3.8 Temperature Sensitivity
3.8.1 Temperature Effects in the Photodiode
The photodiode is simply a reverse-biasedpn junction fabricated as an n-well in thep-substrate.
Electron-hole pairs generated within the n- to p- depletion region are swept across the depletion region by the applied electric field. Carriers generated within one diffusion length of the deple-
tion region are likely to diffuse into the depletion region and similarily contribute to the current.
Electron-hole pairs generated by photons hitting the silicon lattice result in a measurable photocur- rent which is the basis for light detection in CCD and CMOS image sensors. Since the sum of the diffusion lengths in the p- and n- areas is typically larger than the width of the depletion re- gion, photo-induced carrier generation outside the depletion region tends to contribute more to the photocurrent than carrier generation within the depletion region. Electron-hole pairs also can be thermally generated, constituting what is equivalently termed “leakage current” in a diode or “dark current” in a photodiode. Changes in the temperature of the photodiode have little effect on the photocurrent and a significant effect on the dark current. Consequently, at high illumination levels where the photocurrent is orders of magnitude greater than the dark current, temperature has neg- ligible effect on the overall photodiode current. At low illumination levels where the photocurrent is small enough that the dark current is a significant fraction of the total diode current, increased temperatures result in increased dark current and thus a lower signal-to-noise ratio.
260 280 300 320 340 360 380 400
1.08 1.09 1.1 1.11 1.12 1.13
bandgap EG (eV)
temperature (K)
room temperature
bandgap
wavelength
260 280 300 320 340 360 380 4001100
1110 1120 1130 1140 1150
wavelength (nm)
Figure 3.38: The effect of temperature on photo-generated current in the photodiode is negligible.
Left: Bandgap and corresponding wavelength as a function of temperature. The blue line shows how the bandgap of silicon decreases with increasing temperature. The wavelength of photons having an energy equal to the bandgap increases proportionately, as shown by the dashed green line. Right:
The efficiency with which a silicon diode generates photocurrent is a function of frequency. (Plot reprinted with permission from Melles Griot [2].) Both: From the left figure, we can see that a 10◦C shift in temperature results in a 2.7nm shift in the absorption spectrum. From the right figure, we can see that this is only a tiny fraction of the absorption spectrum, which is several hundred nanometers wide.
The photo-generated current is only weakly affected by temperature. Increasing the temperature reduces the bandgapEG as [74]:
EG(T) =EG(0)− αT2 T+β
where EG(0) = 1.16eV, α= 7.02×10−4eV /K, β = 1108K, and the temperatureT is in Kelvin.
Decreasing the bandgap shifts the absorption spectrum of silicon to longer wavelengths. Given the wide absorption spectrum of silicon, in practice this has a negligible effect on responsivity [2] as
shown in fig. 3.38.
Dark current, arising from thermally generated electron-hole pairs, has a clear temperature dependence. This temperature dependence is somewhat complicated as it is a sum of the thermally generated diffusion currents within the n-and p- areas and the drift current within the depletion region, and the two vary differently with temperature.
Within the depletion region, the rate of generation of electron-hole pairsU is governed by [34]:
U ≡ − ni
2τ0
whereni is the intrinsic carrier concentration andτois the effective lifetime within a reverse-biased depletion region. We shall shortly see thatU varies exponentially with temperature because nihas an exponential dependence on temperature, whileτois nearly independent of temperature.
The intrinsic carrier concentrationni can be calculated from:
pn=n2i =NcNve−EG/kT (3.14)
whereEG is the energy gap between the conduction and valence bands:EG = (Ec−Ev). NcandNv
are the effective densities of states in the conduction and valence bands, respectively, and are each proportional toT3/2[74]. The intrinsic carrier concentration depends on temperature approximately in an exponential manner. The actual temperature dependence is somewhat stronger because Nc
andNv also increase with temperature.
The effective lifetimeτo is given by:
τo≡σne(Et−Ei)/kT+σpe(Ei−Et)/kT 2σpσnvthNt
whereσn andσp are the electron and hole capture cross sections,vthis the carrier thermal velocity equal to
3kt/m∗, Nt is the trap density,Et is the trap energy level, and Ei is the Fermi energy level. Only the generation centers whose energy level Et is near the Fermi level Ei contribute significantly to the generation rate, since the generation rate falls exponentially asEt moves away fromEi. Since the centers of generation are indeed near the intrinsic Fermi level,τo will be nearly independent of temperature.
Carriers generated within the depletion region are almost immediately swept away by the electric field. Almost none recombine and the resulting current can be expressed as:
Idep=q|U|W AJ =qni
2τ0W AJ (3.15)
where q is the charge of an electron,W is the width of the depletion region, and AJ is the cross-
sectional area of the pnJunction. Since the rate of electron-hole generationU varies with temper- ature as ni varies with temperature, the component of the thermal current generated within the depletion regionIdep has the same temperature dependence.
Carriers generated outside the depletion region contribute to the dark current by a somewhat different set of physical processes. Once generated, they travel by diffusion until they either recom- bine or diffuse to the edge of the depletion region. Only in the latter case are the carriers swept across the depletion region and thus contribute to the overall dark current. Equations describing the carriers which diffuse to the edge of the depletion region in a reverse-biased diode are [34]:
Idif f,n=qDn
n2i NALn
AJ Idif f,p=qDp
n2i NDLp
AJ (3.16)
The temperature dependence of the diffusion current is the same as that ofn2i [34].
In summary, the dark current has an exponential dependence on temperature. From eqns. 3.15 and 3.14 we see that the thermal current generated within the depletion region varies with temper- ature ase−EG/2kT. Eqns. 3.16 and 3.14 indicate that dark current generated outside the depletion region varies with temperature as e−EG/kT. Near room temperature, thermal electron-hole pair generation within the depletion region dominates the dark current and its temperature dependence is proportional toe−EG/2kT. Around 125◦C, the two mechanisms are of similar magnitude. Above 225◦C, most of the dark current is generated outside the depletion region and its magnitude changes with temperature ase−EG/kT.