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Enhancement of dopant solubility in compound semiconductors during crystal growth
Materials Science in Semiconductor Processing 90 (2019) 259–262
Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Enhancement of dopant solubility in compound semiconductors during crystal growth
T
Ching-Hua Su Materials and Processing Laboratory, EM31 NASA/Marshall Space Flight Center, Huntsville, AL 35812 USA
ARTICLE INFO
ABSTRACT
Keywords: Solubility Dopant Directional solidification Lead telluride
Doping of semiconductors is a process of intentionally incorporating impurity into the materials to adjust and optimize the electrical properties during the processing of semiconductors. The doping level has certain upper limit, which is usually corresponding to the solubility of the dopant in the host material under processing conditions. Sometimes, the maximum solubility level is still not high enough to provide the desired opto-electronic properties and a higher doping level is needed. Hence, enhancing the dopant level is one of the critical issues in the semiconductor industry, especially for those advanced devices made from compound semiconductors, including binary, ternary, as well as multi-component compounds. In this report, we designed a processing method, by simply varying a processing parameter during melt growth, to increase the doping level in the compound semiconductors well above the maximum values obtained under otherwise regular processing procedures and demonstrated it in the melt growth of Cl-doped PbTe.
1. Introduction Doping of semiconductors is a process of intentionally incorporating impurity into semiconducting materials to adjust and optimize the electrical properties of the processed semiconductors. It has been adopted ubiquitously during material processing of semiconductors to meet the technical requirements of the electronic and opto-electronic devices manufactured in the semiconductor industry. The electrical property of semiconductor is dictated by its doping level with certain upper limit, which is usually corresponding to the solubility of the dopant in the host material during the processing of the semiconductors. The solubility limit is fixed by nature through the physical/ chemical interaction between the dopants and the host elements under the processing environment. Sometimes, the maximum solubility level is still not high enough to provide the desired opto-electronic properties and a higher doping level is needed. Therefore, maximizing the dopant level is one of the critical issues in the semiconductor industry, especially for those advanced devices made from compound semiconductors, including binary, ternary, and multi-component compounds. Most of these compound semiconductors consist of two sublattices (A)(B), such as (Cd)(Te), (Hg1-xCdx)(Te), (Cd1-xZnx)(Te1ySey) for the group II-VI compounds, (In)(Sb), (Ga1-xInx)(P) for III-V, (Pb)(Te), (Pb1-xSn)(Te1-ySey) for IV-VI, and (Ag1-xSbx)(Te2) and (Pb1-xyAgxSby)(Te) for the I-V-VI and IV-I-V-VI compounds. In the case of a compound semiconductor, AxBy, formed from x
atoms/moles of element A and y atoms/moles of B, which requires specified electrical properties to satisfy certain electronic and optoelectronic applications. However, the maximum doping level is limited by the solubility of the dopant in the host semiconductor AxBy. In some processes, the concentration of dopant in the starting material, intentionally prepared to exceed its solubility limit, was either quenched or hot-pressed in through the manufacturing process. During the time of device applications, the excessive dopants would precipitate out from the matrix to form a second phase, which reduces the carrier concentration in the matrix as well as hinders the carrier mobility through scattering mechanism from second phase. On the other hand, during the process of melt crystal growth, the material is formed in a quasi-equilibrium condition, which results in homogeneous solid structure in a lower-energy state and, consequently, more thermally stable and mechanically robust [1]. However, even in the case of melt growth by Bridgman technique, the doping efficiency can still be a problem [2]. During the p-type doping of CdTe for the application of solar cell, the extra Phosphorus dopant can incorporate into second phase defects, most likely as Cd3P2, limiting the electrical effectiveness of the dopant. The paper [2] claimed that proper post-processing, annealing regimes, as well as growth parameter manipulation in terms of stoichiometry, cooling rate, etc., can be developed for maximizing solubility. A wider range of doping will provide the materials for the manufacturing of semiconducting devices in other applications, such as thermoelectrics, where the electrical conductivity of compound semiconductors needs to be optimized. The applications of
E-mail address: [email protected]. https://doi.org/10.1016/j.mssp.2018.10.036 Received 9 October 2018; Received in revised form 23 October 2018; Accepted 30 October 2018 1369-8001/ Published by Elsevier Ltd.
Materials Science in Semiconductor Processing 90 (2019) 259–262
C.-H. Su
thermoelectric semiconducting compounds consist of various material systems, including half-Heuslers [3], lead telluride [4–6], germanium telluride [7] and bismuth telluride [8]. In this report, following a thermodynamic analysis on the defect chemistry of compound semiconductors [9] we have designed a processing method, by simply varying a processing parameter during melt growth, to increase the doping level in the compound semiconductors well above the maximum values obtained under otherwise regular processing procedures and demonstrated the method in the melt growth of Cl-doped PbTe. 2. Theoretical concepts The electrical property of semiconductor is dictated by its doping level with certain upper limit, the solubility of the dopant element, which is an inherent nature of the physical-chemical interactions between the dopant and the host elements under the processing environment. The dissolution of dopants in the host material to form a solid solution, is the nature of materials to reduce the Gibbs energy of formation by increasing the entropy term [9]. Therefore, the solubility, i.e., the maximum amount of solute can be dissolved, is zero both at temperature of absolute zero and at the maximum melting temperature due to the phase transition. Along the temperatures in-between, the solubility goes through a maximum as a function of temperature, known as retrograde solubility. Considering a simple case of compound semiconductor, AB, formed from one moles of element A and one moles of B (the results can be easily extended to AxBy), which requires higher electrical conductivity to satisfy certain opto-electronic applications. The result from a thermodynamic defect chemistry derivation [9] for a compound semiconductor AB with a dopant D, which substitutes the sub-lattice of B atom, gives:
µD (B) = µB + RTlnCD (B ) + µDo (B ) (T )
Fig. 1. A schematic phase diagram of the compound semiconductor AB.
also be employed during the process of melt growth, vapor growth, or solid state high temperature sintering of compound semiconductors. Only the results of the melt growth of Cl-doped PbTe will be demonstrated here. For the simple case of compound semiconductor, such as AB, there is always a compositional range, between absolute zero temperature and maximum melting temperature that the solid AB can exist as shown schematically by the phase diagram of A-B in Fig. 1, where the narrow range has been exaggerated. The AB compound has a maximum melting point of TM, at a composition of xB, shown slightly larger than 50 at% in this case. The regular doping process in melt growth usually starts with preparing a homogenized ingot of stoichiometric composition of AB mixed with a certain concentration of dopant. After the sample being heated to above the melting point of TM, the melt is cooled down slowly along the ingot length and D-doped AB compound is grown. As stated early, to increase the dopant content from this regular process, the chemical potential of B during the process needs to be reduced. At a fixed temperature Tg, lower than TM, as shown in Fig. 1, the phase boundaries, from low to high xB, between liquid (L), liquid+solid (L +S), AB solid (ABS), liquid+solid (L+S), and liquid (L),are determined by four different compositions of xB. During the regular melt growth doping process, the melt of starting material, with the stoichiometric composition, will solidify at the maximum melting temperature of TM. Therefore, the chemical potential of B cannot be adjusted to raise the dopant content. However, at a lower temperature Tg, the chemical potential of B, μB, as functions of xB, shown schematically in Fig. 2, increases monotonically with xB in the one-phase region, L or S, and remain constant as μBA and μBB in the twophase (liquid+solid) regions. The chemical potential of B increases tremendously from, μBA, at one end of the solid of composition of xsBA that saturated with A element to, μBB, at the other end of xsBB that saturated with element B. By adopting a doped starting material with a composition of xlBA and solidifying it, the frozen solid, with a composition of xsBA, will have the lowest possible chemical potential of B at the temperature of Tg, and, consequently, a higher doping content. At a fixed temperature, the sum of the chemical potentials of A and B is a stoichiometric invariant over the homogeneity range of the solid compound [9] as shown in Fig. 2. Therefore, the chemical potential of A decreases accordingly from the A-saturated to the B-saturated compositions inside the homogeneity range. Using the same principle, to enhance the concentration of a dopant that substitutes the sub-lattice of A atom, one should lower the chemical potential of its substituting element, i.e., A, under the processing temperature of Tg by employing a doped starting material with a melt composition of xlBB.
(1)
where μD(B) is the chemical potential of dopant D, μB is the chemical potential of B, CD(B) is the dopant concentration, μοD(B) is the excess Gibbs energy of formation for one mole of D substituting one mole of B atoms, R is the gas constant, T is temperature in K. The second term of the equation on the right is basically the entropy for mixing D with B atoms. Since μοD(B) is an inherent material property, the relationship between the dopant concentration, CD(B), and the chemical potentials of D and B under the processing condition can be rearranged as:
CD (B ) = Ae
µD (B) µB RT
(2)
o µD (B ) (T ) RT
is a constant at a fixed temperature. For a prewhere A = e scribed constant μD(B), i.e., under a specific thermodynamic processing condition for the dopant D, the dopant concentration is:
CD (B )
µB
e RT
(3)
which implies that the lower the μB, the higher the dopant concentration. During the process of doping in an elemental semiconductor B, such as the dopant of In substituting Ge lattice [10], the chemical potential of Ge is fixed as that of the pure Ge. From Eq. (3), the concentration of In, CIn, is constant and determined only by the processing condition as shown in Eq. (2). However, for a compound semiconductor, such as AB, the chemical of B varies tremendously across the existing narrow homogeneity range of the compound AB. Hence, the dopant concentration in a compound semiconductor can be raised by lowering the chemical potential of its substituting element under the processing condition. The essence of practicing this principle of maximizing dopant level is to design the crystal growth conditions corresponding to the lowest chemical potential for the substituting element during doping process. This technique of enhancing the dopant level can be applied not only to simple binary compound of AB, but also to ternary, quaternary, as well as multi-components compounds. It can 260
Materials Science in Semiconductor Processing 90 (2019) 259–262
C.-H. Su
Fig. 3. The schematics of a typical initial ampoule position during growth of directional solidification.
Fig. 2. Schematic plots of chemical potentials of A, μA and B, μB, as a function of XB at temperature Tg.
form of 99.999% purity PbCl2. The weighed starting materials were loaded inside fused silica ampoules and sealed under vacuum condition. The ampoule was placed inside a tubular rocking furnace for the melting and mixing of the charge. The ampoules were opened and the homogenized ingots were retrieved for crystal growth. The growth ampoules were made of fused silica of 19 mm OD, 16 mm ID with a slightly tapered end at the growth tip. After the homogenized ingot has been loaded inside, the growth ampoule was sealed under a vacuum condition lower than 10−5 Torr. The growth furnace has four independently controlled electrical-resistance heating zones that provided two temperature plateaus of about 970 °C at the top and 850 °C at the bottom with a thermal gradient of 15 °C/cm in between. As shown in Fig. 3, the homogenized sample in the ampoule is placed inside a furnace with such a thermal profile that, initially, the temperature of the starting material is above the pre-selected growth temperature Tg. As the furnace translation upward, the thermal environment of the ampoule will cool down slowly from the ampoule bottom and solidify the sample from its bottom tip initially and eventually through the whole ingot. After furnace translating about 12 cm, with a rate of 4.88 ± 0.10 mm/h, the solidified samples were cooled down to room temperature by turning off the power to the furnace. Except the different compositions of the starting materials, the crystals were grown using the same process. The grown cylindrical crystals were about 6.3 cm long. To be consistent for the comparison, a rectangular bar with dimension of 2.5 × 2.5 × 13 mm was cut from each crystal boule at location between 2.6 and 2.85 cm from the first freeze tip. The electrical conductivity at 37 °C was determined by measuring the slope of the linear I-V curve measured from 10 data points. After the electrical conductivity measurements, the Cl contents, in the PT-12 and PT-20 samples, were measured by the chemical analysis method of Glow Discharge Mass Spectroscopy (GDMS) provided by Evans Analytical Group (EVG).
3. Experimental The proposed method has been demonstrated in the melt growth of Cl-doping in the IV-VI compound semiconductor of PbTe. The first step in the enhancement of dopant level was to identify the structure of the targeted compound semiconductors and the sub-lattice of the element that will be substituted by the dopant. The dopant Cl, as a Group VII element, substitutes Te lattice site as a donor. Therefore, to reduce the chemical potential of Te, a Pb-rich starting material has been employed to raise the Cl-doping level. From the phase diagram of Pb-Te, at a temperature Tg, lower than the melting point of the compound, find out the composition of the liquidus point having the lower content of the substituting element. The following step is to weigh out the amounts of elements, corresponding to that composition, and to homogenize it with the dopant in a fused silica ampoule for the melt growth of directional solidification. To compare the resultant electrical conductivity and doping levels, two sets of crystals were processed by the regular method as well as by the technique proposed here. As shown in Table 1, the first set of crystals were doped with 0.70 at% Cl. The crystal PT-12 has a starting composition very close to the stoichiometric PbTe with a maximum melting point of 924 °C, whereas the second crystal, PT-20, is Pb-rich and its composition of xPb = 0.5474, which corresponds to a liquidus temperature of about 900 °C from the phase diagram of PbTe [11]. The third crystal PT-21, with the Pb content of xPb = 0.5226, was between that of PT-12 and PT-20 with a liquidus of 911 °C. These three samples have roughly the same Cl doping content of 0.70 at%. In the second set of crystals, PT-8, has a stoichiometric starting composition, whereas the other crystal, PT-23, has a composition of xPb = 0.5464, similar to that of PT-20. Both samples have about the same Cl doping content of 1.0 at%. The Cl-doped PbTe crystals were grown by the un-seeded vertical directional solidification method. The total mass and composition of the samples are listed in Table 1. The starting materials were elements of Pb, 99.9999% purity, Te, 99.99999% purity, and the Cl dopant in the Table 1 Growth parameters and characterization results for five Cl-doped PbTe samples. Crystal
Total mass (g)
Starting composition
Comparison between samples with starting Cl content of 0.70 at% PT-12 97.52 Pb0.4986Te0.4945Cl0.00687 PT-20 98.25 Pb0.5474Te0.4454Cl0.00719 PT-21 97.92 Pb0.5226Te0.4703Cl0.00714 Comparison between samples with starting Cl content of 1.0 at% PT-8 98.57 Pb0.4991Te0.4910Cl0.00988 PT-23 98.51 Pb0.5464Te0.4434Cl0.01017
Liquidus temperature (°C)
Electrical conductivity (S/m)
Measured xsCl
924 900 911
4.15 × 105 8.67 × 105 6.98 × 105
0.00132 0.00354
924 900
5.81 × 105 9.39 × 105
261
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4. Results
shows no dependence on the chemical potential of B,:
µD (i) = RTlnCD (i) + µDo (i) (T )
The results show that, among the starting materials with the same Cl content of 0.70 at%, the crystal, PT-20, grown from Pb-saturated condition at 900 °C, has 2.1 times higher electrical conductivity than that of crystal PT-12, grown from the stoichiometric composition at 924 °C (the regular process). The GDMS data show a 2.7 times higher Cl dopant content xsCl, in the PT-20 sample, which confirms that the increase in electrical conductivity was originated from the Cl dopants, not from other native point defects such as vacancy or interstitial. It also shows that the estimated segregation coefficient, defined as xlCl/xsCl, has reduced from 5.2 for PT-12, to 2.0 for PT-20. The crystal of PT-21, with Pb-content in-between that of PT-12 and PT-20, resulted in an electrical conductivity between them, as expected, and about 1.68 times higher than that of sample PT-12. Comparing the two crystals grown from the initial Cl content of 1 at%, the off stoichiometric sample PT-23 with xPb = 0.5464, has an electrical conductivity about 1.7 times of the sample of PT-8, grown from starting stoichiometric composition. The experiments were a simple test of the claimed method of raising dopant level. The final maximization of dopant level will be determined from several more growth experiments at different Tg with the corresponding starting material compositions to delineate the solidus curve.
(4)
Most of the times, the doping process for melt growth has been practiced by adding the element of dopant to a stoichiometric composition of compound semiconductors as the starting material and the molten sample is directionally solidified. In some cases, off-stoichiometric melt has been employed in the solution growth, such as Traveling Heater Method (THM), with the main purpose of lowering the growth temperature [12]. The novel feature of this report is the concept of raising the dopant concentration in the grown compound semiconductor by lowering the chemical potential of its substituting element under the processing condition. For the melt growth, this can be accomplished by employed a slightly off-stoichiometric starting material and process the growth by the regular solidification process. In the vapor growth, the lowering of the chemical potential of the element can be accomplished either by lowering the partial pressure of that element or by increasing the partial pressures of other elements. The benefits of its application is the possibility of a much wider and flexible range of doping level which can also be applied to almost all of the multicomponents compound semiconductors. The modern advanced optical and electronic semiconducting devices made from compound semiconductors have various commercial applications which require a wide range of electrical property. The method presented here will extend the upper limit of the doping levels to a wider range and, consequently, will provide the materials for the manufacturing of potential semiconducting devices in various applications, including solar cells, where high solubility of dopant is needed to reduce precipitates, and semiconductor lasers, where heavily doping is required, as well as for thermoelectrics, where the peak temperature of figure of merit can be adjusted by electrical conductivity [13].
5. Discussions In applying the method described above, there are few issues need to be noted: a) The selection of Tg should be different for different systems. To maximize the doping level, the data of the homogeneity range of the compound is needed and, in the case of absence of information, several growth experimental results with different Tg might be helpful to optimize the process. b) Various compound semiconductors have their own phase diagrams, depending on the physical/chemical natures of each element involved. Most of the phase diagrams have the properties similar to Figs. 1 and 2 shown above. However, a few systems might have homogeneity ranges shift so much that they are completely outside the stoichiometric composition, either A-rich or B-rich. In this case, it might be complicated to find a temperature Tg that would maximize the dopant level. c) In some other material systems, the homogeneity range can be rather wide for a range of temperature. The crystal grown from the offstoichiometric melt, with a large deviation from stoichiometry, might result in second-phase precipitates during cooling because of the retrograde solubility curve as shown in Fig. 1. A large amount of precipitates might hinder the mobility of electrical carriers and results in low electrical conductivity. d) When selecting the growth temperature Tg, it should be noted that with a starting composition further away from the stoichiometry, as the sample solidifies from the bottom, more extra off-stoichiometric element will be pushed to the final section of the grown ingot, which results in the off-stoichiometric materials with bad crystalline quality, such as precipitates, at the top of the grown ingot. e) When the dopant was incorporated into interstitial site [9], the method claimed here will not work as the chemical potential of interstitial D, as compared to the substitution case presented in Eq. (1),
Acknowledgements The author would like to acknowledge the supports of Space Life and Physical Sciences Division, Human Exploration and Operations Mission Directorate, NASA Headquarters Washington, D.C. United States. References [1] Ching-Hua Su, Mater. Sci. Semicond. Proc. 56 (2016) 94. [2] J.J. McCoy, S.K. Swain, J.R. Sieber, D.R. Diercks, B.P. Gorman, K.G. Lynn, J. Appl. Phys. 123 (2018) 161579. [3] O. Appel, M. Schwall, M. Kohne, B. Balke, Y. Gelbstein, J. Electron. Mater. 42 (2013) 1340. [4] Y. Gelbstein, J. Electron. Mater. 40 (2011) 533. [5] Ching-Hua Su, J. Cryst. Growth 439 (2016) 80. [6] Ching-Hua Su, Curr. Smart Mater. 2 (2017) 3. [7] E. Hazan, N. Madar, M. Parag, V. Casian, O. Ben-Yehuda, Y. Gelbstein, Adv. Electron. Mater. (2015) 1500228. [8] R. Vizel, T. Bargig, O. Beeri, Y. Gelbstein, J. Electron. Mater. 45 (2016) 1296. [9] R.F. Brebrick, Progress in solid state chemistry, 3, Pergamon Press, Oxford, 1967, p. 213. [10] Ching-Hua Su, R.F. Brebrick, J. Phys. Chem. Solids 46 (1985) 963. [11] J.C. Lin, K.C. Hsieh, R.C. Sharma, Y.A. Chang, Bull. Alloy Phase Diagr. 10 (1989) 340. [12] R. Triboulet, Handbook of Crystal Growth, Elsevier, 2015, p. 459. [13] C.-H. Su, Mater. Today Phys. 6 (2018) 1.
262
Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Enhancement of dopant solubility in compound semiconductors during crystal growth
T
Ching-Hua Su Materials and Processing Laboratory, EM31 NASA/Marshall Space Flight Center, Huntsville, AL 35812 USA
ARTICLE INFO
ABSTRACT
Keywords: Solubility Dopant Directional solidification Lead telluride
Doping of semiconductors is a process of intentionally incorporating impurity into the materials to adjust and optimize the electrical properties during the processing of semiconductors. The doping level has certain upper limit, which is usually corresponding to the solubility of the dopant in the host material under processing conditions. Sometimes, the maximum solubility level is still not high enough to provide the desired opto-electronic properties and a higher doping level is needed. Hence, enhancing the dopant level is one of the critical issues in the semiconductor industry, especially for those advanced devices made from compound semiconductors, including binary, ternary, as well as multi-component compounds. In this report, we designed a processing method, by simply varying a processing parameter during melt growth, to increase the doping level in the compound semiconductors well above the maximum values obtained under otherwise regular processing procedures and demonstrated it in the melt growth of Cl-doped PbTe.
1. Introduction Doping of semiconductors is a process of intentionally incorporating impurity into semiconducting materials to adjust and optimize the electrical properties of the processed semiconductors. It has been adopted ubiquitously during material processing of semiconductors to meet the technical requirements of the electronic and opto-electronic devices manufactured in the semiconductor industry. The electrical property of semiconductor is dictated by its doping level with certain upper limit, which is usually corresponding to the solubility of the dopant in the host material during the processing of the semiconductors. The solubility limit is fixed by nature through the physical/ chemical interaction between the dopants and the host elements under the processing environment. Sometimes, the maximum solubility level is still not high enough to provide the desired opto-electronic properties and a higher doping level is needed. Therefore, maximizing the dopant level is one of the critical issues in the semiconductor industry, especially for those advanced devices made from compound semiconductors, including binary, ternary, and multi-component compounds. Most of these compound semiconductors consist of two sublattices (A)(B), such as (Cd)(Te), (Hg1-xCdx)(Te), (Cd1-xZnx)(Te1ySey) for the group II-VI compounds, (In)(Sb), (Ga1-xInx)(P) for III-V, (Pb)(Te), (Pb1-xSn)(Te1-ySey) for IV-VI, and (Ag1-xSbx)(Te2) and (Pb1-xyAgxSby)(Te) for the I-V-VI and IV-I-V-VI compounds. In the case of a compound semiconductor, AxBy, formed from x
atoms/moles of element A and y atoms/moles of B, which requires specified electrical properties to satisfy certain electronic and optoelectronic applications. However, the maximum doping level is limited by the solubility of the dopant in the host semiconductor AxBy. In some processes, the concentration of dopant in the starting material, intentionally prepared to exceed its solubility limit, was either quenched or hot-pressed in through the manufacturing process. During the time of device applications, the excessive dopants would precipitate out from the matrix to form a second phase, which reduces the carrier concentration in the matrix as well as hinders the carrier mobility through scattering mechanism from second phase. On the other hand, during the process of melt crystal growth, the material is formed in a quasi-equilibrium condition, which results in homogeneous solid structure in a lower-energy state and, consequently, more thermally stable and mechanically robust [1]. However, even in the case of melt growth by Bridgman technique, the doping efficiency can still be a problem [2]. During the p-type doping of CdTe for the application of solar cell, the extra Phosphorus dopant can incorporate into second phase defects, most likely as Cd3P2, limiting the electrical effectiveness of the dopant. The paper [2] claimed that proper post-processing, annealing regimes, as well as growth parameter manipulation in terms of stoichiometry, cooling rate, etc., can be developed for maximizing solubility. A wider range of doping will provide the materials for the manufacturing of semiconducting devices in other applications, such as thermoelectrics, where the electrical conductivity of compound semiconductors needs to be optimized. The applications of
E-mail address: [email protected]. https://doi.org/10.1016/j.mssp.2018.10.036 Received 9 October 2018; Received in revised form 23 October 2018; Accepted 30 October 2018 1369-8001/ Published by Elsevier Ltd.
Materials Science in Semiconductor Processing 90 (2019) 259–262
C.-H. Su
thermoelectric semiconducting compounds consist of various material systems, including half-Heuslers [3], lead telluride [4–6], germanium telluride [7] and bismuth telluride [8]. In this report, following a thermodynamic analysis on the defect chemistry of compound semiconductors [9] we have designed a processing method, by simply varying a processing parameter during melt growth, to increase the doping level in the compound semiconductors well above the maximum values obtained under otherwise regular processing procedures and demonstrated the method in the melt growth of Cl-doped PbTe. 2. Theoretical concepts The electrical property of semiconductor is dictated by its doping level with certain upper limit, the solubility of the dopant element, which is an inherent nature of the physical-chemical interactions between the dopant and the host elements under the processing environment. The dissolution of dopants in the host material to form a solid solution, is the nature of materials to reduce the Gibbs energy of formation by increasing the entropy term [9]. Therefore, the solubility, i.e., the maximum amount of solute can be dissolved, is zero both at temperature of absolute zero and at the maximum melting temperature due to the phase transition. Along the temperatures in-between, the solubility goes through a maximum as a function of temperature, known as retrograde solubility. Considering a simple case of compound semiconductor, AB, formed from one moles of element A and one moles of B (the results can be easily extended to AxBy), which requires higher electrical conductivity to satisfy certain opto-electronic applications. The result from a thermodynamic defect chemistry derivation [9] for a compound semiconductor AB with a dopant D, which substitutes the sub-lattice of B atom, gives:
µD (B) = µB + RTlnCD (B ) + µDo (B ) (T )
Fig. 1. A schematic phase diagram of the compound semiconductor AB.
also be employed during the process of melt growth, vapor growth, or solid state high temperature sintering of compound semiconductors. Only the results of the melt growth of Cl-doped PbTe will be demonstrated here. For the simple case of compound semiconductor, such as AB, there is always a compositional range, between absolute zero temperature and maximum melting temperature that the solid AB can exist as shown schematically by the phase diagram of A-B in Fig. 1, where the narrow range has been exaggerated. The AB compound has a maximum melting point of TM, at a composition of xB, shown slightly larger than 50 at% in this case. The regular doping process in melt growth usually starts with preparing a homogenized ingot of stoichiometric composition of AB mixed with a certain concentration of dopant. After the sample being heated to above the melting point of TM, the melt is cooled down slowly along the ingot length and D-doped AB compound is grown. As stated early, to increase the dopant content from this regular process, the chemical potential of B during the process needs to be reduced. At a fixed temperature Tg, lower than TM, as shown in Fig. 1, the phase boundaries, from low to high xB, between liquid (L), liquid+solid (L +S), AB solid (ABS), liquid+solid (L+S), and liquid (L),are determined by four different compositions of xB. During the regular melt growth doping process, the melt of starting material, with the stoichiometric composition, will solidify at the maximum melting temperature of TM. Therefore, the chemical potential of B cannot be adjusted to raise the dopant content. However, at a lower temperature Tg, the chemical potential of B, μB, as functions of xB, shown schematically in Fig. 2, increases monotonically with xB in the one-phase region, L or S, and remain constant as μBA and μBB in the twophase (liquid+solid) regions. The chemical potential of B increases tremendously from, μBA, at one end of the solid of composition of xsBA that saturated with A element to, μBB, at the other end of xsBB that saturated with element B. By adopting a doped starting material with a composition of xlBA and solidifying it, the frozen solid, with a composition of xsBA, will have the lowest possible chemical potential of B at the temperature of Tg, and, consequently, a higher doping content. At a fixed temperature, the sum of the chemical potentials of A and B is a stoichiometric invariant over the homogeneity range of the solid compound [9] as shown in Fig. 2. Therefore, the chemical potential of A decreases accordingly from the A-saturated to the B-saturated compositions inside the homogeneity range. Using the same principle, to enhance the concentration of a dopant that substitutes the sub-lattice of A atom, one should lower the chemical potential of its substituting element, i.e., A, under the processing temperature of Tg by employing a doped starting material with a melt composition of xlBB.
(1)
where μD(B) is the chemical potential of dopant D, μB is the chemical potential of B, CD(B) is the dopant concentration, μοD(B) is the excess Gibbs energy of formation for one mole of D substituting one mole of B atoms, R is the gas constant, T is temperature in K. The second term of the equation on the right is basically the entropy for mixing D with B atoms. Since μοD(B) is an inherent material property, the relationship between the dopant concentration, CD(B), and the chemical potentials of D and B under the processing condition can be rearranged as:
CD (B ) = Ae
µD (B) µB RT
(2)
o µD (B ) (T ) RT
is a constant at a fixed temperature. For a prewhere A = e scribed constant μD(B), i.e., under a specific thermodynamic processing condition for the dopant D, the dopant concentration is:
CD (B )
µB
e RT
(3)
which implies that the lower the μB, the higher the dopant concentration. During the process of doping in an elemental semiconductor B, such as the dopant of In substituting Ge lattice [10], the chemical potential of Ge is fixed as that of the pure Ge. From Eq. (3), the concentration of In, CIn, is constant and determined only by the processing condition as shown in Eq. (2). However, for a compound semiconductor, such as AB, the chemical of B varies tremendously across the existing narrow homogeneity range of the compound AB. Hence, the dopant concentration in a compound semiconductor can be raised by lowering the chemical potential of its substituting element under the processing condition. The essence of practicing this principle of maximizing dopant level is to design the crystal growth conditions corresponding to the lowest chemical potential for the substituting element during doping process. This technique of enhancing the dopant level can be applied not only to simple binary compound of AB, but also to ternary, quaternary, as well as multi-components compounds. It can 260
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Fig. 3. The schematics of a typical initial ampoule position during growth of directional solidification.
Fig. 2. Schematic plots of chemical potentials of A, μA and B, μB, as a function of XB at temperature Tg.
form of 99.999% purity PbCl2. The weighed starting materials were loaded inside fused silica ampoules and sealed under vacuum condition. The ampoule was placed inside a tubular rocking furnace for the melting and mixing of the charge. The ampoules were opened and the homogenized ingots were retrieved for crystal growth. The growth ampoules were made of fused silica of 19 mm OD, 16 mm ID with a slightly tapered end at the growth tip. After the homogenized ingot has been loaded inside, the growth ampoule was sealed under a vacuum condition lower than 10−5 Torr. The growth furnace has four independently controlled electrical-resistance heating zones that provided two temperature plateaus of about 970 °C at the top and 850 °C at the bottom with a thermal gradient of 15 °C/cm in between. As shown in Fig. 3, the homogenized sample in the ampoule is placed inside a furnace with such a thermal profile that, initially, the temperature of the starting material is above the pre-selected growth temperature Tg. As the furnace translation upward, the thermal environment of the ampoule will cool down slowly from the ampoule bottom and solidify the sample from its bottom tip initially and eventually through the whole ingot. After furnace translating about 12 cm, with a rate of 4.88 ± 0.10 mm/h, the solidified samples were cooled down to room temperature by turning off the power to the furnace. Except the different compositions of the starting materials, the crystals were grown using the same process. The grown cylindrical crystals were about 6.3 cm long. To be consistent for the comparison, a rectangular bar with dimension of 2.5 × 2.5 × 13 mm was cut from each crystal boule at location between 2.6 and 2.85 cm from the first freeze tip. The electrical conductivity at 37 °C was determined by measuring the slope of the linear I-V curve measured from 10 data points. After the electrical conductivity measurements, the Cl contents, in the PT-12 and PT-20 samples, were measured by the chemical analysis method of Glow Discharge Mass Spectroscopy (GDMS) provided by Evans Analytical Group (EVG).
3. Experimental The proposed method has been demonstrated in the melt growth of Cl-doping in the IV-VI compound semiconductor of PbTe. The first step in the enhancement of dopant level was to identify the structure of the targeted compound semiconductors and the sub-lattice of the element that will be substituted by the dopant. The dopant Cl, as a Group VII element, substitutes Te lattice site as a donor. Therefore, to reduce the chemical potential of Te, a Pb-rich starting material has been employed to raise the Cl-doping level. From the phase diagram of Pb-Te, at a temperature Tg, lower than the melting point of the compound, find out the composition of the liquidus point having the lower content of the substituting element. The following step is to weigh out the amounts of elements, corresponding to that composition, and to homogenize it with the dopant in a fused silica ampoule for the melt growth of directional solidification. To compare the resultant electrical conductivity and doping levels, two sets of crystals were processed by the regular method as well as by the technique proposed here. As shown in Table 1, the first set of crystals were doped with 0.70 at% Cl. The crystal PT-12 has a starting composition very close to the stoichiometric PbTe with a maximum melting point of 924 °C, whereas the second crystal, PT-20, is Pb-rich and its composition of xPb = 0.5474, which corresponds to a liquidus temperature of about 900 °C from the phase diagram of PbTe [11]. The third crystal PT-21, with the Pb content of xPb = 0.5226, was between that of PT-12 and PT-20 with a liquidus of 911 °C. These three samples have roughly the same Cl doping content of 0.70 at%. In the second set of crystals, PT-8, has a stoichiometric starting composition, whereas the other crystal, PT-23, has a composition of xPb = 0.5464, similar to that of PT-20. Both samples have about the same Cl doping content of 1.0 at%. The Cl-doped PbTe crystals were grown by the un-seeded vertical directional solidification method. The total mass and composition of the samples are listed in Table 1. The starting materials were elements of Pb, 99.9999% purity, Te, 99.99999% purity, and the Cl dopant in the Table 1 Growth parameters and characterization results for five Cl-doped PbTe samples. Crystal
Total mass (g)
Starting composition
Comparison between samples with starting Cl content of 0.70 at% PT-12 97.52 Pb0.4986Te0.4945Cl0.00687 PT-20 98.25 Pb0.5474Te0.4454Cl0.00719 PT-21 97.92 Pb0.5226Te0.4703Cl0.00714 Comparison between samples with starting Cl content of 1.0 at% PT-8 98.57 Pb0.4991Te0.4910Cl0.00988 PT-23 98.51 Pb0.5464Te0.4434Cl0.01017
Liquidus temperature (°C)
Electrical conductivity (S/m)
Measured xsCl
924 900 911
4.15 × 105 8.67 × 105 6.98 × 105
0.00132 0.00354
924 900
5.81 × 105 9.39 × 105
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Materials Science in Semiconductor Processing 90 (2019) 259–262
C.-H. Su
4. Results
shows no dependence on the chemical potential of B,:
µD (i) = RTlnCD (i) + µDo (i) (T )
The results show that, among the starting materials with the same Cl content of 0.70 at%, the crystal, PT-20, grown from Pb-saturated condition at 900 °C, has 2.1 times higher electrical conductivity than that of crystal PT-12, grown from the stoichiometric composition at 924 °C (the regular process). The GDMS data show a 2.7 times higher Cl dopant content xsCl, in the PT-20 sample, which confirms that the increase in electrical conductivity was originated from the Cl dopants, not from other native point defects such as vacancy or interstitial. It also shows that the estimated segregation coefficient, defined as xlCl/xsCl, has reduced from 5.2 for PT-12, to 2.0 for PT-20. The crystal of PT-21, with Pb-content in-between that of PT-12 and PT-20, resulted in an electrical conductivity between them, as expected, and about 1.68 times higher than that of sample PT-12. Comparing the two crystals grown from the initial Cl content of 1 at%, the off stoichiometric sample PT-23 with xPb = 0.5464, has an electrical conductivity about 1.7 times of the sample of PT-8, grown from starting stoichiometric composition. The experiments were a simple test of the claimed method of raising dopant level. The final maximization of dopant level will be determined from several more growth experiments at different Tg with the corresponding starting material compositions to delineate the solidus curve.
(4)
Most of the times, the doping process for melt growth has been practiced by adding the element of dopant to a stoichiometric composition of compound semiconductors as the starting material and the molten sample is directionally solidified. In some cases, off-stoichiometric melt has been employed in the solution growth, such as Traveling Heater Method (THM), with the main purpose of lowering the growth temperature [12]. The novel feature of this report is the concept of raising the dopant concentration in the grown compound semiconductor by lowering the chemical potential of its substituting element under the processing condition. For the melt growth, this can be accomplished by employed a slightly off-stoichiometric starting material and process the growth by the regular solidification process. In the vapor growth, the lowering of the chemical potential of the element can be accomplished either by lowering the partial pressure of that element or by increasing the partial pressures of other elements. The benefits of its application is the possibility of a much wider and flexible range of doping level which can also be applied to almost all of the multicomponents compound semiconductors. The modern advanced optical and electronic semiconducting devices made from compound semiconductors have various commercial applications which require a wide range of electrical property. The method presented here will extend the upper limit of the doping levels to a wider range and, consequently, will provide the materials for the manufacturing of potential semiconducting devices in various applications, including solar cells, where high solubility of dopant is needed to reduce precipitates, and semiconductor lasers, where heavily doping is required, as well as for thermoelectrics, where the peak temperature of figure of merit can be adjusted by electrical conductivity [13].
5. Discussions In applying the method described above, there are few issues need to be noted: a) The selection of Tg should be different for different systems. To maximize the doping level, the data of the homogeneity range of the compound is needed and, in the case of absence of information, several growth experimental results with different Tg might be helpful to optimize the process. b) Various compound semiconductors have their own phase diagrams, depending on the physical/chemical natures of each element involved. Most of the phase diagrams have the properties similar to Figs. 1 and 2 shown above. However, a few systems might have homogeneity ranges shift so much that they are completely outside the stoichiometric composition, either A-rich or B-rich. In this case, it might be complicated to find a temperature Tg that would maximize the dopant level. c) In some other material systems, the homogeneity range can be rather wide for a range of temperature. The crystal grown from the offstoichiometric melt, with a large deviation from stoichiometry, might result in second-phase precipitates during cooling because of the retrograde solubility curve as shown in Fig. 1. A large amount of precipitates might hinder the mobility of electrical carriers and results in low electrical conductivity. d) When selecting the growth temperature Tg, it should be noted that with a starting composition further away from the stoichiometry, as the sample solidifies from the bottom, more extra off-stoichiometric element will be pushed to the final section of the grown ingot, which results in the off-stoichiometric materials with bad crystalline quality, such as precipitates, at the top of the grown ingot. e) When the dopant was incorporated into interstitial site [9], the method claimed here will not work as the chemical potential of interstitial D, as compared to the substitution case presented in Eq. (1),
Acknowledgements The author would like to acknowledge the supports of Space Life and Physical Sciences Division, Human Exploration and Operations Mission Directorate, NASA Headquarters Washington, D.C. United States. References [1] Ching-Hua Su, Mater. Sci. Semicond. Proc. 56 (2016) 94. [2] J.J. McCoy, S.K. Swain, J.R. Sieber, D.R. Diercks, B.P. Gorman, K.G. Lynn, J. Appl. Phys. 123 (2018) 161579. [3] O. Appel, M. Schwall, M. Kohne, B. Balke, Y. Gelbstein, J. Electron. Mater. 42 (2013) 1340. [4] Y. Gelbstein, J. Electron. Mater. 40 (2011) 533. [5] Ching-Hua Su, J. Cryst. Growth 439 (2016) 80. [6] Ching-Hua Su, Curr. Smart Mater. 2 (2017) 3. [7] E. Hazan, N. Madar, M. Parag, V. Casian, O. Ben-Yehuda, Y. Gelbstein, Adv. Electron. Mater. (2015) 1500228. [8] R. Vizel, T. Bargig, O. Beeri, Y. Gelbstein, J. Electron. Mater. 45 (2016) 1296. [9] R.F. Brebrick, Progress in solid state chemistry, 3, Pergamon Press, Oxford, 1967, p. 213. [10] Ching-Hua Su, R.F. Brebrick, J. Phys. Chem. Solids 46 (1985) 963. [11] J.C. Lin, K.C. Hsieh, R.C. Sharma, Y.A. Chang, Bull. Alloy Phase Diagr. 10 (1989) 340. [12] R. Triboulet, Handbook of Crystal Growth, Elsevier, 2015, p. 459. [13] C.-H. Su, Mater. Today Phys. 6 (2018) 1.
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