Device Elements and Circuits for Image Sensors - Essential Principles of Image Sensors - page 27

This leads to the following equations:

∆
∆

φ d

d

φ

=− α φ , =− α φ

x x

( )

− α x − xd

φφ = e = φ e d = α (2.4)

λ

1

λ

0 0

where ϕ 0 denotes the luminous flux density at the silicon surface just before absorption,
the inverse of absorption coefficient α; and d λ is penetration depth, indicating the distance
through which luminous flux density attenuates to 1/ e ( e is the base of natural logarithm)
by absorption. This is an indication of the length required to absorb light to a certain
degree.
Figure 2.20 indicates the wavelength dependence of the absorption coefficient and
penetration depth of silicon. It can be seen that it needs a longer distance to adequately
absorb longer-wavelength light. Compared with red light (around 640 nm), where d λ is
about 3 - 4 μm, blue light (around 440 nm) is as short as 0.3 μm. This means that the
depth required for a photodiode to absorb light efficiently differs greatly, according to
the wavelength. For the use of color imaging, the depth of the photodiode is ordinarily
set to red light, which needs the longest distance lest the sensitivity should be reduced.

2.2.1 np Photodiode on p -Type Substrate

The measured example of spectral response of an np photodiode that is formed on a
p -type substrate, whose cross-sectional diagram is shown in Figure 2.21a, is indicated

Wavelength (nm)

1,000 900 800 700 600 500 400

1.00E+07 10,000

Red Green Blue

1.00E+06 1,000

1.00E+05 100

1.00E+04 10

1.00E+03 1

1.00E+02 0.1

1.00E+01 0.01

1.00E+00
1.00

0.001

1.50 2.00 2.50 3.00 3.50 4.00

Photon energy hν (eV)

FIGURE 2.20
Wavelength dependence of absorption coefficient and penetration depth of silicon.