SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

68 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

Ba++ Ti4+

Displacement of

positive charges with

respect to negative

charges

ferroelectric effect

(b)

Ba++

O– –

Ti4+

Cube corners: Ba++

Cube face centers: O––

Cube center: Ti4+

(a)

Figure 2.25: The structure of a typical perovskite crystal illustrated by examining barium titanate.
(b) The movement of the ions leads to a ferroelectric effect.

A

–

+

– – – – –

+ + + + +

– – – – – –

+ + + + + +

– – – – – –

+ + + + + +

– – – – – –

B

Polarization PA

Interface charge

density = PA –PB

Polarization PB

Figure 2.26: A schematic showing how interface charge density can be produced at heterointer-
faces of two polar materials.

For example, in AlGaN/GaN HFETs , a fixed sheet charge is formed at the heterointerface
due to the the piezoelectric polarization in the strained AlGaN, and the discontinuity in the
spontaneous polarization at the interface (see figure 2.27). To screen the net positive charge
at the AlGaN/GaN junction, a 2DEG is formed. The same effect can also be used to create a
bulk three-dimensional electron slab, as shown in figure 2.28. This is achieved by grading from
GaN to AlGaN, thus spreading the polarization-induced charge over the graded region. The
polarization-induced carrier density,ρπ, is given by the equationρπ=∇·P;herePis the total
polarization in the material. Since the AlGaN composition and polarization are shown to be well-
approximated by Vegard’s law, any desired channel charge profile can be obtained by choosing