Question

A disk-shaped quantum dot 8 nm in diameter is separated from the nearest electrode by       glass with a permittivity of 4.43 x 10^-11 F/m.

1.           Determine the energy needed to increase the charge on the dot by one electron.
2.           Using the rule of thumb for the Coulomb blockade, determine the temperature    below which quantum confinement is possible.

Answer 1

The diameter of a disk is, d=8nm=8×10−9m

    The permittivity of a glass is, ε0=4.43×10−11F/m

Part (a):

The expression for the energy needed to add one electron to dot is,

EC=e22Cdot

.....................(1)

Here, e
is the charge on electron and Cdot

is the quantum dot which is given as,

Cdot=4ε0d.................(2)

Substitute the value of equation (2) in equation (1)

EC=(1.6×10−19)22×4×4.43×10−11×8×10−9EC=9.03×10−21J

Thus, the energy needed to add one electron to dot is 9.03×10−21J

.

Part (b):

By using the rule of thumb for the coulomb blockade is,

T=EC10kB

................(3)

Here, kB
is the Boltzmann constant (1.38×10−23m2kgs−2K−1)

Substitute the values in equation (3)

T=9.03×10−2110×1.38×10−23T=65.4K

Thus, the temperature below which quantum confinement is possible is 65.4K

.