Time resolved photo-luminescent decay characterization of mercury cadmium telluride focal plane arrays

Grant Soehnel

doi:10.1364/OE.23.001256

1. Introduction

Optical detectors function by absorbing photons in the sensor layer and collecting the resulting photo-generated carriers (electron-hole pairs) to produce a signal [1,2]. There is also carrier generation that occurs from thermal energy present in the sensor material that when collected becomes dark current. Carriers recombine via 3 mechanisms illustrated in Fig. 1 [3]. Radiative and auger recombination occur at rates that are intrinsic to the material composition. Radiative recombination produces a photon at the bandgap energy when a carrier spontaneously falls from the conduction band to the valence band. Auger recombination involves an interaction between two or more carriers with one of them falling to the valence band. SRH recombination occurs when a defect or material impurity creates an energy state within the bandgap that facilitates carrier recombination without emitting photons.

Fig. 1 Illustration of the 3 types of carrier recombination.

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The rate of SRH recombination, or equivalently the SRH lifetime, depends on the material quality and can vary among devices or spatially within a device. Defect centers with low SRH lifetimes can produce high dark current or reduced quantum efficiency (QE) once a detector is fabricated. The photons produced from radiative recombination can be detected which provides the opportunity to measure the decay in time of the radiative recombination rate after an optical excitation such as a laser pulse. This data can be analyzed to determine the SRH lifetime. The result is a non-contact measurement technique that can be used to evaluate potential defects and reduced detector performance as soon as a material wafer is fabricated, or at any stage in the processing afterwards up to a hybridized focal plane array (FPA).

2. Carrier recombination simulation

The modeling and experimental data reported in this work is on mercury cadmium telluride (MCT) FPAs. A numerical simulation was developed to determine carrier concentration and recombination rates from equilibrium conditions with a laser pulse excitation. Equations (1) and (2) are used to determine the carrier concentration of both electrons $n$ and holes $p$ after a time step $Δ t$ .

n (t + Δ t) = n (t) + Δ t G_{o p t i c a l} (t) - Δ t (U_{a u g} + U_{r a d} + U_{S R H})

p (t + Δ t) = p (t) + Δ t G_{o p t i c a l} (t) - Δ t (U_{a u g} + U_{r a d} + U_{S R H})

G_{o p t i c a l} (t)

is the optical carrier generation rate, and

U_{a u g}

,

U_{r a d}

, and

U_{S R H}

are the net recombination rates from auger, radiative, and SRH recombination. Equations (3)-(6) are used for the recombination rates [3].

n_{0}

and

p_{0}

are the equilibrium concentrations of electrons and holes, and

n_{i}

is the intrinsic carrier concentration.

n_{1}

and

p_{1}

are the SRH densities which are set equal to

n_{0}

and

p_{0}

for this study due to a lack of knowledge about the nature of the defect states present.

τ_{S R H - n}

and

τ_{S R H - p}

are the SRH lifetimes for electrons and holes, which are set equal to each other and regarded as the primary variable of interest.

B

,

C_{n}

, and

C_{p}

are recombination rate coefficients given by Eqs. (7)-(9) [4–6].

m_{0}

is the mass of an electron, and

m_{c}^{*}

and

m_{v}^{*}

are the effective masses of electrons and holes (in the conduction and valence bands).

| F_{1} F_{2} |

is the overlap integral of the Bloch functions, and its value is not precisely known. A value of 0.2 was used in these simulations.

U_{a u g} = C_{n} (n^{2} p - n_{0}^{2} p_{0}) + C_{p} (n p^{2} - n_{0} p_{0}^{2})

U_{r a d} = B (n p - n_{i}^{2})

U_{S R H} = \frac{(n p - n_{i}^{2})}{τ_{S R H - n} (p + p_{1}) + τ_{S R H - p} (n + n_{1})}

n_{0} p_{0} = n_{i}^{2}

\begin{matrix} B = 5.8 \times 10^{- 13} \sqrt{ε_{\infty}} {(\frac{m_{0}}{m_{c}^{*} + m_{v}^{*}})}^{\frac{3}{2}} (1 + \frac{m_{0}}{m_{c}^{*}} + \frac{m_{0}}{m_{v}^{*}}) \\ \times {(\frac{300}{T})}^{\frac{3}{2}} (E_{g}^{2} + 3 k T E_{g} + 2.75 k^{2} T^{2}) \end{matrix}

\begin{matrix} C_{n} = \frac{(\frac{m_{c}^{*}}{m_{0}}) {| F_{1} F_{2} |}^{2}}{2 n_{i}^{2} (3.8 \times 10^{- 18}) ε_{\infty}^{2} {(1 + \frac{m_{c}^{*}}{m_{v}^{*}})}^{\frac{1}{2}} (1 + \frac{2 m_{c}^{*}}{m_{v}^{*}})} \\ \times {(\frac{E_{g}}{k T})}^{\frac{- 3}{2}} \exp (- \frac{1 + \frac{2 m_{c}^{*}}{m_{v}^{*}}}{1 + \frac{m_{c}^{*}}{m_{v}^{*}}} \frac{E_{g}}{k T}) \end{matrix}

C_{p} = C_{n} [\frac{1 - \frac{3 E_{g}}{k T}}{6 (1 - \frac{5 E_{g}}{4 k T})}]

The intrinsic carrier concentration and band gap for MCT is a function of the temperature

T

and the composition

x

as found in

H g_{(1 - x)} C d_{x} T e

. These two parameters are modeled using Eqs. (10) and (11) [7,8]. The equilibrium carrier concentrations are given by Eqs. (12) and (13) where

N_{D}

and

N_{A}

are the donor and acceptor doping concentrations [2].

E_{g} = - 0.302 + 1.93 x + 5.35 \times 10^{- 4} T (1 - 2 x) - 0.81 x^{2} + 0.832 x^{3}

\begin{matrix} n_{i} = (5.585 - 3.82 x + 1.753 \times 10^{- 3} T - 1.364 \times 10^{- 3} x T) \\ \times 10^{14} E_{g}^{\frac{3}{4}} T^{\frac{3}{2}} \exp (\frac{- E_{g}}{2 k T}) \end{matrix}

n_{0} = \frac{N_{D} - N_{A}}{2} + \sqrt{{(\frac{N_{D} - N_{A}}{2})}^{2} + n_{i}^{2}}

p_{0} = \frac{N_{A} - N_{D}}{2} + \sqrt{{(\frac{N_{A} - N_{D}}{2})}^{2} + n_{i}^{2}}

The simulation is run by setting the initial carrier concentrations to the equilibrium concentrations, and creating a laser pulse

G_{o p t i c a l} (t)

to excite the material. It is assumed that the illumination is circular and of uniform intensity. It is also assumed that charge diffusion rapidly spreads the excitation evenly through the depth of the material such that carrier concentration is always treated as uniform in the illuminated volume of the material. The devices measured were p-n photodiodes, but since they are left unbiased during the experiment, and the p-type implant takes up a very small volume in the n-type absorber, only the n-type material was simulated. Equations (1) and (2) are used to simulate the time resolved deflection and subsequent settling of carrier concentration during and after the laser pulse. Figure 2 shows the result of the simulation using a 10ns 1nJ laser pulse (

λ = 2.5 μ m

) on MCT at 100K with a composition

x = 0.287

. The carrier concentration shown is that of the minority carriers (holes) with a doping concentration

N_{d} = 7 e 14

. The recombination rates of Eqs. (3)-(5) are related linearly, with the square, and with the cube of the excess carrier concentration for SRH, radiative, and auger recombination. As shown by Fig. 2, this causes the auger recombination rate to dominate the total rate during the earliest part of the decay when the carrier concentration is highest followed by the radiative rate, and finally, the SRH rate. Note the time scale is windowed to show the relatively early decay rates and does not show when equilibrium has been reached. A time resolved photo-luminescent (TRPL) decay measurement must be analyzed to extract the SRH lifetime from the measurement of radiative photons. This is challenging because the SRH recombination rate only becomes significant later in the decay when the carrier concentration, recombination rates, and radiative photon flux is relatively low. Pumping the sample with more power does not improve the measurement because it only increases the signal strength immediately after the pulse when the SRH rate is negligible compared to the other two recombination mechanisms. The spatial resolution of the measurement is also limited by the signal to noise ratio because a smaller excitation spot excites less volume in the material which reduces the photo-luminescent signal.

Fig. 2 Carrier recombination simulation using a 10ns 1nJ laser pulse on MCT at 100K with composition x = 0.287.

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3. TRPL decay measurement and analysis

A diagram showing the layout of the TRPL decay experiment is shown in Fig. 3. The pulsed laser is fiber coupled so the end of the fiber can be mounted on motorized stages along with the rest of the optics. A beam splitter is used to create an optical path for the incoming laser excitation and the outgoing photo-luminescence that is read by a single pixel MCT photodiode. A spectral filter in the photo-luminescent path is used to eliminate scattered or reflected laser light. The oscilloscope is set to average mode with 512 averages per measurement.

Fig. 3 Diagram of the TRPL experiment.

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Figure 4 shows 4 examples of TRPL decay traces with varying SRH lifetimes. To evaluate the SRH lifetime, the recombination simulation is used in an optimization with the SRH lifetime as the variable. The simulation output to be compared to the data is the radiative recombination rate $U_{r a d}$ which is scaled to a voltage and normalized to the peak voltage of the oscilloscope trace being evaluated. The optimization metric is the difference between the simulation and the data on a log scale. The noise floor of the oscilloscope is included in the simulation to match the lower limit of the trace data. The initial time for the optimization is also set from 100ns-500ns after the actual laser pulse to avoid any impulse response issues with the oscilloscope data around the laser pulse itself.

Fig. 4 Example oscilloscope trace averages and simulation optimized showing 4 different SRH lifetimes.

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4. FPA lifetime mapping results

The TRPL decay measurement was performed in a 2 dimensional scan to create an SRH lifetime map of a 2048X2048 MCT FPA. This is a shortwave device with a cutoff of ~3.6µm and a cadmium concentration $x = 0.355$ . The device is backside illuminated, so the light must pass through a 0.5mm thick cadmium zinc telluride (CZT) substrate that is transparent to the excitation and photo-luminescent wavelengths. The step size and spot size were both set at 0.5mm for the scan over the entire active surface with the results shown in the top left of Fig. 5. The results show a wide range of spatial features in the SRH lifetime with values ranging from 0.1 to 5µs. The corresponding dark current map for this device is found in the upper right of Fig. 5. The SRH lifetime is clearly inversely related to the dark current, and nearly all spatial features of the lifetime map are present in the dark current map. Higher resolution lifetime scans were performed in a region of interest of the lifetime map that appeared to have fine spatial features. Lifetime maps with spot sizes and scan step sizes of 0.15mm and 0.05mm are shown in the bottom of Fig. 5.

Fig. 5 Carrier lifetime mapping results for shortwave FPA #1 (axis are FPA pixels).

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There is one region in the upper right quadrant of shortwave FPA #1 in which the lifetime is as low as 100ns. This is low enough to reduce the quantum efficiency (QE) of the device which is verified by the region of interest lifetime map and relative response map in Fig. 6. The lifetime map spot size and step size is 0.15mm.

Fig. 6 Lifetime map and relative response map for a region of interest on shortwave FPA #1 (axis are FPA pixels).

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Lifetime mapping was performed for 3 additional FPAs. The lifetime and dark current map for another shortwave FPA is shown in Fig. 7. This FPA also has several defects that have a stronger effect on the QE than the dark current as shown by the relative response map in Fig. 8. Lifetime and dark current maps for 2 midwave FPAs are shown in Fig. 9 and Fig. 10. The cadmium concentration is 0.287 for the midwave arrays providing a cutoff wavelength of ~5.5µm. In both cases, the spatial features found in the lifetime and dark current maps correlate very closely.

Fig. 7 Lifetime and dark current maps for shortwave FPA #2 (axis are FPA pixels).

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Fig. 8 Relative response map for shortwave FPA #2 (axis are FPA pixels).

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Fig. 9 Lifetime and dark current maps for midwave FPA #1(axis are FPA pixels).

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Fig. 10 Lifetime and dark current maps for midwave FPA #2 (axis are FPA pixels).

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5. Conclusions

The lifetime mapping measurement and analysis presented here demonstrates that the SRH lifetime can be used as an indicator of device performance. Dark current and QE are the primary metrics that can be evaluated with a lifetime measurement. Depending on the SRH lifetime being resolved, the spatial resolution of the measurement has been demonstrated as low as 50µm. This is a non-contact and non-destructive measurement that can be applied at any stage in the device fabrication process as soon as a photo-sensitive layer is present. The only requirement is that the absorbing layer is direct band gap to produce enough radiative recombination to detect. This is the case for common infrared absorbing materials. Performing the measurement at each stage of the fabrication process could identify when material defects are introduced.

References and links

1. B. Streetman and S. Banerjee, Solid State Electronic Devices, 5th ed. (Prentice Hall, 2000).

2. S. Sze and K. Ng, Physics of Semiconductor Devices, 3rd ed. (John Wiley & Sons, 2007).

3. S. Rein, Lifetime Spectroscopy, 1st ed. (Springer, 2005).

4. P. K. Saxena, “Modeling and simulation of HgCdTe based p⁺-n-n⁺ LWIR photodetector,” Infrared Phys. Technol. 54(1), 25–33 (2011). [CrossRef]

5. A. Itsuno, J. Phillips, and S. Velicu, “Predicted performance improvement of auger-suppressed HgCdTe photodiodes and p-n heterojunction detectors,” IEEE Trans. Electron. Dev. 58(2), 501–507 (2011). [CrossRef]

6. V. C. Lopes, A. J. Syllaios, and M. C. Chen, “Minority carrier lifetime in mercury cadmium telluride,” Semicond. Sci. Technol. 8(6S), 824–841 (1993). [CrossRef]

7. G. L. Hansen, J. L. Schmit, and T. N. Casselman, “Energy gap versus alloy composition and temperature in Hg_(1-x)Cd_(x)Te,” J. Appl. Phys. 53(10), 7099–7101 (1982). [CrossRef]

8. G. L. Hansen and J. L. Schmit, “Calculation of intrinsic carrier concentration in Hg_(1-x)Cd_(x)Te,” J. Appl. Phys. 54(3), 1639–1640 (1983). [CrossRef]

Time resolved photo-luminescent decay characterization of mercury cadmium telluride focal plane arrays

Abstract

1. Introduction

2. Carrier recombination simulation

3. TRPL decay measurement and analysis

4. FPA lifetime mapping results

5. Conclusions

References and links

Cited By

Figures (10)

Equations (13)

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