Activation Mechanism of the Cyclic Switchover Effect …
635
v F =
m
(3π
2 n)
1 / 3 ,
(9)
where m is the electron mass, n is the concentration of Fermi electrons in the metal,
and è is the Planck constant.
If we express the relaxation time as follows:
τ r =
m
ρne 2 ,
(10)
where e is the elementary charge, and substitute (9) and (10) into (8), we can arrive
at the following relation:
ρl =
(3π
2
)
1 / 3
e 2 n
2 / 3 .
(11)
Assuming that there is one Fermi electron, i.e., one conduction electron, for each
of the copper atoms that form the conduction channel of the Yanson point contact,
we can obtain n = 8.49·10
28 m
−3 . Then, according to (11), we have ρl = 0.658·10
−15
m
2 , which is in agreement with the published data for pure copper: ρl = 0.66·10
−15
m
2 [18–20]. It follows from the available data that for copper at T = 293 K the
resistivity is ρ = 1.673·10
−8
m [21], therefore, the electron mean free path at room
temperature is l = 394 Å, which is in good agreement with the estimation reported
in [22].
To destroy the conduction channel in a GES, it is enough to dissolve a layer of
metal δ pc which is half the channel diameter, that is δ pc = d/ 2. If we estimate the
conduction channel diameter using Sharvin’s equation (7), we can find that
δ pc =
2
√
3π
ρl
R 0
.
(12)
So, the difference δ pc −δ calc can be used as a basic control function in establishing the dependence of the dissolution time τ at of the point-contact conduction
channel on the conduction channel resistance.
To find δ calc from (5), we used Simpson’s method of numerical integration
[23]. Iteration procedures with the termination criterion (δ pc −δ calc )/δ calc ≤
0.01 allowed us to calculate the time of complete interruption of direct conduction
(contact’s lifetime) as a function of the point-contact initial resistance. The obtained
values were compared with the point-contact lifetimes experimentally observed in
the R(t) curves during the self-oscillating switchover process (Fig. 1b). The experimental lifetimes of point contacts were believed to be equal to the lengths of the
sections corresponding to the local minima in the R(t) curves, while the point-contact
resistance was taken as the ordinate values of the sections. Processing of five experimental curves has yielded a dependence of the lifetime of the point-contacts on their
resistance (Fig. 3) with confidence intervals indicated for a confidence probability of
635
v F =
m
(3π
2 n)
1 / 3 ,
(9)
where m is the electron mass, n is the concentration of Fermi electrons in the metal,
and è is the Planck constant.
If we express the relaxation time as follows:
τ r =
m
ρne 2 ,
(10)
where e is the elementary charge, and substitute (9) and (10) into (8), we can arrive
at the following relation:
ρl =
(3π
2
)
1 / 3
e 2 n
2 / 3 .
(11)
Assuming that there is one Fermi electron, i.e., one conduction electron, for each
of the copper atoms that form the conduction channel of the Yanson point contact,
we can obtain n = 8.49·10
28 m
−3 . Then, according to (11), we have ρl = 0.658·10
−15
m
2 , which is in agreement with the published data for pure copper: ρl = 0.66·10
−15
m
2 [18–20]. It follows from the available data that for copper at T = 293 K the
resistivity is ρ = 1.673·10
−8
m [21], therefore, the electron mean free path at room
temperature is l = 394 Å, which is in good agreement with the estimation reported
in [22].
To destroy the conduction channel in a GES, it is enough to dissolve a layer of
metal δ pc which is half the channel diameter, that is δ pc = d/ 2. If we estimate the
conduction channel diameter using Sharvin’s equation (7), we can find that
δ pc =
2
√
3π
ρl
R 0
.
(12)
So, the difference δ pc −δ calc can be used as a basic control function in establishing the dependence of the dissolution time τ at of the point-contact conduction
channel on the conduction channel resistance.
To find δ calc from (5), we used Simpson’s method of numerical integration
[23]. Iteration procedures with the termination criterion (δ pc −δ calc )/δ calc ≤
0.01 allowed us to calculate the time of complete interruption of direct conduction
(contact’s lifetime) as a function of the point-contact initial resistance. The obtained
values were compared with the point-contact lifetimes experimentally observed in
the R(t) curves during the self-oscillating switchover process (Fig. 1b). The experimental lifetimes of point contacts were believed to be equal to the lengths of the
sections corresponding to the local minima in the R(t) curves, while the point-contact
resistance was taken as the ordinate values of the sections. Processing of five experimental curves has yielded a dependence of the lifetime of the point-contacts on their
resistance (Fig. 3) with confidence intervals indicated for a confidence probability of