1. Introduction

X-ray image sensor is a new application field of CMOS image sensor and widely used in medical radiography and scientific research^[1-3]. The use of CMOS sensors in X-ray detection is a desirable technique shift due to their inherent characteristics of lower power consumption, lower cost and higher system integration. Most of the CMOS X-ray sensors are indirect sensors that need a scintillation layer to convert the incident X-ray into visible fluorescent light which can then be collected by the photodiode. CsI(Tl) crystal is the most widely used scintillation for its high light yield (55000 photons/MeV) and non-hygroscopicity^[4]. The X-ray used in the medical field is about 5 to 140 keV^[5], and the converted fluorescence intensity is about 0.9 to 26 lux^[6]. The main difficulty in the CMOS X-ray sensor is the detection of the weak fluorescence and the following process to assemble the scintillation with the CMOS image sensor. The low X-ray exposures mean that a CMOS-compatible photodiode should possess the performance of high sensitivity, good linearity and low dark current, while the requirement for the dynamic range is not so strict^[7]. The fluorescence emission spectrum of CsI(Tl) crystal ranges from 400 to 800 nm with a peak at about 550 nm^[8]. It is important to design a photodiode that has a spectral response coinciding with the spectral response of CsI(T1) in order to get the maximum sensitivity of X-ray sensor. In standard N-well CMOS process there are three kinds of PN junctions, namely N⁺/P_sub, P⁺/N_well and P⁺/N_well/P_sub photodiodes. P⁺/N_well/P_sub double junction photodiode is chosen because it has the least dark current compared with N⁺/P_sub and N_well/P_sub photodiodes^[9].

2. Double junction photodiode structure and modeling

Cross sections of the three compatible photodiodes in N-well CMOS process are shown in Fig. 1.

As shown in Fig. 1, the P⁺/N_well and N_well/P_sub photodiodes are in fact a single PN junction and P⁺/N_well/P_sub is in fact two parallel junctions. The diagrammatic sketch of PN junction photodiode is shown in Fig. 2.

For incident light of wavelength $\lambda$, the total current density in the cross section of $X=X_{\rm j}$ is^[10]

$$\begin{equation} \begin{split} J_{\rm tot} {}& =q\frac{T_{\rm total }P_{\rm in}\lambda \alpha}{Ahc} {\rm e}^{-\alpha X_{\rm j}} \left[1-\frac{1}{1+\alpha L_{\rm p}}{\rm e}^{-\alpha W}\right]+qp_{\rm n0} \frac{D_{\rm p}}{L_{\rm p}} \\[2mm]& \approx q \frac{T_{\rm total }P_{\rm in}\lambda \alpha }{Ahc} {\rm e}^{-\alpha X_{\rm j}} \left[1-\frac{1}{1+\alpha L_{\rm p}}{\rm e}^{-\alpha W}\right]. \\ \end{split} \end{equation}$$

(1)

Here T_total is transmission coefficient, P_in is the optical power of incident light, $\lambda$ is wavelength of incident light, α is absorption coefficient of silicon, X_j is the distance from depletion border of P region to the surface of semiconductor, P_n0 is the hole concentration at the boundary of N type area and depletion layer, L_p is the diffusion length of hole out of depletion layer, A is the area of photo-excited region, h is Planck constant, c is the speed of light in vacuum circumstances. Sometimes the term $qp_{\rm n0} \frac{D_{\rm p}}{L_{\rm p}}$ is omitted since the diffusion current density is far less than the drift current density.

Next we will research the photoelectric response of P⁺/N_well/P_sub. The diagrammatic sketch of P⁺/N_well/P_sub photodiode is shown in Fig. 3. The P⁺ region and P_sub region are connected together, so the P⁺/N_well/P_sub photodiode can be seen as two parallel PN junctions with different junction depth. The total photocurrent consists of the following four parts: the drift current in the depletion layer of N_well, the diffusion current in the bottom of N_well, the drift current in the depletion layer of P_sub, and the diffusion current in the bottom of P_sub.

The doping concentration of P⁺ is much larger than that of N_well and the doping concentration of N_well is much larger than that of P_sub. The width of the depletion layer is expressed as follows:

$$\begin{equation} W_{\rm n}=\sqrt {\frac{2\varepsilon _{\rm r} \varepsilon _0 V_{\rm D1} }{qN_{\rm D}}}, \end{equation}$$

(2)

$$\begin{equation} W_{\rm p}=\sqrt {\frac{2\varepsilon _{\rm r} \varepsilon _0 V_{\rm D2} }{qN_{\rm A} }} . \end{equation}$$

(3)

Here $\varepsilon_{\rm r}$ is relative permittivity of silicon, $\varepsilon_{0}$ is permittivity of vacuum, V_D1 is the contact potential of P⁺/N_well, V_D2 is the contact potential of N_well/P_sub, N_D is the doping concentration of N_well, and N_A is the doping concentration of P_sub.

For P⁺/N_well/P_sub photodiode the total photocurrent density J_tot consists of two parts as shown in Eq. (4).

$$\begin{equation} J_{\rm tot}=J_{\rm tot1}+J_{\rm tot2}, \end{equation}$$

(4)

where J_tot1 is photocurrent density collected by P⁺/N_well, and J_tot2 is photocurrent density collected by N_well/P_sub photodiode.

From the PN junction photoelectric model it can be deduced that the N_well/P_sub photoelectric model is

$$\begin{equation} \begin{split} J_{\rm tot2} {}& =q\frac{T_{\rm total}P_{\rm in}\lambda \alpha }{Ahc} {\rm e}^{-\alpha X_{\rm jn}} \left[1-\frac{1}{1+\alpha L_{\rm n}}{\rm e}^{-\alpha W_{\rm p}}\right]+qn_{\rm p0} \frac{D_{\rm n}}{L_{\rm n}} \\[2mm]& \approx q\frac{T_{\rm total}P_{\rm in}\lambda \alpha }{Ahc} {\rm e}^{-\alpha X_{\rm jn}} \left[1-\frac{1}{1+\alpha L_{\rm n}}{\rm e}^{-\alpha W_{\rm p}}\right]. \\ \end{split} \end{equation}$$

(5)

The term $qn_{\rm p0} \frac{D_{\rm n}}{L_{\rm n}}$ in Eq. (5) can also be omitted because the diffusion current density is far less than the drift current density.

For P⁺/N_well PN junction, similar to the deduction of PN junction photodiode it can be derived that the photocurrent density collected by N_well is

$$\begin{equation} \begin{split} J_{\rm drift1} {}& =\int_{X_{\rm p^+}}^{X_{\rm p^+}+W_{\rm n}} {G(x){\rm d}x} \\[2mm]& =q\frac{T_{\rm total}P_{\rm in}\lambda \alpha }{Ahc}\left[{\rm e}^{-\alpha X_{\rm p+}}-{\rm e}^{-\alpha (W_{\rm n}+X_{\rm p+})}\right]. \\ \end{split} \end{equation}$$

(6)

Here $G(x)$ is the generation rate of photon-generated carrier at a distance of $x$ from surface. When $x_{\rm p^+}+w_{\rm n}$ $<$ $x$ $<$ $x_{\rm jn}$, the width of non depletion layer in N$_{\rm well}$ is $x_{\rm jn}$ -($x_{\rm p^+}+ w_{\rm n}$) $=$ 0.8 -(0.15 $+$ 0.1) $=$ 0.55 $\mu$m $\ll$ $L_{\rm p}$($=$ 100 $\mu$m), and from the PN junction photodiode model we know that the diffusion current density is far less than drift current density, therefore the diffusion photocurrent density in N$_{\rm well}$ can be omitted. The photocurrent density of P$^+$/N$_{\rm well}$/P$_{\rm sub}$ double junction photodiode can be expressed as

$$\begin{equation} \begin{split} J_{\rm tot} = {}&J_{\rm tot1}+J_{\rm tot2} \\[1.5mm] ={}&q\frac{T_{\rm total}P_{\rm in}\lambda \alpha }{Ahc}{\rm e}^{-\alpha X_{\rm jn}} \left(1-\frac{1}{1+\alpha L_{\rm n}}{\rm e}^{-\alpha W_{\rm p+}}\right) \\[1.5mm]&{} + q\frac{T_{\rm total}P_{\rm in}\lambda \alpha }{Ahc} \left[{\rm e}^{-\alpha X_{\rm p+}}-{\rm e}^{-\alpha (W_{\rm n}+X_{\rm p+})}\right] \\[1.5mm] ={}&q\frac{T_{\rm total}P_{\rm in}\lambda \alpha }{Ahc} \left[{\rm e}^{-\alpha X_{\rm jn}}-\frac{1}{1+\alpha L_{\rm n}} {\rm e}^{-\alpha (W_{\rm p}+X_{\rm jn})}\right. \\[1.5mm]&{}+ \left. {\rm e}^{-\alpha X_{\rm p+}}-{\rm e}^{-\alpha (W_{\rm n}+X_{\rm p+})}\right]. \\ \end{split} \end{equation}$$

(7)

Typical values of minority lifetime $\tau$, diffusion coefficient D, diffusion length L are shown in Table 1. Set N_p+ = 10¹⁹ cm^-3, N_Nwell = 10¹⁷ cm^-3, N_Psub = 10¹⁵ cm^-3, X_p⁺ = 0.15 μm, X_jn = 0.8 μm and it can be calculated V_D1 = 0.8 V, V_D2 = 0.7 V and W_n = 0.1 μm, W_p = 0.9 μm according to Eqs. (3) and (4).

Using the parameters in Table 1 and Eq. (7), the relationship of α and $\lambda$ refer to bibliography^[11], the normalized simulated spectral responses of P⁺/N_well, N_well/P_sub, P⁺/N_well/P_sub photodiodes are shown in Fig. 4. The spectrum of P⁺/N_well photodiode ranges from 350 to 1000 nm with a peak value at 450 nm. The spectrum of N_well/P_sub photodiode ranges from 400 to 1000 nm with a peak at 600 nm. The spectrum of P⁺/N_well/P_sub photodiode ranges from 300 to 1000 nm with a peak at 550 nm. P⁺/N_well/P_sub photodiode has the largest response compared with P⁺/N_well and N_well/P_sub photodiodes because it can absorb both short and long wavelengths.

As shown in Fig. 4, the absorbing peak of P⁺/N_well/P_sub photodiode is about 550 nm and its spectrum is very close to the fluorescence spectrum of CsI(Tl) scintillation, so it can improve the quantum detecting efficiency and further increase the sensitivity of the sensor. It also shows the photocurrent of P⁺/N_well/P_sub photodiode at 550 nm is about 1.5 times that of N_well/P_sub photodiode and 5 times that of P⁺/N_well photodiode respectively.

3. Results and discussion

In CSMC 0.5 μm n-well CMOS processes, three different structure photodiodes P⁺/N_well, P⁺/N_well/P_sub, and improved P⁺/N_well/P_sub are constructed. The improved P⁺/N_well/P_sub photodiode is realized by adding a guarding ring using poly1 layer between the bird's beak and the active area of the photodiode so as to increase the distance between them and inhibit the leaked current from the bird's beak to the active region, and in this way the dark current induced by the bird's beak is reduced ^{[12, 13]}.

Structure of the improved P⁺/N_well/P_sub photodiode is shown in Fig. 5.

The response of P⁺/N_well/P_sub photodiode with active area of 100 × 100 μm² under a white LED lamp was tested using Keithley 4200 semiconductor parameter characterization. The measurement was undertaken at a fixed bias to reduce the reverse bias voltage transition noise of the 4200 machine itself. Dark current of the three photodiodes was measured at the reverse bias voltage from 0.5 to 5 V in steps of 0.5 V and the average dark current of each kind of photodiode is shown in Fig. 6. Average dark current is the mean value of 10 measurements. It is shown that the improved P⁺/N_well/P_sub photodiode has the least dark current about 6.5 pA and P⁺/N_well photodiode about 13 pA and P⁺/N_well/P_sub photodiode about 11 pA. This proves that optimizing the method to reduce dark current is feasible.

Photocurrent of the three photodiodes at 100 lux white LED illumination was measured and results are shown in Fig. 7. The photocurrent of P⁺/N_well/P_sub photodiode is slightly larger than the improved P⁺/N_well/P_sub photodiode and P⁺/N_well photodiode has the least photocurrent since it has only a shallow P⁺/N_well junction to absorb the incident light while P⁺/N_well/P_sub photodiode has two junctions to absorb incident light. Comparison of the average dark current and photocurrent at 100 lux illumination under reverse voltage range from 0 to 5 V of these photodiodes is shown in Table 2. For a photodiode in X-ray sensor IC the dark current is the most important parameter because it can't be improved by pixel architecture or peripheral circuitry, so the improved P⁺/N_well/P_sub photodiode is the most suitable photodiode in X-ray sensor IC.

From Table 2 it can be seen that the improved P⁺/N_well/P_sub photodiode has the best performance comprehensively because it has the least dark current and good photoelectric response. The reason that the improved P⁺/N_well/P_sub produces less photocurrent than P⁺/N_well/P_sub results from the fact that the guard ring occupies a size of only a few pixels. In fact, for improved P⁺/N_well/P_sub photodiode the real photo-sensitive area is about 98 × 98 μm², smaller than 100 × 100 μm² of P⁺/N_well/P_sub photodiode. The sensitivity of improved P⁺/N_well/P_sub photodiode was measured at white LED illumination and the result is shown in Fig. 8.

From Fig. 8 it can be measured that the sensitivity of the improved P⁺/N_well/P_sub photodiode is about 20 pA/lux.

The response of improved P⁺/N_well/P_sub photodiode to monochromatic light of wavelength 405, 532, 633 and 808 nm is also measured by laser beam. The testing result is shown in Fig. 9.

As shown in Fig. 9, the improved P⁺/N_well/P_sub double junction photodiode has a larger response at 532 nm than the other three incident wavelengths. The sensitivity of 405 nm, 532 nm, 633 nm and 808 nm is about 1 × 10^-9, 2 × 10^-8, 3 × 10^-10, 2 × 10^-10 A· m²/W respectively. The indirect X-ray detector uses CsI(Tl) scintillation to convert the X-ray into fluorescence and is further detected by the semiconductor. The spectrum of excited fluorescence ranges from 400 nm to 800 nm and has a peak at about 550 nm. The improved P⁺/N_well/P_sub double junction photodiode has a matched spectrum response to that of CsI(Tl) fluorescence and can improve the sensitivity of X-ray detection.

To test the performance the CMOS X-ray sensor IC using P⁺/N_well/P_sub double junction photodiode, a CMOS image sensor was designed and fabricated in CSMC 0.5 μm process. Capacitive transimpedance amplifier (CTIA) pixel architecture was used to have a large and controllable charge to voltage conversion gain ^{[14, 15]} and is shown in Fig. 10. Correlated double sampling (CDS) technique was integrated in the chip to reduce the reset noise^[16]. The microphotograph of the chip is shown in Fig. 11.

The X-ray sensor was realized by coupling the CsI(Tl) scintillation to the fabricated CMOS IC by transparent glue of optimum refractive index. The surface of the CsI(Tl) scintillation is covered with bonder to isolate the interference of ambient light. The thickness of the CsI(Tl) is 1 mm.

The X-ray sensor was irradiated by X-rays from SHIMADZU XRD-6000 X-ray unit with a copper anode target. The irradiation intensity I of X-ray against tube voltage U and tube current i can be expressed as following:

$$\begin{equation} I=kiZU^n. \end{equation}$$

(8)

Here k is a constant coefficient about (1.1-1.4) × 10^-9. n is nearly equal to 2, and Z is the atomic number of the target: for copper it is 29. I is in unit of J/(s· m²) or W/m². The average X-ray photon energy excited from a copper target is about 8.05 keV.

The sensitivity of the assembled CMOS X-ray sensor is measured at 60 μs integration time and the testing results are shown in Table 3. The output voltage value is the average value of five measurements. Sensitivity measurement result of the assembled X-ray sensor is shown in Fig. 13.

As shown in Fig. 12, the sensor shows a good linearity when the incident X-ray intensity increases gradually. The slope of the fitted curve is 0.21, meaning the sensitivity of the designed X-ray sensor is 0.21 V· m²/W at 60 μs integration time. Main parameters of the present CMOS X-ray sensor are summarized in Table 4.

4. Conclusion

In this paper a monolithic CMOS X-ray sensor was presented for indirect X-ray detection. An improved P⁺/N_well/P_sub photodiode was proposed to match the fluorescence of CsI(Tl) scintillation and keep low dark current. It has characteristics of low dark current, large photocurrent response and matched spectral response to the spectrum of CsI(Tl) fluorescence. The monolithic CMOS X-ray sensor IC consisting of improved P⁺/N_well/P_sub photodiode and CTIA pixel architecture with high charge-to-voltage gain was designed. A CMOS X-ray sensor was assembled based on the designed IC directly coupled with CsI(Tl) scintillation. The measured X-ray sensitivity is about 0.21 V· m²/W under X-ray irradiation from a Cu target. It can also be calculated that each pixel produces about 5097e charge upon 8.05 keV X-ray photon during 60 μs integration time. To our knowledge this is the first time an improved P⁺/N_well/P_sub photodiode combined with CTIA pixel architecture has been proposed in a monolithic CMOS X-ray sensor.