SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

10.6. MAGNETIC SEMICONDUCTORS AND SPINTRONICS 507

GaSb

InAs

GaSb

• –
  
  
  • Fe Gate Fe
  
  
  
  

x

y

z

Ferromagnetic metal

contact injection

Figure 10.14: A schematic of a spin transistor in which electrons with a selected spin are injected
into a 2-dimensional channel.

device it is possible to inject electrons or holes in a spin selected state using ferromagnetic
contacts. In figure 10.14a we show a spin-transistor in which spin selected electrons are injected
from an Fe contact acting as a source. The magnetized contact injects electrons with spin selected
by the magnetization field and maintain this spin state as they travel throughout the device. The
spin transistor exploits quantum interference effects with two nuances: i) spin select electrons
can be injected into a transistor channel; ii) spin splitting of spin-up and spin-down states causes
the two spin state electrons to have a differentk-vector which can be controlled by a gate bias to
create interference effects.
Using the geometry shown in figure 10.14a, electrons are injected into the 2-dimensional
channel with a spin polarized along the+xdirection. These electrons may be written in terms
of the spin-up (positivez-polarized) and spin-down (negativez-polarized) states

〈x|→

1

√

2

(〈↑|+〈↓|) (10.6.4)

Now consider the possibility where the energy of the spin-up and spin-down electrons is different
as shown in figure 10.15. The splitting in the spin-up and spin-down states can occur due to
external magnetic fields or internal spin-orbit effects combined with lack of inversion symmetry.
These effects are strongest in narrow bandgap semiconductors where the conduction band states
are influenced by thep-type valence band states.