Electronic signal detection

The basic task of electronic signal detection is the precise measure-ment of voltage signals offering low noise levels and a wide dynamic range. These input voltage signals have either been produced by the conversion of photocharge into a voltage, for example by employing a capacitance, or they are the result of more elaborate photocharge preprocessing as was already described here. The output of signal de-tection electronics is usually a voltage that should be proportional to the input voltage over a large dynamic range. An important property of the signal detection electronics is that its output should have very low impedance, that is, the output voltage should be stable and must not depend on the amount of current drawn. As we will see in what follows, the electronic signal detection noise is today’s limiting factor in increasing an image sensor’s sensitivity and its dynamic range.

5.5.1 Signal-to-noise (SNR) and dynamic range

For a numerical description of the voltage or charge-noise performance of an electronic circuit, two values are often used, thesignal-to-noise ratioSNR and thedynamic rangeDR. The SNR is defined by comparing

5.5 Electronic signal detection 131

VD

Msense

Mload

Vf

Vbias

Vg

VD

Msense

Vf

Vg

Rload

C C

Figure 5.14: Schematic diagram of the source follower circuit realized with a resistor (left) or with a so-called active load MOSFET (right). This is the most often used electronic circuit for photocharge detection in semiconductor image sensors. Photocharge deposited on the gate capacitance leads to a gate voltage Vg, which in turn produces a linear change in output voltageVf.

an actual signal levelVwith its rms noise∆V, according to:

SNR=20¹⁰log V

∆V (5.4)

The DR compares the maximum signal levelVmaxwith the minimum rms noise level (∆Vmin), in an image sensor typically obtained in the dark

DR=20¹⁰log Vmax

∆Vmin (5.5)

As an example, consider a CCD image sensor whose maximum charge (“full well charge”) is 50,000 electrons, and for which a dark noise of 50electrons rms is observed. This image sensor has a dynamic range of 60dB.

It should be mentioned that the preceding definitions of SNR and DR in image sensors are not consistent with usage elsewhere in optical physics: As the measured voltage at the image sensor’s output is usu-ally proportional to the incident optical power, a factor of 10in front of the logarithm should be used instead of the employed factor 20.

However, because electrical engineers are used to associating power only with the square of voltage levels, the definitions given here are the ones employed almost exclusively for all image sensor specifications.

5.5.2 The basic MOSFET source follower

Although elaborate circuits exist for the desired conversion of volt-age signals into other voltvolt-age signals, most imvolt-age sensors employ the simplest type of voltage measurement circuits, theMOSFET source fol-lower. As shown in Fig.5.14, this circuit consists of just one transis-tor and one resistransis-tor, which is often implemented as another transistransis-tor

called active load [27]. The output voltage of this source follower circuit is essentially given by

Vout=f Vin−V0 (5.6)

with a transistor-dependent multiplication factorf of 0.6-0.8 and an offset voltage V0 of several hundred millivolts. In practice, one or a few such source follower stages are employed in series, to obtain low enough output impedance while maintaining the required read-out speed. At first sight it is surprising that such a simple circuit with a gain of less than unity is used in high-sensitivity image sensors. The reason for this is that the photocharge conversion gain is provided by the effective input capacitance, which is kept as small as possible. To-day’s best image sensors have an effective input capacitance of around 15 fF, corresponding to a voltage increase of around 10µV per electron.

Taking the circuits’ overall gain of less than unity into account, one ar-rives at the so-called sensitivity of the image sensor, expressed inµV per electrons. Typical sensitivities of state-of-the-art CCD and CMOS image sensors are between 5 and 10µV per electron.

5.5.3 Noise sources in MOSFETs

Based on a source follower circuit, a typical output stage of an image sensor consists of the components shown in Fig.5.15. The photocharge is transported to a diffusion (either the output diffusion of a CCD or the photodiode itself) that is connected to the gate of the source-follower MOSFET. Before measurement of each individual photocharge packet, the diffusion and the connected gate are biased to a reference voltage using a so-called reset MOSFET. Three main noise sources can be iden-tified in such a circuit [26], whose influences are referenced back to the input of the source-follower MOSFET, contributing to an effective rms charge measurement uncertainty∆Q.

Reset or kTC noise. The channel of the reset transistor exhibits John-son noise similar to an ordinary resistor. This causes statistical fluc-tuations in the observed reset voltage levels, which result in effective charge noise∆Qresetgiven by

∆Qreset=

kT C (5.7)

for the effective input capacitanceC, at temperatureT, and using Boltz-mann’s constantk.

Flicker or 1/f noise. Statistical fluctuations in the mobility and charge carrier concentration of the source follower transistor’s channel cause

5.5 Electronic signal detection 133

reset Vreset

output diffusion

C VD

Mreset

Msense

Mload

Vout

V_bias

Figure 5.15: Complete single-stage output circuit of a typical image sensor, consisting of a floating diffusion, a reset transistor, and a single-stage source follower as shown in Fig.5.14.

an effective charge noise∆Qflickerdescribed by

∆Qflicker∝C

I^AB

gm²f CoxW L (5.8) at frequency f, for current I, bandwidth B, transistor length L, and widthW, oxide capacitanceCox, process-dependent flicker noise con-stantA, which is typically between 0.5 and 2, and the transistor’s trans-conductancegm.

Thermal noise. Johnson noise in the source follower transistor’s chan-nel can also be referred back to the input, resulting in thermally gener-ated charge noise∆Qthermalgiven by

∆Qthermal=C

4kT Bα

gm (5.9)

using the same parameters as in the preceding.

In practice, the first two noise sources can be essentially eliminated by a signal-processing technique calledcorrelated double sampling(CDS) [28]: Reset noise is canceled by a two-stage process, in which the diffu-sion is preset to a reference voltage and a first measurement is made of this voltage level. In a second step, the photocharge is transferred to the diffusion, and a second measurement is made. The difference be-tween these two measurements is free of reset noise and contains only information about the photocharge of interest. Because CDS is a tem-poral high-pass filter, flicker noise with its low-frequency dominance is effectively canceled at the same time.

The thermal noise contribution cannot be reduced using signal proc-essing techniques, and it is obvious from Eq. (5.9) what can be done to minimize thermal noise. Reduction of temperature (in astronomical applications down to -120°C) not only lowers charge noise levels [29]

but thedark current contribution can be reduced to values as low as one electron per day per pixel. As a rule of thumb, dark current in silicon doubles for each increase in temperature of around 8–9 °C.

Often the reduction in temperature is combined with a reduction of the readout bandwidth to 50–100 kHz, leading to a charge noise level of around one electron [30]. Another technique of bandwidth reduction is the repetitive, nondestructive measurement of photocharge with out-put signal averaging, as carried out in the Skipper CCD [31]. Charge noise levels of 0.3 electrons rms have been obtained in this way. As can be seen in Eq. (5.9) the dominant factor in noise performance is the effective input capacitance. This has been lowered to values of less than 1 fF using the so-called double-gate MOSFET [32], corresponding to a sensitivity of more than 200µV per electron and an effective charge noise level of less than one electron at room temperature and at video frequencies. The maximum photocharge such an output stage can han-dle is about 10,000 electrons, the DR is limited to about 80 dB.