Understanding dark current in pixels of silicon photomultipliers.pdf

Understanding dark current in pixels of silicon photomultipliers

R. Pagano, S. Lombardo and S. Libertino CNR-IMM

Strada VIII Zona Industriale, 5, 95121, Catania, Italy [email protected]

G. Valvo, G. Condorelli, B. Carbone, D.N. Sanfilippo and G. Fallica

IMS-R&D STMicroelectronics, Stradale Primosole, 50 95121 Catania, ITALY

Abstract Silicon photomultipliers are nowadays considered a promising alternative to conventional vacuum tube photomultipliers. The physical mechanisms operating in the device need to be fully explored and modeled to understand the device operational limits and possibilities. In this work we study the dark current behavior of the pixels forming the Si photomultiplier as a function of the applied overvoltage and operation temperature. The data are well modeled by assuming that dark current is caused by current pulses triggered by events of diffusion of single minority carriers (mostly electrons) injected from the boundaries of the active area depletion layer (dominating at temperatures above 0C) and by thermal emission of carriers from Shockley-Read-Hall defects in the depletion layer (dominating at temperatures below 0C).

I. INTRODUCTION Silicon Photomultipliers (SiPMs) are a very promising

alternative to conventional photomultipliers (PM) thanks to some interesting characteristics: they are insensitive to magnetic fields, hence can be used in environments with high fields; their operation voltage is far lower, and they ensure better robustness and reliability than PM; they are much cheaper than their traditional counterpart [1-2].

SiPM structure consists in a parallel array of equal single pixels, each one made of a silicon p-n junction avalanche photodetector with an integrated resistor. The SiPM is biased above the breakdown voltage, that is, each pixel is operated in Geiger mode, above the breakdown voltage (BV) of the p-n junction. The junction is carefully doped in order to have breakdown only in the central active area of the pixel, used for the photon detection, and by the avalanche mechanism (not by Zener). To understand the photon detection concept, let us assume to bias such junction above breakdown with a fast voltage step. In this condition, if no carrier is present in the depletion region the junction is highly sensitive to the detection of single photons. In fact, if the photon is absorbed by creating an electron-hole pair, both carriers will start to drift in the high field region of the depletion layer and, being the voltage above breakdown, this drift will result with a 100% probability in the impact generation of a second e-h pair, and so on, up to the build-up of the junction avalanche.

The avalanche is limited by the buildup of a limiting space charge in the depletion layer which decreases the field [3]. Moreover, since the photodector has a resistor in series, when the avalanche current flows through the resistor, the voltage applied to the junction drops below BV. It quenches the avalanche, the current decreases to zero, and the voltage across the p-n junction increases again above BV. The pixel is ready again to detect the arrival of a new photon. Clearly, all the transients recorded are the result of both capacitive effects and (generally faster) avalanche build-up characteristic times.

Such ideal picture is strongly modified by the occurrence of phenomena leading to dark current, generally attributed to generation effects from Shockley-Read-Hall (SRH) defects in the depletion layer, afterpulsing effects, and diffusion of carriers from the quasi-neutral boundaries of the p-n junction [4].

The purpose of this work is to understand the behavior of dark current in single pixels of SiPMs, by separately taking into account the contribution given by the avalanche build-up and quenching, and the effect of generation / diffusion of carriers in the depletion layer in order to provide a detailed understanding of the current-voltage (IV) curves. We propose a physical model of the I-V above breakdown voltage able to reproduce the voltage and temperature dependence of the current for the studied devices.

II. DEVICE STRUCTURE Devices were realized by STMicroelectronics on silicon

epitaxial n-type wafers and formed from planar microcells. An implanted p-layer forms an enrichment region which defines both the active area and the breakdown voltage (BV) of the junction. The anode is contacted by sinkers created around the photodiode active area by means of a high-dose boron implantation. The cathode is given by the diffusion of arsenic from a doped in-situ thin polysilicon layer deposited on the top of the structure. The quenching resistor, made from low-doped polysilicon, is integrated on the cathode of the cell itself. Thin optical trenches filled with oxide and metal surround the pixel active area in order to reduce electro-optical

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coupling effects (crosstalk) between adjacent microcells. A double-layer antireflective coating made of silicon oxide and silicon nitride enhances the spectral response of the device in the blue and near ultraviolet wavelength ranges. The pixels have a square geometry with an active area side of 40x40 m2 [5]. Figure 1 shows a schematic drawing of the pixel, with the structure of the p-n junction. The depletion region relevant for photon detection is the one below the enrichment layer, where the field is higher, being larger the doping level.

III. RESULTS AND DISCUSSION

The current-voltage (I-V) curves of single cell reverse biased in the region 24V 36V, in dark, as a function of the device temperature, from -25C to 65C are reported in Fig. 2. Breakdown is clearly visible at voltages of 27-29 V, with the well known increase of the BV with the temperature.

Though the measurements show steady-state I-V curves, the time resolved analysis of the current at the oscilloscope at a fixed bias above BV reveals that the time averaged breakdown current of Fig. 2 is indeed a random sequence of current spikes. Fig. 3 shows such spikes in a semilog time scale at various bias levels at room temperature.

Each I-t curve is indeed the average of 1000 traces. It is evident that after an initial spike the current has an exponential decrease with time, with the same characteristic time as the voltage level is changed. These dark counts are attributed to generation and / or diffusion from quasi neutral boundaries of a single free carrier which initiate the avalanche in a short time scale.

The current, however, does not go immediately to zero since there is the displacement current due to diode capacitance recharge to the pristine voltage level. In such a picture the integrated current signal, usually referred to as gain, is approximately equal to:

!

G =Q

q=2C

qVPOL " BV( ) (1)

where C is the effective pixel capacitance, VPOL the applied

Figure 1. Schematic of SiPM cell.

Figure 2. I-V curves in reverse voltage as a function of the device temperature from -25C (white square) up to 65 C (magenta circles).

bias, and q the elementary charge. The factor 2 is needed since we detect both the initial current spike due to avalanche build-up and quenching, followed by the recharge of the diode effective capacitance. According to this picture, the time constant of the exponential I vs. t trace after the initial current spike should simply be equal to C=RquenchC, where Rquench is the value of the quenching resistance. Such interpretation is confirmed by the excellent agreement between the experimental time constants and the C values. The agreement is also found when temperature is changed. In such case Rquench varies because of the temperature dependence of the resistance value of the integrated resistor [6], but still the measured time constants are perfectly consistent with the C values.

According to this picture the measured DC current (Fig. 2) can then simply evaluated as:

( ) ( ) ( ) dDC ATVfTVqGTVI !!= ,~

,, (2)

where

!

f DC is the frequency of dark events per unit area, i.e., events of generation and / or diffusion from quasi neutral boundaries of single free carriers into the active detection volume of the photodetector, and Ad is the corresponding detection area. G is the product of

!

G of Eq. (1) times the probability Pa that an injected free carrier actually initiates the avalanche.

The gain G can be evaluated as the integral of signals such as those of Fig. 3 from 0 to 3-4 times C. In particular Fig. 4 reports the measured gain evaluated by integration from 0 to 160 ns as a function of voltage for a number of temperatures. In the same figure we also report the theoretical gain 2C(V-BV)/q evaluated at a single temperature (-25C). Only one model curve is calculated for clarity, and the others corresponding to the higher temperatures are simply obtained by shifting the first one to the right because of the temperature dependence of BV.

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Figure 3. Dark Current as a function of time for biases ranging from -30V (lowest line) up to 34 V (highest line) acquired at room temperature.

We first note that the model is quite close to the data (curve at -25 C) but the experimental curve is non linear, with an approximately quadratic trend with voltage. The super-linear behavior is also observed at higher temperatures, without any particular change of trend, except for the well known shift of BV as temperature increases. The non linear behavior of gain is an important feature of SiPMs and we have investigated this issue in further detail. In particular we have measured the gain by an alternative, independent method, hereafter proposed. From Eq. (2) it is easy to estimate the photodetector current under illumination Ilight. In fact one expects that:

!

I l ight = q "G " f DC + QE "

f photon( ) " Ad ## q "G "QE " f photon " Ad

(3)

where fPhot is the photon flux incident on the pixel and QE is the corresponding external quantum efficiency. If we are in a condition where fPhot >> fDC, G can be evaluated as:

!

G =ILight

f photon "QE " Ad. (4)

As already underlined G in Eqs. (2)-(4) is the product of G (Eq.(1)) times Pa, so the two parameters coincide only if Pa is one, i.e., 100% probability to trigger the avalanche.

Figure 5 reports an example of I-V characteristics of a SiPM pixel under illumination with laser light at 659 nm at flux levels ranging from 2.2 nW/cm2 up to 22 W/cm2. Above BV the pixel operates linearly up to about 200 nW/cm2, and a tendency to signal saturation is evident above such intensity. The saturation above 200 nW/cm2 is well explained by dead time effects, of the order of 200 ns as shown in Fig. 3.

Data such as those of Fig. 5 allow to evaluate G by using Eq. (4). By assuming a QE value of 0.15 at the 659 nm laser wavelength [7] we determine G and the results are shown in Fig. 6. In particular the figure shows the comparison between

Figure 4. Gain as a function of voltage. The dashed line is the theoretical gain evaluated at -25C.

the

!

G values with those of G and the linear model of Eq. (1). It is evident a surprisingly good match between G and

!

G at high voltage, while a small difference is observed at low voltages.

We now proceed in our analysis by discussing the dark count frequency fDC. Ideally with no SRH center generating free carriers in the detection volume, fDC should at least be equal to the frequency of free carrier injection from the quasi-neutral boundaries, given by the well known expression:

!

f DIF =ni2Dn

N aLn=

Dn

" n#

ni2

N a (5)

where ni is intrinsic carrier concentration, Na is the dopant concentration at the depletion layer boundary of the enrichment, Dn is the electron diffusivity and Ln is the diffusion length.

Figure 5. IV characteristics in reverse voltage in dark (dark) and under illumination from 2.2 nW/cm2 (green) to 22 W/cm2 (blue)

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If we also assume the presence of defects, the related emission frequency is given by the well known SRH expression:

!

f TH = N dif "W " #n "$n "T2 "exp %

Ec - ETkT

&

' (

)

* + (6)

where Ndif is the defect concentration, W the depletion layer width, n an universal constant, n the defect cross-section, EC-ET the defect ionization energy, T the temperature, and k the Boltzmann constant.

Figure 7 shows the comparison between the experimental dark I-V characteristics and the model, by assuming the G values of Fig. 6. The agreement between data and model is extremely good. We fit the data both as a function of voltage and as a function of temperature by assuming the well known relationship between carrier diffusivity and mobility, and Ln = 10 m, n=1100 cm2/Vs, and Na= 1.5e16 cm-3 in Eq. (5), while for thermal diffusion (Eq. (6)) we have assumed Ndif = 1e9 cm-3, EC-ET = 0.54 eV, n = 1.6e-15 cm2, with the universal constant n = 1.78e21 cm-2s-2K-2 as reported in [8]. The remarkable agreement between data and model is obtained by assuming quite reasonable values of the fit parameters, and this suggests that the present model catches quite well the behavior of the device. We also note that these devices present a dark current only limited by carrier diffusion already at quite low temperatures, essentially almost at 0 C, indicating a remarkably low SRH defect concentration (of the order of 1e9 cm-3).

IV. CONCLUSIONS

In this paper we have reported on the realization of Silicon Photomultipliers, we have described a physical model on the dark count rate of SiPM single pixels, and we have compared this model to experimental data taken on SiPM realized by

Figure 6. Gain as a function of voltage for temperatures from -25C up to 65C: dots are data reported in Fig.4, lines the gain determined from eq. (4) as described in text.. The results are compared with the model of eq. (1)

Figure 7. Comparison of the experimental I-V curves (circle) in reverse voltage and the physical model as (lines) a function of the device temperature from -25C (white) up to 65 C (magenta)

STMicroelectronics. The model fits nicely the data and demonstrates that state-of-the-art SiPM can have at room temperature a dark current rate limited only by carrier diffusion.

ACKNOWLEDGMENTS CNR authors gratefully acknowledge partial grant support

by IMS R&D, STMicroelectronics.

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