5.3. Thermionic emission
305
x
U x
W
x =
C
Figure 5.1: Energy diagram for thermionic emission.
x > 0 represents the vacuum. The solid curve is the potential energy U (x).
We consider a single electron with energy W inside the bulk emitter material with x ≤ 0. We approximate the potential energy
U (x) by a square barrier. The problem of scattering of matter
waves by a square barrier in one dimension is treated in many
books on elementary quantum mechanics, see for example Liboff
[59].
Inside the bulk material with x ≤ 0 the wave function is a superposition of a right-propagating incident wave plus a left-propagating
reflected wave. This is represented by
+ik 1 x
−ik 1 x
u(x ≤ 0) = a + e
+ a − e
,
(5.21)
where the complex constants a + and a − have yet to be determined. The direction of propagation can be verified by forming
the complete wave function ψ(x, t) given by
iW t/¯ h
ψ(x, t) = u(x) e
,
(5.22)
305
x
U x
W
x =
C
Figure 5.1: Energy diagram for thermionic emission.
x > 0 represents the vacuum. The solid curve is the potential energy U (x).
We consider a single electron with energy W inside the bulk emitter material with x ≤ 0. We approximate the potential energy
U (x) by a square barrier. The problem of scattering of matter
waves by a square barrier in one dimension is treated in many
books on elementary quantum mechanics, see for example Liboff
[59].
Inside the bulk material with x ≤ 0 the wave function is a superposition of a right-propagating incident wave plus a left-propagating
reflected wave. This is represented by
+ik 1 x
−ik 1 x
u(x ≤ 0) = a + e
+ a − e
,
(5.21)
where the complex constants a + and a − have yet to be determined. The direction of propagation can be verified by forming
the complete wave function ψ(x, t) given by
iW t/¯ h
ψ(x, t) = u(x) e
,
(5.22)