Sensing of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 64

a

E c

2DEG

E c

E c

E F

+

E v

E v E v

b

source gate drain

2DEG

n +

n -AlGaAs

GaAs

Fig. 2.6 ( a ) Formation of a 2DEG and ( b ) the HEMT transistor

The 2DEG has a carrier density of 2 10 11 -2 10 12 cm 2 and a mobility of
10 7 cm 2 =Vs. This sheet of ballistic electrons forms a channel in a FET transistor
if additional processing defines the source and drain electrodes, the n C doping
beneath their respective areas, and the gate electrode. The latter has the role of
depleting the electrons in the 2DEG in the presence of a negative applied voltage.
The HEMT transistor is schematically represented in Fig. 2.6 b. It is similar to a
MOSFET where the SiO 2 layer at the Si=SiO 2 interface corresponds to the wider
semiconductor. Although the inversion layer in MOSFET has the properties of a
2DEG, like in the case of AlGaAs/GaAs heterostructures, the quality of the Si=SiO 2
interface is inferior than in AIII-BV compounds or nitrides, and therefore, many
2DEG properties are lost in MOSFETs at room temperature.
Natori ( 1994 ) developed the first theory of the ballistic HEMT and found analytic
expressions for channel charges and the saturation current. The HEMT ballistic
transport was explored further (Wang and Lundstrom 2003) by generalizing the
analytic model of ballistic transistors ( Rahman et al. 2003 ). This theory relies on
the fact that the channel is located at the top of the barrier between source and drain
because the gate voltage reduces the barrier height to control the density of electrons
in the channel. The ballistic FET is modeled classically in the channel region, a
quantum mechanical analysis being necessary only if tunneling is accounted for.
Tunneling always worsens the MOSFET's and HEMT's properties.
In the Datta-Lundstrom model of HEMT, which takes into consideration only
the top of the source-drain barrier and models classically the transport in the
channel, the carrier distribution function at the top of the barrier is composed of
two halves corresponding to equilibrium injection of electrons in the source and
drain (see Fig. 2.7 a). The key parameters of the equivalent circuit model of the
HEMT, displayed in Fig. 2.7 b, are the three capacitors C S , C D ,andC G , representing,
respectively, the effects of source, drain, and gate electrodes on the top of the barrier.