SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

508 CHAPTER 10. COHERENT TRANSPORT AND MESOSCOPIC DEVICES

Spin-down Spin-up

k( ) k( )

Ec + E

Ec – E

Ec

k

EF

Figure 10.15: A schematic of the band profile of spin-up and spin-down electrons. At the Fermi
energy thek-vector for spin-up and spin-down electrons are different.

The position of the Fermi level is the same for the spin-up and spin-down states as shown in
figure 10.15. We have

EF = Ec−ΔE+

^2 k^2 (↓)

2 m∗

= Ec+ΔE+

^2 k^2 (↑)

2 m∗

(10.6.5)

As the electrons move down the channel the phase difference between spin-up and spin-down
electrons changes according to the usual wave propagation equation

Δθ=[k(↑)−k(↓)]L (10.6.6)

whereLis the channel length. The drain contact acts as a spin filter and only accepts electron
states with spin in thex-direction. Thus the current flows ifΔθ=2nπ. Otherwise the current
value is lower. Thus the spin transistor essentially behaves as an electrooptic modulator where
the phase is controlled by the gate voltage which controlsEF.