SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

APPENDIX C. DENSITY OF STATES 533

ky

kx

kz

–k k

2 dk = k space between k and k + dk

k

2 πk dk = area between circles

with radii k and k + dk

4 πk^2 dk = volume between surfaces of

spheres with radii k and k + dk

2D system

3D system

1D system

ky

kx

} dk

} dk

k

0

dk dk

(a)

(b)

(c)

Figure C.3: Geometry used to calculate density of states in three, two, and one dimensions. By
finding thek-space volume in an energy interval betweenEandE+dE, one can find the number
of allowed states.