SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

8.6. POLAR MATERIALS AND STRUCTURES 389

GaN

Ga face

N face

(0001)

-Qπ

+Qπ

+Qπ

+Qπ

-Qπ

-Qπ}

ΣQ=0

(a)

-Qπ

+Qπ

(c)

(b)

+Qscr

-Qscr

Figure 8.18: (a) Stick-ball representation of Wurtzite GaN crystal structure. (b) Classical model
of polarization charge in a polar material such as GaN. (c) Crystal will draw in charge to screen
the polarization dipole - From M. J. Murphy et al, MRS Internet J. Nitride Semicond. Res. 4S1,
G8.4(1999)

heteroepitaxially (on sapphire, Si, or SiC substrates). The material at the substrate / thin film
interface is highly defective and therefore capable of trapping mobile charges. We will assume
that the effect of the backgroundn-type doping on the electric field profile within the material
is negligible compared to the electric field generated by the polarization charges. We will also
ignore the effects of surface states on the electrical properties of the material. Both of these
effects will be considered later.
In the absence of surface states, as the material becomes thicker, the electric field in the ma-
terial (given by the slope of the conduction and valence band) will remain constant until the
valence band crosses the Fermi level, as shown in figure 8.19b. The thickness of the filmdcrat
which this occurs is given simply by

dcr=

Eg

eEπ

=

3 .4eV

1 .6MeV/cm

215 A ̊ (8.6.3)

whereEg =3.4eVis the bandgap of GaN. Onced>dcr, holes begin to accumulate at
the surface (created by generation across the gap), leading to an equal electron concentration
which drifts to the substrate-epi interface (the GaN N-face), creating a screening dipole. This is
illustrated in figure 8.19c. The magnitude of the screening chargeQscrincreases continuously