Referring now to FIGS. 1 and 2 illustrating the prior-art two dimensional (2D) pixel architectures. FIG. 1, shows the cleaved pixel design with device area being about 1 mm×1 mm. The key motivation for this design is as follows. Spatial independence of the scintillation flux on the pixel photodiodes should be ensured, so that the readout would be the same irrespective of where the interaction occurs in the volume of pixel. Due to the high refractive index of InP, only a small fraction of radiation impinging on the side surface from a random point will escape, while most of the radiation will be internally reflected and eventually reach the absorbing photodiode. If the pixels were not cleaved and instead a planar array as grown was used, this will be resulted in the following situation. The signal would be shared between neighboring pixels in the amount that depends on the position of the interaction. The main disadvantage of this prior art design, is the large area of the photodiode (1 mm2) which translates into a large diode capacitance (about 50 pF) that places stringent demands on the electronic amplifiers in the flip-chip readout Si circuitry.
Referring now to FIG. 2 illustrating a prior art integrated pixel architecture. In this design, diodes form an array of squares or hexagons. The explosion symbol reflects the position of an interaction event, assumed to be a distance h deep into the scintillator body. FIG. 2 illustrates the alternative prior-art design which addresses the issue of low capacitance. The idea is to make an array of photo-diodes of much smaller area, without cleaving. The full power of planar integrated technology is then deployed. For example, if 100 μm×100 μm diodes are used, instead of the current 1 mm×1 mm, the capacitance goes down by two orders of magnitude. However, the number of photons collected by a single pixel decreases, albeit by a smaller amount. The reason that the number of photons decreases is because photons generated by a single ionization event (a Compton or photoelectric interaction in the given slab) are now shared by several 2D pixels. The total area of illuminated pixels is of the order h2, where h is the distance from the interaction region to the top surface of the detector, i.e. the surface where the epitaxial photodiodes are located. Inasmuch as h2<<1 mm2, the amount of photons received by a single 100 μm×100 μm pixel decreases by the smaller amount, compared to the 100-fold decrease in the area. The integrated pixel design thus enhances the charge per capacitance ratio. This implies a higher voltage developed in a single diode in response to receiving the scintillating radiation and therefore the higher signal to noise ratio. This prior art design provides the capability of assessing the deposited energy by the analysis of the ratio of signals received by the central diode (the one closest to the location of an ionization event) and its nearest neighbors.
To better understand the collection of photons in the integrated-pixel architecture, it has been noted that the propagation of scintillating radiation in the body of n-doped InP scintillator is diffusive, as shown by the research in room temperature experiments. Most of the scintillation photons reaching the detectors surface are not photons directly generated by the electrons and holes at the site of the gamma particle interaction, but photons that have been re-absorbed and re-emitted a multiple number of times. The motion of light form the initial interaction site to the detector is a random and characterized by a mean free path of about λ=100 μm (in the samples of doping n=6·1018 cm−3 at room temperature). The corresponding diffusion coefficient of light can be estimated as D=λ2/τ≈105 cm2/s, where τ=(Bn)−1≈1 ns is the radiative recombination time and B≈1.2×10−10 cm3/s is the radiative recombination constant in InP. This estimate justifiably assumes that light propagation between the absorption/re-emission sites is practically instantaneous.
To estimate the illumination area by an interaction event that occurs a distance h deep into the scintillator, the diffusion equation has been solved for the density of photons N({right arrow over (r)},t):
                              D          ⁢                                    ∇              2                        ⁢                          N              ⁡                              (                                                      r                    →                                    ,                  t                                )                                                    =                              ∂            N                                ∂            t                                              (        1        )            with the boundary condition, N(z=0,t)=0, of absorbing detector surface and the initial condition N({right arrow over (r)},t=0)=N0δ({right arrow over (r)}−{right arrow over (r)}0), where {right arrow over (r)}0=(0,0,−h). Using the known Green's function of the diffusion equation (1), it was found the resultant flux density j({right arrow over (r)},t) [cm−2 s−1] through the detector surface (the boundary plane) in the form of
                                          j            ⁡                          (                              r                ,                t                            )                                ≡                                    -              D                        ⁢                                          ∂                N                                            ∂                z                                                    =                                                            N                0                            ⁢              h                                                      t                ⁡                                  (                                      4                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    Dt                                    )                                                            3                /                2                                              ⁢                      exp            (                          -                                                                    r                    2                                    +                                      h                    2                                                                    4                  ⁢                                                                          ⁢                  Dt                                                      )                                              (        2        )            
It has been observed that the flux density decays radially from the epicenter as a Gaussian function of width d=√{square root over (Dt)}. For the total pulse duration T=h2/2D=v·τ, where v is the average number of the absorption/re-emission events, we have d=√{square root over (2DT)}=h≈λ√{square root over (T/τ)}=λ√{square root over (v)}. In the experiments at room temperature, h≈300 μm and v≈10, so that the Gaussian width of the flux distribution is about 3λ≈h. Both estimates, d=h and d=λ√{square root over (v)} give roughly the same width.
In the above-discussed prior art, all embodiments of the scintillator, the capacitance of the epitaxial PIN diode has been determined by the volume of its charge collection, and therefore it scales with the area of the pixel. Thus, there has been a need for a new architecture that provides a substantially smaller capacitance for same collection volume, the architecture which provides substantially higher pixel sensitivity.
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