SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

390 CHAPTER 8. FIELD EFFECT TRANSISTORS

(a) (b)

n-GaN Substrate

Growth direction

(0001)

+Qπ

-Qπ

EF

EC

EV

Defective

region

dcr 0

n-GaN Substrate

+Qπ

-Qπ

EF

EC

EV

dcr 0

n-GaN Substrate

+Qπ

-Qπ

EF

EC

EV

dcr 0

+Qscr

-Qscr

(c)

Figure 8.19: Schematic diagram of ann-type GaN sample along with charge profile and band
diagram (a) during the initial stages of growth, (b) ford=dcr, and (c) ford>dcr.

with epitaxial layer thickness. The evolution of the screening charge with distance is obtained
by recognizing that the maximum voltage across the structure is the bandgap of the material, or

1

e

Eg=|E|·d=

(

Qπ−Qscr



)

d (8.6.4)

Qscr=Qπ−

Eg

ed

(8.6.5)

Asd→∞,Qscr→Qπ, or in other words for very thick samples the polarization dipole is fully
screened.
If we now assume that there exists a surface donor state, a very similar situation develops,
except that instead of holes providing the positive screening charge, ionized surface donors do.
These states pin the Fermi level at the surface to create a built-in voltage equal to the donor