- Email: [email protected]
GaSb superlattice infrared detectors
Accepted Manuscript Capacitance-Voltage Investigation of Low Residual Carrier Density in InAs/ GaSb Superlattice Infrared Detectors J. Schmidt, F. Rutz, V. Daumer, R. Rehm PII: DOI: Reference:
S1350-4495(16)30678-8 http://dx.doi.org/10.1016/j.infrared.2017.04.008 INFPHY 2272
To appear in:
Infrared Physics & Technology
Received Date: Revised Date: Accepted Date:
28 November 2016 30 January 2017 15 April 2017
Please cite this article as: J. Schmidt, F. Rutz, V. Daumer, R. Rehm, Capacitance-Voltage Investigation of Low Residual Carrier Density in InAs/GaSb Superlattice Infrared Detectors, Infrared Physics & Technology (2017), doi: http://dx.doi.org/10.1016/j.infrared.2017.04.008
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Capacitance-Voltage Investigation of Low Residual Carrier Density in InAs/GaSb Superlattice Infrared Detectors J. Schmidt, F. Rutz, V. Daumer, R. Rehm Fraunhofer Institute for Applied Solid State Physics, Freiburg (Germany)
Abstract Capacitance-voltage (CV) analysis was performed on homojunction InAs/GaSb superlattice photodiodes for the mid-infrared spectral range around 5 µm. The CV investigation was carried out over a wide temperature range from 80 K up to 200 K, for two nominally identical samples from two different epitaxy systems. The characterizations were carried out with a refined measurement setup, considering the impedance range, the measured frequency range and the accessible temperature range. For the calculated residual carrier density in the nid-region of the diodes values in the low 1014 cm−3 and 1015 cm−3 ranges were found, respectively. Keywords: InAs/GaSb T2SL, MWIR, Capacitance-Voltage Investigation, Residual Carrier Density 1. Introduction Since the first proposal [1] the InAs/GaSb type-II superlattice material system has been proven to be a promising choice for a variety of applications Email address: [email protected] (J. Schmidt) Preprint submitted to Proceedings of the QSIP 2016
January 30, 2017
in the field of infrared (IR) detection. By choosing the thickness of each InAs and GaSb layer, the effective cutoff wavelength can be tailored from about 3 µm to far above 12 µm, which makes it ideally suited for the design of infrared detectors. Superlattice photodiodes are used for the detection in the mid-infrared regime [2], in the long-wavelength regime [3] and also in combining different cutoff wavelengths in one detector such as dual-color devices [4]. For minority charge carrier devices like photodiodes, the residual carrier density is very important for the device performance. It defines the width of the space charge region as well as the minority carrier lifetime in the nonintentionally doped (nid) region. The charge carrier density in the nid-region of a pin-diode directly impacts the most important dark current contributions, namely the diffusion current, the generation recombination current, the direct tunneling current and also the trap-assisted tunneling current. To fit existing dark current models to measured data, i.e., understanding the limiting mechanisms in the device under test [5], the residual carrier density is a crucial parameter. In this paper, we have investigated the residual carrier density in photodiodes based on broken-gap type-II superlattice consisting of alternating layers of GaSb and InAs. The samples were grown by molecular beam epitaxy (MBE) on 3” (100) GaSb substrates with a classical pin-homojunction diode design (see figure 1). In the n-doped superlattice the donor concentration is Nd ≈ 1017 cm−3 , followed by a non-intentionally doped intrinsic region, with a very low residual carrier density. The p-doped superlattice comprises a doping density of Na ≈ 1016 cm−3 .
2
p-contact
EC EF EV
p
p-doped SL nid-SL
n-doped SL
z
n-contact
n E
GaSb-substrate
Figure 1: Schematic depiction of a pin-homojunction superlattice (SL) diode with the band edge profile.
We compare material grown on a multi-wafer system (MBE 1) and a singlewafer system (MBE 2). Both samples are designed to have a 5 µm cutoff wavelength at 77 K, where the cutoff wavelength is extracted from the responsivity spectrum at half of the maximum value. The residual carriers are p-type, as shown in ref. [6] for a superlattice composition of 10 monolayers InAs and 10 monolayers GaSb per period, which is similar to our design. This was confirmed by Hall measurements for a temperature range from 80 K up to around 200 K. For higher temperatures n-type conduction is observed. The p-type nature of the intrinsic region of our diodes is supported by responsivity measurements, which exhibit no dependence on bias voltage for moderate reverse biases. After growth, the material is mesa etched, passivated using a dielectric passivation and metallized with an ohmic contact layer and a gold bonding metal, enabling electrical connections based on standard gold-wire ball bonding. Quadratic test diodes with different sizes are fabricated for electro-optical investigation of the material. In this work, the presented data were obtained on diodes with an area of A = 400 × 400 µm2 . To extract the residual charge-carrier density, a capacitance-voltage (CV) 3
measurement technique is used. 2. Capacitance-Voltage Measurement The frequency dependent impedance of a reverse-biased diode is measured in order to extract the depletion-region capacitance, as previously reported in ref. [7]. CV profiling is optimally suited to measure the electrically active charge carrier density even for low carrier densities down to 1014 cm−3 . However, it is not possible to determine the carrier polarity using the CVtechnique. To calculate the residual carrier density the well known relation 2 A 2 Na + Nd = · (Vbi − VD ), (1) C eεr ε0 Na · Nd between the depletion-region capacitance C and the doping concentrations Na and Nd for the acceptor and donor densities is used [7]. Here εr = 15.4 denotes the dielectric constant of the material [7], ε0 is the vacuum permittivity, Vbi is the built in potential of the homojunction and VD is the voltage drop over the diode. The area of the diodes is represented as A and e denotes the elementary charge. Since Nd Na , the expression
Na +Nd Na ·Nd
in equation 1
simplifies to 1/Na . For moderate reverse biases equation 1 yields a direct relation between the residual carrier density Na and the depletion-region capacitance C of the diodes. The inverse residual charge carrier density 1/Na can be derived from the slope of the linear relationship of (A/C)2 as a function of the bias voltage VD . 3. Equivalent-Circuit Model An appropriate equivalent circuit model is required in order to accurately determine the capacitance and minimize the error from the non-ideal mea4
surement setup. Usually, a two-component equivalent circuit model consisting of either a parallel resistor or a series resistor and a capacitance is used. These equivalent circuit models differ from the actually measured impedance either for high or for low frequencies. Therefore, we use a three-component equivalent-circuit model consisting of a capacitor and a series resistor as well as a parallel resistor. For this equivalent-circuit model the frequency dependent complex impedance Z(ω) is given by RP Z(ω) = RS + −i 1 + (RP ωC)2
RP2 ωC 1 + (RP ωC)2
,
(2)
where ω is the angular frequency. For this equivalent-circuit C represents the depletion-region capacitance of the diode. The parallel resistance RP is attributed to the dark resistance of the diode and RS is the effective series resistance of the measurement. An additional series inductance accounting for the bonding wire does not need to be included in the equivalent circuit model. A typical inductance would only affect the device impedance in the GHz range, which is not addressed in this paper. 4. Experiment CV measurements are performed over a wide temperature range from 80 K to roughly 200 K, in order to extract the residual carrier density. The used setup consisted of a cryostat with a custom designed sample holder and a Keysight E4990A impedance analyzer. The contacting of the samples is done by a 50 Ω coaxial four-terminal technique. An optimal shielding of the setup is achieved by connecting the shield of the coaxial cables right at the sample position. To ensure very low stray capacitances of the wires 5
and the setup, an open/short-calibration is performed directly on the sample die. Our setup allows to measure an impedance range from about 40 mΩ to 100 MΩ. The accessible frequencies cover the wide range from 20 Hz to 5 MHz, which provides enough features of the impedance and phaseshift to extract the sample capacitance using a suitable equivalent-circuit model. Our setup combined with the large test diodes maximizes the ratio of the sample capacitance to stray capacitances, which is an essential feature for precisely quantifying the residual charge-carrier density. The magnitude of the impedance as well as the phaseshift are measured over a reverse bias voltage range at a constant temperature to vary the width of the spacecharge region. Furthermore, the dark current Id of the investigated diodes is measured using an Agilent 4156C parameter analyzer. By measuring the dark current of the diode, it is possible to calculate the internal voltage drop VD over the diode using the series resistance RS and the externally applied bias voltage Vext , as VD = Vext − RS · Id . 5. Results Figure 2 demonstrates the measured data with the fitted three component model as an example for a temperature of 120 K and 100 mV reverse bias for the sample from MBE 1. The measured impedance |Z| and phaseshift ϑ are transformed into their real (<{Z(ω)} = |Z| · cos(ϑ)) and imaginary (={Z(ω)} = |Z| · sin(ϑ)) equivalent, in order to be fitted using equation 2. The black triangles represent the measured impedance with the red line as the fitted impedance according to the three component model, the measured 6
2 0 M B E 1 , 1 2 0 K , - 1 0 0 m V B ia s P h a s e s h if t : m e a s u re d f it
I m p e d a n c e ( Ω)
1 0
5
1 0
4
Im p e d a n c e : m e a s u re d f it
-2 0 -4 0 -6 0 -8 0
R e a l: C = 2 0 .4 p F Im a g in a r y : C = 2 0 .7 p F
1 0
0
3
1 0
2
1 0
P h a s e s h ift ( ° )
6
1 0
3
4
1 0 1 0 F re q u e n c y (H z )
5
1 0
6
-1 0 0
Figure 2: Exemplary fitted impedance and phaseshift at 120 K and a reverse bias voltage of 100 mV for MBE 1.
phaseshift (blue circles) with the magenta line as the fit. At low frequencies the constant impedance and zero phaseshift indicate an ohmic resistance, which is the dark resistance of the diode. For increasing frequencies a decrease in the impedance and phaseshift approaching almost −90◦ shows a capacitance that is attributed to the depletion-region capacitance. For high frequencies the phaseshift rises again, while the impedance saturates. This indicates the influence of the series resistance. The values for the capacitance shown in the plot are derived from the fit of the real and imaginary part of the complex impedance, respectively. Both values deviate by only one percent, which is a strong indicator that the used model is a valid description for the investigated structures. The depletion-region capacitance over the entire bias range can be determined by fitting the data for every measured bias voltage. Figure 3 shows the calculated capacitance versus the measured bias voltage
7
3 2
C a p a c ita n c e ( p F )
M B E 1 , 1 2 0 K
R e Im
2 8
2 4
2 0
-0 .5
-0 .4 -0 .3 -0 .2 -0 .1 In te r n a l b ia s v o lta g e ( V )
0
Figure 3: Capacitance versus internal bias voltage at 120 K for MBE 1, with the capacitance extracted from the real and imaginary part from equation 2 in black and red, respectively
at 120 K. The capacitance calculated from the real and imaginary part of the complex impedance are in good accordance to each other for every measured bias voltage, so in the following their average is used as the depletion-region capacitance. Using equation 1 a linear fit to the (A/C)2 data from figure 4 is done to extract the carrier density in the fitted bias voltage interval. For low reverse bias voltages the nid-region is being depleted, whereas for increasing biases the p-doped superlattice starts to get depleted. Figure 4 (left) shows the data for the sample from the multi-wafer MBE system for 120 K. Here the residual carrier density is calculated as 2.5 · 1014 cm−3 with a doping density of 1.5 · 1016 cm−3 for the p-doped superlattice. Figure 4 (right) shows the same plot for the single-wafer MBE system for 120 K, where the linear fit is optimized for a residual carrier density of the nid-region of 1.1 · 1015 cm−3 and
8
y6
pVdoped SL: yf5xyu cm
7
8
bARCi² byu bm²RFi²i
7
bARCi² byu bm²RFi²i
yu
8
bARCi²Vaverage fit bintrinsici fit bpVdoped SLi
MBE yg y2u K
V3
6 4
y4
Residual carrier density: 2f5xyu cm
2 V2
Vyf5 Vy Vuf5 Internal bias voltage bVi
7 6 5
u
y6
pVdoped SL: 2f2xyu cm
V3
4 3 2
V3
bARCi²Vaverage fit bintrinsici fit bpVdoped SLi
MBE 2g y2u K
y V2
y5
Residual carrier density: yfyxyu cm
V3
Vyf5 Vy Vuf5 Internal bias voltage bVi
u
Figure 4: (A/C)2 versus internal bias voltage with linear fit for intrinsic and p-doped superlattice in red and blue respectively, both at 120 K. Left: MBE 1, right: MBE 2.
a carrier density of the p-doped superlattice of 2.2 · 1016 cm−3 . The p-doping concentration is in good accordance with the target design values being an indicator for the validity of the used approach to calculate the charge-carrier density. Figure 5 shows the residual charge-carrier density over the inverse temperature for the entire measured temperature range as red triangles for MBE 1 and black circles for MBE 2. The error bars result from the error of the linear fit of equation 1 to the depletion-region capacitances and the error of the fit of the capacitance using equation 2. The carrier densities for both samples are nearly constant over a wide temperature range. Towards higher temperatures the carrier densities approach the intrinsic carrier densities ni which are represented by red and black lines for MBE 1 and MBE 2, respectively. Our residual carrier densities are compared with published data from other groups in figure 5 in the saturation region between 150 K and 80 K. The data presented in figure 5 has been limited to samples with comparable cutoff wavelength. For MBE 2, the single-wafer system, the value of about
9
1 6
1 0
1 5
R e s id u a l c a r r ie r d e n s ity
(c m
-3
)
1 0
n i( T )
1 0
M B E M B E A . H P . C C . C G . C
1 4
n i( T )
1 0
1 3
4
6
8
1 2 o o d e t h r is to l e rv e ra h e n e t
a l. ( 2 0 0 e t a l. ( 2 e t a l. ( 2 a l. ( 2 0 1
1 0
1 2
6 ) 0 1 0 0 3 )
[7 ] 0 ) [8 ] 9 ) [9 ] [1 0 ]
1 4
1 0 0 0 /T e m p e ra tu re (1 /K )
Figure 5: Temperature dependent residual charge-carrier density with the intrinsic chargecarrier density ni for two MBE systems. In the saturation region between 150 K and 80 K mean values of 2.4 · 1014 cm−3 and 1.3 · 1015 cm−3 are found for MBE 1 and MBE 2, respectively. Compared to literature data the lowest residual carrier density is found for MBE 1.
1.3 · 1015 cm−3 is in good accordance to the different reported values. For 80 K it is almost the same, as was reported in ref. [8] and [9]. Other reported values are 6 · 1014 cm−3 [7] and more recently around 4.5 · 1014 cm−3 [10]. The residual carrier density for MBE 1, the multi-wafer MBE system is 2.4 · 1014 cm−3 , showing the lowest residual carrier density reported in literature so far for mid-wavelength infrared InAs/GaSb type-II superlattices. With these techniques it is possible to monitor the residual carrier density for different MBE systems and samples to ensure optimal quality in our epitaxy process. To further improve our understanding of the processes and the material system we are now able to use our measured residual carrier density as an input parameter to perform highly accurate dark current analysis. 10
6. Summary By refining the measurement setup it is possible to reliably measure the impedance and phaseshift of InAs/GaSb type-II superlattice photodiodes over a wide temperature range from 80 K up to around 200 K. We use a three-component equivalent-circuit model to fit the measured impedance and phaseshift in order to refine the extraction of the voltage dependent depletionregion capacitance. From the capacitance, the residual carrier density is obtained. The chosen approach yields reliable values for the carrier density. With these values we are able to evaluate different MBE systems. For our single-wafer MBE system we obtain values of 1.3 · 1015 cm−3 for the residual carrier density, whereas the residual carrier density in the multi-wafer MBE system has been determined to 2.4 · 1014 cm−3 , which is the lowest reported residual carrier density so far. This low residual carrier density reveals an excellent material quality of the measured diodes, which shows the high potential for the InAs/GaSb type-II superlattice material system. The refined measurement setup and method allows a valuable investigation of the material and therefore the monitoring and further improvement of the material quality. With these improvements, new detector designs can be realized to further improve the electro-optical performance of InAs/GaSb superlattice photodiodes. Acknowledgments The authors thank S. Fibelkorn, T. Henkel, W. Luppold and J. Niemasz for assistance in detector processing. We also thank N. Kohn and M. Wauro
11
for epitaxy of the detector material. Project funding by the German Federal Ministry of Defense is gratefully acknowledged.
12
[1] D. L. Smith, C. Mailhiot, Proposal for strained type II superlattice infrared detectors, Journal of Applied Physics 62 (6) (1987) 2545–2548. doi:10.1063/1.339468. [2] L. H¨oglund, C. Asplund, R. Marcks von W¨ urtemberg, A. Gamfeldt, H. Kataria, D. Lantz, S. Smuk, E. Costard, H. Martijn, Advantages of T2SL: results from production and new development at IRnova, Proc. of SPIE Vol. 9819 (2016) 98190Z. doi:10.1117/12.2227466. [3] D. Z. Ting, A. Soibel, J. Nguyen, L. Hoglund, A. Khoshakhlagh, S. B. Rafol, S. a. Keo, A. Liao, J. M. Mumolo, J. K. Liu, S. D. Gunapala, Type II superlattice barrier infrared detector, Proc. of SPIE Vol. 8154 (2011) 81540L–1. doi:10.1117/12.896240. [4] M. Walther, R. Rehm, J. Fleissner, J. Schmitz, J. Ziegler, W. Cabanski, R. Breiter, InAs/GaSb type-II short-period superlattices for advanced single and dual-color focal plane arrays, Proceedings of SPIE 6542 (2007) 654206–654206–8. doi:10.1117/12.719227. [5] R. Rehm, F. Lemke, J. Schmitz, M. Wauro, M. Walther, Limiting dark current mechanisms in antimony-based superlattice infrared detectors for the long-wavelength infrared regime, Proc. of SPIE Vol. 9451 (2015) 94510N. doi:10.1117/12.2177091. [6] L. Konczewicz, S. Contreras, H. A¨ıt-Kaci, Y. Cuminal, J.-B. Rodriguez, P. Christol, Effect of pressure on electrical properties of short period InAs/GaSb superlattice, Physica Status Solidi (B) 246 (3) (2009) 643– 647. doi:10.1002/pssb.200880520. 13
[7] A. Hood, D. Hoffman, Y. Wei, F. Fuchs, M. Razeghi, Capacitancevoltage investigation of high-purity InAs/GaSb superlattice photodiodes, Applied Physics Letters 88 (5) (2006) 1–3. doi:10.1063/1.2172399. [8] P. Christol, C. Cervera, R. Chaghi, H. A¨ıt-Kaci, J. B. Rodriguez, L. Konczewicz, S. Contreras, K. Jaworowicz, I. Ribet-Mohamed, Electronic Properties of InAs/GaSb Superlattice Detectors to Evaluate High Temperature Operation, Proc. of SPIE Vol. 7608 (2010) 76081U–76081U–11. doi:10.1117/12.840853. [9] C. Cervera, J. B. Rodriguez, J. P. Perez, H. At-Kaci, R. Chaghi, L. Konczewicz, S. Contreras, P. Christol, Unambiguous determination of carrier concentration and mobility for InAs/GaSb superlattice photodiode optimization, Journal of Applied Physics 106 (3). doi:10.1063/1.3191175. [10] G. Chen, a. M. Hoang, S. Bogdanov, a. Haddadi, P. R. Bijjam, B.-M. Nguyen, M. Razeghi, Investigation of impurities in type-II InAs/GaSb superlattices via capacitance-voltage measurement, Applied Physics Letters 103 (3) (2013) 033512. doi:10.1063/1.4813479.
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Highlights:
Capacitance-voltage analysis was performed on InAs/GaSb superlattice infrared pinphotodiodes.
The measurements were carried out over a wide frequency range and a wide temperature range.
The residual carrier density was calculated using a three component equivalent-circuit model and a refined measurement setup.
Two nominally equal samples from two different MBE systems were compared, one showing a very low residual carrier density in the low 1014 cm-3 range.
1
S1350-4495(16)30678-8 http://dx.doi.org/10.1016/j.infrared.2017.04.008 INFPHY 2272
To appear in:
Infrared Physics & Technology
Received Date: Revised Date: Accepted Date:
28 November 2016 30 January 2017 15 April 2017
Please cite this article as: J. Schmidt, F. Rutz, V. Daumer, R. Rehm, Capacitance-Voltage Investigation of Low Residual Carrier Density in InAs/GaSb Superlattice Infrared Detectors, Infrared Physics & Technology (2017), doi: http://dx.doi.org/10.1016/j.infrared.2017.04.008
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Capacitance-Voltage Investigation of Low Residual Carrier Density in InAs/GaSb Superlattice Infrared Detectors J. Schmidt, F. Rutz, V. Daumer, R. Rehm Fraunhofer Institute for Applied Solid State Physics, Freiburg (Germany)
Abstract Capacitance-voltage (CV) analysis was performed on homojunction InAs/GaSb superlattice photodiodes for the mid-infrared spectral range around 5 µm. The CV investigation was carried out over a wide temperature range from 80 K up to 200 K, for two nominally identical samples from two different epitaxy systems. The characterizations were carried out with a refined measurement setup, considering the impedance range, the measured frequency range and the accessible temperature range. For the calculated residual carrier density in the nid-region of the diodes values in the low 1014 cm−3 and 1015 cm−3 ranges were found, respectively. Keywords: InAs/GaSb T2SL, MWIR, Capacitance-Voltage Investigation, Residual Carrier Density 1. Introduction Since the first proposal [1] the InAs/GaSb type-II superlattice material system has been proven to be a promising choice for a variety of applications Email address: [email protected] (J. Schmidt) Preprint submitted to Proceedings of the QSIP 2016
January 30, 2017
in the field of infrared (IR) detection. By choosing the thickness of each InAs and GaSb layer, the effective cutoff wavelength can be tailored from about 3 µm to far above 12 µm, which makes it ideally suited for the design of infrared detectors. Superlattice photodiodes are used for the detection in the mid-infrared regime [2], in the long-wavelength regime [3] and also in combining different cutoff wavelengths in one detector such as dual-color devices [4]. For minority charge carrier devices like photodiodes, the residual carrier density is very important for the device performance. It defines the width of the space charge region as well as the minority carrier lifetime in the nonintentionally doped (nid) region. The charge carrier density in the nid-region of a pin-diode directly impacts the most important dark current contributions, namely the diffusion current, the generation recombination current, the direct tunneling current and also the trap-assisted tunneling current. To fit existing dark current models to measured data, i.e., understanding the limiting mechanisms in the device under test [5], the residual carrier density is a crucial parameter. In this paper, we have investigated the residual carrier density in photodiodes based on broken-gap type-II superlattice consisting of alternating layers of GaSb and InAs. The samples were grown by molecular beam epitaxy (MBE) on 3” (100) GaSb substrates with a classical pin-homojunction diode design (see figure 1). In the n-doped superlattice the donor concentration is Nd ≈ 1017 cm−3 , followed by a non-intentionally doped intrinsic region, with a very low residual carrier density. The p-doped superlattice comprises a doping density of Na ≈ 1016 cm−3 .
2
p-contact
EC EF EV
p
p-doped SL nid-SL
n-doped SL
z
n-contact
n E
GaSb-substrate
Figure 1: Schematic depiction of a pin-homojunction superlattice (SL) diode with the band edge profile.
We compare material grown on a multi-wafer system (MBE 1) and a singlewafer system (MBE 2). Both samples are designed to have a 5 µm cutoff wavelength at 77 K, where the cutoff wavelength is extracted from the responsivity spectrum at half of the maximum value. The residual carriers are p-type, as shown in ref. [6] for a superlattice composition of 10 monolayers InAs and 10 monolayers GaSb per period, which is similar to our design. This was confirmed by Hall measurements for a temperature range from 80 K up to around 200 K. For higher temperatures n-type conduction is observed. The p-type nature of the intrinsic region of our diodes is supported by responsivity measurements, which exhibit no dependence on bias voltage for moderate reverse biases. After growth, the material is mesa etched, passivated using a dielectric passivation and metallized with an ohmic contact layer and a gold bonding metal, enabling electrical connections based on standard gold-wire ball bonding. Quadratic test diodes with different sizes are fabricated for electro-optical investigation of the material. In this work, the presented data were obtained on diodes with an area of A = 400 × 400 µm2 . To extract the residual charge-carrier density, a capacitance-voltage (CV) 3
measurement technique is used. 2. Capacitance-Voltage Measurement The frequency dependent impedance of a reverse-biased diode is measured in order to extract the depletion-region capacitance, as previously reported in ref. [7]. CV profiling is optimally suited to measure the electrically active charge carrier density even for low carrier densities down to 1014 cm−3 . However, it is not possible to determine the carrier polarity using the CVtechnique. To calculate the residual carrier density the well known relation 2 A 2 Na + Nd = · (Vbi − VD ), (1) C eεr ε0 Na · Nd between the depletion-region capacitance C and the doping concentrations Na and Nd for the acceptor and donor densities is used [7]. Here εr = 15.4 denotes the dielectric constant of the material [7], ε0 is the vacuum permittivity, Vbi is the built in potential of the homojunction and VD is the voltage drop over the diode. The area of the diodes is represented as A and e denotes the elementary charge. Since Nd Na , the expression
Na +Nd Na ·Nd
in equation 1
simplifies to 1/Na . For moderate reverse biases equation 1 yields a direct relation between the residual carrier density Na and the depletion-region capacitance C of the diodes. The inverse residual charge carrier density 1/Na can be derived from the slope of the linear relationship of (A/C)2 as a function of the bias voltage VD . 3. Equivalent-Circuit Model An appropriate equivalent circuit model is required in order to accurately determine the capacitance and minimize the error from the non-ideal mea4
surement setup. Usually, a two-component equivalent circuit model consisting of either a parallel resistor or a series resistor and a capacitance is used. These equivalent circuit models differ from the actually measured impedance either for high or for low frequencies. Therefore, we use a three-component equivalent-circuit model consisting of a capacitor and a series resistor as well as a parallel resistor. For this equivalent-circuit model the frequency dependent complex impedance Z(ω) is given by RP Z(ω) = RS + −i 1 + (RP ωC)2
RP2 ωC 1 + (RP ωC)2
,
(2)
where ω is the angular frequency. For this equivalent-circuit C represents the depletion-region capacitance of the diode. The parallel resistance RP is attributed to the dark resistance of the diode and RS is the effective series resistance of the measurement. An additional series inductance accounting for the bonding wire does not need to be included in the equivalent circuit model. A typical inductance would only affect the device impedance in the GHz range, which is not addressed in this paper. 4. Experiment CV measurements are performed over a wide temperature range from 80 K to roughly 200 K, in order to extract the residual carrier density. The used setup consisted of a cryostat with a custom designed sample holder and a Keysight E4990A impedance analyzer. The contacting of the samples is done by a 50 Ω coaxial four-terminal technique. An optimal shielding of the setup is achieved by connecting the shield of the coaxial cables right at the sample position. To ensure very low stray capacitances of the wires 5
and the setup, an open/short-calibration is performed directly on the sample die. Our setup allows to measure an impedance range from about 40 mΩ to 100 MΩ. The accessible frequencies cover the wide range from 20 Hz to 5 MHz, which provides enough features of the impedance and phaseshift to extract the sample capacitance using a suitable equivalent-circuit model. Our setup combined with the large test diodes maximizes the ratio of the sample capacitance to stray capacitances, which is an essential feature for precisely quantifying the residual charge-carrier density. The magnitude of the impedance as well as the phaseshift are measured over a reverse bias voltage range at a constant temperature to vary the width of the spacecharge region. Furthermore, the dark current Id of the investigated diodes is measured using an Agilent 4156C parameter analyzer. By measuring the dark current of the diode, it is possible to calculate the internal voltage drop VD over the diode using the series resistance RS and the externally applied bias voltage Vext , as VD = Vext − RS · Id . 5. Results Figure 2 demonstrates the measured data with the fitted three component model as an example for a temperature of 120 K and 100 mV reverse bias for the sample from MBE 1. The measured impedance |Z| and phaseshift ϑ are transformed into their real (<{Z(ω)} = |Z| · cos(ϑ)) and imaginary (={Z(ω)} = |Z| · sin(ϑ)) equivalent, in order to be fitted using equation 2. The black triangles represent the measured impedance with the red line as the fitted impedance according to the three component model, the measured 6
2 0 M B E 1 , 1 2 0 K , - 1 0 0 m V B ia s P h a s e s h if t : m e a s u re d f it
I m p e d a n c e ( Ω)
1 0
5
1 0
4
Im p e d a n c e : m e a s u re d f it
-2 0 -4 0 -6 0 -8 0
R e a l: C = 2 0 .4 p F Im a g in a r y : C = 2 0 .7 p F
1 0
0
3
1 0
2
1 0
P h a s e s h ift ( ° )
6
1 0
3
4
1 0 1 0 F re q u e n c y (H z )
5
1 0
6
-1 0 0
Figure 2: Exemplary fitted impedance and phaseshift at 120 K and a reverse bias voltage of 100 mV for MBE 1.
phaseshift (blue circles) with the magenta line as the fit. At low frequencies the constant impedance and zero phaseshift indicate an ohmic resistance, which is the dark resistance of the diode. For increasing frequencies a decrease in the impedance and phaseshift approaching almost −90◦ shows a capacitance that is attributed to the depletion-region capacitance. For high frequencies the phaseshift rises again, while the impedance saturates. This indicates the influence of the series resistance. The values for the capacitance shown in the plot are derived from the fit of the real and imaginary part of the complex impedance, respectively. Both values deviate by only one percent, which is a strong indicator that the used model is a valid description for the investigated structures. The depletion-region capacitance over the entire bias range can be determined by fitting the data for every measured bias voltage. Figure 3 shows the calculated capacitance versus the measured bias voltage
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3 2
C a p a c ita n c e ( p F )
M B E 1 , 1 2 0 K
R e Im
2 8
2 4
2 0
-0 .5
-0 .4 -0 .3 -0 .2 -0 .1 In te r n a l b ia s v o lta g e ( V )
0
Figure 3: Capacitance versus internal bias voltage at 120 K for MBE 1, with the capacitance extracted from the real and imaginary part from equation 2 in black and red, respectively
at 120 K. The capacitance calculated from the real and imaginary part of the complex impedance are in good accordance to each other for every measured bias voltage, so in the following their average is used as the depletion-region capacitance. Using equation 1 a linear fit to the (A/C)2 data from figure 4 is done to extract the carrier density in the fitted bias voltage interval. For low reverse bias voltages the nid-region is being depleted, whereas for increasing biases the p-doped superlattice starts to get depleted. Figure 4 (left) shows the data for the sample from the multi-wafer MBE system for 120 K. Here the residual carrier density is calculated as 2.5 · 1014 cm−3 with a doping density of 1.5 · 1016 cm−3 for the p-doped superlattice. Figure 4 (right) shows the same plot for the single-wafer MBE system for 120 K, where the linear fit is optimized for a residual carrier density of the nid-region of 1.1 · 1015 cm−3 and
8
y6
pVdoped SL: yf5xyu cm
7
8
bARCi² byu bm²RFi²i
7
bARCi² byu bm²RFi²i
yu
8
bARCi²Vaverage fit bintrinsici fit bpVdoped SLi
MBE yg y2u K
V3
6 4
y4
Residual carrier density: 2f5xyu cm
2 V2
Vyf5 Vy Vuf5 Internal bias voltage bVi
7 6 5
u
y6
pVdoped SL: 2f2xyu cm
V3
4 3 2
V3
bARCi²Vaverage fit bintrinsici fit bpVdoped SLi
MBE 2g y2u K
y V2
y5
Residual carrier density: yfyxyu cm
V3
Vyf5 Vy Vuf5 Internal bias voltage bVi
u
Figure 4: (A/C)2 versus internal bias voltage with linear fit for intrinsic and p-doped superlattice in red and blue respectively, both at 120 K. Left: MBE 1, right: MBE 2.
a carrier density of the p-doped superlattice of 2.2 · 1016 cm−3 . The p-doping concentration is in good accordance with the target design values being an indicator for the validity of the used approach to calculate the charge-carrier density. Figure 5 shows the residual charge-carrier density over the inverse temperature for the entire measured temperature range as red triangles for MBE 1 and black circles for MBE 2. The error bars result from the error of the linear fit of equation 1 to the depletion-region capacitances and the error of the fit of the capacitance using equation 2. The carrier densities for both samples are nearly constant over a wide temperature range. Towards higher temperatures the carrier densities approach the intrinsic carrier densities ni which are represented by red and black lines for MBE 1 and MBE 2, respectively. Our residual carrier densities are compared with published data from other groups in figure 5 in the saturation region between 150 K and 80 K. The data presented in figure 5 has been limited to samples with comparable cutoff wavelength. For MBE 2, the single-wafer system, the value of about
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1 6
1 0
1 5
R e s id u a l c a r r ie r d e n s ity
(c m
-3
)
1 0
n i( T )
1 0
M B E M B E A . H P . C C . C G . C
1 4
n i( T )
1 0
1 3
4
6
8
1 2 o o d e t h r is to l e rv e ra h e n e t
a l. ( 2 0 0 e t a l. ( 2 e t a l. ( 2 a l. ( 2 0 1
1 0
1 2
6 ) 0 1 0 0 3 )
[7 ] 0 ) [8 ] 9 ) [9 ] [1 0 ]
1 4
1 0 0 0 /T e m p e ra tu re (1 /K )
Figure 5: Temperature dependent residual charge-carrier density with the intrinsic chargecarrier density ni for two MBE systems. In the saturation region between 150 K and 80 K mean values of 2.4 · 1014 cm−3 and 1.3 · 1015 cm−3 are found for MBE 1 and MBE 2, respectively. Compared to literature data the lowest residual carrier density is found for MBE 1.
1.3 · 1015 cm−3 is in good accordance to the different reported values. For 80 K it is almost the same, as was reported in ref. [8] and [9]. Other reported values are 6 · 1014 cm−3 [7] and more recently around 4.5 · 1014 cm−3 [10]. The residual carrier density for MBE 1, the multi-wafer MBE system is 2.4 · 1014 cm−3 , showing the lowest residual carrier density reported in literature so far for mid-wavelength infrared InAs/GaSb type-II superlattices. With these techniques it is possible to monitor the residual carrier density for different MBE systems and samples to ensure optimal quality in our epitaxy process. To further improve our understanding of the processes and the material system we are now able to use our measured residual carrier density as an input parameter to perform highly accurate dark current analysis. 10
6. Summary By refining the measurement setup it is possible to reliably measure the impedance and phaseshift of InAs/GaSb type-II superlattice photodiodes over a wide temperature range from 80 K up to around 200 K. We use a three-component equivalent-circuit model to fit the measured impedance and phaseshift in order to refine the extraction of the voltage dependent depletionregion capacitance. From the capacitance, the residual carrier density is obtained. The chosen approach yields reliable values for the carrier density. With these values we are able to evaluate different MBE systems. For our single-wafer MBE system we obtain values of 1.3 · 1015 cm−3 for the residual carrier density, whereas the residual carrier density in the multi-wafer MBE system has been determined to 2.4 · 1014 cm−3 , which is the lowest reported residual carrier density so far. This low residual carrier density reveals an excellent material quality of the measured diodes, which shows the high potential for the InAs/GaSb type-II superlattice material system. The refined measurement setup and method allows a valuable investigation of the material and therefore the monitoring and further improvement of the material quality. With these improvements, new detector designs can be realized to further improve the electro-optical performance of InAs/GaSb superlattice photodiodes. Acknowledgments The authors thank S. Fibelkorn, T. Henkel, W. Luppold and J. Niemasz for assistance in detector processing. We also thank N. Kohn and M. Wauro
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for epitaxy of the detector material. Project funding by the German Federal Ministry of Defense is gratefully acknowledged.
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[1] D. L. Smith, C. Mailhiot, Proposal for strained type II superlattice infrared detectors, Journal of Applied Physics 62 (6) (1987) 2545–2548. doi:10.1063/1.339468. [2] L. H¨oglund, C. Asplund, R. Marcks von W¨ urtemberg, A. Gamfeldt, H. Kataria, D. Lantz, S. Smuk, E. Costard, H. Martijn, Advantages of T2SL: results from production and new development at IRnova, Proc. of SPIE Vol. 9819 (2016) 98190Z. doi:10.1117/12.2227466. [3] D. Z. Ting, A. Soibel, J. Nguyen, L. Hoglund, A. Khoshakhlagh, S. B. Rafol, S. a. Keo, A. Liao, J. M. Mumolo, J. K. Liu, S. D. Gunapala, Type II superlattice barrier infrared detector, Proc. of SPIE Vol. 8154 (2011) 81540L–1. doi:10.1117/12.896240. [4] M. Walther, R. Rehm, J. Fleissner, J. Schmitz, J. Ziegler, W. Cabanski, R. Breiter, InAs/GaSb type-II short-period superlattices for advanced single and dual-color focal plane arrays, Proceedings of SPIE 6542 (2007) 654206–654206–8. doi:10.1117/12.719227. [5] R. Rehm, F. Lemke, J. Schmitz, M. Wauro, M. Walther, Limiting dark current mechanisms in antimony-based superlattice infrared detectors for the long-wavelength infrared regime, Proc. of SPIE Vol. 9451 (2015) 94510N. doi:10.1117/12.2177091. [6] L. Konczewicz, S. Contreras, H. A¨ıt-Kaci, Y. Cuminal, J.-B. Rodriguez, P. Christol, Effect of pressure on electrical properties of short period InAs/GaSb superlattice, Physica Status Solidi (B) 246 (3) (2009) 643– 647. doi:10.1002/pssb.200880520. 13
[7] A. Hood, D. Hoffman, Y. Wei, F. Fuchs, M. Razeghi, Capacitancevoltage investigation of high-purity InAs/GaSb superlattice photodiodes, Applied Physics Letters 88 (5) (2006) 1–3. doi:10.1063/1.2172399. [8] P. Christol, C. Cervera, R. Chaghi, H. A¨ıt-Kaci, J. B. Rodriguez, L. Konczewicz, S. Contreras, K. Jaworowicz, I. Ribet-Mohamed, Electronic Properties of InAs/GaSb Superlattice Detectors to Evaluate High Temperature Operation, Proc. of SPIE Vol. 7608 (2010) 76081U–76081U–11. doi:10.1117/12.840853. [9] C. Cervera, J. B. Rodriguez, J. P. Perez, H. At-Kaci, R. Chaghi, L. Konczewicz, S. Contreras, P. Christol, Unambiguous determination of carrier concentration and mobility for InAs/GaSb superlattice photodiode optimization, Journal of Applied Physics 106 (3). doi:10.1063/1.3191175. [10] G. Chen, a. M. Hoang, S. Bogdanov, a. Haddadi, P. R. Bijjam, B.-M. Nguyen, M. Razeghi, Investigation of impurities in type-II InAs/GaSb superlattices via capacitance-voltage measurement, Applied Physics Letters 103 (3) (2013) 033512. doi:10.1063/1.4813479.
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Highlights:
Capacitance-voltage analysis was performed on InAs/GaSb superlattice infrared pinphotodiodes.
The measurements were carried out over a wide frequency range and a wide temperature range.
The residual carrier density was calculated using a three component equivalent-circuit model and a refined measurement setup.
Two nominally equal samples from two different MBE systems were compared, one showing a very low residual carrier density in the low 1014 cm-3 range.
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