Thursday, March 02, 2017

Theoretical Frame Rate Limit of Si Image Sensor

Open source Sensors journal publishes a paper "The Theoretical Highest Frame Rate of Silicon Image Sensors" by Takeharu Goji Etoh, Anh Quang Nguyen, Yoshinari Kamakura, Kazuhiro Shimonomura, Thi Yen Le, and Nobuya Mori from Osaka and Ritsumeikan Universities, Japan.

"The frame rate of the digital high-speed video camera was 2000 frames per second (fps) in 1989, and has been exponentially increasing. A simulation study showed that a silicon image sensor made with a 130 nm process technology can achieve about 10^10 fps. The frame rate seems to approach the upper bound. Rayleigh proposed an expression on the theoretical spatial resolution limit when the resolution of lenses approached the limit. In this paper, the temporal resolution limit of silicon image sensors was theoretically analyzed. It is revealed that the limit is mainly governed by mixing of charges with different travel times caused by the distribution of penetration depth of light. The derived expression of the limit is extremely simple, yet accurate. For example, the limit for green light of 550 nm incident to silicon image sensors at 300 K is 11.1 picoseconds. Therefore, the theoretical highest frame rate is 90.1 Gfps (about 10^11 fps)."

After the simplifications of equations mostly based on the photocarriers travel time to the collection node, "the expression of the temporal resolution limit is reduced to an extremely simple form:"

Δτ = 6.12 δ

where δ is the average light penetration depth
∆τ is the temporal resolution limit
The units of ∆τ and δ are, respectively, ps and µm.

The paper's conclusion:

"The temporal resolution limit of silicon image sensors is theoretically derived. The limit is mainly governed by mixing of charges with different travel times caused by the distribution of penetration depth of light. The final expression is ∆τ = 6.12 δ, which may be unbelievably simple, but sufficiently accurate. Now, the target is clear. It is time to give it a try to break it."


  1. Interesting work, and I really like their style. However, I need to point out that the depth resolution of most ToF-cameras is already better than 3.4 cm (assuming 850nm illumination, 18.7µm penetration depth, 114ps temporal resolution).


    1. Actually, most ToF cameras deal with pulses 10ns and longer. They determine the distance from these pulses phases and delays. At that pulse length, their depth resolution is not limited by the photocarrier travel time.

  2. Nice work, I would like to know the relationship between delta (t) and frames per second. For instance, how 11.1 ps correspond to 90.1 Gfps?

  3. Actually the result here is the same as for most high speed photodetectors for optical communications. The absorption depth spread )or multiplication region depth, leads to a temporal spread and hence a speed limit. (Another bonus for short absorption length materials!) I wish the authors worked a little harder on references, not only for the relationship to optical communications, but also for work on high speed image sensors. Practical limits are more on readout rate, unless (mostly) only burst (local storage) image sensors are considered. Stacked structures have always been considered a solution for this since the days of Z-plane and other hybrid topologies. Stacked BSI CIS allows a lot of these early pipe dreams of the old days to be realized today.

  4. Thank you very much for your comments. As far as I know, the explicit expression of the temporal resolution limit has not been theoretically derived. The problem can be formulated with no approximation. However, it is expressed by an implicit equation and should be numerically calculated to intuitively understand the characteristics. The expressions shown in this paper are all explicit and give a very good insight to the problem at a glance, though the final one is too simple to understand the physics. As you wrote, the analysis can be generally applied or extended to other photoelectron conversion layers.

    1. hi Etoh-san. I don't think any expression has been derived for limit of frame rate for an image sensor. However, as I noted, a similar calculation has been done for photodetectors many times. For example, see the chapter in Sze, Physics of Semiconductor Devices on Photodetectors - Photodiodes. (page 758 in the 2nd edition, 1981, eq 34) where the f(3dB) frequency is given as ~0.4av where a is the absorption coefficient and v is the saturation velocity. Putting in a=1e4 (green) and v=1e7 gives 40GHz, surprisingly close to the 90GHz above. This is in a textbook in 1981. The original work was done much earlier, perhaps 1950's or 60's.

    2. Thank you very much, Eric-san. I will go through the prior works on the photodiodes.


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