SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

392 CHAPTER 8. FIELD EFFECT TRANSISTORS

n-GaN Substrate

+Qπ

-Qπ

EF

EC

EV

+eNDD

(b)

+

EDD

(a)

0 dGaN

-Qscr

++ ++ ++ ++

0 wd dGaN

ionized

donors

electrons

Figure 8.21: Schematic diagram of (a) a thickn-type GaN sample along with (b) the corre-
sponding charge profile and band diagram when surface states and the donor charge are taken
into account.

IfeNDD>Qπ,thenQπwill be fully screened when(EC−EDD)−(EC−EF)is very close
to zero, or in other words whenEDDis very close toEF. Analogous to the previous case of
screening via holes,

NDD+ =Qπ−

EDD

ed

(8.6.8)

whereEDD/eis now the built-in voltage as opposed toEg/e.
We have ignored the effects of the donor charge in the analysis until now because we were
seeking to understand the formation of the screening dipole. Figure 8.21 shows the band diagram
of a thickn-type GaN film. Experimental evidence has shown that the surface of GaN indeed
has a neutral level,EDD, which is currently assumed to be the position of the surface donor.
Since the GaN is considered to be very thick, the energy bands must be flat (zero electric field).
The surface negative polarization charge−Qπis balanced by the sum of the positively charged
ionized surface statesNDD+ and the areal density of charges in the depletion regionNd·w,or

Qπ=NDD+ +Nd·w (8.6.9)