SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

116 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

Ec

Ev –x 1

x 2 Ec

Ev

–x 1 0x 2

x

(a)

(b)

Available empty

states (holes) in

valence band

Electrons in

conduction band

Eg

++++++ –––––––––

Tunnel barrier

Figure 3.12: (a) A schematic showing the band profile for ap–njunction. An electron in the
conduction band can tunnel into an unoccupied state in the valence band or vice versa. (b) The
potential profile seen by the electron during the tunneling process.

The exponent for the tunneling probability is (m∗(GaAs) = 0.065 m 0 ;m∗(InAs)

∼0.02 m 0 ;Eg(GaAs) = 1.5 eV;Eg(InAs) = 0.4 eV) for GaAs

−

4 ×(2× 0. 065 × 0. 91 × 10 −^30 kg)^1 /^2 (1. 5 × 1. 6 × 10 −^19 J)^3 /^2

3 ×(1. 6 × 10 −^19 C)(1. 05 × 10 −^34 Js)(2× 107 V/m)

= − 160

The tunneling probability is exp(−160)∼=0. For InAs the exponent turns out to be−12.5

and the tunneling probability is

T= exp (− 12 .5) = 3. 7 × 10 −^6

In InAs the band-to-band tunneling will start becoming very important if the field is

∼ 2 × 105 V/cm.