EFFECT OF ISLAND LENGTH ON THE COULOMB MODULATION IN SINGLE-ELECTRON TRANSISTORS

We have studied single-electron transistors with island lengths of 2, 10, 20, 30, and 40 mu m and with high-resistance tunnel junctions to m inimize the effects of cotunneling and electron self-heating. With lon ger islands, there is a marked reduction of the gate modulation of the Coulomb blockade width. According to orthodox theory, the width of th e Coulomb blockade at T = 0 is equal to e/C-Sigma, and it falls approx imately exponentially with k(B)T/E-c, where E-c = e(2)/2C(Sigma), and C-Sigma is the total capacitance. Based on numerical calculations and analytic estimates, we conclude that the modulation reduction is mainl y due to the large increase in stray capacitance between the island an d the leads as the island length is increased, and not to some more su btle nonequilibrium effect. When the increased capacitance is combined with the effect of electron heating, the Coulomb modulation is rapidl y reduced. This work also demonstrates the need to take stray capacita nce into account in addition to intrinsic junction capacitance even in structures that are only a few mu m long. [S0163-1829(98)07307-X].