1. Introduction
Group-III nitrides are semiconductor materials that are expected to play a revolutionary role in modern optoelectronics and high-power, high-temperature electronics. Development of the technological base for growth and processing of these materials demands detailed knowledge of their physical properties. Much effort has been made in the recent years to examine various characteristics and parameters of GaN, AlN, InN and their ternary compounds. Some carefully selected results are summarized in reference Reference Edgar[1]. However, the scientific field related to group-III nitrides has broadened so quickly that the appearance of such books does not keep pace with the needs of the nitride community. More ongoing development of the reference database is desirable both for fundamental and applied studies covering growth, processing and characterization of these promising materials.
In this paper we make an attempt to develop a self-consistent database of thermodynamic properties of group-III nitrides and the species related to growth of these materials. Part of the data is taken from the reliable sources. The rest of the data are either refined using new information on the properties of the nitrides and relevant species available from the literature or presented here for the first time.
The organization of the paper is as follows. In Section 2 we explain the notation used throughout the paper and give the main expressions for calculation of thermodynamic functions of the materials. Section 3 gives a short guide to the database. In Section 4 we discuss the origin of the thermodynamic properties of the species refined or obtained in this paper.
2. Notation and general relationships
The Gibbs free energy G(P,T) of a certain species as a function of pressure P and temperature T is defined by the expression
where G0(P0,T) is the Gibbs thermodynamic potential taken at the standard pressure P 0 = 1 atm. For G0(P0,T) we use the standard approximation accepted in the reference books Reference Gurvich, Veyts and Alcock[2] Reference Gurvich, Veyts, Alcock and Alcock[3] Reference Gurvich, Veyts and Alcock[4]. According to these works the temperature dependence of G0(P0,T) can be approximated by a polynomial
Here H(298 K) is the standard formation enthalpy of the species (for elemental species this value is defined to be equal to zero) corresponding to the standard temperature T 0 = 298.15 K, Φ(x) is the so called reduced Gibbs free energy. The polynomial approximation (2) differs from those used in JANNAF tables or in well-known database “Chemkin”. By special comparison we have found that our polynomial form provides more a more accurate approximation of the thermodynamic properties of various species in a wide temperature range.
Using the array of coefficients φ,φ−2 …φ3 one can calculate the enthalpy H(T), entropy S(T) and specific heat Cp(T) of the species corresponding to the standard pressure P 0 = 1 atm and arbitrary temperature
In this paper thermodynamic functions of materials are calculated by commonly accepted methods discussed in detail in Reference Gurvich, Veyts and Alcock[2]. For gaseous species the molecular constants (bond lengths, angles between the bond directions, oscillation frequencies etc.), either taken from literature or estimated (in the case of lack of experimental information), are used in the calculations. Therewith the “rigid rotator – harmonic oscillator” approximation is applied to account for internal rotational degrees of freedom of molecules.
3. Organization of the database
For convenience the thermodynamic database of the materials involved into growth of group-III nitrides is split into seven tables Reference Edgar[1]. In Table 1 the data on elemental materials are collected. Table 2 and Table 3 contain the data on group-III hydrides and chlorides respectively. Table 4 presents the data on gaseous group-III metal-organic compounds. In Table 5 the data on various (first of all, gaseous) species which are either nitrogen carrying precursors or byproducts of chemical reactions are given. Table 6 contains thermodynamic properties of the adducts forming during MOVPE or HVPE growth of group-III nitrides. And, finally, in Table 7 properties of solid and gaseous binary nitrides are presented. Every table contains in separate columns
-
• The chemical notation for the species
-
• The phase state of the species: solid (s), liquid (l) or gaseous (g)
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• The temperature range where the polynomial approximation (2) is proven to be valid
-
• The formation enthalpy H(298 K) of the species corresponding to the standard temperature T 0 = 298.15 K, and seven coefficients φ,φ−2…φ3 measured in J/mol·K to provide the Gibbs free energy measured in J/mol
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• A reference to the work where the corresponding thermodynamic data have been reported (there is no reference in this column if the thermodynamic properties are refined or estimated in this paper)
Table 1 Thermodynamic properties of elemental materials related to growth of group-III nitrides.
Table 2 Thermodynamic properties of group-III hydrides.
Table 3 Thermodynamic properties of group-III chlorides.
Table 4 Thermodynamic properties of group-III metal-organic compounds.
Table 5 Thermodynamic properties of compound species related to growth of group-III nitrides. (*) Indexes s- and a- denotes the molecules C2H2 having different bond configurations: HC=CH and H2C=C respectively.
Table 6 Thermodynamic properties of adducts related to growth of group-III nitrides.
Table 7 Thermodynamic properties of group-III nitrides.
Table 1s Thermodynamic properties of elemental materials related to growth of group-III nitrides (ChemKin format).
Table 2s Thermodynamic properties of group-III hydrides (ChemKin format).
Table 3s Thermodynamic properties of group-III chlorides (ChemKin format).
Table 4s Thermodynamic properties of group-III metal-organic compounds (ChemKin format).
Table 5s Thermodynamic properties of compound species related to growth of group−III nitrides (ChemKin format). (*) Indexes s- and a- denotes the molecules C2H2 having different bond configurations: HC=CH and H2C=C respectively.
Table 6s Thermodynamic properties of adducts related to growth of group−III nitrides (ChemKin format).
Table 7s Thermodynamic properties of group−III nitrides (ChemKin format).
Thermodynamic properties of 44 species – Al(s), Al(l), Al(g), Al2(g), AlH(g), AlH2(g), AlH3(g), AlN(g), CH(g), CH2(g), CH3(g), CH4(g), s-C2H2(g), C2H4(g), C2H5(g), C2H6(g), Cl(g), Cl2(g), H(g), H2(g), HCl(g), HN3(g), In(s), In(l), In(g), InH(g), Ga(s), Ga(l), Ga(g), GaH(g), GaCl(g), GaCl2(g), GaCl3(s), GaCl3(l), GaCl3(g), Ga2Cl6(g), N(g), N2(g), NH(g), NH2(g), NH3(g), N2H2(g), N2H4(g), NH4Cl(s) – are taken from references Reference Gurvich, Veyts and Alcock[2] Reference Gurvich, Veyts, Alcock and Alcock[3] Reference Gurvich, Veyts and Alcock[4] Reference Stull and Prophet[5]. For these components no special comments will be made. The properties of 31 other species (including adducts forming during MOVPE and HVPE process) – AlN(s), AlCH3(g), Al(CH3)3(g), Al2(CH3)6(g), a-C2H2(g), GaH2(g), GaH3(g), GaN(s), GaN(g), GaCH3(g), Ga(CH3)3(g), InH2(g), InH3(g), InN(s), InCH3(g), In(CH3)3(g), Al·NH3(g), AlCH3·NH(g), (AlCH3·NH)3(g), Al(CH3)3·NH3(g), (Al(CH3)2·NH2)3(g), (Al·N)3, (Al(CH3)2·NH2)2(Ga(CH3)2·NH2)(g), (Al(CH3)2·NH2)(Al(CH3)2·NH2)2(g), Ga·NH3(g), GaCH3·NH(g), Ga(CH3)3·NH3(g), (GaCH3·NH)3(g), (Ga(CH3)2·NH2)3(g), (Ga·N)3, GaCl3·NH3(g) – are either refined or derived in this paper. For these species the thermodynamic data are attended by necessary comments given in Section 4.
All the data are verified for self-consistency and therefore can be used for thermodynamic calculations.
4. Comments
In this section we make short comments on the thermodynamic properties of various species and the way in which these properties are estimated. The main species are arranged in alphabetical order, the adducts are considered at the end of section.
4.1 AlCH3(g) monomethylaluminum (MMA)
Molecules AlCH3 (MMA) have been observed experimentally in the gas phase Reference Srinivas, Sulze and Schwarz[6]. Thermodynamic functions of MMA are obtained using molecular constants calculated theoretically in references Reference Fox, Ray, Rubesin and Schaefer[7] Reference Jin, Xie and Schaefer[8] Reference Jin, Xie and Schaefer[9]. According to these works the molecule MMA in the ground X1A1 state has the structure of C3V symmetry. Formation enthalpy of MMA is calculated using the value of Al–CH3 bond energy estimated by comparison of the bond energies in such pairs of molecules as AlCH3 and GaCH3, Al(CH3)3 and Ga(CH3)3. This procedure is applied because theoretical estimation of the formation enthalpy of MMA carried out in reference Reference Fox, Ray, Rubesin and Schaefer[7] results in an evidently underestimated value (this was mentioned by authors of reference Reference Fox, Ray, Rubesin and Schaefer[7] themselves). Our data are in a reasonable agreement with those obtained in reference Reference Tirtowidjojo and Pollard[10].
4.2 Al(CH3)3(g) trimethylaluminum (TMA)
Thermodynamic functions of Al(CH3)3 are calculated using the molecular constants taken from experimental Reference Atiya, Grady, Russel and Claxton[11] Reference Kvisle and Rytter[12] Reference Kvisle and Rytter[13] Reference O’Brien and Ozin[14] Reference Almenningen, Halvorsen and Haaland[15] Reference Ogawa[16] Reference Ogawa, Hirota and Miyazava[17] and theoretical Reference Atiya, Grady, Russel and Claxton[11] studies. According to these works, the TMA molecule in the ground X1A1 state has the structure of D3h symmetry. The formation enthalpy of TMA is taken after reference Reference Glushko[18]. Earlier thermodynamic functions of TMA were calculated in reference Reference Mosin and Golosova[19] using approximate values of molecular constants and in reference Reference Tirtowidjojo and Pollard[10]. Our data are in a reasonable agreement with the results of both these works.
4.3 Al2(CH3)6(g)
Thermodynamic properties of gaseous Al2(CH3)6 are calculated using the molecular constants obtained experimentally in references Reference Kvisle and Rytter[13] Reference Almenningen, Halvorsen and Haaland[15] Reference Ogawa[16] Reference Ogawa, Hirota and Miyazava[17] Reference Ohishi and Shimanouchi[20] Reference Gray[21]. According to these works the Al2(CH3)6 molecule in the ground X1A1 state has the structure of D2h symmetry. The formation enthalpy of Al2(CH3)6 is taken from reference Reference Glushko[18].
Earlier thermodynamic functions of Al2(CH3)6 were calculated in reference Reference Mosin and Golosova[19] using approximate values of molecular constants and in reference Reference Tirtowidjojo and Pollard[10]. The value of entropy at 298.15 K given in Reference Tirtowidjojo and Pollard[10] is lower than that accepted in the current work. The cause of the discrepancy could not be revealed since the authors of reference Reference Tirtowidjojo and Pollard[10] did not refer to their source of data on molecular constants. The formation enthalpy of Al2(CH3)6 reported in reference Reference Tirtowidjojo and Pollard[10] is somewhat lower than that recommended in reference Reference Glushko[18], although it remains within the experimental error bars.
4.4 AlN(s)
The specific heat Cp(T) of solid AlN has been measured by different groups in the temperature range of 50-300 K. The results are summarized in reference Reference Edgar[1] and plotted in Figure 1 (numerical values are given also in the Data file 1). These data were used in references Reference Gurvich, Veyts and Alcock[4] Reference Stull and Prophet[5] for calculation of thermodynamic functions of solid AlN. We refine the thermodynamic properties of AlN accounting for the results of AlN specific heat measurements carried out in the temperature range of 2.6-300 K Reference Kotschenko, Demidenko, Paschinkin, Yachmenev and Sabanova[22] (the data on specific heat are shown in Figure 1 and also given in the Data file 2). The formation enthalpy of AlN is taken according to references Reference Gurvich, Veyts and Alcock[4] Reference Stull and Prophet[5].
Figure 1. Specific heat of solid AlN as a function of temperature (after reference Reference Edgar[1] and reference Reference Kotschenko, Demidenko, Paschinkin, Yachmenev and Sabanova[22]).
Free evaporation of AlN in vacuum has been investigated in reference Reference Dreger, Dadape and Margrave[23]. The evaporation of AlN is found to be congruent. The total pressure of evaporating species (Al and N2) measured at different temperatures is shown in Figure 2 and numerical data given in Data file 3. Comparison to thermodynamic calculations (the solid line in Figure 2) shows that the evaporation of AlN is kinetically limited. Due to this kinetic effect the experimental data on AlN evaporation can not be used for estimation of thermodynamic properties of this compound.
Figure 2. Total pressure (sum of Al and N2 partial pressures) measured during free evaporation of AlN in vacuum by torsion method Reference Dreger, Dadape and Margrave[23]. For comparison the result of thermodynamic calculation of the total pressure is plotted in the figure.
4.5 a-C2H2(g) vinylidene
Thermodynamic properties of vinylidene are calculated using the molecular constants found in theoretical and experimental studies Reference Dreger, Hamilton and Schaefer[24] Reference Evin, Ho and Lineberger[25]. According to the results of these studies the vinylidene molecule has a configuration of C2V symmetry in the ground state. The formation enthalpy of vinylidene is determined using the formation enthalpy of s-C2H2(g) Reference Gurvich, Veyts and Alcock[4] and the isomerization energy of acetylene- vinylidene – 43 kcal/mol obtained in references Reference Dreger, Hamilton and Schaefer[24] Reference Evin, Ho and Lineberger[25]
4.6 GaCH3 monomethylgallium (MMG)
Thermodynamic functions for gaseous GaCH3 (MMG) are calculated using molecular constants determined in experimental Reference Lafleur and Parnis[26] and theoretical Reference Block and Trachtman[27] Reference Trachtman, Beede and Bock[28] Reference Hoffman, Sherrill and Schaefer[29] studies of the molecules MMG and CH3GaH Reference Knight, Banisaukas, Babb and Davidson[30] Reference McKee[31]. According to these works the molecule GaCH3 in the ground X1A1 state has the configuration of C3V symmetry. The formation enthalpy of MMG is calculated using the value of the Ga–CH3 bond energy determined while studying the pyrolysis of trimethylgallium (Ga(CH3)3) Reference Jacko and Price[32] Reference Oikawa, Tsuda, Morishita, Mashita and Kuniga[33]. Theoretical calculation of this energy Reference Block and Trachtman[27] gave a remarkably underestimated value. Earlier thermodynamic functions of MMG were reported in reference Reference Tirtowidjojo and Pollard[10]. Our data are in a reasonable agreement with the results of this work.
4.7 Ga(CH3)3(g) trimethylgallium (TMG)
Thermodynamic functions of gaseous Ga(CH3)3 (TMG) are calculated using the molecular constants determined both experimentally Reference Kvisle and Rytter[13] Reference Hall, Woodward and Ebswarth[34] Reference Durig and Chatterjee[35] Reference Beagly, Schmidling and Steer[36] Reference Coates and Downs[37] and theoretically Reference Block and Trachtman[27] Reference Trachtman, Beede and Bock[28]. According to these studies the TMG molecule in the ground X1A1 state has the configuration of D3h symmetry. Formation enthalpy of TMG is taken from reference Reference Glushko[18]. Earlier thermodynamic properties of TMG have been estimated in Reference Mosin and Shaulov[38] and Reference Tirtowidjojo and Pollard[10] using the approximate values of the molecular constants. Our data agree with the results obtained in reference Reference Tirtowidjojo and Pollard[10].
4.8 GaH2(g)
Molecular constants of gaseous GaH2 are determined using the experimental data of references Reference Knight, Banisaukas, Babb and Davidson[30] Reference Downs and Pulham[39] Reference Pulumbi, Mijoule, Manceron and Bouteiller[40] Reference Xiao, Hauge and Margrave[41] and results of theoretical calculations carried out for molecules GaH2 Reference Knight, Banisaukas, Babb and Davidson[30] Reference Downs and Pulham[39] Reference Pulumbi, Mijoule, Manceron and Bouteiller[40] Reference McKee[31] Reference Treboux and Barthelat[42] Reference Bock, Dobbs, Mains and Trachtman[43] Reference Balasubramanian[44] and Ga2H4 Reference Lammortsma and Leszczynski[45]. According to the experimental and theoretical results the molecule GaH2 in the ground state X2A1 has a non-linear configuration of C2V symmetry. We calculate the formation enthalpy of GaH2 using the value of Ga–H bond energy in the molecule GaH2 obtained theoretically in Reference Balasubramanian[44] Reference Kim and Balasubramanian[46]. Recently thermodynamic functions of GaH2 have been estimated in Reference Reference Tirtowidjojo and Pollard[10]. The authors of Reference Tirtowidjojo and Pollard[10] reported the value of entropy of GaH2 at 298.15 K as well as the polynomial approximation of the specific heat which agree well with our estimates. However, the formation enthalpy of GaH2 – H(298 K) = 164 kJ/mol accepted in Reference Tirtowidjojo and Pollard[10] exceeds significantly the value obtained in this work. This is related to overestimation in reference Reference Tirtowidjojo and Pollard[10] the Ga–H bond energy in the molecule GaH2 – 273.6 kJ/mol instead 171.5 kJ/mol as follows from the theoretical calculations of references Reference Balasubramanian[44] Reference Kim and Balasubramanian[46].
4.9 GaH3(g)
Molecular constants of gaseous GaH3 are taken from experimental Reference Downs and Pulham[39] Reference Pullumbi, Bouteiller, Manceron and Mijoule[47] and theoretical Reference Downs and Pulham[39] Reference Bock, Dobbs, Mains and Trachtman[43] Reference Balasubramanian[44] Reference Pullumbi, Bouteiller, Manceron and Mijoule[47] Reference Souter, Andrew, Downs, Green, Ma and Schaefer[48] Reference Barone, Orlandini and Adamo[49] Reference Cheung, Ma and Li[50] Reference Shen and Schaefer[51] Reference Schwerdtfeger, Heath, Dolg and Bennet[52] Reference Dobbs, Trachtman, Bock and Cowley[53] studies of molecules GaH3 and Ga2H6 Reference Souter, Andrew, Downs, Green, Ma and Schaefer[48] Reference Barone, Orlandini and Adamo[49]. According to the results obtained in these works the molecule GaH3 in the ground state X1A1 has a flat configuration of D3h symmetry. We calculate the formation enthalpy of GaH2 using the value of Ga–H bond energy in the molecule GaH3 obtained theoretically in reference Reference Balasubramanian[44] Reference Kim and Balasubramanian[46]. Thermodynamic functions of gaseous GaH3 have been reported also in reference Reference Tirtowidjojo and Pollard[10]. The value of entropy of GaH3 at 298.15 K and the polynomial approximation for specific heat agree well with our data. The formation enthalpy of GaH3 – H(298 K) = 108 kJ/mol accepted in reference Reference Tirtowidjojo and Pollard[10] is significantly less than the value obtained in this work. This is related to the underestimation in reference Reference Tirtowidjojo and Pollard[10] of the Ga–H bond energy in the molecule GaH3 – 273.6 kJ/mol instead 338.7 kJ/mol predicted based on theoretical calculations Reference Balasubramanian[44] Reference Kim and Balasubramanian[46].
4.10 GaN(s)
The specific heat Cp(T) of solid GaN has been measured by calorimetry in the temperature interval of 5–60 K Reference Kotschenko, Demidenko, Sabanova, Yachmenev, Gran and Radchenko[54] and in the temperature interval of 55–300 K Reference Demidenko, Kotschenko, Sabanova and Gran[55]. The experimental data obtained in these works are shown in Figure 3 and given numerically in Data file 4. For comparison in Figure 3 is shown the approximation of the specific heat versus temperature recommended in reference Reference Edgar[1].
Figure 3. Specific heat of solid GaN versus temperature Reference Kotschenko, Demidenko, Sabanova, Yachmenev, Gran and Radchenko[54] Reference Demidenko, Kotschenko, Sabanova and Gran[55].
Thermodynamic properties of solid GaN are determined using the experimental data on specific heat Reference Kotschenko, Demidenko, Paschinkin, Yachmenev and Sabanova[22] Reference Kotschenko, Demidenko, Sabanova, Yachmenev, Gran and Radchenko[54] Reference Demidenko, Kotschenko, Sabanova and Gran[55] and the enthalpy increment of GaN Reference Itagaki and Yamaguchi[56]. We take the formation enthalpy of GaN averaged over two values – one of them based on the calorimetric measurements of GaN heat of burning Reference Hahn and Juza[57], the other obtained using the 3rd law and the experimental data of reference Reference Thurmond and Logan[58]. The value accepted in reference Reference Glushko[18] is an underestimate. This was pointed out by authors of reference Reference Evseeva and Zenkevich[59], where results of reference Reference Hahn and Juza[57] were discussed in regard to the determination of the formation enthalpy of solid InN. The thermodynamic functions of GaN reported in references Reference Barin, Knacke and Kubashewski[60] Reference Shinkarev, Andreeva and Schaulov[61] were obtained using rough estimates of the GaN specific heat, entropy and formation enthalpy; therefore they are not quite accurate.
Langmuir (free) evaporation of GaN in vacuum has been studied in reference Reference Munir and Searcy[62]. The evaporation was found to be congruent. The total pressure of the evaporating species (Ga and N2) was measured versus temperature by a torsion-effusion method. The results of the measurements are plotted in Figure 4 and given numerically in Data file 5. Comparison to thermodynamic calculations (the solid line in Figure 4) shows that the evaporation of GaN is kinetically limited. Due to this limitation the experimental data on GaN evaporation can not be used for estimation of the thermodynamic properties of this compound.
Figure 4. Total pressure (sum of Ga and N2 partial pressures) measured during free evaporation of GaN in vacuum by torsion-effusion method Reference Munir and Searcy[62]. For comparison the result of thermodynamic calculation of the total pressure is plotted in the figure.
4.11 GaN(g)
There is no information on the molecular constants of gaseous GaN. To calculate the thermodynamic functions of GaN(g) we use the oscillation frequencies and interatomic distance estimated in references Reference Shinkarev, Andreeva, Pesotskyi and Schaulov[63] Reference Krasnov[64] assuming by analogy with AlN(g) that the ground state of GaN molecule is X2Π. The formation enthalpy of gaseous GaN is calculated by using the dissociation energy of the molecule equal to 523 kJ/mol as determined in reference Reference Guido and Girly[65]. Thermodynamic functions of gaseous GaN reported in reference Reference Shinkarev, Andreeva, Pesotskyi and Schaulov[63] have been calculated using the molecular constants obtained in references Reference Shinkarev, Andreeva, Pesotskyi and Schaulov[63] Reference Krasnov[64]. The formation enthalpy of GaN(g) was not determined in reference Reference Shinkarev, Andreeva, Pesotskyi and Schaulov[63].
4.12 InCH3 monomethylindium (MMI)
We could not find in the literature any information on the molecular constants of gaseous InCH3 (MMI). That is why we estimate these constants assuming in analogy with MMA and MMG that the MMI molecule in the ground state X1A1 state has the configuration of C3V symmetry. The formation enthalpy of MMI is found using the value of In-CH3 bond energy extracted in reference Reference Jacko and Price[66] from the experimental data on pyrolysis of In(CH3)3.
4.13 In(CH3)3(g) trimethylindium (TMI)
Thermodynamic functions of gaseous In(CH3)3 (TMI) are calculated using the molecular constants obtained in experimental studies Reference Hall, Woodward and Ebswarth[34] Reference Blake and Cradock[67] Reference Fjeldberg, Haaland, Seip, Shen and Weidlein[68] Reference Barbe, Hencher, Shen and Tuck[69] Reference Vranka and Amma[70] Reference Amma and Rundle[71] Reference Pauling and Laubengayer[72]. According to these works the TMI molecule in the ground X1A1 state has the configuration of D3h symmetry. To determine the value of formation enthalpy of TMI we use the experimental data on the formation enthalpy of solid In(CH3)3 as well as the heat of In(CH3)3(s) sublimation Reference Clark and Price[73] Reference Laubengayer and Gilliam[74]. Earlier rough estimations of thermodynamic properties of TMI have been made in reference Reference Malkova and Pashinkin[75].
4.14 InH2(g)
Thermodynamic functions of gaseous InH2 are calculated on the base of molecular constants measured in references Reference Downs and Pulham[39] Reference Pulumbi, Mijoule, Manceron and Bouteiller[40] and theoretically calculated in reference Reference Pulumbi, Mijoule, Manceron and Bouteiller[40]. According to these works the molecule InH2 in the ground X2A1 state has non-linear configuration of C2V symmetry. The formation enthalpy of InH2 is estimated using the value of In–H bond energy in the InH2 molecule calculated in reference Reference Balasubramanian and Tao[76].
4.15 InH3(g)
The thermodynamic functions of gaseous InH3 are calculated using the molecular constants determined in experimental Reference Downs and Pulham[39] Reference Pullumbi, Bouteiller, Manceron and Mijoule[47] and theoretical studies Reference Pulumbi, Mijoule, Manceron and Bouteiller[40]. According to these works the molecule InH3 in the ground X1A1 state has a flat configuration of D3h symmetry. The formation enthalpy of InH3 is estimated using the value of the In–H bond energy in the InH3 molecule calculated in reference Reference Balasubramanian and Tao[76].
4.16 InN(s)
There is no experimental information on thermodynamic properties of solid InN. The published data on InN evaporation Reference Gordienko and Fenochka[77] Reference McChesney, Bridenbaugh and O’Connor[78] Reference Evseeva and Zenkevich[59] Reference Vorobjev, Evseeva and Zenkevich[79] cannot be used to determine the enthalpy of InN formation since equilibrium conditions were not met in these experiments. Evaporation of InN occurs with decomposition into the liquid and gas phases starting at least from 450oC Reference Kotschenko, Demidenko, Paschinkin, Yachmenev and Sabanova[22]. No experimental data on Langmuir evaporation of InN in vacuum are available at the present time.
The value of H(298 K) estimated using the heat of InN burning Reference Hahn and Juza[57] and accepted in Reference Thurmond and Logan[58] is apparently underestimated (this was mentioned by the authors of reference Reference Evseeva and Zenkevich[59] who especially analyzed the work Reference Hahn and Juza[57]) and cannot serve as the basis for estimation of properties of InN. That is why we take the available data on the properties of other III-V compounds and use the analogy method Reference Kireev[80] to extrapolate the respective thermodynamic functions of InN.
4.17 Adducts formed while mixing gaseous group-III compounds and ammonia
Spectral investigations of the chemical reactions between Al atoms in a ground electron state and NH3 molecules Reference Howard, Joly, Edwards, Singer and Logan[81], theoretical studies of Al·NH3 adducts Reference Sakai[82] Reference Davy and Jaffrey[83] and numerous experimental data Reference Ault[84] Reference Watari, Shimuzin, Aida and Takayama[85] Reference Muller[86] Reference Andersen, Forgaard and Haaland[87] Reference During, Breadly and Odom[88] Reference Durig, Chatterjee, Li, Jaliliam, Zozulin and Odom[89] Reference Golubinskaya, Golubinskii, Mastryukov, Vilikov and Bregadze[90] Reference Greenwood, Storr and Wallbridge[91] Reference Shriver, Amster and Taylor[92] Reference Shriver and Parry[93] Reference Greenwood, Storr and Wallbridge[94] Reference Almond, Jenkins, Rice and Yates[95] Reference Leib, Emerson and Oliver[96] Reference Almond, Drew, Jenkins and Rice[97] Reference Almond, Drew, Jenkins and Rice[97] Reference Beachley, Royster, Arhar and Rheingold[98] Reference Sauls, Hurley, Interrante, Machetti and Maciel[99] Reference Interrante, Sigel, Garbauskas, Hejna and Slack[100] provide evidence of the formation in the gaseous mixture of metal-organic group-III compounds and ammonia of such adducts as TMA·NH3 and TMG·NH3 . With gradual liberation of methane these adducts transform into the radicals DMA·NH2 and DMG·NH2 which, in turn, can combine into the complexes (DMA·NH2)3, (DMG·NH2)3, (DMA·NH2)2(DMG·NH2) and (DMA·NH2)(DMG·NH2)2 . Further liberation of CH4 molecules is assumed from these complexes with their transition into (MMA·NH)3, (MMG·NH)3, (MMA·NH)2(MMG·NH), (MMA·NH)(MMG·NH)2, and then into gaseous polymers of (Al·N)3, (Ga·N)3, (Al·N)2(Ga·N), (Al·N)(Ga·N)2 type. Below the thermodynamic properties of some of these adducts are estimated. In addition the properties of GaCl3·NH3, which can be formed during hydride vapor phase epitaxy of GaN, are discussed.
4.17.1. AlNH3(g)
The molecular constants of gaseous Al·NH3 necessary for estimation of thermodynamic functions are taken from theoretical studies Reference Sakai[82] Reference Davy and Jaffrey[83]. According to these works the molecule Al·NH3 in the ground X1A1 state has configuration of C3V symmetry. The formation enthalpy of Al·NH3 is found using the value of Al–NH3 bond energy calculated theoretically in Reference Sakai[82] Reference Davy and Jaffrey[83].
4.17.2. GaNH3(g)
There is no information on molecular constants of the gaseous Ga·NH3 adduct. In analogue with Al·NH3 we assume that molecule Ga·NH3 is stable in the ground X1A1 state and has the structure of C3V symmetry. Molecular constants of Ga·NH3 are found by extrapolation of the corresponding constants for the pairs TMA and TMG, TMA·NH3 and TMG·NH3, Al·NH3 and Ga·NH3 . The formation enthalpy of Ga·NH3 is calculated using the estimated value of the Ga–NH3 bond energy. The estimation procedure is based on a comparison of the values of bond energies in the pairs of molecules Al·NH3 and Ga·NH3, TMA·NH3 and TMG·NH3 .
4.17.3. Al(CH3)3·NH3(g)
Thermodynamic functions of gaseous Al(CH3)3·NH3 (or TMA·NH3) are calculated using the molecular constants found both experimentally Reference Ault[84] Reference Watari, Shimuzin, Aida and Takayama[85] Reference Muller[86] Reference Andersen, Forgaard and Haaland[87] and theoretically Reference Muller[86] Reference Jungwirth and Zahradnik[101] Reference March, Hamilton, Xie and Schaefer[102]. According to these studies the molecule Al(CH3)3·NH3 in the ground X1A1 state has the configuration of C3V symmetry. The formation enthalpy of Al(CH3)3·NH3 is determined using the value of TMA-NH3 bond energy obtained in references Reference Muller[86] Reference Andersen, Forgaard and Haaland[87] Reference March, Hamilton, Xie and Schaefer[102] Reference Sauls, Interrante and Ziang[103] Reference Zaouk, Salvetat, Sakaya and Maury[104] Reference Henrickson, Duffy and Egman[105].
4.17.4. Ga(CH3)3·NH3(g)
Molecular constants of gaseous Ga(CH3)3·NH3 (or TMG·NH3) needed for estimation of the thermodynamic functions are taken from experimental studies Reference During, Breadly and Odom[88] Reference Durig, Chatterjee, Li, Jaliliam, Zozulin and Odom[89] Reference Golubinskaya, Golubinskii, Mastryukov, Vilikov and Bregadze[90] Reference Greenwood, Storr and Wallbridge[91] Reference Shriver, Amster and Taylor[92] Reference Shriver and Parry[93] Reference Greenwood, Storr and Wallbridge[94] Reference Almond, Jenkins, Rice and Yates[95]. According to the results of these works the molecule Ga(CH3)3·NH3 in the ground X1A1 state has the structure of C3V symmetry. The formation enthalpy of Ga(CH3)3·NH3 is obtained through the TMG–NH3 bond energy determined in references Reference Zaouk, Salvetat, Sakaya and Maury[104] Reference Leib, Emerson and Oliver[96].
4.17.5. (Al(CH3)2·NH2)3(g)
Thermodynamic properties of (Al(CH3)2·NH2)3 or (DMA·NH2)3 are calculated using the molecular constants taken from experimental studies of (DMA·NH2)3 Reference Interrante, Sigel, Garbauskas, Hejna and Slack[100], (DMG·NH2)3 Reference Almond, Drew, Jenkins and Rice[97] Reference Beachley, Royster, Arhar and Rheingold[98], (DMA·NH2)2 Reference Almond, Drew, Jenkins and Rice[97], TMA·NH3, TMG·NH3 and theoretical investigations of DMA·NH2 Reference Muller[86] and (HAl·NH)3 Reference Fink and Richards[106]. In accordance with these works it is accepted that in the ground state X1A the complex (DMA·NH2)3 has non-flat ring configuration of C1 symmetry. The formation enthalpy of (DMA·NH2)3 is found using the experimental data of reference Reference Sauls, Interrante and Ziang[103].
4.17.6. (Ga(CH3)2·NH2)3(g)
Thermodynamic properties of (Ga(CH3)2·NH2)3 or (DMG·NH2)3 are calculated using the molecular constants taken from experimental studies of (DMG·NH2)3 Reference Almond, Drew, Jenkins and Rice[97] Reference Beachley, Royster, Arhar and Rheingold[98], (DMG·NH2)2 Reference Almond, Drew, Jenkins and Rice[97], and TMG·NH3 . According to these works the complex (DMG·NH2)3 in the ground state X1A has non-flat ring configuration of C1 symmetry. There is no information on the formation enthalpy of (DMG·NH2)3. We estimate this value by comparison the formation energies of the pairs (DMA·NH2)3 and (DMG·NH2)3, TMA·NH3 and TMG·NH3 .
4.17.7. (Al(CH3)2·NH2)2(Ga(CH3)2·NH2)(g) and (Al(CH3)2·NH2)(Ga(CH3)2·NH2)2(g)
The complexes (Al(CH3)2·NH2)2(Ga(CH3)2·NH2) and (Al(CH3)2·NH2)(Ga(CH3)2·NH2)2 have not been studied. The molecular constants of these species as well as their formation enthalpies are calculated using extrapolation of corresponding data on the properties of (Al(CH3)2·NH2)3 and (Ga(CH3)2·NH2)3 adducts.
4.17.8. AlCH3NH(g) and GaCH3NH(g)
Decomposition of TMA·NH3 and TMG·NH3 can lead to appearance of gaseous radicals AlCH3·NH and GaCH3·NH which, in turn, can combine into the ring complexes (AlCH3·NH)3 and (GaCH3·NH)3 . There is no information on molecular constants of these species in literature. We estimate them using corresponding data obtained for molecules TMA·NH3, TMG·NH3, DMA·NH2, DMG·NH2, MMA, MMG, Al·NH3, Ga·NH3, HGaCH3 and HAlCH3 . Therewith we assume that molecules AlCH3·NH(g) and GaCH3·NH(g) in the ground X1A state have an asymmetric configuration of C1 symmetry. The formation enthalpies of AlCH3·NH(g) and GaCH3·NH(g) are estimated based on experimental data for TMA·NH3 and TMG·NH3 decomposition obtained in references Reference Muller[86] Reference Sauls, Interrante and Ziang[103] Reference Sauls, Hurley, Interrante, Machetti and Maciel[99].
4.17.9. (AlCH3·NH)3(g) and (GaCH3·NH)3(g)
Thermodynamic functions of gaseous (AlCH3·NH)3 and (GaCH3·NH)3 are calculated based on molecular constants estimated using results of experimental and theoretical studies of (AlH·NH)3, (DMA·NH2)3, (DMG·NH2)3, (DMG·NH2)2(DMA·NH2), TMA·NH3 and TMG·NH3 . Therewith is assumed that molecules considered in their ground states have asymmetric configuration of C1 symmetry. The formation enthalpies are estimated using the results of study of TMA·NH3 and TMG·NH3 decomposition accompanied by release of methane Reference Muller[86] Reference Sauls, Interrante and Ziang[103] Reference Sauls, Hurley, Interrante, Machetti and Maciel[99].
4.17.10. (AlN)3 and (GaN)3
Ring molecular complexes (Al·N)3 and (Ga·N)3 are assumed to be the final products in the chain of consequent adduct formation when mixing group-III metal-organic compounds and ammonia. The thermodynamic functions of these molecules are calculated using the estimated values of molecular constants. For this we use the results of experimental and theoretical studies of AlH·NH3 Reference Fink and Richards[106], (BH·NH)3 Reference Gurvich, Veyts and Alcock[4] and (B·N)3 Reference Martin, El-Yazal, Francois and Gijbels[107] Reference Martin, El-Yazal and Francois[108]. We also assume that in their ground states the molecules (Al·N)3 and (Ga·N)3 have a flat structure of D3h symmetry. Formation enthalpies of (Al·N)3 and (Ga·N)3 are estimated on the base of studies of TMA·NH3 and TMG·NH3 decomposition with simultaneous release of methane Reference Muller[86] Reference Sauls, Interrante and Ziang[103] Reference Sauls, Hurley, Interrante, Machetti and Maciel[99].
4.17.11. GaCl3·NH3
Thermodynamic properties of GaCl3·NH3 are calculated using the molecular constants experimentally found in Reference Hargittai, Hargittai and Spiridonov[109] Reference Taylor and Riethmiller[110]. According to these works the GaCl3·NH3 molecule has in the ground state X1A1 a configuration of C3V symmetry. The formation enthalpy of GaCl3·NH3 is determined using the value of formation enthalpy of solid GaCl3·NH3 as well as the evaporation enthalpy of liquid GaCl3·NH3 recommended in Reference Glushko[18]. The enthalpy of GaCl3·NH3(s) melting necessary for the calculations is estimated by a method proposed in reference Reference Morachevsky and Sladkov[111].
5. Summary
In conclusion, a database of thermodynamic properties of group-III nitrides and substances related to growth of these materials is developed in this paper. A polynomial approximation of the reduced Gibbs free energy as a function of temperature corresponding to the standard pressure of 1 atm is given for 75 species. Among them data for 31 species (including adducts frequently formed during vapor phase epitaxy) are either refined or obtained here for the first time. Using the polynomial one can calculate temperature dependencies of enthalpy, entropy and specific heat of a certain species. The database is checked for self-consistency and therefore can be used for thermodynamic calculations.
