The simulation and optimization of the internal quantum efficiency of GaSb thermophotovoltaic cells with a box-shaped Zn diffusion profile

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The simulation and optimization of the internal quantum efficiency ofGaSb thermophotovoltaic cells with a box-shaped Zn diffusion profile

Hong Ye n, Yue Shu, Liangliang TangDepartment of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230027, PR China

a r t i c l e i n f o

Article history:Received 12 December 2013Received in revised form1 March 2014Accepted 6 March 2014Available online 3 April 2014

Keywords:GaSb thermophotovoltaic cellBox-shaped Zn diffusion profileInternal quantum efficiency

a b s t r a c t

Based on a GaSb thermophotovoltaic (TPV) cell with a box-shaped Zn diffusion profile, a theoreticalmodel of the generation and drift of the photogenerated minority carriers in the cell was established,and the internal quantum efficiency (IQE) of the cell was predicted with the classical semiconductortheory. The calculated results agreed well with the measurements. It is determined that reducing thefront surface recombination velocity (Sn) could improve the IQE of the emitter region, whereasincreasing the lifetime of holes (τh) could improve the IQE of the base region. The Zn diffusion durationhas a large influence on the IQE at short wavelengths below 1200 nm. Compared with the IQE for the 5 hdiffusion time, the IQE of the 2 h counterpart was improved dramatically. Front surface etching couldincrease the IQE at short wavelengths below 700 nm while there was a decrease in the IQE forwavelengths above 700 nm. Thus, front surface etching is not necessary for a cell with a box-shaped Zndiffusion profile because the IQE for the near infrared wavelengths are the most important. Thecalculated results were elucidated by analyzing the distribution of the minority carriers generated in thecell and their recombination processes.

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1. Introduction

Gallium antimonide (GaSb) is a type of direct bandgap III–Vsemiconductor material. Due to the low bandgap (0.72 eV), GaSb isespecially suitable for fabricating infrared devices. Its applicationsinclude thermophotovoltaic (TPV) cells [1–3], infrared detectors[4], quantum rings [5,6] and Hall devices [7]. The fabrication ofTPV cells is a notably important application of GaSb material.Studies have shown that it is feasible to use a simple diffusionmethod to prepare the PN junction for most of the sphalerite-structured III–V semiconductor compounds [8–10].

Zn diffusion is one of the most important procedures for thepreparation of GaSb TPV cells [11–17]. Prior to the diffusion, thediffusion source and the N-GaSb substrate should be placed inthe same vessel and heated in a vacuum or inert gas environmentto create the vapor of the diffusion source, which diffuses into theN-GaSb substrate and creates a P-type layer. In this way, the PNjunction can be formed. Using different Zn diffusion sources anddiffusion methods can produce different Zn diffusion profiles[12,13]. There are two modes to realize Zn diffusion in GaSb: theclosed mode and the pseudo-closed mode. In the closed mode, an

ampoule is used to hold the sample and the diffusion sourcematerial. When Zn–Ga alloy pellets are used as the diffusionsource and the diffusion temperature is maintained at approxi-mately 500 1C, a box-shaped Zn diffusion profile is obtained [14].When using the pseudo-closed mode, a graphite box is generallyused to hold the samples, and a kink-and-tail-shaped Zn diffusionprofile can be formed. Over the past decade, several kink-and-tail-shaped Zn diffusion profiles have been obtained from several typesof diffusion sources at different temperatures [14–16].

Compared with the box-shaped Zn diffusion profile, the kink-and-tail profile has a high Zn concentration diffusion front formed by thedissociative mechanism. However, the tail portion of the kink-and-tail profile nearly coincides with the box profile because both of themare formed by the kick-out mechanism [14]. Rajagopalan et al.performed front surface etching on GaSb wafers having kink-and-tail shaped Zn diffusion profiles. The depth of the front surfaceetching was approximately 0.4 μm, nearly equal to the depth of thekink point in the kink-and-tail profile. They fabricated GaSb TPV cellsfrom the etched wafers, and the cells showed good performance [18].Fraas et al. etched the PN junctions of the kink-and-tail-shaped GaSbwafers from 0.5 to 0.1 μm and fabricated excellent GaSb TPV cellswith an external quantum efficiency (EQE) up to 80% in thewavelength range from 1 to 1.6 μm [19]. Subsequently, Fraas et al.developed a double-diffusion process using a Zn–Ga diffusion sourceto make excellent GaSb TPV cells while avoiding the etch back

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n Corresponding author.E-mail address: [email protected] (H. Ye).

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requirement [20]. From these, it can be speculated that GaSb wafershaving a box-shaped Zn diffusion profile can also be used to fabricateTPV cells of considerable efficiency.

Martin et al. calculated the internal quantum efficiency (IQE) of aGaSb TPV cell with a kink-and-tail-shaped Zn diffusion profile [21,22].However, the box-shaped counterpart has not yet been systematicallystudied. In this work, the IQE of a GaSb TPV cell with a box-shaped Zndiffusion profile was calculated, and the results were fit to themeasured data by adjusting the front surface recombination velocityand the hole lifetime. The effects of these two parameters on the IQEof the cell were also discussed. In addition, the effects of the diffusionduration and front surface etching depth on the results wereinvestigated, and the results were clearly explained by an analysisof the transformation of photons to carriers.

2. Calculation model

The structure of a TPV cell can be divided into three parts: theemitter region (ER), the depletion region (DR) and the base region(BR), as shown in Fig. 1. The ER is a P-type semiconductor, whichreceives the photon irradiation, and its width is WER. The BR is anN-type semiconductor whose width is WBR. The DR is the PNjunction of the semiconductor with a width of WDR. The directionof the built-in electrostatic field in this region is opposite to thedirection of the potential difference outside the cell.

Before calculating the IQE of the cell, the boundaries of eachregion should be determined. Thus the potential difference of thebuilt-in electrostatic field VD should first be determined. Accordingto the classical semiconductor theory, VD can be expressed as [23]

VD ¼ kTq

lnNDNA

n2i

ð1Þ

In Eq. (1), k¼ 1:38� 10�23 J=K is the Boltzmann constant; T isthe absolute temperature; q is the electron charge; ni is theintrinsic carrier concentration, which represents the concentrationof the intrinsic excited electrons or holes and is independent of thedoping level ( for GaSb, ni ¼ 1:4� 1012 cm�3 when T¼300 K[22]); and ND and NA are the concentrations of the donor andacceptor ions, i.e., the doping density of Te and Zn, respectively.

The position of the DR can be obtained by solving the Poissonequation, which can be written as [24]

d2V1ðxÞdx2 ¼ qNA

εsðxERoxoxADÞ

d2V2ðxÞdx2 ¼ �qND

εsðxADoxoxDRÞ

9>=>; ð2Þ

In Eq. (2), xAD is the depth of the PN junction, which separatesthe positive and negative charges in the DR, as shown in Fig. 1. xER

and xDR are the left and right boundaries of the DR, respectively.V1ðxÞ and V2ðxÞ are the electric potentials of the P-type portion andthe N-type portion of the DR, respectively. εs represents theabsolute permittivity of the material, which can be calculated asεs ¼ εrε0, where ε0 ¼ 8:854� 10�12 F=m is the permittivity ofvacuum, and εr is the positive permittivity of the material (forGaSb, εr ¼ 15:69).

To solve Eq. (2), the following boundary conditions are neces-sary:

EðxERÞ ¼ �dV1ðxÞdx jx ¼ xER ¼ 0

EðxDRÞ ¼ �dV2ðxÞdx jx ¼ xDR ¼ 0

9=; ð3Þ

V1ðxERÞ ¼ 0V2ðxDRÞ ¼ VD

V1ðxADÞ ¼ V2ðxADÞ

9>=>; ð4Þ

Z xAD

xERNAdx¼

Z xDR

xADNDdx ð5Þ

Eq. (3) represents the zero electric field intensity at theboundaries of the DR. Eq. (4) means that the range of the electricpotential in the DR is from 0 to VD, and the potential is continuousat xAD. Eq. (5) denotes that the sum of negative charges in theP-type region of the DR is equal to the positive counterpart in theN-type region, as shown in the inset in Fig. 1. Combined withthe above boundary conditions, Eq. (2) can be solved, and thevalues of xER and xDR can be obtained. Thus, the boundarypositions of each region can be determined.

The total IQE of the cell is composed of three parts [21,22,25]:

QEðλÞ ¼ QEERðλÞþQEDRðλÞþQEBRðλÞ ð6ÞIn Eq. (6), QEERðλÞ, QEDRðλÞ, andQEBRðλÞ represent the IQEs of

the ER, DR and BR, respectively. The calculation methods for thethree regions will be introduced successively below.

Due to the non-constant diffused Zn concentration, the ER ischaracterized by the presence of a position-dependent built-inelectrostatic field EEðxÞ. It can be calculated as the sum of twocomponents, one due to the doping profile gradient and the otherbased on the semiconductor's position-dependent bandgap

EEðxÞ ¼1q

kTNAðxÞ

dNAðxÞdx

þdEgðxÞdx

� �ð7Þ

In Eq. (7), NAðxÞ represents the diffused concentration of Zn,EgðxÞ is the bandgap of GaSb changing with NAðxÞ. dEgðxÞ=dxrepresents the narrowing of the electrical bandgap in P-GaSb, asdescribed in [22]

dEgðxÞ=dx¼ 1� 10�8 N1=3A ð8Þ

W W W

ER(P-type)

DR BR(N-type)

x0 x x x x

x xx

N

N

Depth

N

o

Fig. 1. The cell model and the range of each region.

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The rate at which minority carriers are generated, G(x,λ), is afunction of the semiconductor absorption coefficient αðλÞ and theincident spectral irradiance ΦΙΝðλÞ:Gðx; λÞ ¼ΦINðλÞ αðλÞ expð�αðλÞxÞ ð9Þ

In Eq. (9), α is the absorption coefficient, and a set of data forthe absorption coefficient α is given in [22]. With this generationterm, the concentration of the photogenerated carriers generatedin this region, n(x), is calculated by solving the minority carriercontinuity equation with the quasi-equilibrium approximation[23]:

ddx

qnðxÞμeðxÞEEðxÞþkTμeðxÞdnðxÞdx

� �¼ q

nðxÞ�n0ðxÞτeðxÞ

�Gðx; λÞ� �

ð10Þ

In Eq. (10), μe represents the electron mobility in the ER. Anempirical equation is given in [22] to obtain μe from the concen-tration and temperature:

μeðND; TÞ ¼ μmin ;eþμmax ;eð300=TÞθ1;e �μmin ;e

1þðND=Nref ;eðT=300Þθ2;e Þαeð11Þ

In Eq. (11), μmin ;e ¼ 1050 cm2=V s, μmax ;e ¼ 5650 cm2=V s,Nref ;e ¼ 2:8� 1017 cm�3, αe ¼ 1:05, θ1;e ¼ 2:0, and θ2;e ¼ 2:8. Atroom temperature (T¼300 K), Eq. (11) can be simplified to

μeðND; TÞ ¼ μmin ;eþμmax ;e�μmin ;e

1þðND=Nref ;eÞαeð12Þ

In Eq. (10), τe represents the electron lifetime, which can bedescribed as [25]

1τtot;e

¼ 1τSRH;e

þ 1τAuger;e

þ 1τRadiative;e

ð13Þ

As shown in Eq. (13), three factors should be considered whencalculating τe: the Shockley–Read–Hall (SRH) recombination, theAuger recombination and the Radiative recombination. In Eq. (13),τSRH;e ¼ 10 ns, τAuger;e ¼ ðCAuger;e � N2

AÞ�1, and τRadiative;e ¼ ðBopt � NAÞ�1,with the constants: CAuger;e ¼ 5� 10�30 cm6=s, Bopt ¼ 8:5�10�11 cm3=s[22]. As shown in Fig. 2, when the doping concentra-tion is high – up to 1020 cm�3 – Auger recombination is the majorfactor in determining τe. However, when the doping concentrationis low, such as 1017 cm�3, SRH recombination is the major factorfor τe. Therefore, the total lifetime of the minority carrier willdecrease dramatically when the doping concentration increases.

In Eq. (10), n0ðxÞ represents the minority carrier density with-out illumination. The relationship between the concentrations ofelectrons and holes in a semiconductor can be written as

np¼ n2i ð14Þ

In Eq. (14), n and p represent the concentrations of electronsand holes, respectively. Therefore, n0ðxÞ can be described as

n0ðxÞ ¼n2i

NAð15Þ

At this point, all of the parameters in Eq. (10) are known.The boundary conditions of Eq. (10) are

at the ER edge (x¼ xER)

nðxERÞ�n0ðxERÞ ¼ 0 ð16Þat the surface (x¼0)

qnð0Þμeð0ÞEEð0ÞþkTμeð0Þdnð0Þdx

� �¼ qSn½nð0Þ�n0ð0Þ� ð17Þ

In Eq. (17), Sn represents the front surface recombinationvelocity. It differs significantly among the wafers, and it is difficultto measure directly. However, the results can be fit to themeasured data to obtain its value [21,22].

Once the Zn diffusion profile is known, Eq. (10) can be solved.The IQE of the ER is computed by evaluating the minority currentdensity Jeðx; λÞ at the ER edge (x¼ xER) [21]

QEERðλÞ ¼Jeðx; λÞqΦINðλÞ

¼ ½qnðxÞμeðxÞEEðxÞþkTμeðxÞðdnðxÞ=dxÞ�jx ¼ xER

qΦINðλÞð18Þ

The DR contribution is calculated assuming that each photonabsorbed within its spatial limit generates an electron–hole paircontributing to the final photocurrent density [22]

QEDRðλÞ ¼Z WER þWDR

WER

αðλÞexpð�αðλÞxÞdx

¼ exp½�αðλÞWER�ð1�exp½�αðλÞWDR�Þ ð19ÞThe BR is characterized by a constant dopant concentration

(ND) and a width (WBR) much larger than the hole diffusion length(Lh). Thus, its IQE can be calculated with the classical expressionfrom the Hovel formulation [26]

QEBRðλÞ ¼αðλÞLh

1þαðλÞLhexp½�αðλÞðWERþWDRÞ� ð20Þ

In Eq. (20), the hole diffusion length Lh can be described as

Lh ¼ffiffiffiffiffiffiffiffiffiffiffiDhτh

pð21Þ

In Eq. (21), τh represents the lifetime of holes. As wasperformed for Sn of the ER, the calculated IQE results should befit to the measured data to obtain the value of τh. Dh represents thedrift speed of holes in the BR, and according to the Einsteinrelation

Dh ¼ ðkT=qÞμh ð22ÞIn Eq. (22), μh represents the hole mobility. An empirical

equation is given to obtain μh from the concentration andtemperature [22]

μhðNA; TÞ ¼ μmin ;hþμmax ;hð300=TÞθ1;h �μmin ;h

1þðNA=Nref ;hðT=300Þθ2;h Þαhð23Þ

In Eq. (23), μmin ;h ¼ 190 cm2=V s, μmax ;h ¼ 875 cm2=V s,Nref ;h ¼ 9� 1017 cm�3, αh ¼ 0:65, θ1;h ¼ 1:7, and θ2;h ¼ 2:7. Atroom temperature (T ¼ 300 K), Eq. (23) can be simplified to

μhðND; TÞ ¼ μmin ;hþμmax ;h�μmin ;h

1þðNA=Nref ;hÞαhð24Þ

3. Experiment verification

To fabricate GaSb cells with a box-shaped Zn diffusion profile,the closed diffusion mode should be adopted. For each diffusion,

1E17 1E18 1E19 1E2010-2

10-1

100

101

102

103 SRH

Auger

Radiative

Total

Min

ority

Car

rier L

ifetim

e /n

s

Doping Concentration /cm-3

Fig. 2. The minority carrier lifetime in the emitter region (ER) versus the dopingconcentration.

H. Ye et al. / Solar Energy Materials & Solar Cells 125 (2014) 268–275270

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an ampoule was used to hold the Zn–Ga alloy pellets and theN-GaSb wafer, and the experimental apparatus is shown in Fig. 3.The diffusion sources are Zn–Ga alloy pellets, and the N-GaSbsubstrate is doped with Te at a concentration of 4� 1017 cm�3.After preparation, the ampoule is sealed and evacuated to reach ahigh vacuum (�10�6 Torr). The furnace used for the closed Zndiffusion mode should be vertical. Thus the shape and size of theampoule should be designed according to the temperature dis-tribution of the diffusion furnace in vertical direction, to maintaina stable temperature of the N-GaSb substrate during the heatingperiod. Additionally, the proper distance between the diffusionsources and the N-GaSb substrate is approximately 4 cm. Underthe above conditions, the Zn–Ga alloy pellets were heated at500 1C for 2 h and 5 h, and two GaSb wafers with box-shaped Zndiffusion profiles were fabricated. The diffusion profiles weremeasured by a CAMECA IMS4F secondary ion mass spectrometer(SIMS). Focused Csþ primary ion beams were used to bombard thesurface of the diffused GaSb sample, and the sputtered ZnCsþ

secondary ions were collected. Thus, the concentration of Zn as a

function of depth could be obtained for each sample. The resultsare shown in Fig. 4.

The intersection point of the concentration profiles of Zn and Teis the center of the DR, i.e., xAD. xAD of the 2 h diffusion profileshown in Fig. 4 is 0:24 μm. While calculating the potentialdifference of the built-in electrostatic field, the integral averageresult of NA should be used because the Zn doping level is notuniform. Therefore, NA should be described as

NA ¼Z xAD

0NAdx=xAD ð25Þ

The P-type portion of the DR can be approximated by a lineargradient junction because the range of the DR is very smallcompared to the whole diffusion profile, as shown in the insets(a) and (b) in Fig. 4, and the N-type portion of the DR has auniform Te doping profile. Thus, the Poisson equation (Eq. (2)) canbe written as

d2V1ðxÞdx2 ¼ qNA

εs¼ qαZnðxAD � xÞþND

εsðxERoxoxADÞ

d2V2ðxÞdx2 ¼ �qND

εs ðxADoxoxDRÞ

9>=>; ð26Þ

In Eq. (26), αZn represents the gradient of the Zn concentration.In the P-type portion of DR, αZn is assumed to be constant and canbe approximated by the derivative of the Zn concentration profileat xAD. The boundary condition in Eq. (5) can be described asZ xAD

xERNAdx¼

xAD�xER2

αþND

� �ðxAD�xERÞ

¼NDðxDR�xADÞ ¼Z xDR

xADNDdx ð27Þ

Following the steps for calculation described above, the resultsof the left and right boundary positions of the DR arexER ¼ 0:22 μm and xDR ¼ 0:29 μm, respectively. For the 5 h diffu-sion profile shown in Fig. 4, xAD is 0:53 μm, and the correspondingleft and right boundary positions of DR are xER ¼ 0:50 μm andxDR ¼ 0:57 μm, respectively.

By the calculation methods introduced in Section 2, the IQEs ofthe ER, DR and BR can be obtained. The IQE of the cell with a 2 hFig. 3. A schematic diagram of the closed mode Zn diffusion experiment.

0.0 0.2 0.4 0.6 0.8 1.0 1.2

1E16

1E17

1E18

1E19

1E20

1E21 Zn (500 , 2h) Zn (500 , 5h) Te (4 1017cm-3)

Con

cent

ratio

n /c

m-3

Depth / m

0

1x10

2x10

3x10

4x10

5x10

0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29

0.50 0.52 0.54 0.56 0.580.0

5.0x10

1.0x10

1.5x10

2.0x10

xDR

xAD

xER

xDR

xAD

xER

N-typeP-type

Depletion Region

Zn Te

Con

cent

ratio

n /c

m

Zn Te

N-typeP-type

Depletion Region

Con

cent

ratio

n /c

m

Depth / m

Depth / m

Fig. 4. The box profiles obtained from 2 h and 5 h Zn diffusions. Insets (a) and (b) represent the enlargement of the depletion regions (DRs) of the 2 h and 5 h Zn diffusions,respectively.

H. Ye et al. / Solar Energy Materials & Solar Cells 125 (2014) 268–275 271

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diffusion shown in Fig. 4 is calculated first. As described above, thefront surface recombination velocity (Sn) and the hole lifetime (τh)are difficult to measure. To obtain their values, the calculatedresults need to be fit to the measured data. A second order finitedifference numerical method was used to solve the minoritycarrier continuity equation (Eq. (11)), and the values of Sn and τhobtained by fitting to the measured results are Sn ¼ 8� 105 m=sand τh ¼ 1:65 ns. The calculated IQE results are shown in Fig. 5.The calculated profile essentially coincides with the measuredcounterpart.

4. Results and discussion

The front surface recombination velocity (Sn) and the holelifetime (τh) are important parameters that should be taken intoaccount while fabricating cells. The value of Sn reflects the loss rateof the photogenerated minority carriers at the front surface of theER, and the value of τh reflects the counterpart in the BR. Both aredirectly related to the fraction of electrical energy that is trans-ferred from the photogenerated minority carriers. The effects of Snand τh on the IQE results are shown in Figs. 6 and 7, respectively.

The effect of Sn on the IQE of the cell is shown in Fig. 6. Asshown in Fig. 6(a), the effect of Sn on the IQE of the cell issignificant in the range from 1� 104 to 1� 107 m=s. The influencemainly concentrates in the short wavelength band below 800 nm.There is some influence at wavelengths from 800 to 1600 nm, andthere is little influence above 1600 nm. The IQE decreases when Sn

increases. Fig. 6(b) clearly shows that these phenomena aredirectly caused by the effect of Sn on the IQE of the ER.

The effect of τh on the IQE of the cell is shown in Fig. 7. Fig. 7(a) shows that the effect of τh on the IQE of the cell is considerablein the range from 0.01 to 100 ns [27,28]. The influence is mainlyconcentrated in the wavelength range from 800 to 1800 nm, andthe influence at wavelengths from 1200 to 1600 nm is especiallylarge. However, there is little influence at short wavelengths below800 nm. The IQE increases with τh. It is clear in Fig. 7(b) that thesephenomena are directly caused by the effect of τh on the IQE of theBR. Therefore, the conclusion can be drawn from Figs. 6 and 7 thatwe should endeavor to decrease Sn and improve τh to obtain ahigher IQE of the cell. The parameters of our cell are Sn ¼ 8�105 m=s and τh ¼ 1:65 ns, and there is still considerable room forimprovement. For Sn, a passivation treatment can be applied onthe front surface of the cell. Thus, the recombination sourceformed by surface impurities can be removed, to decrease Sn[29]. As for τh, its value is directly related to the quality of the GaSbwafer. When using GaSb wafers of poor quality to fabricate TPVcells, the performance of the cells will decrease because the latticeconstant of the wafer has an enormous effect on the SRH lifetimeof holes (τSRH;h) [28]. Therefore, high-quality GaSb wafers shouldbe chosen to fabricate TPV cells to have a high value of τh.

To investigate the effect of the diffusion duration on theperformance of the cell, the IQE of the cell was calculated withthe 5 h diffusion profile shown in Fig. 4, using the same Sn and τhfrom fits of the 2 h diffusion profile. The results are shown in Fig. 8.The comparison of the total IQEs of the cells is shown in Fig. 8(a),whereas Fig. 8(b), (c) and (d) shows the comparisons of the IQEs ofthe ER, DR and BR, respectively. As shown in Fig. 8(a), the total IQEof the cell decreases dramatically at short wavelengths below1200 nm when the diffusion duration is increased from 2 to 5 h.However, there is little influence at wavelengths above 1200 nm.When the diffusion duration increases, the IQE of the ER willdecrease at wavelengths below 800 nm, whereas it increases atwavelengths from 800 to 1800 nm (Fig. 8(b)). However, the latterincrement is offset by the reduction of the IQE of the BR in thesame wavelength range (Fig. 8(d)). Additionally, the IQE of the DRdecreases at wavelengths from 600 to 1200 nm (Fig. 8(c)). Andfinally the total IQE shows the trend of a sharp decrease at shortwavelengths. To explain the IQE phenomena of the differentdiffusion durations, the Lambert–Beer law should be introduced

� lg T ¼ kbc ð28Þ

where T is the transmittance of the incident light, k is the molarabsorption coefficient, b and c represent the depth of the

400 600 800 1000 1200 1400 1600 18000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 Measured IQE ER IQE DR IQE BR IQE Total IQE

IQE

Wavelength /nm

Fig. 5. The comparison of the calculated IQE results and the measured data.

0.0

0.2

0.4

0.6

0.8

1.0

Sn=1e3 Sn=1e4 Sn=1e5 Sn=1e6 Sn=1e7 Sn=1e8

Tota

l IQ

E

Wavelength /nm400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

0.0

0.2

0.4

0.6

0.8

1.0

Sn=1e3 Sn=1e4 Sn=1e5 Sn=1e6 Sn=1e7 Sn=1e8

ER IQ

E

Wavelength /nm

Fig. 6. The effect of Sn on the IQE of the cell. (a) The effect on the total IQE and (b) the effect on the IQE of the ER.

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absorption layer and the concentration of the light absorbingsubstance, respectively. As the doping concentration of Zn can beignored, GaSb can be regarded as the major light absorbingsubstance, which has a constant concentration. If it is assumedthat each photon absorbed can generate a minority carrier so longas its energy is larger than the bandgap of GaSb, the concentrationof the minority carriers generated will have an exponentialrelationship with depth. As shown in Fig. 9, in the ER, the minoritycarriers generated by 500 nm and 600 nm incident photonsconcentrate in the surface region (depth from 0 to 0.2 μm). As

for the 5 h Zn diffusion profile, the Zn concentration is high – up to1020 cm�3 – in this region (Fig. 4), so the lifetime of the minoritycarriers is very short, as depicted in Fig. 2. Thus, the loss of theminority carriers is remarkable, leading to a lower IQE in thiswavelength range for the ER of the cell fabricated with the 5 h Zndiffusion compared to that of the 2 h Zn diffusion counterpart.However, the distribution of the minority carriers generated by800 nm and 900 nm incident photons is nearly uniform withdepth. Thus the minority carriers generated in the ER for the 5 hZn diffusion are far more plentiful than for the 2 h counterpart,

0.0

0.2

0.4

0.6

0.8

1.0

h=0.01 ns

h=0.1 ns

h=1 ns

h=10 ns

h=100 ns

Tota

l IQ

E

Wavelength /nm400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

0.0

0.2

0.4

0.6

0.8

h=0.01 ns

h=0.1 ns

h=1 ns

h=10 ns

h=100 nsBR

IQE

Wavelength /nm

Fig. 7. The effect of τh on the IQE of the cell. (a) The effect on the total IQE and (b) the effect on the IQE of the BR.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2h

5h

Tota

l IQ

E

Wavelength /nm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2h

5h

DR

IQE

Wavelength /nm

0.0

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E

Wavelength /nm

Fig. 8. The comparison of the IQE of the cell for different diffusion durations. (a) The comparison of the total IQE of the cell, (b)–(d) the comparisons of the IQE of the ER, DRand BR, correspondingly.

H. Ye et al. / Solar Energy Materials & Solar Cells 125 (2014) 268–275 273

Author's personal copy

and the IQE will also be higher at wavelengths above 800 nm.743 nm is a critical value, at which the IQE of the ER for the 5 h Zndiffusion equals that of the 2 h counterpart. The Zn diffusionduration has little effect on the width of the DR, thus when theDR is closer to the surface, the ratio of the minority carriersgenerated by short wavelength photons in the DR will increase.Therefore, in the short wavelength range, the IQE of the DR willincrease. However, the Zn diffusion duration has little effect on theIQE of the DR in the long wavelength range because the distribu-tion of minority carriers is uniform with depth in this range. Theminority carriers generated in the BR can be regarded as arisingfrom the photons passing through the ER and the DR. With a DRcloser to the surface, the number of photons generating minoritycarriers in the BR will increase. Thus, the IQE of the BR willincrease.

Surface etching is an important art in fabricating TPV cells. Itseffect on the IQE was analyzed with the 2 h diffusion profile. The

results are shown in Fig. 10. The positions of the two surface etchingdepths on the diffusion profile are marked in Fig. 10(a), and the effectof the surface etching depth on the total IQE of the cell is shown inFig. 10(b). The experimental results are shown in Fig. 10(c), whereasthe effects of the surface etching depth on the IQE of the ER, DR andBR are shown in Fig. 10(d), (e) and (f), respectively. As shown inFig. 10(b), after 0.05 μm surface etching, the total IQE of the cellincreases at short wavelengths below 651 nm, whereas it decreasesat wavelengths above 651 nm. However, the total IQE of the celldecreases over the whole wavelength range when etched 0.10 μm.The comparison of the measured EQEs of the untreated wafer andthat with 5 min of surface etching is shown in Fig. 10(c). It is clearlyshown that although the values of IQE and EQE are not directlycomparable, the change trends of the calculated results in Fig. 10(b) and the measured results in Fig. 10(c) after shallow surfaceetching are in good agreement. Additionally, the EQE results mea-sured by Rajagopalan et al. also showed a similar phenomenon [18].Fig. 10(d)–(f) shows that when etched 0.05 μm, there is only a slightincrement of the IQEs of the DR and the BR. Thus the change trend ofthe total IQE is mainly caused by the change in the ER. In the ER, theIQE increases below 651 nm and decreases above 651 nm, and thetotal IQE of the cell shows the same trend. However, when etched0.10 μm, the IQEs of the ER and the DR decrease sharply. Though theIQE of the BR increases, the total IQE of the cell decreases throughoutthe whole wavelength range. The value of the concentration of thegenerated minority carriers divided by the number of incidentphotons versus depth is shown in Fig. 11. The minority carriersgenerated by short wavelength photons concentrate in the surfacearea of the ER. When etched 0.05 μm, the high Zn dopant concen-tration in this region is removed, and the IQE of the ER increases inthe short wavelength range. However, the distribution of theminority carriers generated by long wavelength photons is uniform.The surface etching reduces the number of the minority carriersgenerated in the ER significantly, and the IQE of the ER decreases.651 nm is a critical value at which the IQE of the ER will not changeafter 0.05 μm surface etching. However, when etched 0.10 μm, the

0.00.0

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Right Edge of ERwith 5h Zn Diffusion

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Min

ority

Car

riers

/ In

cide

nt P

hoto

ns

Depth / m0.1 0.2 0.3 0.4 0.5 0.6

Fig. 9. The effect of the Zn diffusion duration on the ratio of minority carriersgenerated by photons of different wavelengths versus depth.

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Tota

l IQ

E

Wavelength /nm

Without Etch Etch1: Depth=0.05 m Etch2: Depth=0.10 m

ER IQ

E

Without Etch Etch1: Depth=0.05 m Etch2: Depth=0.10 m

BR

IQE

Without Etch Etch1: Depth=0.05 m Etch2: Depth=0.05 m

DR

IQE

Wavelength /nm Wavelength /nmWavelength /nm

Without Etch Etch 5 mins

EQE

Wavelength /nm

Fig. 10. The effect of the surface etching depth on the IQE of the cell. (a) The surface etching positions, (b) the effect on the total IQE, (c) the experimental results for the EQEof the cell, (d)–(f) the effect on the IQE of the ER, DR and BR, correspondingly.

H. Ye et al. / Solar Energy Materials & Solar Cells 125 (2014) 268–275274

Author's personal copy

number of the minority carriers generated in the ER decreasesthroughout the entire wavelength range, thus, the IQE also decreases.The IQE of the DR and BR increases with the surface etching depthbecause the DR and BR will become closer to the surface of the cell.Therefore, the front surface etching is unnecessary for the GaSb cellwith a box-shaped Zn diffusion profile, because the near infrared IQEis the most important.

5. Conclusions

A detailed calculation model to evaluate the IQE of GaSb TPVcells has been established adopting the classical semiconductortheory, and the IQEs of GaSb TPV cells with box-shaped Zndiffusion profiles have been calculated. The calculated resultsagree notably well with the measured data. The results indicatethat to improve the IQE of the cell below 800 nm, surfacepassivation is necessary to reduce Sn, and to improve the IQEabove 800 nm, a high-quality GaSb wafer with a large τh should bechosen to fabricate the cell. When decreasing the Zn diffusionduration, the PN junction of the cell becomes shallower, the IQE ofthe cell increases for short wavelengths below 1200 nm. Addi-tionally, when the surface etching depth is approximately 0.05 μm,the IQE of the cell increases at short wavelengths below 651 nmand decreases at long wavelengths above 651 nm, which is provenby the experimental measurement. However, when surfaceetching depth reaches approximately 0.10 μm, the IQE of the cellpresents a decreasing trend throughout the whole wavelengthrange, indicating that surface etching is not necessary for GaSbcells with box-shaped Zn diffusion profiles.

Acknowledgments

This work was funded by the National Basic Research Programof China (Grant no. 2009CB939904) and the FundamentalResearch Funds (Grant no. 20120013) for the Central Universities.

References

[1] K. Qiu, A.C.S. Hayden, Development of a novel cascading TPV and TE powergeneration system, Appl. Energy 91 (2012) 304–308.

[2] A. Niv, Z.R. Abrams, M. Gharghi, C. Gladden, X. Zhang, Overcoming thebandgap limitation on solar cell materials, Appl. Phys. Lett. 100 (2012).

[3] X. Wu, H. Ye, J.X. Wang, Experimental analysis of cell output performance for aTPV system, Sol. Energy Mater. Sol. Cells 95 (2011) 2459–2465.

[4] Y. Ashuach, Y. Kauffmann, C. Saguy, S. Grossman, O. Klin, E. Weiss,E. Zolotoyabko, Quantification of atomic intermixing in short-period InAs/GaSb superlattices for infrared photodetectors, J. Appl. Phys. 113 (2013).

[5] W.H. Lin, K.W. Wang, Y.A. Liao, C.W. Pao, S.Y. Lin, The formation mechanismsand optical characteristics of GaSb quantum rings, J. Appl. Phys. 114 (2013).

[6] M.C. Wagener, P.J. Carrington, J.R. Botha, A. Krier, Simulation of the enhancedinfrared photoresponse of type-II GaSb/GaAs quantum ring solar cells, Appl.Phys. Lett. 103 (2013).

[7] I. Knez, R.R. Du, G. Sullivan, Finite conductivity in mesoscopic Hall bars ofinverted InAs/GaSb quantum wells, Phys. Rev. B 81 (2010).

[8] S.P. Chang, Fabrication of simple GaAs solar cell by Zn diffusion method, Adv.Mater. Res. 684 (2013) 312–316.

[9] H. Ye, L.L. Tang, Y.L. Ma, Experimental and theoretical investigation of zincdiffusion in N-GaSb, Chin. Sci. Bull. 55 (2010) 2489–2496.

[10] A. Hoglund, C.W.M. Castleton, S. Mirbt, Diffusion mechanism of Zn in InP andGaP from first principles, Phys. Rev. B 77 (2008).

[11] T. Schlegl, O.V. Sulima, A.W. Bett, The influence of surface preparation on Zn-diffusion processes in GaSb, in: A. Gopinath, T.J. Coutts, J. Luther (Eds.),Thermophotovoltaic Generation of Electricity, 2004, pp. 396–403.

[12] V.S. Sundaram, P.E. Gruenbaum, Zinc diffusion in GaSb, J. Appl. Phys. 73 (1993)3787–3789.

[13] A.W. Bett, S. Keser, O.V. Sulima, Study of Zn diffusion into GaSb from thevapour and liquid phase, J. Cryst. Growth 181 (1997) 9–16.

[14] H. Ye, L. Tang, K.J. Li, The intrinsic relationship between the kink-and-tail andbox-shaped zinc diffusion profiles in n-GaSb, Semicond. Sci. Technol. 28(2013).

[15] S.P. Nicols, H. Bracht, M. Benamara, Z. Liliental-Weber, E.E. Haller, Mechanismof zinc diffusion in gallium antimonide, Phys. B: Condens. Matter 308–310(2001) 854–857.

[16] O.V. Sulima, A.W. Bett, M.G. Mauk, B.Y. Ber, P.S. Dutta, Diffusion of Zn in TPVmaterials: GaSb, InGaSb, InGaAsSb and InAsSbP, in: T.J. Coutts, G. Guazzoni, J.Luther (Eds.), Thermophotovoltaic Generation of Electricity, 2003, pp. 402–413.

[17] K. Sunder, H. Bracht, S.P. Nicols, E.E. Haller, Zinc and gallium diffusion ingallium antimonide, Phys. Rev. B 75 (2007).

[18] G. Rajagopalan, N.S. Reddy, H. Ehsani, I.B. Bhat, P.S. Dutta, R.J. Gutmann,G. Nichols, O. Sulima, A simple single-step diffusion and emitter etchingprocess for high-efficiency gallium-antimonide thermophotovoltaic devices,J. Electron. Mater. 32 (2003) 1317–1321.

[19] L.M. Fraas, G.R. Girard, J.E. Avery, B.A. Arau, V.S. Sundaram, A.G. Thompson,J.M. Gee, GaSb booster cells for over 30-percent efficient solar-cell stacks,J. Appl. Phys. 66 (1989) 3866–3870.

[20] L.M. Fraas, V.S. Sundaram, J.E. Avery, P.E. Gruenhaum, E. Malocsay, III–V solarcells and doping processes, US Patent Number 5217539, June 8, 1993.

[21] C. Algora, D. Martin, Modelling and manufacturing GaSb TPV converters, in:T.J. Coutts, G. Guazzoni, J. Luther (Eds.), Thermophotovoltaic Generation ofElectricity, 2003, pp. 452–461.

[22] D. Martin, C. Algora, Temperature-dependent GaSb material parameters forreliable thermophotovoltaic cell modelling, Semicond. Sci. Technol. 19 (2004)1040–1052.

[23] H.F. Wolf, Semiconductors, Wiley-Interscience, New York, 1971.[24] I.D. Mayergoyz, Solution of the nonlinear Poisson equation of semiconductor-

device theory, J. Appl. Phys. 59 (1986) 195–199.[25] G. Stollwerck, O.V. Sulima, A.W. Bett, Characterization and simulation of GaSb

device-related properties, IEEE Trans. Electron Devices 47 (2000) 448–457.[26] J. Wiley, Semiconductors and Semimetals, 10, Academic Press, NY (1975) 91.[27] G. Benz, R. Conradt, Auger recombination in GaAs and GaSb, Phys. Rev. B 16

(1977) 843–855.[28] D. Donetsky, G. Belenky, S. Svensson, S. Suchalkin, Minority carrier lifetime in

type-2 InAs–GaSb strained-layer superlattices and bulk HgCdTe materials,Appl. Phys. Lett. 97 (2010).

[29] A. Cuevas, P.A. Basore, G. GiroultMatlakowski, C. Dubois, Surface recombina-tion velocity of highly doped n-type silicon, J. Appl. Phys. 80 (1996)3370–3375.

0.00 0.05 0.10 0.15 0.20 0.250.0

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Right Edge of ERwith Surface Etching 0.05 m

Right Edge of ERwithout Surface Etching

Min

ority

Car

riers

/ In

cide

nt P

hoto

ns

Depth / m

Fig. 11. The effect of the front surface etching depth on the ratio of minoritycarriers excited by photons of different wavelengths versus depth.

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