SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

8.5. CHARGE CONTROL MODEL FOR THE MODFET 383

0

z

EF

E 0

E 1

V

edi

eV(z)=E 2 z−eVdi−

Figure 8.16: Band structure of the HFET channel region represented as a triangular potential
well.

For the case of(EF−E 0 )/kBT≥ 1 ,weget

ns·

e

kBT

·

1

Ds

=

EF−E 0

kBT

(8.5.9)

or

EF−E 0 =

e

Ds

ns=

π^2

m∗

ns (8.5.10)

ForEF−E 0 ≈eVdi−,weget

Vdi−=

(

π^2

em∗

)

=ans (8.5.11)

This tells us thateVdi−, the amount that the conduction band drops below the Fermi energy
at the heterointerface, increases linearly withns. The coefficientain equation 8.5.11 is clearly
material dependent since it varies withm∗. By examining the band diagram and the electric field
profile near the channel, we can calculateΔd.

Vdi−=ans=E 2 ·Δd=

ens



·Δd (8.5.12)

Δd=

a

e

(8.5.13)

Typical values ofΔdare 80A for the AlGaAs/GaAs system, 50 ̊ A for the AlInAs/GaInAs, and ̊
20 A for the AlGaN/GaN system and the Si/SiO ̊ 2 2 system. When calculating the band diagram
of a HEMT, one of two boundary conditions are typically used: