SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

2.9. DOPING IN POLAR MATERIALS 65

Intrinsic range

Si

Nd= 10^15 cm–3

1000 300 200 100 75 50

500

1017

10

10

10

10

16

15

14

13

0 4 8 12 16 20

Saturation range

Freeze-out

range

1000/T (K–^1 )

E ni

LECTRON

DENSITY

n

(cm

–3

)

TEMPERATURE (K)

Nd= 10^16 cm–2

Figure 2.22: Electron density as a function of temperature for a Si sample with donor impurity
concentration of 1015 cm−^3.

2.9 DOPING IN POLAR MATERIALS

Semiconductors such as GaN, In, and AlN are called polar materials since they can have net
polarization due to a shift in the cation and anion sublattices. In unstrained zinc-blende structures
the cation and anion sublattices are arranged in such a way that there is no net polarization in
the material. However, in the wurtzite crystal (like InN, GaN, AlN) the arrangement of the
cation and anion sublattices can be such that there is a relative movement from the ideal wurtzite
position to produce a “spontaneous polarization” in the crystal which becomes very important
for heterostructures. This effect is illustrated in figure 2.24. Also given in table 2.4 are the values
of the spontaneous polarization which is aligned along the c-axis of the crystal.
In addition to spontaneous polarization is another phenomena which can lead to polarization in
the material. Strain can cause a relative shift between the cation and anion sublattices and create
net polarization in the material. This is the piezoelectric effect. In figure 2.25 we show how
the movement of rows can cause polarization effect by looking at the structural arrangements of
atoms in barium titanate.