SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

496 CHAPTER 10. COHERENT TRANSPORT AND MESOSCOPIC DEVICES

1

0.1

0.01

0.001

0.0001

0.00001

0 0.25 0.50 0.75 1

26 Å

ELECTRON ENERGY (eV)

T

RANSMISSION COEFFICIENT

26 Å

1.2 eV

m* = 0.04 m 0

m* = 0.15 m 0

50 Å

well

barrier

Resonant effects in tunneling

Figure 10.6: Transmission coefficient as a function of electron longitudinal energy for a double
barrier structure

The wavevectork 1 is given by
^2 k^21
2 m∗

=E

While tunneling through a single barrier has no interesting feature, tunneling through a double
barrier structure has interesting resonances as can be seen from the expression forT 2 B. The cal-
culated transmission probability as a function of longitudinal electron energy for a typical double
barrier is shown in figure 10.6. The sharp peaks in the transmission probability correspond to
resonant tunneling through the quasi-bound states in the quantum well formed between the two
barriers. The tunneling probability reaches unity at energies corresponding to the quasi-bound
states in the quantum well. To calculate the current density in the system we note that

J = nev

=

e

4 π^3 

∫∞

0

dk

∫∞

0

d^2 kt

[

f(E)−f(E

′

)

]

T(E)

∂E

∂k

(10.3.6)