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Optik 125 (2014) 2395–2399

Contents lists available at ScienceDirect

Optik

jo ur nal homepage: www.elsev ier .de / i j leo

esearch on quantum efficiency of transmission-mode InGaAshotocathode

uchun Jina, Benkang Changa,∗, Hongchang Chengb, Jing Zhaoa, Mingzhu Yanga,inlong Chena, Guanghui Haoa

Institute of Electronic Engineering and Optoelectronic Technology, Nanjing University of Science & Technology, Nanjing 210094, ChinaKey Laboratory of Low Light Level Technology of COSTIND, Xi’an 710065, China

r t i c l e i n f o

rticle history:eceived 22 May 2013ccepted 16 October 2013

a b s t r a c t

To investigate the quantum efficiency of high performance transmission-mode InGaAs photocathode, thequantum efficiency curve is fitted by using the multilayer optical thin film theory and the first principlecalculation. A series of the performance parameters are obtained with the relative error less than 5%.

eywords:nGaAs photocathodeuantum efficiencyirst principle calculationack interface recombination velocity

It indicates that the thickness of the emission layer is 0.7–0.9 �m, the thickness of the window layer is0.1–0.3 �m. Meanwhile the results from the first principle calculation are proved to be reliable as well. Inaddition, the long-wave response will increase and the highest integral sensitivity will be obtained whenthe thickness of the emission layer is the optimum value. For the InGaAs photocathode, the back interfacerecombination velocity mainly leads to the low integral sensitivity, which is caused by the material latticemismatch.

. Introduction

The negative electron affinity (NEA) InGaAs photocathode hasany advantages of large emission current density, concentrative

mitting electron energy distribution and low dark current. Its bandap Eg goes with In component from 0.35 eV of InAs to 1.43 eV ofaAs, which corresponding to the cutoff wavelength of 3.5 �m and.87 �m [1,2]. By using the InGaAs photocathode, a near infraredensitivity image intensifier can be produced which the responseavelength range can be perfectly matched with the night sky spec-

rum. Therefore, the InGaAs photocathode has always been one ofhe hot topics in the night vision field.

In order to satisfy the need of the semiconductor laser radar andaser-assisted night vision systems, the US Litton System developed

InGaAs photocathode for the first time in 1993 [3,4]. The spec-ral response of the transmission-mode InGaAs photocathode canxtend its long-wavelength threshold to 1.06 �m, and the quan-um efficiency of InGaAs photocathode above 900 nm is apparentlyigher than that of GaAs photocathode and S20 cathode. In 2002, US

TT reported the variable spectral response curve of transmission-

ode InGaAs photocathode with the changing of In content [5].

ubsequently, the Photonics (France), Katod company (Russian)6], Andor company (US), Hamamatsu Corporation (Japan) and

∗ Corresponding author. Tel.: +86 18601401072; fax: +86 025 84315177.E-mail addresses: jinmuchun@163.com (M. Jin), bkchang@mail.njust.edu.cn

B. Chang).

030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved.ttp://dx.doi.org/10.1016/j.ijleo.2013.10.086

© 2013 Elsevier GmbH. All rights reserved.

the North Night-Vision Technology Group Co., Ltd. (NNVTG) fromChina were carrying out the study of the InGaAs photocathode andachieved certain results. The InGaAs photocathode integral sensi-tivity was 575 �A lm−1 and the radiant sensitivity at 1.06 �m ofwavelength was 0.043 mA W−1 produced by NNVTG [7].

For the InGaAs photocathode, the performance parametersinfluencing on the quantum efficiency can be obtained by fittingto the experiment curve, such as the electron escape probability,the electron diffusion length and the back interface recombinationvelocity, which could be used to estimate the performance of cath-ode and guide the design of structure. In this paper, the extinctioncoefficient and refractive index, which taking a part in fitting thequantum efficiency curve, are calculated by the first principle. Then,the range of parameters is gotten that can affect photoelectric emis-sion properties. The influences of the active layer thickness and theback interface recombination velocity on the integral sensitivity areanalyzed at last.

2. Theoretical calculation

In our work, the transmission-mode InGaAs photocathode isgrown by MBE and regarded as four layers of structure: InGaAsactive layer, GaAlAs window layer, Si3N4 antireflection layer and

glass substrate, as shown in Fig. 1. The active layer has a thicknessof 0.9 �m with p-type Zn-doping concentration of 1×1019 cm−3,the window layer has a thickness of 0.3 �m with concentration of2×1018 cm−3 and the antireflection layer has a thickness of 0.1 �m.

2396 M. Jin et al. / Optik 125 (2014) 2395–2399

2

l

˛

wtro

R

T

A

wi

[

Ewisrrtto

tpaapsbttaFvsvi

1 2 3 40

1

2

3

4

5

6

Energy (e V)

Com

plex

Inde

x of

Ref

ract

ion

kn

Fig. 1. Diagram of InGaAs photocathode module [7].

.1. Optical property

The absorption coefficient of InGaAs active layer can be calcu-ated by [8]

= 4�k

�(1)

here � is the wavelength of the incident photons, k is the extinc-ion coefficient. By using multilayer optical thin film theory [9], theeflectivity, transmissivity and absorptivity of InGaAs photocath-de can be calculated by

hv =(

ngB − C

ngB + C

)·(

ngB − C

ngB + C

)∗(2)

hv = 4ngn0

(ngB + C) · (ngB + C)∗ (3)

hv = 1 − Rhv − Thv (4)

here ng is the refractive index of the glass, n0 is the refractivendex of the air. B and C are obtained by following matrix

B

C

]=

⎛⎝ 3∏

j=1

[cos ıj i · sin ıj/�j

i · �j sin ıj cos ıj

]⎞⎠ ·

[1

n0

](5)

very 2 × 2 characteristic matrix represents a thin film layer,hich means the parameters of the matrix contain the optical

nformation of the layer and the last 2 × 1 matrix represents theubstrate medium. In the characteristic matrix, ıj = 2��jdj cos �j/�epresents the optical path between adjacent layers. �j = nj − ikj

epresents the complex index of refraction, nj and kj are the refrac-ive index and extinction coefficient of the j layer. dj stands for thehickness of the layer, �jx represents the refraction angle which isbtained by law of refraction �j sin �j = �j+1 sin �j+1.

In the calculation of the absorption coefficient and reflectivity,he refractive index and extinction coefficient of the In0.1Ga0.9Ashotocathode is obtained by first principle. First of all, we chose

2 × 1 × 1 super cell model which having 7 Ga atoms, 8 As atomsnd 1 In atom. The In atoms accounting for 12.5% means 0.1 com-onents. InGaAs sphalerite unit cell is F43m space group with Td2ymmetry [10]. The lattice constant is 0.56938, which is obtainedy law of Vegard. After that, the calculations were performed withhe quantum mechanics program of CASTEP based on density func-ion theory (DFT) [11]. The Broyden Flecher Goldfarb Shanno (BFGS)lgorithm was used to optimize the structures of the crystal models.inally, we found the calculated value is lower than the theoretical

alue after compared, this is because the band gap in the localizedtate instead of the excited state during calculations. The correctedalue of the refractive index and extinction coefficient are shownn Fig. 2.

Fig. 2. The refractive index and extinction coefficient of InGaAs photocathode.

2.2. Quantum efficiency

Considering with the boundary condition, the formula of quan-tum efficiency was solved from the one-dimensional diffusionequation as follows [12]

Y(hv) = P(1 − R)˛Ld exp(−ˇTw)

˛2hvL2

d− 1

×{

˛Dn + SV

(Dn/Ld) cosh(Te/Ld) + SV sinh(Te/Ld)

−exp(−˛Te)

[SV cosh(Te/Ld) + (Dn/Ld) sinh(Te/Ld)

](Dn/Ld) cosh(Te/Ld) + SV sinh(Te/Ld)

− ˛Ld exp(−˛Te)

}(6)

where P is the electron escape probability, R is the reflectivity ofthe photocathode, Ld is electron diffusion length, SV is the inter-face recombination velocity, Dn is the electron diffusion coefficient,Te and Tw are the thickness of the active layer and window layerrespectively. and are the absorption coefficient of the activelayer and window layer respectively, wherein R is a wavelength-related function calculated by the extinction coefficient and therefractive index using an optical film matrix theory.

The spectral response curve is obtained by the relationship withY(hv) as shown in the following formula

YT (hv) ≈ 1.24 S(�)�

(7)

where S(�) is the spectral response value, � is the wavelength ofthe incident photon.

3. Experimental curve and fitting results

The experimental quantum efficiency curve for InGaAs pho-tocathode is shown in Fig. 3, the spectral response ranges from400 nm to1100 nm.

The parameters of the spectral response curve are shown inTable 1, in which the integral sensitivity reached 558.82 �A lm−1.After that, the structural parameters for the photocathode wereresearched by fitting the experimental curve.

It clearly to see that the quantum efficiency curve has beenaffected by many parameters, such as electron escape probabil-ity, electron diffusion length, back interface recombination velocity,electron diffusion coefficient, reflectivity, the component, thicknessand absorption coefficient of the active layer and window layer,respectively. For a given photocathode, R, Te, Tw, ˛, and In% had

been determined, though P, Ld, Sv, Dn, ˇ, and Al% were not pre-cise. Starting with an initial value, P and Ld were changing withina set range [13]. The band gap was determined by the conditionof shortwave cut-off for quantum efficiency. The component of Al

M. Jin et al. / Optik 125 (2014) 2395–2399 2397

Table 1The computing results of quantum efficiency for transmission-mode InGaAs photocathode.

esponse/mA W−1 The peak position/nm The integral sensitivity/�A lm−1

795 558.82

wE

E

wttAetwtr

ct

naTetpad

qStp

4

clttv

wd

400 600 80 0 10 00 120 010-4

10-3

10-2

10-1

100

Wavelength (nm)

Qua

ntum

Eff

icie

ncy

(%)

Fitting CurveExperimental Curve

The starting wavelength/nm The cut-off wavelength/nm The peak r

440 1065 47.8

as obtained with 0.5–0.63 as well as absorption coefficient usingq. (8) [14].

g = 1.9 + 0.125x + 0.143x2 (8)

here x is the component of Al. In this calculation, the thickness andhe refractive index were set to be 0.1 �m and 2.06 �m respectively,he obtained values R, ˛, were dealt with cubic interpolation.fter all the parameters had been set, we calculated the quantumfficiency for every group of the fitting parameter, and drew theheoretical curve by the software program in order to compareith the experimental curve. When the discrepancy between the

wo curves is within a certain range, we considered this group iseasonable value.

For the InGaAs photocathode, we dealt the quantum efficiencyurve with the least square method, made the relative error lesshan 5%, got the range of fitting parameters as shown in Table 2.

It’s hard to make accurate for the growth control of the thick-ess on InGaAs photocathode, so the range of the thickness forctive layer and window layer are 0.7–0.9 �m and 0.1–0.3 �m.he electron escape probability is 0.32 by cubic interpolation. Thelectron diffusion length is 1.9 �m. The back interface recombina-ion velocity is about 107 cm s−1, which is decided by the complexreparation process and serious lattice mismatch between InGaAsnd GaAlAs. Related to the property of the material, the electroniffusion coefficient is 90 cm2/s for InGaAs photocathode.

One reasonable group of parameters was chose to calculate theuantum efficiency, if Te = 0.7 �m, Tw = 0.2 �m, P = 0.32, Ld=1.9 �m,v = 107 cm s−1. In this case, the fitting relative error is minimizedo 2.9% and the fitting curve is shown in Fig. 4. The fitting resultsroved the reliability of first principle calculations as well.

. Discussion

The quantum efficiency of transmission-mode InGaAs photo-athode will change significantly as the changing of the emissionayer thickness Te, which is shown in Fig. 5. We set the window layero be 0.2 �m, the electron escape probability to be 0.32, the elec-ron diffusion length to be 1.9 �m, the back interface recombination

7 −1

elocity to be 10 cm s .As can be seen from Fig. 5, the spectral response increases

ith the increasing of Te in the long-wavelength section, butecreases in the short-wavelength section. This shows that there

400 500 60 0 70 0 800 900 10 00 110 010-1

100

101

102

Wavelength (nm)

Qua

ntum

Eff

icie

ncy

(%)

Fig. 3. The spectral response curve of InGaAs photocathode.

Fig. 4. The experimental curve and fitting curve of quantum efficiency fortransmission-mode InGaAs photocathode.

is a reasonable thickness of emitting layer which is between thelength of absorption and the electron diffusion length, the thin Te isnot conducive to fully absorption for light, while the thick Te causesthe photoelectrons generated by light cannot diffuse to the surfaceand escape. Therefore, for the fitting InGaAs photocathode, anappropriate increase of the emission layer thickness will increasethe quantum efficiency at 1.06 �m.

In the case of different electron diffusion length, the integralsensitivity curve of the transmission-mode InGaAs photocathodewith the change of active layer thickness as shown in Fig. 6. We setthe window layer to be 0.2 �m, the electron escape probability tobe 0.32, the back interface recombination velocity to be 107 cm s−1.It can seen that the optimal value of thickness increases with theincreasing of the diffusion length, but the influence of thicknesson the integral sensitivity is weak in the condition of large diffu-sion length. When the emission layer thickness is small enough(<0.5 �m), the incident light cannot be fully absorbed which resultsa low integral sensitivity. When the emission layer thickness is toolarge (>1.7 �m), high-energy photoelectron cannot diffuse into thesurface which also led to the decreasing of the integral sensitivity.

According to the results mentioned above, the integral sensitivityis 570 �A lm−1 when the active layer thickness is 1.2 �m and theelectron diffusion length is 1.9 �m.

400 600 80 0 10 00 120 010-4

10-3

10-2

10-1

100

Qua

ntum

Eff

icie

ncy

(%)

Te=0.5μmTe=0.7μmTe=1.0μm

Wavelength (nm)

Fig. 5. The influence of active layer thickness on the quantum efficiency for InGaAsphotocathode.

2398 M. Jin et al. / Optik 125 (2014) 2395–2399

Table 2The fitting results of quantum efficiency for transmission-mode InGaAs photocathode.

The thickness ofactive layer/�m

The thickness ofwindow layer/�m

The component ofwindow layer

Electron escapeprobability

Electron diffusionlength/�m

Back interfacerecombination

−1

0.7–0.9 0.1–0.3 0.5–0.63

0 1 2 3 4 50

100

200

300

400

500

600

Thickness (μm)

Ld=1.2μmLd=1.9μmLd=3.0μm

Inte

gral

Sen

sitiv

ity (μ

A/lm

)

Ft

efwteebsittsfmttfwbi

Ft

ig. 6. The transmission-mode InGaAs photocathode integral sensitivity curve withhe change of active layer thickness.

The back interface recombination velocity has an impact on thentire absorption band for photocathode. When the back inter-ace recombination velocity is large, the electrons generated inindow layer will be recombined totally at the back interface of

he transmission-mode InGaAs photocathode, so the amount oflectrons generating in the active layer would decrease. Thus, it’sssential for transmission-mode photocathode to have a favorableack interface recombination velocity. We calculated the integralensitivity with the change of back interface recombination veloc-ty for different electron diffusion length as shown in Fig. 7 whenhe window layer is 0.2 �m, the active layer is 0.7 �m, the elec-ron escape probability is 0.32. It can be seen that, the integralensitivity is almost a maximum constant when the back inter-ace recombination velocity under 105 cm s−1. It is going to be a

inimum constant after a rapid decay of back interface recombina-ion velocity between 105 and 107 cm s−1. It is not difficult to findhat the integral sensitivity is 560 �A lm−1 when the back inter-ace recombination velocity is 107 cm s−1, which is in accordance

ith the results mentioned above. Meanwhile it proves that the

ack interface recombination velocity is a key factor leading to lowntegral sensitivity for transmission-mode InGaAs photocathode.

100

105

1010400

600

800

1000

1200

1400

Back Interface Recombination Velocity (cm/s)

Ld=1.2μmLd=1.9μmLd=3.0μm

Inte

gral

Sen

sitiv

ity (μ

A/lm

)

ig. 7. The transmission-mode InGaAs photocathode integral sensitivity curve withhe change of back interface recombination velocity.

velocity/cm s

0.32 1.9 107

The interface characteristics are mainly affected by the dopingconcentration. Low hole concentration at interface will increase theback interface recombination velocity. Higher carbon concentra-tion at the interface will cause the radiation electron trap increaseduring the growth of InGaAs, which affecting the back interfacerecombination velocity [15]. On the other hand, the InGaAs is lat-tice mismatched to GaAlAs. When the In mole value x ≥ 0.1, thematched critical thickness is 200 A far less than the thickness ofactive layer. Caused by the lattice mismatch, defects will affect theelectron diffusion length [5] and the back interface recombinationvelocity, which need to further study.

5. Conclusion

In this paper, the quantum efficiency curve of transmission-mode InGaAs photocathode was fitted by using the multilayeroptical thin film theory and the first principle calculation. A seriesof structural parameters were obtained with the relative erroris 2.9% at last. The Al composition is 0.63, the surface escapeprobability is 0.32, the electron diffusion length is 1.9 �m, theback interface recombination velocity is 107 cm s−1 which vali-date the first principle calculation is reasonable. In addition, theinfluence of active layer thickness on the quantum efficiency ofInGaAs photocathode had been simulated combining with the fit-ting results, the long-wave response would be enhanced and theintegral sensitivity would be the highest when the emission layerthickness was a reasonable value. Most of all, the back interfacerecombination velocity is a key factor leading to low integral sensi-tivity for transmission-mode InGaAs photocathode. How to reducethe back interface recombination velocity is an important way toimprove the integral sensitivity of InGaAs photocathode in futurework.

Acknowledgment

This work is financed by the National Nature Science Foundationof China (Grant No. 60871012).

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