Infrared Physics & Technology 45 (2004) 181–189

www.elsevier.com/locate/infrared

Calculation of the R0A product in nþ–n–p and pþ–p–nGaInAsSb infrared detectors

Tian Yuan a,1, Soo-Jin Chua a,b,*, Yixin Jin c

a Department of Electrical and Computer Engineering, Center for Optoelectronics, National University of Singapore,

Singapore 119260, Singaporeb Institute of Materials Research and Engineering, National University of Singapore, Singapore 119260, Singapore

c Changchun Institute of Physics, Chinese Academy of Sciences, Changchun 130021, PR China

Received 29 April 2002

Abstract

In this paper, the zero-bias resistance areas product R0A is calculated in the nþ–n–p and pþ–p–n Ga0:8In0:2As0:81Sb0:19infrared detectors, on the base of the material parameters in the three layers. The calculated results show that pa-

rameters in the heavily doped layer in the different structures have different influences on R0A. Moreover, R0A in the nþ–n–p structure is higher than that in the pþ–p–n structure because the higher carrier concentration in the nþ-region for

the nþ–n–p structure improves R0A whereas the one in the pþ-region for the pþ–p–n structure reduces R0A.� 2003 Elsevier Ltd. All rights reserved.

Keywords: R0A; Photodetectors; GaxIn1�xAs1�ySby; Parameters

1. Introduction

In recent years, the quaternary alloys GaIn-

AsSb lattice matched to GaSb substrates have

been increasing interest in infrared (IR) optoelec-tronic devices for spectral range 2–5 lm [1]. Such

devices have many important applications, in-

cluding gas spectroscopy analysis, remote sensing

* Corresponding author. Address: Department of Electrical

and Computer Engineering, Center for Optoelectronics, Na-

tional University of Singapore, Singapore 119260, Singapore.

Tel.: +65-68744784; fax: +65-67797454.

E-mail address: elecsj@nus.edu.sg (S.-J. Chua).1 Current address: Microelectronic Centre, School of Electri-

cal and Electronic Engineering, Nanyang Technological Uni-

versity, 639798 Singapore.

1350-4495/$ - see front matter � 2003 Elsevier Ltd. All rights reserv

doi:10.1016/j.infrared.2003.09.003

of gas pollutants, light–wave communication sys-

tem using fluoride glass fibers, as well as a number

of medical applications. GaInAsSb alloys have

already shown their capabilities to achieve efficient

lasers [2] and detectors [3–5]. One of the importantfigures of merit in the detectors is the zero-bias

resistance areas product R0A because the value ofR0A directly affects the detector performance ex-pressed by the detectivity D�. Lin et al. [6] reported

the experimental results of R0A less than 100 X cm2

in GaInAsSb detector. However, very little infor-

mation can be provided from literature about the

theoretical analysis of R0A for these material de-tectors.

In this paper, the zero-bias resistance areas

product R0A is calculated based on the differentdevice structures (nþ–n–p and pþ–p–n) and the

ed.

182 T. Yuan et al. / Infrared Physics & Technology 45 (2004) 181–189

related material parameters. The results show:

which is the optimal structure out of the two

structures and what are junction depths and car-

rier concentrations that would maximize R0A. Thetwo different structures are quantitatively com-

pared and R0A is checked by the influence of thecarrier concentrations and the junction depths in

the three layers of each structure, as well as the

surface recombination velocities on the two sur-

faces for each structure. Furthermore, on the basis

of the theoretical calculation, some optimum

conditions are proposed to maximize R0A for de-tectors. These results are important for the fabri-

cation of detectors.

2. Device structure and theoretical model

We consider the structures of nþ–n–p and

pþ–p–n Ga0:8In0:2As0:81Sb0:19 detectors shown in

Fig. 1, in which the lattice of Ga0:8In0:2As0:81Sb0:19alloys is matched to GaSb [7]. In the p–n junction,four kinds of noise mechanism: Auger, Radia-

tive, Generation–recombination (G–R) and tun-

neling, are considered and expressed by R0A. Thesecontributions to R0A all add in parallel and theexpressions are given in the previous paper [8]. In

isotype nþ–n and pþ–p junctions, the basic as-

sumptions are made as follows:

(1) The nþ- or pþ-region is heavily doped such that

the depletion region for the nþ–n or pþ–p

dttn +

(a)

rpS

reSe

rnn Snn

rpn+

SpWpWn

W npWnn

pnn+

Fig. 1. The two structures fo

junction exists in the low-doped region [9].

They are shown in Fig. 1. G-R noise in the

nþ–n (or pþ–p) depletion region is considered.

(2) The effective interface recombination velocities

Spp and Snn located at the pþ–p and nþ–n junc-tions are introduced. They are derived to take

into account the minority-carrier behavior in

the heavily doped pþ- and nþ-layers [10,11].

(3) Compared to the major carrier concentration

in the heavily doped layer, the minority-carrier

concentration is very low; additionally the

minority-carrier diffusion mechanism is deter-

mined by the interface recombination velocity.Therefore, Auger and radiative noise mecha-

nisms in the heavily doped regions are ne-

glected.

(4) The tunneling mechanism across nþ–n and

pþ–p junctions is neglected.

The interface recombination velocities Spp andSnn are valid for the arbitrary pþ–p and nþ–n high-low junctions [11]:

Spp ¼pDepþpþLepþ

repþ coshdpþLepþ

� �þ sinh dpþ

Lepþ

� �

repþ sinhdpþLepþ

� �þ cosh dpþ

Lepþ

� � ð1Þ

Snn ¼nDpnþnþLpnþ

rpnþ coshtnþLpnþ

� �þ sinh tnþ

Lpnþ

� �

rpnþ sinhtnþLpnþ

� �þ cosh tnþ

Lpnþ

� � ð2Þ

where D ¼ KTl=q, L ¼ ðDsÞ1=2, r ¼ SL=D.

dp+dt

(b)

Wn

re p+

Se

rpp Spp

pWp

Wnp Wpp

p+n p

r a GaInAsSb detector.

T. Yuan et al. / Infrared Physics & Technology 45 (2004) 181–189 183

3. Calculated results and discussion

The calculations have been performed on the

nþ–n–p and pþ–p–n Ga0:8In0:2As0:19Sb0:81 infrared

detectors operated at 300 K. The basic parametersare shown in Table 1 and the related parameters

have been evaluated in the same way as in the

previous papers [7,8]. For practical calculation, the

r and Nf in the p–n and pþ–p (or nþ–n) junc-tions are assumed to be the same. Parameters

Table 1

Basic parameters for the nþ–n–p and pþ–p–n structures

Basic parameters T ¼ 300 K, x ¼ 0:8, Nf ¼ 1014 cm�3

nþ–n–p structure

nþ-region n-region p-

Carrier concentration (cm�3) 5· 1018 1018 10

Width (lm) 0.5 2 5

Mobility (cm2/V s) 1000 1000 24

Surface recombination

velocity (m/s)

0 0

Nf and r are respectively the trap density and capture cross-section in

1013 1014 1015 1016 1017 1018100

101

102

103

104

(R0A)Auger

(R0A)rad

(R0A)GRnp

(R0A)GRpp

(R0A)total

p+ =n=1018 cm-3

Nf σ s =0.1cm-1

N f σs =0.01cm- 1

R0A

(ohm

-cm

2 )

p(cm- 3 )(a) (

Fig. 2. The dependence of ðR0AÞtotal and its components on: (a) thecentration for the pþ–p–n structure.

except for mobilities, such as carrier concentra-

tions, widths, surface recombination velocities,

have been calculated to show how these parame-

ters affect R0A.

3.1. R0A in the pþ–p–n structure

Fig. 2 shows R0A and its components in the pþ–p–n structure as functions of p- and n-side carrier

concentrations, with other parameters in Table 1

, rs ¼ 10�15 cm2

pþ–p–n structure

region pþ-region p-region n-region

17 1018 1017 1018

0.5 5 2

0 240 240 1000

0 0

the depletion region.

1015 1016 1017 1018 1019101

102

103

(R 0A)Auger

(R 0A)rad

(R 0A)GRnp

(R 0A)GRpp

(R 0A)total

p+ =1018 cm- 3 p=1017 cm-3

R0A

(ohm

-cm

2 )

n(cm- 3 )b)

p-side carrier concentration (p) and (b) the n-side carrier con-

184 T. Yuan et al. / Infrared Physics & Technology 45 (2004) 181–189

keeping constants. Moreover, ðR0AÞGRpp , ðR0AÞGRnpand ðR0AÞtotal with Nf ¼ 1013 cm�3 and r ¼10�15 cm2 are also plotted in Fig. 2(a). In Fig. 2(a),

all of R0A components contribute to ðR0AÞtotal inNf ¼ 1014 cm�3 and r ¼ 10�15 cm2, especially in

p > 1016 cm�3. In the range of p < 1016 cm�3,ðR0AÞtotal is mainly determined by the G-R noise inthe p–n junction, while other noise components

have a little contribution. Because of ðR0AÞGR /1=rNf [8], ðR0AÞGR and ðR0AÞtotal are increased if rand Nf are reduced, which is similar to that in then–p GaInAsSb detector [8]. In Fig. 2(a), the

maximum value of ðR0AÞtotal are obtained at p ¼1017 cm�3. Based on this condition, Fig. 2(b) showsthe dependence of ðR0AÞtotal and its components onthe n-side carrier concentration. ðR0AÞtotal dependson all the components in n > 1016 cm�3; in n <1016 cm�3, ðR0AÞtotal is mainly limited by ðR0AÞGRnp.With increasing n, ðR0AÞtotal rises up and keeps aconstant in n > 1018 cm�3. No tunneling mecha-

nism appears in Fig. 2 because the direct tunneling

mechanism needs a necessary factor that bothn- and p-type semiconductor materials must be

degenerate. For the Ga0:8In0:2As0:19Sb0:81 alloy,

the degeneracy state is in p > 1018 cm�3 and n >1016 cm�3.

Fig. 3 shows the dependence of ðR0AÞtotal on thep-side carrier concentration with the pþ-side car-

rier concentration (pþ), width (dpþ) and surfacerecombination velocity (Se) as parameters, underthe condition of other parameters in Table 1

keeping constants. ðR0AÞtotal is obviously reducedwith increasing pþ, dpþ and Se. The pþ-side pa-rameters affect ðR0AÞAuger and ðR0AÞrad in the p-sidethrough Spp and ðR0AÞtotal. With increasing the p-side carrier concentration, the maximum value of

ðR0AÞtotal is obtained at p ¼ 1017 cm�3, therefore

the carrier concentration in the pþ-side should behigher than 1017 cm�3. In the p–n homojunction

structure, ðR0AÞtotal, associated with the Auger andradiative mechanisms [8], is strongly reduced by

the p-side surface recombination velocity, In the

triple-layer structure, it is hoped that the interface

recombination velocity can be reduced with a

heavily doped layer. In Fig. 3(c), although

ðR0AÞtotal markedly decreases in the range ofSe > 104 m/s, with the increasing of Se from 0 to

102 m/s, ðR0AÞtotal almost does not change. This

indicates that the Spp is limited by the parametersin the heavily doped layer more or less. In addi-

tion, ðR0AÞtotal in Fig. 3(a) strongly decreases atpþ ¼ 1021 cm�3 and in p > 1018 cm�3 because the

tunneling mechanism appears in this part.

Fig. 4 shows ðR0AÞtotal with the change of thep-side width (d). ðR0AÞtotal decreases with the thickerwidth in the p-side only in the range of p > 1016

cm�3. This result is caused by Auger and radiative

noise mechanisms because only both of them are

related with p-side width [12]. As shown in Fig. 2,

these two noise mechanisms affect ðR0AÞtotal in therange of p > 1016 cm�3. Fig. 5 shows the depen-

dence of ðR0AÞtotal on the n-side carrier con-centration with the n-side width (t) and surfacerecombination velocity (Sp) as parameters. Al-though ðR0AÞtotal has a little decreasing with in-creasing t and Sp, its optimum value is not affectedby these two parameters in n > 1018 cm�3. There-

fore, if the n-side carrier concentration is higher

than 1018 cm�3, the influence of these two para-

meters in the n-side on ðR0AÞtotal can be neglected.This result is advantageous of the device fabrica-

tion because the limitation of these two parameters

is canceled.

3.2. R0A in the nþ–n–p structure

Fig. 6 shows ðR0AÞtotal and its components in thenþ–n–p structure as functions of p- and n-sidecarrier concentrations with other parameters in

Table 1 keeping constants. Moreover ðR0AÞGRnnand ðR0AÞtotal with the different nþ are also plottedin Fig. 6(b). The different ðR0AÞGRnn and ðR0AÞtotalare marked as the number 1, 2 and 3. In Fig. 6(a),

in the range of 1016 cm�3 < p < 1018 cm�3,

ðR0AÞtotal is dominated by all components and itsmaximum value is obtained. In p < 1016 cm�3,ðR0AÞGRnp controls ðR0AÞtotal, while in p > 1018

cm�3, ðR0AÞtunnel controls ðR0AÞtotal and the tun-neling mechanism strongly reduces ðR0AÞtotal. InFig. 6(b), with the change of n, all of the R0Acomponents contribute to ðR0AÞtotal. The tunnelingmechanism does not appear because the the p-side

material is in the nondegeneracy state with p lessthan 1017 cm�3. With the change of nþ, ðR0AÞAugerand ðR0AÞrad should be changed through Snn, butthese two mechanisms do not. With increasing nþ,

1013 1014 1015 1016 1017 1018 1019

1

10

100 n=1018 cm-3

p+ =1018 cm-3

1019

1021R0A

(ohm

-cm

2 )

p(cm-3)(a)1013 1014 1015 1016 1017 10180

20

40

60

80

100

120

140 p+ =n=1018 cm-3

dp+ =0.5 µm

1 5

R0A

(ohm

-cm

2 )

p(cm-3)(b)

1013 1014 1015 1016 1017 101810- 3

10- 2

10- 1

100

101

102

103

102

Se=0(m/s)

108

104

p+ =n=1018 cm-3

R0A

(ohm

-cm

2 )

p(cm-3)(c)

Fig. 3. The dependence of ðR0AÞtotal on the p-side carrier concentration with the pþ-side: (a) carrier concentration (pþ), (b) width (dpþ )and (c) surface recombination velocity (Se) as parameters for the pþ–p–n structure.

T. Yuan et al. / Infrared Physics & Technology 45 (2004) 181–189 185

the peak of ðR0AÞtotal rises and shifts to the high nbecause the peak of ðR0AÞGRnn changes in that way.That is, the high nþ-side carrier concentration is

conducive to improve ðR0AÞtotal. With the variety

of Sp and tnþ , ðR0AÞtotal never changes and theirinfluence on ðR0AÞtotal will be neglected. The in-fluence of the parameters in the nþ-side for the nþ–

n–p structure is completely opposite to that of the

1013 1014 1015 1016 10170

20

40

60

80

100

120

140 p+=n=1018cm-3

d=5µm

8

10

R0A

(ohm

-cm

2 )

p(cm- 3 )

Fig. 4. The dependence of ðR0AÞtotal on the p-side carrier con-centration with the p-side width (d) as a parameter for the pþ–p–n structure.

1015 1016 1017 101820

40

60

80

100

120

140

160p+=1018cm-3 p=1017cm-3

t=0.5µm 5

R0A

(ohm

-cm

2 )

n(cm-3)(a)

Fig. 5. The dependence of ðR0AÞtotal on the n-side carrier concentrativelocity (Sp) as parameters for the pþ–p–n structure.

186 T. Yuan et al. / Infrared Physics & Technology 45 (2004) 181–189

parameters in the pþ-side for the pþ–p–n structure.

We will discuss later. Because the influence of the

n-side width on ðR0AÞtotal in the nþ–n–p structure issimilar to that in the pþ–p–n structure, it is ne-

glected here.

Fig. 7 shows the influence of the p-side pa-rameters (Se and d) on ðR0AÞtotal for the nþ–n–pstructure. The parameters Se and d are only relatedwith Auger and radiative mechanisms. The high Seand d reduce ðR0AÞAuger and ðR0AÞrad [12], thereforeðR0AÞtotal decreases. Moreover, the peak of

ðR0AÞtotal shifts to the high p in Fig. 7(a), on thecontrary to the low p in Fig. 7(b). Compare Fig.7(a) with Fig. 3(c), except that ðR0AÞtotal in the nþ–n–p structure is a little higher than that in the pþ–

p–n structure at Se ¼ 0, ðR0AÞtotal in the pþ–p–nstructure is obviously higher than that in the nþ–

n–p structure. Therefore, it is useful to add a

heavily doped layer on the p-side surface for

weakening the influence of the surface recombi-

nation on ðR0AÞtotal.

p+=1018cm-3 p=1017cm-3

1015 1016 1017 10180

20

40

60

80

100

120

140

160

Sp=0(m/s)

102

R0A

(ohm

-cm

2 )

n(cm-3)(b)

on with the n-side: (a) width (t) and (b) surface recombination

1014 1015 1016 1017 1018 1019 102010-2

10-1

100

101

102

103

104

105

n+=5 X1018cm-3 n=1018 cm-3

(R 0 A)Auger

(R 0 A)rad

(R 0 A)GRnp

(R 0 A)GRnn

(R 0 A)tunnel

(R 0 A)total

R0A

(ohm

-cm

2 )

R0A

(ohm

-cm

2 )

p(cm-3)(a)1015 1016 1017 1018 1019

101

102

103

3

2

1

1 n+ =1018cm-3

2 5X1018

3 1019

p=1017cm-3 3

2

1

(R 0 A)Auger

(R 0 A) Rad (R 0 A)

GRnp

(R 0 A) GRnn (R 0 A) total

n(cm-3)(b)

Fig. 6. The dependence of ðR0AÞtotal and its components on: (a) the p-side carrier concentration (p) and (b) the n-side carrier con-centration (n) for the nþ–n–p structure as well as ðR0AÞGRnn with the variety of the nþ-side carrier concentration (nþ).

1014 1015 1016 1017 1018 1019 102010-4

10-3

10-2

10-1

100

101

102

103

108

104

102

Se=0(m/s)

n+=5X1018cm-3 n=1018cm-3

R0A

(ohm

-cm

2 )

p(cm-3)(a)1014 1015 1016 1017 1018 1019 102010-2

10-1

100

101

102

103 n+=5X1018cm-3 n=1018cm-3

d=2µm

5

10

R0A

(ohm

-cm

2 )

p(cm-3)(b)

Fig. 7. The dependence of ðR0AÞtotal on the p-side carrier concentration with the p-side: (a) surface recombination velocity (Se) and(b) width (d) as parameters for the nþ–n–p structure.

T. Yuan et al. / Infrared Physics & Technology 45 (2004) 181–189 187

10-1 100 101 102 103 104 105 106 107 108101

102

103

104

105

Snn

Spp

Spp(

or S

nn) (

m/s

)Se(or Sp)(m/s)

Fig. 8. The dependence of the interface recombination veloci-

ties Spp and Snn on the Se and Sp for the pþ–p–n and nþ–n–pstructures respectively.

188 T. Yuan et al. / Infrared Physics & Technology 45 (2004) 181–189

4. Discussion

Now we discuss why the opposite results are

shown in Figs. 3(a) and 6(b), and why Sp and tnþhave not any influence on ðR0AÞtotal in the nþ–n–pstructure. At nþ ¼ 5� 1018 cm�3, Lhnþ is to be

0.0136 lm, and it will continue decreasing with theincreasing of nþ, which can be considered as

Lhnþ tnþ . Therefore Snn in Eq. (2) can be ap-proximated by Snn ¼ nLhnþ

nþsnþwhich is not related to Sp

and tnþ in the nþ–n–p structure (snþ is the minor-ity-carrier lifetime in the nþ-side). Thus, Sp and tnþcould not change ðR0AÞAuger and ðR0AÞrad throughSnn and thereby ðR0AÞtotal could not be affected forthe nþ–n–p structure. In addition, based on Ref.

[8], it can be calculated that snþ is determined bys1Auger in the n-type material [13,14], so that Snn is

further approximated by Snn / n

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ n2i

ðnþÞ2

r. In the

range of nþ > 1018 cm�3, there exists nþ ni andSnn / n. This result shows that nþ almost does notaffect Snn, and thereby not affect ðR0AÞAuger andðR0AÞrad in the nþ–n–p structure. However withincreasing the nþ-side carrier concentration,

ðR0AÞGR and ðR0AÞtotal are increased in Fig. 6(b).On the contrary, in the pþ–p–n structure, Lepþ isequal to 31.2 lm at pþ ¼ 1018 cm�3 and to 0.032

lm at pþ ¼ 1021 cm�3. This shows that with in-

creasing pþ, the variety of the relationship between

Lepþ and dpþ is changed from Lepþ dpþ to Lepþ dpþ . Therefore, in the pþ–p–n structure, the influ-ence of each parameter in the pþ-side on ðR0AÞAugerand ðR0AÞrad associated with Spp could not be ne-glected, and correspondingly, ðR0AÞtotal is changedby the variety of the parameters in the pþ-side.

Fig. 8 shows the variety of Spp and Snn with Seand Sp respectively. As above discussions, Snn isnot affected by Sp, which shows a horizontal line inFig. 8. However Spp increases in 10 < Se < 107 m/s.The two limiting values of the surface recombi-

nation velocity are S ¼ 0 and S ¼ 1. The formerimplies an ideal ohmic contact whereas the latter

means an ideal majority-carrier contact. In prac-

tice, the contact at the pþ-region surface of a

pþ–p–n structure is a nonideal majority-carrier

contact and is found to have a value of Se that isfinite and greater than zero. In Fig. 8, although Spp

has a high value (>10 m/s) in Se < 10 m/s, Spp isobviously lower than Se in Se > 10 m/s. This resultdemonstrates that adding a layer will effectivelyreduce the influence of the surface recombination

on GaInAsSb photodetectors. In Ref. [6], the au-

thors have mentioned that the surface leakage

current is an important factor to influence R0A,which increases as the surface recombination is

suppressed. Basing on our simulation results, we

provide a suitable structure to limit the surface

recombination. In addition, utilizing the high-lowjunction can minimize minority-carrier recombi-

nation losses [15]. Therefore the detectors proper-

ties are improved for triple-layer structures.

5. Conclusion

In this paper, four kinds of noise mechanismsare considered for R0A in the nþ–n–p and pþ–p–nGa0:8In0:2As0:81Sb0:19 infrared photodetectors.

ðR0AÞtotal with these noise mechanisms are calcu-lated based on the material parameters in the three

T. Yuan et al. / Infrared Physics & Technology 45 (2004) 181–189 189

layers. The main conclusions can be drawn from

the above study as follows:

(1) In the pþ–p–n structure, the parameters in the

pþ-side affect ðR0AÞAuger and ðR0AÞrad throughSpp and hence ðR0AÞtotal. The high ðR0AÞtotal isobtained with the low carrier concentration

and the surface recombination velocity as well

as the thin width in the pþ-side. In addition,

the thick width in the p-side reduces

ðR0AÞtotal. However, although ðR0AÞtotal has alittle decreasing with the thick width and the

high surface recombination velocity in the

n-side, the optimum value of ðR0AÞtotal couldnot be affected by these two parameters in

the n-side carrier concentration higher than

1018 cm�3.

(2) In the nþ–n–p structure, the nþ-side carrier

concentration is required to be as high as pos-

sible in order to obtain the high ðR0AÞtotal andat the same time, the carrier concentration in

the n-side should be increased, while the widthand the surface recombination in the nþ-side

and n-side almost do not influence ðR0AÞtotal.In addition, the low surface recombination

velocity and the thin width in the p-side is

required to obtain the high ðR0AÞtotal.(3) Compared the influence of the surface recom-

bination velocity in the pþ-side in the pþ–p–n

structure with that in the p-side in the nþ–n–p structure on ðR0AÞtotal, it is found that, exceptthat ðR0AÞtotal in the nþ–n–p structure is a littlehigher than that in the pþ–p–n structure at

Se ¼ 0, ðR0AÞtotal in the pþ–p–n structure is ob-viously higher than that in the nþ–n–p struc-

ture. This result indicates that it is useful to

add a heavily doped layer on the p-side surface

for weakening the influence of the surface re-

combination on ðR0AÞtotal.

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