper four peaks. They could not explain the position of the lowest peak, however. To ac- count for this fact, Luban et al. s proposed a one- parameter family of anharmonic oscillator potentials which differs from the harmonic one only in a zone of ra- dius ( 15 nm around the axis of the device. Bryant' proposed another explanation, accounting for variable lateral confinement in the emitter (collector) and the well. Starting from the harmonic-oscillator splitting of AF-b0„=25 meV in the quantum box and of AF. „, t — 1 meV in the contacts, he concluded that the I. 5 4 Cl 1 4 Q 4 0. 5 V 0 0. 5 0. 7 0. 8 0. 9 FIG. 1. Ultrasmall double-barrier structure. The conduction core is about five times smaller than the physical dimensions of the structure. Voltage (V) FIG. 2. Current-voltage characteristics of the device obtained with E, 43 meV, AEb„25 meV, a 5 meV, a 0007, and r,/r, 10. In the inset schematic low-temperature current- voltage characteristics are shown, obtained by Read et ai. (Ref. 4). The peaks are grouped in two sets A, and B„n -0, 1, 2. The number n of the peak denotes the number of the electrons in the well. 5895 1990 The American Physical Society