- Email: [email protected]
Photoconduction spectroscopy of p-type GaSb films
Physica B 407 (2012) 1656–1659
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Photoconduction spectroscopy of p-type GaSb films M.W. Shura n, V. Wagener, J.R. Botha, M.C. Wagener Department of Physics, P.O. Box 77000, Nelson Mandela Metropolitan University, Port Elizabeth 6031, South Africa
a r t i c l e i n f o
a b s t r a c t
Available online 28 September 2011
Excess carrier lifetimes (77 K) have been measured as function of the absorbed flux density in undoped p-type gallium antimonide films (GaSb/GaAs) using steady state photoconductivity measurements with the illumination wavelength of 1.1 mm. Using the results from Hall effect measurements along with the relations describing the lifetimes of the excess minority carriers in the bulk of the films and at the surface, the theoretical values of the effective excess carrier lifetime in the materials were also calculated. Discrepancies between the experimental and theoretical results were described using a two-layer model, by considering the variation in the charge distribution within the layer due to the presence of surface states, as well as the band offset between the layer and the substrate. Theoretical modeling of the experimental result yields values of different parameters such as band bending at the surface, minimum value of Shockley–Read–Hall lifetime and maximum value of the surface recombination velocity. & 2011 Elsevier B.V. All rights reserved.
Keywords: GaSb Photoconductivity Lifetime Recombination Concentration
1. Introduction Gallium antimonide (GaSb) and related compounds are direct band-gap semiconductors suitable for fabricating high-frequency electronic devices and optoelectronic devices. Undoped GaSb is usually p-type with a thermal equilibrium concentration of holes ranging from 1015 to 1017 cm 2 s 1[1,2]. It has been the subject of active discussion in the literature for more than four decades [1–4]. The photo response of this material makes it very useful in the design of a variety of device architectures, including photo detectors, resonant tunneling structures and other quantum devices [2,3,5] The performance of the material in this case depends on the lifetime of free charge carriers generated by the interaction of light with the material, referred to as the excess carrier lifetime (t). The excess carrier lifetime is in general determined by the recombination rate of the minority charge carriers in the bulk of the material bulk and at the surface. Several experimental techniques have been used to extract the excess carrier lifetime of photo-generated charge carriers. The simplest and the most commonly used method is steady state photoconductivity measurements [2,3]. Using this technique it is possible to extract the effective excess carrier lifetime (teff) resulting from both the bulk and surface recombination processes. This paper focuses on the measurement and modeling of the dependence of the excess carrier lifetime on absorbed photon flux density in undoped p-type GaSb/GaAs films. The discrepancy between the results obtained from steady photoconductivity
n
Corresponding author. Tel.: þ27 735163767. E-mail address: [email protected] (M.W. Shura).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.09.110
measurements and values expected from the theory is resolved using a two-layer model. Steady state photoconductivity measurements have been shown to be unaffected by trapping temperatures at high temperature [1], in the present work the effect of trapping is neglected and a single excess carrier lifetime and/or excess carrier concentration is used in the analysis of our work.
2. Theory For a steady state photoconductivity, the excess carrier generation rate (Go) is equal to their recombination rate (R), so that the photo-generated carrier concentration Dn in the entire sample is given as [7]
Dn ¼ Go tef f ¼
DF b
tef f :
ð1Þ
Here b is the thickness of the sample and DF is the total absorbed photon flux density in the sample, which is described in terms of the incident photon flux density Fo as
DF ¼ Fo ð1RÞð1eab Þ:
ð2Þ 4
1
The absorption coefficient a has a value of 2.34 10 cm at a wavelength of 1.1 mm at 77 K as calculated using the relation of its dependence on photon energy analyzed for direct band gap semiconductors [5,8,9]. The reflection coefficient R was taken as 0.34 for GaSb at 77 K [2,3,9]. The change in the sample conductivity due to illumination is given by [7]
Ds ¼ eðmn þ mp Þ
DF b
tef f ,
ð3Þ
M.W. Shura et al. / Physica B 407 (2012) 1656–1659
1657
EC E1
ES
po1 << p1 ∆VL
Surface
∆Vs Vo
RL
po2 >> p2 EF EV b2
b1
Fig. 1. (a) Diagram illustrating a simple photoconductivity circuit and basic parameters used to describe the two layer system. (b) Band edge diagram for the two layer system.
where e is the elemental charge and mn and mp are the electron and hole mobilities, respectively. Fig. 1(a) contains the sample and the circuit diagrams used for photoconductivity measurements in this work. A variable load resistor RL is connected in series with the sample being studied. A battery of constant voltage Vo ¼6 V was used in all measurements. Rp is the resistance of the sample during illumination called the photo resistance of the sample. Taking into account Eqs. (1) and (3) along with Ohm’s law for this circuit we obtain
tef f ¼
ð1 þRL =Rp Þ Di , we Eo ðmn þ mp Þ DF
ð4Þ
where Di is the photo-generated current, w is the width of the sample and Eo is the dark electric field. The simplified form of the well known radiative (tR), Shockley–Read–Hall (tSRH) and Auger (tA) excess carrier recombination lifetimes are described in terms of the thermal equilibrium carrier concentration po and Dn for p-type bulk material as [6–13]
tR ¼
1 , C R ðp3 þ DnÞ
tSRH ¼ tno þ
tpo Dn , p3 þ Dn
tA ¼
1 C pa ðpo þ DnÞ2
:
ð5Þ
The radiative recombination coefficient CR has a value of 10 11 cm3/s at 77 K as calculated using the expression derived by Van Roosbroeck and Shockley [8,10,14,17] and Cpa is the hole Auger capture coefficient that involves the split-off valence band, which is dominant in GaSb. Typical values of Cpa is 10 24 cm6/s at 77 K [15,18] The parameters tno and tpo are the Shockley– Read–Hall lifetimes for electrons and holes when the recombination center is empty and filled with electrons, respectively. The surface carrier recombination velocity is also given for p-type material as [8,11]. 1 1 Dns ¼ , þ S Sno Spo ðp3s þ Dns Þ
ð6Þ
where Sno and Spo are the surface recombination velocities of electrons and holes when the surface state is empty and fully occupied by electrons, respectively. S has the constant values Sno at low injection levels and SnoSpo/(Sno þ Spo) at higher injection levels. The Shockley–Read–Hall lifetime tSRH also takes on constant values tno at low injection levels and tno þ tpo at high injection levels. Hence, tSRH can be substituted by tno or tno þ tpo [7] in the description of the DF dependence of the bulk lifetime (tbulk). Taking any of these values does not affect the value of tbulk, since both tno and tpo are very large as compare to teff, Eq. (5) along with Eq. (1) and the well known relation for the bulk excess carrier lifetime of the semiconductor [7,11] yield 1
tbulk
2 DF DF 1 ¼ C R p3 þ tbulk þ C pa p3 þ tbulk þ , b b tno
ð7Þ
or
2 CR b 2 C p 1 b tbulk þ p2o þ R o þ tbulk C pa tno C pa DF C pa DF 2 1 b ¼ 0, ð8Þ C pa DF
t3bulk þ 2po þ
where po is the thermal equilibrium hole concentration. The solution of Eq. (8) is rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 b 2D 3 þ B þ B2 þ A3 B þ B2 þ A3 , tbulk ¼ ð9Þ 3 DF where !2 2 CR D CR 1 1 p ffiffiffi , A¼ þ , D ¼ po þ 3 3 C pa tno 2C pa 2 3C pa 3 D DF þAD : B ¼ 4 3 2bC pa Eqs. (7)–(9) describe the dependence of tbulk on DF. In most of our GaSb/GaAs samples, the values of the effective excess carrier lifetimes given by tef f ¼ 1=ðð1=tbulk Þ þð2S=bÞÞ predict a constant excess carrier lifetime of about 1–10 ns at very low injection levels. However, the results of steady state photoconductivity measurements show that the value of teff has a maximum value about 1–10 ms at very low injection levels and decreases strongly with increasing injection level. This discrepancy suggests that an additional mechanism must be involved. One possibility would be a variation in the carrier concentration within the layer. It is expected that the presence of surface states, as well as the band offset between the layer and the substrate, will cause some degree of carrier depletion at the surface and the interface. Thus, in order to resolve the discrepancy between the measured lifetimes and the above theoretical predictions, a two-layer model is introduced. Fig. 1(a) and (b) depict the sample parameters and energy band diagram used to describe the two-layer system. The thicknesses of the total depletion region (i.e. surface and interface, referred to as layer 1) and the bulk region (layer 2) are represented by b1 and b2, respectively. Due to the band edge energy variation in layer 1 from 0 to Es before illumination, the hole thermal equilibrium concentration (po1) in layer 1 will fall exponentially from the equilibrium value po2 in the bulk (layer 2) to that at the surface, given by pos ¼po2exp( Es/kT). Hence at any position in layer 1 where the energy band bending is E, the value of po1 is given by E ð10Þ po1 ðEÞ ¼ po2 exp kT where T is the temperature and k Boltzmann’s constant.
M.W. Shura et al. / Physica B 407 (2012) 1656–1659
The effective value of po1(E), which corresponds to the average thermal equilibrium effective carrier lifetime in layer 1 is now evaluated as follows. Since the po1 dependence of t1eff is only through the radiative and Auger carrier lifetime t1R and t1A in layer 1, the average thermal equilibrium value of t1R and t1A, denoted by t1RA can be calculated using the following relation: Z 1 Es t1RA ¼ t1RA ðEÞdE: ð11Þ Es 0 Upon using relation (11) along with Eqs. (10) and (7) (by neglecting the effects of DF for very low injection level), t1RA can be expressed in terms of Esas " !# C pa p2o2 þ C R po2 expðEs =kTÞ C pa kT expðEs =kTÞ1 : t1RA ¼ 2 ln ES C R po2 C pa p2o2 þ C R po2 CR
103 3
102 Excess carrier Lifetime (μs)
1658
101
1 4
100
Layer 1 Layer 2 Surface Effective b = 4.7μm po2= 2x1016cm-3 po1= 1014cm-3
10-1 10-2 10-3
2
ð12Þ The value of po1 is then obtained using relations (7), (10) and (12) for DF E0 as " sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# 4C pa Cn : ð13Þ po1 ¼ 1 1 þ 2 2C pa C n t1RA Eq. (13) along with Eq. (7) yields the DF dependence of the excess effective carrier lifetime t1eff in layer 1. No surface recombination was taken into account in the separate simulation of the excess carrier lifetimes in layers 1 and 2. Using the sum of parallel photo-generated currents in layers 1 and 2
Di ¼ Di1 þ Di2 ,
ð14Þ
along with the relations (1), (3) and Ohm’s law, tbulk can be easily described as
tbulk ¼
t1ef f DF1 þ t2ef f DF2 DF1 þ DF2
:
ð15Þ
Here DF1 and DF2 are the photon flux densities absorbed in layers 1 and 2 respectively, given by
DF1 ¼ Fo ð1RÞð1eab1 Þ,
ð16Þ
DF2 ¼ Fo ð1RÞðeab1 eab Þ:
ð17Þ
For simplicity it was assumed that the reflectivity of the GaSb surface is the same as that of the hetero-interface with GaAs. Taking into account Eq. (15) along with Eq. (6) yields the effective excess carrier lifetime teff in the sample. Fig. 2 shows the absorbed flux density dependence of teff in the entire sample. Curve 1 represents the decreasing in t1eff in layer 1 as DF increases and when DF1t1eff/b1 4po1 and curve 2 describes the constant value of t2eff when DF2t2eff/b2 opo2 in layer 2. Curve 3 illustrates the change in surface recombination lifetime from its low level value b/2Sno to its high level injection value b(Sno þSpo)/ 2SnoSpo. Curve 4 represents the DF dependence of the net teff in the entire sample, resulting from the recombination effect in both layers 1 and 2, the surface and the interface between the layer and the substrate. The shape of curve 4 correlates well with the experimental results obtained in this study, as shown and discussed in Section 4.
3. Experiment All the samples used in this work were p-type GaSb grown by metal-organic vapor phase epitaxy (MOVPE) on semi-insulating GaAs substrate using triethylgallium and trimethylantimony in our laboratory. The thicknesses of the samples are 1.4 mm, 3.8 mm and 4.7 mm. The growth temperatures for the three samples were 625 1C, 500 1C and 625 1C and the corresponding V/III ratios were 1.0, 1.8 and 1.2, respectively. For the Hall Effect measurements, the wafers were cut into square samples of dimensions about
10-4 1011
1013 1015 1017 1019 1021 1023 Absorbed Flux Density ∆Φ (cm-2s-1)
1025
Fig. 2. Absorbed photon flux dependence of excess carrier lifetime in various parts of the sample.
5 mm 5 mm and four ohmic contacts were deposited on the corners in the Van der Pauw configuration using indium [3]. For photoconductivity measurements the wafers were cut into samples of size about 2 mm 5 mm and two ohmic contacts were deposited on the edges using indium soldering and/or silver paste. The edges of the samples and the contacts were masked and immersed in liquid nitrogen, so that illumination fell only on the exposed surface between the two contacts through a waveguide. A halogen lamp that provides a maximum photon flux density at about 1.1 mm was used as the source of illumination. Ruled diffraction gratings of 600 lines/mm and peak efficiencies of 75% in the primary wavelength region 600 to 2500 nm were employed to measure the photo-signal at 1.1 mm. A set of different long pass filters were used between the source and the gratings to block higher order wavelengths. A commercial InGaAs photo-detector (sensitive in the range 0.7 to 1.8 mm) was placed at the position occupied by the sample to measure the incident photon flux density. Different neutral density filters were used to vary the illumination levels. For the modulation of the incident light on the sample a mechanical chopper was used. The induced AC photo signal was phase-sensitively separated by a lock-in amplifier. For the best detection of small signals the load resistances were adjusted according to the sample resistance. In order to saturate the photo-response signal, the modulation frequency was chosen to be as low as possible (10–30 Hz).
4. Results and discussion Fig. 3(a) illustrates the contribution of the bulk and the surface of the semiconductor on teff, while (b) shows the simulation (solid lines) of the experimental data (symbols) for teff versus DF for GaSb/GaAs layers of different thickness. To perform the process of curve fitting, first the data of DF was described using Eq. (2). Then the effective carrier lifetimes determined experimentally (Eq. (4)) were plotted. The theoretical results of teff versus DF (using the combination of Eqs. (6) and (15)) were plotted on the same graph. Before starting the fitting process, Es was kept at its maximum value and the influence of tSRH and S on teff was reduced by changing tno and Sno until the theoretical curve lies above the experimental data. Next, by changing the value of Es, the theoretical curve was moved closer towards the experimental data. At this stage of the simulation, either the theoretical curve would fit the experimental data in the entire range of flux densities, or it
M.W. Shura et al. / Physica B 407 (2012) 1656–1659
101
102 101 10
Excess carrier lifetime(μs)
Excess carrier Lifetime(μs)
103
Bulk Effective Surface Experimental
0
10-1 10-2 10
1659
T =77K λ= 1.1μm Samples A B C
100
10-1
-3
10-4 11 10
10
13
10
15
10
17
10
19
10
21
10
23
10
25
10-2 1012
Absorbed Flux density ∆Φ (cm-2s-1)
10
14
10
16
10
18
Absorbed Flux Density ∆Φ (cm-2s-1)
Fig. 3. (a) Effects of the bulk and surface on the flux dependence of the effective carrier lifetime (lines). The data points were measured for a sample with thickness 4.7 mm. (b) Experimental data (symbols) and simulations (lines) of the effective lifetime as function of photon flux density for three GaSb/GaAs samples, labeled A, B and C.
Table 1 List of quantities and their values obtained by theoretical modeling of the experimental results. Quantities
Value
Sample label
A
B
C
70 30 40– 60 1–2
70 40 20– 30 5–10
45 40 10– 15 5–10
77 K Energy band bending (meV) Thickness of layer 1(nm) Effective Shockley–Read–Hall lifetime (micro second) Surface Recombination velocity (cm s 1)
would fit the data for higher flux densities, while still lying above the experimental data for lower flux densities. The first case is an indication of a negligible contribution from SRH and surface recombination to the lifetime. In the second case, the fit could be improved by adjusting the values of tSRH and/or S. In both cases, by adjusting tSRH and S until they started to influence the quality of the fit, it was possible to estimate the minimum and maximum possible values of tSRH and S, respectively, but difficult to predict, which parameter is dominant, since they have the same effect. The values of some quantities like b1, Es, and the estimated ranges for the values of tSRH and S extracted from the simulations are shown in Table 1. The values of the band bending at the surface is in complete agreement with the results obtained from measurements of the GaSb surface band bending potential from magneto-transport characteristics of GaSb–InAs–AlSb quantum wells [16]. Lower values surface recombination velocities ranging from 6–210 cm/s are reported on p-type c-Si and in GaInAsSb/AlGaAsSb hetero-structures [19,20].
5. Conclusions To investigate the photo response of undoped p-type GaSb/ GaAs, the carrier lifetimes of the photo-generated carriers were measured as function of the absorbed flux density, using steady state photoconductivity measurements. When the experimental results were analyzed using the results from Hall effect measurements along with the relations describing the lifetimes of the excess minority carriers in the bulk of the films and at the surface,
a huge discrepancy was observed in the magnitude and the photon flux dependence of the photo-generated carrier lifetimes. Discrepancies between the experimental and theoretical results were described using a two-layer model, by assuming a variation in the charge distribution within the layer due to the presence of surface states, and the band offset between the layer and the substrate. Finally we like to emphasize that the two-layer system used for the first time to determine the injection level dependence of the excess carrier lifetime appears to be well matched to the experimental results. However, further work is required to establish the validity of the proposed model.
Acknowledgements This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and the Technology and the National Research Foundation, South Africa and the financial support of the Nelson Mandela Metropolitan University. References [1] C.C. Ling, M.K. Lui, S.K. Ma, X.D. Chen, S. Fung, C.D. Beling, Appl. Phys. Lett. 85 (2004) 384. [2] A. Rakoviska, V. Berger, X. Markadet, B. Vinter, K. Bouzehoune, D. Kaplan, Semicond. Sci. Technol. 15 (2000) 34. [3] G. Sarusi, A. Zemel, D. Eger, J. Appl. Phys. 72 (1992) 2312. [4] A. Subekti, JMS 5 (2000) 1. [5] D. Martin, C. Algora, Semicond. Sci. Technol. 19 (2004) 1040. [6] R.N. Zitter, Phys. Rev. 112 (1958) 852. [7] A. Cuevas, D. Macdonald, Sol. Energy 76 (2004) 255. [8] R.K. Lal, P. Chakrabarti, Prog. Cryst. Growth Charact. Mater. 52 (2006) 33. [9] D.E. Aspens, A.A. Studna, Phys. Rev. B 27 (1983) 985. [10] A. Rogalski, Z. Orman, Infrared Physics 25 (1985) 551. [11] D.K. Schroder, IEEE Trans. Electron Devices 44 (1997) 160. [12] O.L. Curtis Jr., Phys. Rev. 172 (1968) 773. [13] W. Shockley, W.T. Read, Phys. Rev. 87 (1952) 835. [14] W. Shockley, W. Van Roosbroeck, Phys. Rev. 94 (1954) 1558. [15] A. Haug, J. Phys. C: Solid State Phys. 17 (1984) 6191. [16] P.A. Folkes, G. Gumbs, W. Xu, M. Taysing-Lara, Appl. Phys. Lett. 89 (2006) 202113. [17] C.A. Wang, G. Nichols, Auger and Radiative Recombination Coefficients in 0.55 eV InGaAsSb, Massachusetts Institute of Technology, Lexington, 2004. [18] A. Sugimura, J. Appl. Phys. 51 (1980) 4405. [19] P. Saint-Cast, D. Kania, M. Hofmann, J. Benick, J. Rentsch, R. Preu, Appl. Phys. Lett. 95 (2009) 151502. [20] C.A. Wanga, D.A. Shiau, Appl. Phys. Lett. 86 (2005) 101910.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Photoconduction spectroscopy of p-type GaSb films M.W. Shura n, V. Wagener, J.R. Botha, M.C. Wagener Department of Physics, P.O. Box 77000, Nelson Mandela Metropolitan University, Port Elizabeth 6031, South Africa
a r t i c l e i n f o
a b s t r a c t
Available online 28 September 2011
Excess carrier lifetimes (77 K) have been measured as function of the absorbed flux density in undoped p-type gallium antimonide films (GaSb/GaAs) using steady state photoconductivity measurements with the illumination wavelength of 1.1 mm. Using the results from Hall effect measurements along with the relations describing the lifetimes of the excess minority carriers in the bulk of the films and at the surface, the theoretical values of the effective excess carrier lifetime in the materials were also calculated. Discrepancies between the experimental and theoretical results were described using a two-layer model, by considering the variation in the charge distribution within the layer due to the presence of surface states, as well as the band offset between the layer and the substrate. Theoretical modeling of the experimental result yields values of different parameters such as band bending at the surface, minimum value of Shockley–Read–Hall lifetime and maximum value of the surface recombination velocity. & 2011 Elsevier B.V. All rights reserved.
Keywords: GaSb Photoconductivity Lifetime Recombination Concentration
1. Introduction Gallium antimonide (GaSb) and related compounds are direct band-gap semiconductors suitable for fabricating high-frequency electronic devices and optoelectronic devices. Undoped GaSb is usually p-type with a thermal equilibrium concentration of holes ranging from 1015 to 1017 cm 2 s 1[1,2]. It has been the subject of active discussion in the literature for more than four decades [1–4]. The photo response of this material makes it very useful in the design of a variety of device architectures, including photo detectors, resonant tunneling structures and other quantum devices [2,3,5] The performance of the material in this case depends on the lifetime of free charge carriers generated by the interaction of light with the material, referred to as the excess carrier lifetime (t). The excess carrier lifetime is in general determined by the recombination rate of the minority charge carriers in the bulk of the material bulk and at the surface. Several experimental techniques have been used to extract the excess carrier lifetime of photo-generated charge carriers. The simplest and the most commonly used method is steady state photoconductivity measurements [2,3]. Using this technique it is possible to extract the effective excess carrier lifetime (teff) resulting from both the bulk and surface recombination processes. This paper focuses on the measurement and modeling of the dependence of the excess carrier lifetime on absorbed photon flux density in undoped p-type GaSb/GaAs films. The discrepancy between the results obtained from steady photoconductivity
n
Corresponding author. Tel.: þ27 735163767. E-mail address: [email protected] (M.W. Shura).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.09.110
measurements and values expected from the theory is resolved using a two-layer model. Steady state photoconductivity measurements have been shown to be unaffected by trapping temperatures at high temperature [1], in the present work the effect of trapping is neglected and a single excess carrier lifetime and/or excess carrier concentration is used in the analysis of our work.
2. Theory For a steady state photoconductivity, the excess carrier generation rate (Go) is equal to their recombination rate (R), so that the photo-generated carrier concentration Dn in the entire sample is given as [7]
Dn ¼ Go tef f ¼
DF b
tef f :
ð1Þ
Here b is the thickness of the sample and DF is the total absorbed photon flux density in the sample, which is described in terms of the incident photon flux density Fo as
DF ¼ Fo ð1RÞð1eab Þ:
ð2Þ 4
1
The absorption coefficient a has a value of 2.34 10 cm at a wavelength of 1.1 mm at 77 K as calculated using the relation of its dependence on photon energy analyzed for direct band gap semiconductors [5,8,9]. The reflection coefficient R was taken as 0.34 for GaSb at 77 K [2,3,9]. The change in the sample conductivity due to illumination is given by [7]
Ds ¼ eðmn þ mp Þ
DF b
tef f ,
ð3Þ
M.W. Shura et al. / Physica B 407 (2012) 1656–1659
1657
EC E1
ES
po1 << p1 ∆VL
Surface
∆Vs Vo
RL
po2 >> p2 EF EV b2
b1
Fig. 1. (a) Diagram illustrating a simple photoconductivity circuit and basic parameters used to describe the two layer system. (b) Band edge diagram for the two layer system.
where e is the elemental charge and mn and mp are the electron and hole mobilities, respectively. Fig. 1(a) contains the sample and the circuit diagrams used for photoconductivity measurements in this work. A variable load resistor RL is connected in series with the sample being studied. A battery of constant voltage Vo ¼6 V was used in all measurements. Rp is the resistance of the sample during illumination called the photo resistance of the sample. Taking into account Eqs. (1) and (3) along with Ohm’s law for this circuit we obtain
tef f ¼
ð1 þRL =Rp Þ Di , we Eo ðmn þ mp Þ DF
ð4Þ
where Di is the photo-generated current, w is the width of the sample and Eo is the dark electric field. The simplified form of the well known radiative (tR), Shockley–Read–Hall (tSRH) and Auger (tA) excess carrier recombination lifetimes are described in terms of the thermal equilibrium carrier concentration po and Dn for p-type bulk material as [6–13]
tR ¼
1 , C R ðp3 þ DnÞ
tSRH ¼ tno þ
tpo Dn , p3 þ Dn
tA ¼
1 C pa ðpo þ DnÞ2
:
ð5Þ
The radiative recombination coefficient CR has a value of 10 11 cm3/s at 77 K as calculated using the expression derived by Van Roosbroeck and Shockley [8,10,14,17] and Cpa is the hole Auger capture coefficient that involves the split-off valence band, which is dominant in GaSb. Typical values of Cpa is 10 24 cm6/s at 77 K [15,18] The parameters tno and tpo are the Shockley– Read–Hall lifetimes for electrons and holes when the recombination center is empty and filled with electrons, respectively. The surface carrier recombination velocity is also given for p-type material as [8,11]. 1 1 Dns ¼ , þ S Sno Spo ðp3s þ Dns Þ
ð6Þ
where Sno and Spo are the surface recombination velocities of electrons and holes when the surface state is empty and fully occupied by electrons, respectively. S has the constant values Sno at low injection levels and SnoSpo/(Sno þ Spo) at higher injection levels. The Shockley–Read–Hall lifetime tSRH also takes on constant values tno at low injection levels and tno þ tpo at high injection levels. Hence, tSRH can be substituted by tno or tno þ tpo [7] in the description of the DF dependence of the bulk lifetime (tbulk). Taking any of these values does not affect the value of tbulk, since both tno and tpo are very large as compare to teff, Eq. (5) along with Eq. (1) and the well known relation for the bulk excess carrier lifetime of the semiconductor [7,11] yield 1
tbulk
2 DF DF 1 ¼ C R p3 þ tbulk þ C pa p3 þ tbulk þ , b b tno
ð7Þ
or
2 CR b 2 C p 1 b tbulk þ p2o þ R o þ tbulk C pa tno C pa DF C pa DF 2 1 b ¼ 0, ð8Þ C pa DF
t3bulk þ 2po þ
where po is the thermal equilibrium hole concentration. The solution of Eq. (8) is rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 b 2D 3 þ B þ B2 þ A3 B þ B2 þ A3 , tbulk ¼ ð9Þ 3 DF where !2 2 CR D CR 1 1 p ffiffiffi , A¼ þ , D ¼ po þ 3 3 C pa tno 2C pa 2 3C pa 3 D DF þAD : B ¼ 4 3 2bC pa Eqs. (7)–(9) describe the dependence of tbulk on DF. In most of our GaSb/GaAs samples, the values of the effective excess carrier lifetimes given by tef f ¼ 1=ðð1=tbulk Þ þð2S=bÞÞ predict a constant excess carrier lifetime of about 1–10 ns at very low injection levels. However, the results of steady state photoconductivity measurements show that the value of teff has a maximum value about 1–10 ms at very low injection levels and decreases strongly with increasing injection level. This discrepancy suggests that an additional mechanism must be involved. One possibility would be a variation in the carrier concentration within the layer. It is expected that the presence of surface states, as well as the band offset between the layer and the substrate, will cause some degree of carrier depletion at the surface and the interface. Thus, in order to resolve the discrepancy between the measured lifetimes and the above theoretical predictions, a two-layer model is introduced. Fig. 1(a) and (b) depict the sample parameters and energy band diagram used to describe the two-layer system. The thicknesses of the total depletion region (i.e. surface and interface, referred to as layer 1) and the bulk region (layer 2) are represented by b1 and b2, respectively. Due to the band edge energy variation in layer 1 from 0 to Es before illumination, the hole thermal equilibrium concentration (po1) in layer 1 will fall exponentially from the equilibrium value po2 in the bulk (layer 2) to that at the surface, given by pos ¼po2exp( Es/kT). Hence at any position in layer 1 where the energy band bending is E, the value of po1 is given by E ð10Þ po1 ðEÞ ¼ po2 exp kT where T is the temperature and k Boltzmann’s constant.
M.W. Shura et al. / Physica B 407 (2012) 1656–1659
The effective value of po1(E), which corresponds to the average thermal equilibrium effective carrier lifetime in layer 1 is now evaluated as follows. Since the po1 dependence of t1eff is only through the radiative and Auger carrier lifetime t1R and t1A in layer 1, the average thermal equilibrium value of t1R and t1A, denoted by t1RA can be calculated using the following relation: Z 1 Es t1RA ¼ t1RA ðEÞdE: ð11Þ Es 0 Upon using relation (11) along with Eqs. (10) and (7) (by neglecting the effects of DF for very low injection level), t1RA can be expressed in terms of Esas " !# C pa p2o2 þ C R po2 expðEs =kTÞ C pa kT expðEs =kTÞ1 : t1RA ¼ 2 ln ES C R po2 C pa p2o2 þ C R po2 CR
103 3
102 Excess carrier Lifetime (μs)
1658
101
1 4
100
Layer 1 Layer 2 Surface Effective b = 4.7μm po2= 2x1016cm-3 po1= 1014cm-3
10-1 10-2 10-3
2
ð12Þ The value of po1 is then obtained using relations (7), (10) and (12) for DF E0 as " sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# 4C pa Cn : ð13Þ po1 ¼ 1 1 þ 2 2C pa C n t1RA Eq. (13) along with Eq. (7) yields the DF dependence of the excess effective carrier lifetime t1eff in layer 1. No surface recombination was taken into account in the separate simulation of the excess carrier lifetimes in layers 1 and 2. Using the sum of parallel photo-generated currents in layers 1 and 2
Di ¼ Di1 þ Di2 ,
ð14Þ
along with the relations (1), (3) and Ohm’s law, tbulk can be easily described as
tbulk ¼
t1ef f DF1 þ t2ef f DF2 DF1 þ DF2
:
ð15Þ
Here DF1 and DF2 are the photon flux densities absorbed in layers 1 and 2 respectively, given by
DF1 ¼ Fo ð1RÞð1eab1 Þ,
ð16Þ
DF2 ¼ Fo ð1RÞðeab1 eab Þ:
ð17Þ
For simplicity it was assumed that the reflectivity of the GaSb surface is the same as that of the hetero-interface with GaAs. Taking into account Eq. (15) along with Eq. (6) yields the effective excess carrier lifetime teff in the sample. Fig. 2 shows the absorbed flux density dependence of teff in the entire sample. Curve 1 represents the decreasing in t1eff in layer 1 as DF increases and when DF1t1eff/b1 4po1 and curve 2 describes the constant value of t2eff when DF2t2eff/b2 opo2 in layer 2. Curve 3 illustrates the change in surface recombination lifetime from its low level value b/2Sno to its high level injection value b(Sno þSpo)/ 2SnoSpo. Curve 4 represents the DF dependence of the net teff in the entire sample, resulting from the recombination effect in both layers 1 and 2, the surface and the interface between the layer and the substrate. The shape of curve 4 correlates well with the experimental results obtained in this study, as shown and discussed in Section 4.
3. Experiment All the samples used in this work were p-type GaSb grown by metal-organic vapor phase epitaxy (MOVPE) on semi-insulating GaAs substrate using triethylgallium and trimethylantimony in our laboratory. The thicknesses of the samples are 1.4 mm, 3.8 mm and 4.7 mm. The growth temperatures for the three samples were 625 1C, 500 1C and 625 1C and the corresponding V/III ratios were 1.0, 1.8 and 1.2, respectively. For the Hall Effect measurements, the wafers were cut into square samples of dimensions about
10-4 1011
1013 1015 1017 1019 1021 1023 Absorbed Flux Density ∆Φ (cm-2s-1)
1025
Fig. 2. Absorbed photon flux dependence of excess carrier lifetime in various parts of the sample.
5 mm 5 mm and four ohmic contacts were deposited on the corners in the Van der Pauw configuration using indium [3]. For photoconductivity measurements the wafers were cut into samples of size about 2 mm 5 mm and two ohmic contacts were deposited on the edges using indium soldering and/or silver paste. The edges of the samples and the contacts were masked and immersed in liquid nitrogen, so that illumination fell only on the exposed surface between the two contacts through a waveguide. A halogen lamp that provides a maximum photon flux density at about 1.1 mm was used as the source of illumination. Ruled diffraction gratings of 600 lines/mm and peak efficiencies of 75% in the primary wavelength region 600 to 2500 nm were employed to measure the photo-signal at 1.1 mm. A set of different long pass filters were used between the source and the gratings to block higher order wavelengths. A commercial InGaAs photo-detector (sensitive in the range 0.7 to 1.8 mm) was placed at the position occupied by the sample to measure the incident photon flux density. Different neutral density filters were used to vary the illumination levels. For the modulation of the incident light on the sample a mechanical chopper was used. The induced AC photo signal was phase-sensitively separated by a lock-in amplifier. For the best detection of small signals the load resistances were adjusted according to the sample resistance. In order to saturate the photo-response signal, the modulation frequency was chosen to be as low as possible (10–30 Hz).
4. Results and discussion Fig. 3(a) illustrates the contribution of the bulk and the surface of the semiconductor on teff, while (b) shows the simulation (solid lines) of the experimental data (symbols) for teff versus DF for GaSb/GaAs layers of different thickness. To perform the process of curve fitting, first the data of DF was described using Eq. (2). Then the effective carrier lifetimes determined experimentally (Eq. (4)) were plotted. The theoretical results of teff versus DF (using the combination of Eqs. (6) and (15)) were plotted on the same graph. Before starting the fitting process, Es was kept at its maximum value and the influence of tSRH and S on teff was reduced by changing tno and Sno until the theoretical curve lies above the experimental data. Next, by changing the value of Es, the theoretical curve was moved closer towards the experimental data. At this stage of the simulation, either the theoretical curve would fit the experimental data in the entire range of flux densities, or it
M.W. Shura et al. / Physica B 407 (2012) 1656–1659
101
102 101 10
Excess carrier lifetime(μs)
Excess carrier Lifetime(μs)
103
Bulk Effective Surface Experimental
0
10-1 10-2 10
1659
T =77K λ= 1.1μm Samples A B C
100
10-1
-3
10-4 11 10
10
13
10
15
10
17
10
19
10
21
10
23
10
25
10-2 1012
Absorbed Flux density ∆Φ (cm-2s-1)
10
14
10
16
10
18
Absorbed Flux Density ∆Φ (cm-2s-1)
Fig. 3. (a) Effects of the bulk and surface on the flux dependence of the effective carrier lifetime (lines). The data points were measured for a sample with thickness 4.7 mm. (b) Experimental data (symbols) and simulations (lines) of the effective lifetime as function of photon flux density for three GaSb/GaAs samples, labeled A, B and C.
Table 1 List of quantities and their values obtained by theoretical modeling of the experimental results. Quantities
Value
Sample label
A
B
C
70 30 40– 60 1–2
70 40 20– 30 5–10
45 40 10– 15 5–10
77 K Energy band bending (meV) Thickness of layer 1(nm) Effective Shockley–Read–Hall lifetime (micro second) Surface Recombination velocity (cm s 1)
would fit the data for higher flux densities, while still lying above the experimental data for lower flux densities. The first case is an indication of a negligible contribution from SRH and surface recombination to the lifetime. In the second case, the fit could be improved by adjusting the values of tSRH and/or S. In both cases, by adjusting tSRH and S until they started to influence the quality of the fit, it was possible to estimate the minimum and maximum possible values of tSRH and S, respectively, but difficult to predict, which parameter is dominant, since they have the same effect. The values of some quantities like b1, Es, and the estimated ranges for the values of tSRH and S extracted from the simulations are shown in Table 1. The values of the band bending at the surface is in complete agreement with the results obtained from measurements of the GaSb surface band bending potential from magneto-transport characteristics of GaSb–InAs–AlSb quantum wells [16]. Lower values surface recombination velocities ranging from 6–210 cm/s are reported on p-type c-Si and in GaInAsSb/AlGaAsSb hetero-structures [19,20].
5. Conclusions To investigate the photo response of undoped p-type GaSb/ GaAs, the carrier lifetimes of the photo-generated carriers were measured as function of the absorbed flux density, using steady state photoconductivity measurements. When the experimental results were analyzed using the results from Hall effect measurements along with the relations describing the lifetimes of the excess minority carriers in the bulk of the films and at the surface,
a huge discrepancy was observed in the magnitude and the photon flux dependence of the photo-generated carrier lifetimes. Discrepancies between the experimental and theoretical results were described using a two-layer model, by assuming a variation in the charge distribution within the layer due to the presence of surface states, and the band offset between the layer and the substrate. Finally we like to emphasize that the two-layer system used for the first time to determine the injection level dependence of the excess carrier lifetime appears to be well matched to the experimental results. However, further work is required to establish the validity of the proposed model.
Acknowledgements This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and the Technology and the National Research Foundation, South Africa and the financial support of the Nelson Mandela Metropolitan University. References [1] C.C. Ling, M.K. Lui, S.K. Ma, X.D. Chen, S. Fung, C.D. Beling, Appl. Phys. Lett. 85 (2004) 384. [2] A. Rakoviska, V. Berger, X. Markadet, B. Vinter, K. Bouzehoune, D. Kaplan, Semicond. Sci. Technol. 15 (2000) 34. [3] G. Sarusi, A. Zemel, D. Eger, J. Appl. Phys. 72 (1992) 2312. [4] A. Subekti, JMS 5 (2000) 1. [5] D. Martin, C. Algora, Semicond. Sci. Technol. 19 (2004) 1040. [6] R.N. Zitter, Phys. Rev. 112 (1958) 852. [7] A. Cuevas, D. Macdonald, Sol. Energy 76 (2004) 255. [8] R.K. Lal, P. Chakrabarti, Prog. Cryst. Growth Charact. Mater. 52 (2006) 33. [9] D.E. Aspens, A.A. Studna, Phys. Rev. B 27 (1983) 985. [10] A. Rogalski, Z. Orman, Infrared Physics 25 (1985) 551. [11] D.K. Schroder, IEEE Trans. Electron Devices 44 (1997) 160. [12] O.L. Curtis Jr., Phys. Rev. 172 (1968) 773. [13] W. Shockley, W.T. Read, Phys. Rev. 87 (1952) 835. [14] W. Shockley, W. Van Roosbroeck, Phys. Rev. 94 (1954) 1558. [15] A. Haug, J. Phys. C: Solid State Phys. 17 (1984) 6191. [16] P.A. Folkes, G. Gumbs, W. Xu, M. Taysing-Lara, Appl. Phys. Lett. 89 (2006) 202113. [17] C.A. Wang, G. Nichols, Auger and Radiative Recombination Coefficients in 0.55 eV InGaAsSb, Massachusetts Institute of Technology, Lexington, 2004. [18] A. Sugimura, J. Appl. Phys. 51 (1980) 4405. [19] P. Saint-Cast, D. Kania, M. Hofmann, J. Benick, J. Rentsch, R. Preu, Appl. Phys. Lett. 95 (2009) 151502. [20] C.A. Wanga, D.A. Shiau, Appl. Phys. Lett. 86 (2005) 101910.