Biophotonics_Concepts_to_Applications

Example 5.6

(a) The quantum efficiency for InGaAs is around 90 % for the wavelength

range 1300 nm <λ< 1600 nm. Show that in this wavelength range the

responsivityR= 7.25× 105 λ.

(b) Show that at 1300 nm the responsivityR= 0.92 A/W.

(c) At wavelengths higher than 1600 nm the photon energy is not sufficient

to excite an electron from the valence band to the conduction band. If the

material In0.53Ga0.47As has an energy gap Eg= 0.73 eV, what is the

cutoff wavelength?

(d) Why does the responsivity drop off at low wavelengths?

Solution:

(a) From Eq. (5.8)

R¼

gq

hm

¼

gqk

hc

¼

ðÞ 0 : 90 ðÞ 1 : 6  10 ^19 Ck

ðÞ 6 : 625  10 ^34 JsðÞ 3  108 m=s

¼ 7 : 25  105 k

(b) From the above equation, at 1300 nm

R¼½ 7 : 25  105 ðA=WÞ=mŠð 1 : 30  10 ^6 mÞ¼ 0 :92 A=W

(c) From Eq. (5.4)

kcðlmÞ¼

hc

Eg

¼

1 : 240

0 : 73

¼ 1 : 70 lm

InGaAs

Ge

Si

0.7 0.9 1.1 1.3 1.5 1.7

0.2

0.4

0.6

0.8

1.0

Wavelength (μm)

Responsivity (A/W)

Fall off due to

insufficient

photon energy

Fall off due to most

absorption in the

p region

Fig. 5.4 Comparison of the
responsivity and quantum
efficiency as a function of
wavelength forpin
photodiodes constructed of
three different materials

126 5 Fundamentals of Optical Detectors