Negative differential capacitance of quantum dots

Abstract

The dependence of charges accumulated on a quantum dot under an external voltage bias is studied. The charge is sensitive to the changes of number of filled levels and the number of conducting levels ͑channels͒. We clarify that there are two possible outcomes of applying a bias. ͑a͒ The number of conducting channels increases, but the number of filled levels decreases. ͑b͒ The number of filled levels increases or does not change while the number of conducting channels ͑levels͒ increases with the bias. In case ͑b͒, charges are generally expected to increase monotonically with the applied bias. We show, however, that this expectation may not materialize when the electron transmission coefficients depend on bias. Numerical evidences and a theoretical explanation of this negative differential capacitance, i.e., charges accumulated on a quantum dot decrease with applied bias, are presented. The capacitance of a quantum dot ͑QD͒ has been the subject of many studies.1,2 This is largely due to the fact that classical results derived from a macroscopic system are not applicable to a system of nanometer scale at which electron levels are discrete and the density of state is finite. So far, most studies have been on modifications of classical capacitance due to the finite density of states and electron tunneling, such as fluctuation of differential capacitance with respect to the gate voltage.3 However the nonlinear chargevoltage characteristics 4,5 has been less studied. A QD can be viewed as a potential well which is capable of accommodating electrons. Figure 1 is a schematic diagram of a QD connected to two external leads. The two leads can have different electrochemical potentials, and their difference is called the external bias on the dot. At nonzero bias, a tunneling current may pass through the QD while the electric charges on the QD can also vary with bias. There are three possible ways of applying a bias. Without losing generality, let us assume the electrochemical potential of the left lead L is no less than that of right lead R , i.e., L у R . The first way is to raise L while one keeps R unchanged as shown in Fig. 1͑b͒. The dashed line is electrochemical potentials of two leads at zero bias. The second way is to lower R , but L does not change. This is shown in Fig. 1͑c͒. The third way is to raise L and to lower R simultaneously as shown in Fig. 1͑d͒. Experimentally, all three ways described in Fig. 1 can be realized easily by controlling the gate voltage of the QD. Here we shall be interested in how the charge Q(V) on the QD change with the bias V. Intuitively, the behavior Q(V) depends on how a bias V is applied.An electron on the dot must occupy on one energy level. At zero temperature, there are three types of energy levels. One is the empty levels on which there are no electrons. They are the levels above L . The second type is the filled levels below R . The third type is conducting levels ͑chan-nels͒ which are between R and L , and are partially filled by electrons. In the case of Fig. 1͑b͒, as the exte...

Silicon quantum dots embedded in a SiO2matrix: From structural study to carrier transport properties

“…Thus, at high V b , the charge accumulated on a conductive energy level decreases with increasing V b , since the ratio between the incoming and outcoming transmission coefficient decreases with V b . 26 NDR almost does not appear in the largest QD [ Fig. 7(b)] due to a reduced presence of isolated peaks in the DOS, as reported in Figs. 7(e)-7(f).…”

“…Different structural models have been proposed to describe SiQDs and optical, structural, and electrical properties have been widely reported using density functional theory (DFT). [16][17][18][19][20][21][22][23] From a fundamental point of view many novel electronic transport phenomena have been discovered, such as a staircaselike current-voltage (I-V) characteristic, 24 Coulomb blockade oscillation, 25 negative differential resistance, 4,26 or the Kondo effect. 27 Researchers have mostly concentrated on the study of single and two QDs using the nonequilibrium Green's functions formalism (NEGFF) 26,[28][29][30] with one level of energy and constant transition rates.…”

Energetics and carrier transport in doped Si/SiO2quantum dots

“…Approximations must be adopted in order to limit the computational effort, like using a reduced system size, or employing a simplified approach. Most of the available studies on single-and two-QDs have been performed by using nonequilibrium Green functions formalism (NEGFF) with constant transition rates between QDs and one energy level per QD [31][32][33][34][35][36] , and by using tunneling transmission coefficients with planar Si/SiO 2 values for the barrier height, and bulk-Si band gap. [37][38][39][40] Here we make use of a different approach, 41-43 based on the transfer Hamiltonian formalism and non-coherent rate equations to describe the current, that takes into account the local potential due to the QD charge, com-V FIG.…”

Spin interference and the Fano effect in electron transport through a mesoscopic ring side-coupled with a quantum dot

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