4 Coulomb blockade

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80 4 Coulomb blockade J [arb. u.] 0 2 4 6 8 V Fig. 4.7. Coulomb staircase: voltage-current curves of an asymmetric junction at low temperature (T =0.01EC) at different gate voltages VG =0,VG =0.25EC, and VG =0.5EC. Dashed line shows the change at higher temperature T =0.1EC. Voltage is in units of EC/|e|. 4.3.5 Contour plots. Stability diagrams To analyze the experiments the contour plots of the current J(V,VG) (Fig. 4.8) and the differential conductance dJ/dV (V,VG) (Fig. 4.9) are very useful. The characteristic structures of Coulomb blockade (so-called Coulomb diamonds) are well pronounced in these pictures. The white rhombic-shaped regions are the regions of Coulomb blockade. At zero temperature there is no current, one state with n electrons is stable with respect to tunneling. For example, near the point V = VG = 0 the state n = 0 is stable. If one changes the gate voltage, the other charge states become stable. At large enough bias voltage the stability is lost and sequential tunneling events produce a finite current. The contour plots, as well as a schematic representations of the boundaries of the stability region in the (V,VG) plane, are often called stability diagrams. While both left and right tunneling events should be suppressed, there are two stability conditions, obtained directly from the tunneling rates (4.35), (4.38) |e| n − 1
V 4 2 0 -2 4.3 Single-electron transistor 81 -4 -2 -1 0 VG 1 2 Fig. 4.8. Contour plot of the current. where V = VL − VR is the bias voltage, and VGL = VG − VL, VGR = VG − VR are the voltages between the gate and the leads. These inequalities show that if the system leaves the stability region at finite bias voltage V , the new state with n = n ± 1, which occurs as a result of tunneling through one junction, is also unstable with respect to tunneling through the other junction. As a result, the systems returns back to the state n, and the cycle is started again, thus the current flows through the system. V 4 2 0 -2 -4 -2 -1 0 VG 1 2 Fig. 4.9. Contour plot of the differential conductance. 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 0.3 0.1 0
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Page 21 and 22: 4.5 Cotunneling 4.5 Cotunneling 87
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Page 25: Additional reading 4.7 Problems 91

4 Coulomb blockade

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