- Email: [email protected]
Feasibility study of the chemical vapour transport of ternary compound semiconductor thin films
Thin Solid Films, 193/194 (1990) 943-950
943
FEASIBILITY STUDY OF T H E C H E M I C A L VAPOUR T R A N S P O R T O F T E R N A R Y C O M P O U N D S E M I C O N D U C T O R T H I N FILMS K. BALAKRISHNAN, B. VENGATESAN, N. KANNIAH AND P. RAMASAMY
Crystal Gro~,th Centre, Anna University, Madras 600025 (India)
A general thermodynamic model to fix the minimum source temperature Ts and minimum deposition temperature Td for the efficient transport of ternary compounds has been proposed. The proposed model has been verified experimentally with CulnS2 and CulnSe2. The influence of temperature and transporting agent on chemical vapour transport has been accounted for. The efficiencies of the different transporting agents have been accounted for on the basis of bond energy values.
1. INTRODUCTION The chemical vapour transport (CVT) technique is successfully employed for growing crystals and depositing thin films of relatively non-volatile materials. Of the many aspects of CVT that have received practical and theoretical attention, the choice of solvent components ("transport agents") for the transport of a particular solid and the establishment of the optimum growth conditions are important problems. The exploratory work needed to achieve the desired result, when carried out in an empirical, trial-and-error fashion, will often be ineffective and time consuming. The slowness of the empirical approach arises from the many experimental variables which can affect the results, coupled to the time needed to set up and run an experiment before it can be evaluated. Even when a useful system is known or can be guessed from experience, a good deal of experimentation may be necessary to obtain satisfactory results and to optimize the conditions. There is obviously much to be gained when suitable solvent components and growth conditions can be chosen on a theoretical basis. However, the existing theoretical models ~'2 are not adequate to explain the successful deposition of ternary chalcogenides. The thermodynamic analysis of CVT is very useful in solving the following problems: (1) prediction of source temperature and deposition temperature; (2) selection of a suitable transporting agent. In the present work, an attempt has been made to consider the thermodynamic analysis of the CVT of ternary chalcogenides taking the elements as the source 01M0-6090/90/$3.50
© ElsevierSequoia/Printedin The Netherlands
944
K. BAI AKRISHNANt't al.
materials. Predictions of minimum source temperature 7~ and minimum deposition temperature T,~for the deposition ofchalcogenides (CulnS z and CuInSe2) have been made on the basis of this proposed model. The influence of temperature and transporting agent concentration has also been accounted for. This model has also been extended to predict the experimental conditions for the deposition of CulnS, and CulnS% with hydrogen iodide as the transporting agent. The elticiencies of the different transporting agents have been accounted for on the basis of the bond energy' values. Further. this model can be used to study the minimum source temperature and minimum deposition temperature for other chalcogcnides. Thi,,, model is a general model for the deposition of ternary semiconductors as thin lilms or single crystals. In addition to the above theoretical work. single-crystal thin platelcts of ('ulnS2 and CulnSe2 have been deposited by' the CVT technique using iodine as the transporting agent to confirm the present theoretical predictions. 2.
FI!ASIBII.I[~
S I'[,DY
()1.
Till!
('11!!MI('AI
X,'AP()L/R
I RANSI'(}RI
(~1
II'RNARY
('OM P()t ]NI)S
Ifa ternary compound is to bc effectively transported through the gas phase in a closed system, an equilibrium constant Kp near unity is not the only st, lticicnt condition. Since the vapour pressure of the ternary chalcogenide at the experimental conditions is negligible, the gas phase is assumed to contain volatile binary gaseous species. Further, the question of the conditions for the efl'ective transport of the ternary chalcogenide can be answered if free energy change AG functions of all possible solid to gas phase equilibrium reactions in the transport systems are known. A feasibility study of the transport o f a ternary compound therefore reduces to the evaluation of the AG functions of such reactions. 3.
API"I.I('ATI()N ()1 T i n - I'R(IP(}SFI) M(H)I.II. I t ) ( ' u I n S ,
3. I. Pre¢fiction o [ t h c source tctnpcruturc 7~
When the constituent elements, namely copper, indium and sulpht, r in the case of CulnS2. are taken in the stoichiomctric proportions together with the transporting agent, iodine at the source end, they react to form the gaseous binary iodides and sulphur at high temperature. All these gaseous species diffuse into the colder deposition zone owing to the drop in temperature. At the deposition zone they react back to form the ternary chalcogenide with the release of iodine. The iodine liberated dill'uses back to the source end to form the metal iodides once again Ithe feasibility of the formation of ternary compound in preference to the constituent elements is discussed in Section 3.2): Culs)+ In(s)+ 2S(s) ~ 212(gJTz'('ul(g)+ Inl3(g)-~ S_,(g) ('U lnSe(s)+
212~g)
~1)
Clearly the gas phase during a ( ' V T reaction contains the gallic species as during a hypothetical transport of the constituent elements occurring simulta-
CHEMICAL VAPOUR TRANSPORT OF TERNARY SEMICONDUCTORS
945
neously. The hypothetical transport reactions of the elements are represented below: Cu(s) + S(s) + ~12(g) ~ CuI(g) + ~S2(g )
(2)
In(s) + S(s) +~: 12(g)~----Inl3(g) + ½S2(g)
(3)
In general the AG function is given by the equation
AG = AG'+RTInKp where AG ~ is the standard free energy change, R the gas constant, T (K) the temperature and K the equilibrium constant. The free energy function for the formation of ternary compound from the binary iodides and sulphur can be represented as AGI = AG~ + R T I n K p l with pl(12) 2
KPl
pl(Cul)pl(lnl3)pl(S2 )
The following relationships are evident from stoichiometry of eqn. (1): pl(S2) =
pI(Cul) = pl(Inl 3)
(4)
Therefore pl(12) 2
Kpl - pl(Cul)3 At equilibrium AG1 = 0 and
-AG'; = RTlnKpl = RTln~ - AG~ = RT{2 In p l ( I 2 )
--
pl(I2) 2
3 In pt(Cui)}
(5)
Similarly, the A G 2 function for eqn. (2) is given by AG 2 =
AG'~+ R
T In ~p2(CuI)p2(S2)0"5} ~ p2(i2)0, s
(6)
The values of the partial pressures from eqn. (4) are introduced into eqn. (6): PE(CUI) =
pl(Cul)
p2(52) = Pt(S2) =
pl(Cul)
P2(12) = p l ( I 2 )
~, (p,(CuI)pl(CuI)°5) AG2 = AG'j + a t , n ] ~ (
AG'~+RTIn[ p,(12)o. 5 j AG2 = AG'2+ RT{I.5 In pt(Cul)-0.5 In p~(I2)}
(7)
K. BAI.AKRISHNAN e l al.
946
C o m b i n a t i o n ofeqns. (5)and (7)gives the tinal result: A(; 2 = AG 2 +0.5A(/I-f 0.5RTInpI(12)
(8)
Similar calculations for eqn. 13) result in AG.~ = A G . ~ + 0 . 5 A G I 0 . 5 R ' l ' l n p l [ 1 2 l
(91
For any spontaneous reaction, AG should be negative. The ternary c o m p o u n d CulnS2 will be deposited at the deposition end only when AG z and AGs values are negative. The corresponding AG values arc calculated by substituting the values of A l l and AS AG 2 = +19461
19.8T (-0.5RTInp(I 2)
(10)
A G e = - 86 082 + 23.4T-- 0.5R T In p(I 2)
(I I)
A ( ; 2 becomes negative at any temperature higher than 1025 K for an iodine concentration of 5 m g c m 3, whereas A(/3 is negative at any temperature below 3990 K ff)r an iodine concentration of 5 mg cm ~. Hence, if the source temperature is kept below 1025 K, Cul will not be transported. This leads to an incongruent ( ' V T ofCulnS2. ForcongruentCV'lofCulnSewithl 2 { S m g c m b at the transportmg agent, the source temperature must be kept above 1025 K. The same procedure has been applied to predict the m i n i m u m source temperature of CulnS2 with H1 and ('ulnSe2 with 12 and HI as the transporting agents ('Fable I).
IA BI.II 1 PRII)I(lhl)
("~*mpoulld
VA[ U I ' S ()1 M I N I M U M
.%'ollrc("
5a)tR,t I AND
I)1 ['(15,1111Vx,
II MI'I~RAItIRI5~,
1)anv).rt
/5"cdt( led
f'rcd, h'd
tl~( "111
DIDIIIIIIttll
/tIHIIIIII,fDI
I'.(K)
II~IK)
(.'ul nS., ('ulnS,
('u:ln:N ('u:ln:S
1, Ill
1025 1640
S44 1480
('ulnSe, ('ulnSe.,
('u:ln:Sc Cu:ln:Se
1, III
901 1250
S35 I I(R)
3.2. P r e d i c t i o n o[dcf)oA'ilioII t(,mt)('rdlurc
The constituent elements react with the iodine to form gaseous binary halides and sulphur according to tile equation Cu(s) + Inls) + 2S(s)+ 212(81 ~- C u l ( g ) + Inl 3(g)+ S2(g)
t 121
These gaseous binary iodides and sulphur diffuse to the colder deposition zone owing to the temperature gradient. At the colder deposition zone, two reactions are possible: ( ' u l ( g ] + I n l s ( g ) + S,(g)~--~C'u(s) ~ In(s) ~ 2S(s)+212(g)
(13)
Cul(g) + lnl 3(g) + S2(g) . : ('ulnS2(s) + 212(g)
(14)
CHEMICAL VAPOUR TRANSPORT OF TERNARY SEMICONDUCTORS
947
The estimated value of the free energy change for reactions (13) and (14) assuming Kp = 1 for the effective transport are AGI4 (cal m o l - 1) = - 3 4 0 3 4 + 4 0 . 3 T
(15)
AGI5 (cal m o l - 1) = _ 100474+43.9T
(16)
and
As shown by eqn. (15), AG 14 becomes negative at any temperature below 844 K and the deposition of the elements is possible. However, if the ternary compound is to be effectively transported, the formation of the elements can be avoided by maintaining the deposition zone temperature Td above 844 K. In the present experimental investigation Td is maintained at 1048 K and the corresponding AG values at 1048 K are AGt4 = + 8200 cal m o l - 1 AG 15 = - 54 467 cal mol - t
(17)
From these values it is very clear that reaction (13) is not feasible but reaction (14) is spontaneous at 1008 K. Hence the ternary compound is formed at 1048K in preference to the constituent elements. Thus the proposed model is able to fix the minimum deposition temperature Td as 844 K in the case o f C V T of CulnS2 with 12 (5 mg cm - 3) as the transporting agent. In the CVT of CulnSe2 using iodine as the transporting agent, the formation of elements can be avoided by maintaining the deposition zone temperature Td above 835 K. The results are presented in Table I. 4.
RESULTS AND DISCUSSION
4.1. Criteria to f i x the source temperature
From thermodynamical calculations, the feasibility of any chemical reaction can be predicted. A reaction is feasible only if the AG value for that reaction is negative. The transport of the ternary compound is feasible only if AG values of all the reactions are negative. Thus, in the case of transport of CulnS 2, even though AG 3 is negative at normal experimental temperatures, AG2 becomes negative at a source temperature of 1025 K at the iodine concentration of 5 mg cm 3. Thus the transport of CulnS 2 is possible only if the source temperature is maintained above a minimum value of 1025 K. Hence this model enables prediction of the essential criteria to fix the source temperature of the CVT technique. This model also explains the incongruent CVT of CulnS2 below 1025 K. Paorici et al. 3 have grown CulnS2 single crystals by taking elements in stoichiometric ratio as the source material together with iodine as the transporting agent at the minimum source temperature of I I 3 0 K . However, in the present investigation, the platelets have been deposited at a lower temperature of 1073 K. According to this theoretical model, it is possible to deposit CulnS2 platelets at any source temperature higher than 1025 K. Present experimental results confirm that
948
g,. B A I . A K R I S I ' I N A N t't
~;1[.
CulnS2 can be successfully deposited at any appreciable transport rate even at a source temperature of 1073 K. The experimental details are discussed in Seclion 5. it is not necessary to go for a higher temperature range to carr) out the transport. Thus the proposed theoretical model enables the minimum source temperature for the CVT of ternary chalcogenides to be lixed. 4.Q. Iodilt~'." lhc hc.st lratl.s]~orlitl L, ~l.~Oll t#ttotl.ff halos, on.s /or the ~/lemi~~l/ tal)ottr tran.v~ort ~ff ternary ('hah'o~eni(k,.~ In the literature several transporting agents such as (_'1,, Br 2, I,, HCI. HBr and HI have been reported for the transport of binary and ternary compounds~:
A(s)+ B(sj4 2Y(s) q- 2X2(g)-:=: AX(g) + BX ~(g)+ Y,(g) A BY2(s)+ 2Xz(g)
(IN)
w h e r e A B Y , i s a l - I l l Vl compound and X is the halogen. For a better transport of the ternary chalcogenidcs the following t~vo stages are important: (a) the conversion of the elements into volatile halide and chalcogen at the source zone: (b) the formation of the ternary compound from the ,, olatile halides and chalcogen at the deposition zone. l-he tirst stage involves the tission of the bonds in elements and I,. When the same elements are transported using different transporting agents, the elticiencv of the transport reaction depends on the X--X bond energy of the transporting agent. The halogen with the It, west bond energy will easily form the gaseous halides and is a more efficient transporting agent. From the bond energy values (I--l, 36 kcal tool ~: CI--CI. 58 kcal tool ~ Br--Br. 46 kcal mol 115,it is clear that I,. which has the lowest bond energy, will undergo tission easily and will form the binary iodides much more easily. During the formation of binary halides such as Cui and Inl.~, heat energ.~ is released owing to the bond formation. From the bond energy values (Cu-- 1.76 kcal tool ~: Cu--Br, 84 kcal tool ~: ( ' u - CI. 92 kcal tool ~1~"'. it is clear that the formation of iodides, which have low bond energies, involves the release of low heat energy compared with the corresponding bromides and chlorides. Hence iodides are comparatively less stable and require lower heat energy to be dissociated with the tission of the (_'u--I bond. In the second stage, the tormation of the ternary compound in the deposition zone involves the tission of A--X, B - X . Y - Y bonds. Once again the halides with the lowest bond energies will undergo easier fission, i.e. a lower energy is required tO effect the bond fission; on comparing the bond energies of the different halides, iodides (Cu--I, 76 kcal tool ~: In--I, 82 kcal tool ~ have the lowest bond energies. They will easily undergo tission at ,'t much lower temperature than the corresponding chlorides and bromides. Thus the formation of a ternary cornpound is feasible at a much lower energy only in the case of iodides. Since the formation of halides in the tirst stage and dissociation of halides leading to the formation of ternary compound in the second s t a g e a r e feasible at a much lower temperature only in the case of iodides, iodine is the best transporting agent among the halogens for the CVT of ternary compounds.
C H E M I C A L V A P O U R T R A N S P O R T OF T E R N A R Y S E M I C O N D U C T O R S
949
4.3. Effect of source temperature and transporting agent concentration The values of AGz and AG 3 depend on the partial pressure of iodine and temperature as represented in eqns. (10) and (1 I). The dependence of AG2 on the amount of iodine at any constant temperature and on the temperature for a fixed iodine concentration is represented in Fig. 1. The transport of the ternary compound is more feasible at a lower concentration of the transporting agent, as revealed by the negative AG2 value even at the much lower temperature of 1025 K. The partial pressure of iodine depends on the temperature. Since the partial pressure is in the logarithmic term, the influence of the partial pressure of iodine is comparatively less than that of temperature. AG2 is initially positive and becomes negative when the temperature is above a particular value. As revealed by the graph, this temperature depends on the amount of iodine taken in the ampoule. For the iodine concentration of 5 mg cm - 3, AG2 becomes negative at any temperature above 1025 K for CulnS2. Thus the formation of CuI is spontaneous only above the temperature of 1025 K in the case of transport of CulnS2 with iodine. Since the formation of Inl 3 is spontaneous under normal experimental conditions, the transport reaction depends only on the formation of gaseous CuI. Similar calculations for the transport of CulnSc2 show that the effect of source temperature and transporting agent concentration are similar to those for CulnS2. IODINE I
i
CONCENTRATION ( mg/cm 3 ) 2
3
!
!
4
5
i
6
i
i
Iodine concentration roll / crn3
200~
A -1 B -2 C -3 O-4 E -S
1SOC lOOC
gg5 K
E o
0 d
10~15K
-500
!
-1000 -I 500 -2000
A
gg5
l 1005
1 101S
I 1025
i
TEMPERATURE ( K )
Fig. I. The variation in AG2with temperatureand iodineconcentration(CuinS2).
950
K. BAI.AKRISHNAN ~'/' a/.
It was found that the minimum source temperature for the transport of ('ulnSce is 901 K at the iodine concentration of 5 mg cm ~ 5. EXPERIMI'ZNI'AL I)ETAII.S
Platelets of CulnS, and ('ulnSe 2 have been deposited by the CVT technique using iodine as the transporting agent. F'or the deposition of ('ulnSe, the high purity elements copper, indium and sulphur in stoichiometric ratio and trace amounts of iodine have been placed in a quartz tube. The quartz tube was evacuated to a vacuum of 10 5 Torr and then sealed off and then placed in a horizontal kanthal coiled double-zone furnace. Zone temperatures were maintained correct to + I (" by' means of t~.o Masibus temperature controllers. The deposition zone was cleaned initially by keeping the temperature higher than the source zone temperature for 24 h. After this the temperature gradient was reversed, and the source temperature and deposition temperature were kept constant at 830 C and 800 (" respectively. Platelets of C u l n S : were formed on the colder tip of the ampoule after 100 h. Ct, lnSce was deposited in the same way. from the elements together with iodine as the transporting agent, keeping the source temperature and deposition temperature at 810 C a n d 7 7 0 ('respectively. 6. ( ' ( ) N ( ' I . t l S I ( I N
The proposed general thcrmodynamic model helps to tix the minimum source temperature and minimum dcposition temperature for the effective transport of ternary compounds. The experimental results for the transport of ('ulnS2 and CulnSe 2 are in good accordance with the predictions of the proposed model. The influence of temperature is much more critical than that of the transporting agent concentration. The theoretical considerations on the basis of bond energy values predict that iodine is the best transporting agent among halogens for the transport of ternary chalcogcnides. A( ' K N O W I . I ! I ) G M I i N T
One of the authors {K.B.) is grateful to the University Grants ('ommission for the award of a Junior Research Fellowship. RH-I!RI-N('I!S
I 2 3 4 5 6 7
I".l!mmcncggcr,.I.('rv',l, Grnulh.,¢ 4(196~1135. l . . & . ~Vchmcir, ,I. ('r.1 ~I. O'ro~t III,/5 (I~)7~) 341. ('. Paorici. I.. Z a n o t t i and M . ( ' u r t h . / . ('r~l. Rr.~. ]~'clmM., 17i 19S2~ql7 II. Schafer. ('lwmi(,gtl Trun.sp~*rt Reucli, m.~. A c a d e m i c Press. Nev, h'ork. I q 6 4 l I. J. Emeleus and A. (}. Sharpe, .'!,lodern ..I.Vwct~ ,!I luorganic ('hcmt.~tr~. ELI:IS, I.ondon. 197"~ A . D . John. Lau~c'.~ tlumlbook ,*1 (']wnli.~trl. Mc(-ira~,~,-I till. New York. I I th cdn.. I C)71. P. 1.. S,.mi. "l'extb¢~ok ,{llm,r~amc ('lwnli.~lrt. Sultan ( ' h a n d . New Delhi. 19g5
943
FEASIBILITY STUDY OF T H E C H E M I C A L VAPOUR T R A N S P O R T O F T E R N A R Y C O M P O U N D S E M I C O N D U C T O R T H I N FILMS K. BALAKRISHNAN, B. VENGATESAN, N. KANNIAH AND P. RAMASAMY
Crystal Gro~,th Centre, Anna University, Madras 600025 (India)
A general thermodynamic model to fix the minimum source temperature Ts and minimum deposition temperature Td for the efficient transport of ternary compounds has been proposed. The proposed model has been verified experimentally with CulnS2 and CulnSe2. The influence of temperature and transporting agent on chemical vapour transport has been accounted for. The efficiencies of the different transporting agents have been accounted for on the basis of bond energy values.
1. INTRODUCTION The chemical vapour transport (CVT) technique is successfully employed for growing crystals and depositing thin films of relatively non-volatile materials. Of the many aspects of CVT that have received practical and theoretical attention, the choice of solvent components ("transport agents") for the transport of a particular solid and the establishment of the optimum growth conditions are important problems. The exploratory work needed to achieve the desired result, when carried out in an empirical, trial-and-error fashion, will often be ineffective and time consuming. The slowness of the empirical approach arises from the many experimental variables which can affect the results, coupled to the time needed to set up and run an experiment before it can be evaluated. Even when a useful system is known or can be guessed from experience, a good deal of experimentation may be necessary to obtain satisfactory results and to optimize the conditions. There is obviously much to be gained when suitable solvent components and growth conditions can be chosen on a theoretical basis. However, the existing theoretical models ~'2 are not adequate to explain the successful deposition of ternary chalcogenides. The thermodynamic analysis of CVT is very useful in solving the following problems: (1) prediction of source temperature and deposition temperature; (2) selection of a suitable transporting agent. In the present work, an attempt has been made to consider the thermodynamic analysis of the CVT of ternary chalcogenides taking the elements as the source 01M0-6090/90/$3.50
© ElsevierSequoia/Printedin The Netherlands
944
K. BAI AKRISHNANt't al.
materials. Predictions of minimum source temperature 7~ and minimum deposition temperature T,~for the deposition ofchalcogenides (CulnS z and CuInSe2) have been made on the basis of this proposed model. The influence of temperature and transporting agent concentration has also been accounted for. This model has also been extended to predict the experimental conditions for the deposition of CulnS, and CulnS% with hydrogen iodide as the transporting agent. The elticiencies of the different transporting agents have been accounted for on the basis of the bond energy' values. Further. this model can be used to study the minimum source temperature and minimum deposition temperature for other chalcogcnides. Thi,,, model is a general model for the deposition of ternary semiconductors as thin lilms or single crystals. In addition to the above theoretical work. single-crystal thin platelcts of ('ulnS2 and CulnSe2 have been deposited by' the CVT technique using iodine as the transporting agent to confirm the present theoretical predictions. 2.
FI!ASIBII.I[~
S I'[,DY
()1.
Till!
('11!!MI('AI
X,'AP()L/R
I RANSI'(}RI
(~1
II'RNARY
('OM P()t ]NI)S
Ifa ternary compound is to bc effectively transported through the gas phase in a closed system, an equilibrium constant Kp near unity is not the only st, lticicnt condition. Since the vapour pressure of the ternary chalcogenide at the experimental conditions is negligible, the gas phase is assumed to contain volatile binary gaseous species. Further, the question of the conditions for the efl'ective transport of the ternary chalcogenide can be answered if free energy change AG functions of all possible solid to gas phase equilibrium reactions in the transport systems are known. A feasibility study of the transport o f a ternary compound therefore reduces to the evaluation of the AG functions of such reactions. 3.
API"I.I('ATI()N ()1 T i n - I'R(IP(}SFI) M(H)I.II. I t ) ( ' u I n S ,
3. I. Pre¢fiction o [ t h c source tctnpcruturc 7~
When the constituent elements, namely copper, indium and sulpht, r in the case of CulnS2. are taken in the stoichiomctric proportions together with the transporting agent, iodine at the source end, they react to form the gaseous binary iodides and sulphur at high temperature. All these gaseous species diffuse into the colder deposition zone owing to the drop in temperature. At the deposition zone they react back to form the ternary chalcogenide with the release of iodine. The iodine liberated dill'uses back to the source end to form the metal iodides once again Ithe feasibility of the formation of ternary compound in preference to the constituent elements is discussed in Section 3.2): Culs)+ In(s)+ 2S(s) ~ 212(gJTz'('ul(g)+ Inl3(g)-~ S_,(g) ('U lnSe(s)+
212~g)
~1)
Clearly the gas phase during a ( ' V T reaction contains the gallic species as during a hypothetical transport of the constituent elements occurring simulta-
CHEMICAL VAPOUR TRANSPORT OF TERNARY SEMICONDUCTORS
945
neously. The hypothetical transport reactions of the elements are represented below: Cu(s) + S(s) + ~12(g) ~ CuI(g) + ~S2(g )
(2)
In(s) + S(s) +~: 12(g)~----Inl3(g) + ½S2(g)
(3)
In general the AG function is given by the equation
AG = AG'+RTInKp where AG ~ is the standard free energy change, R the gas constant, T (K) the temperature and K the equilibrium constant. The free energy function for the formation of ternary compound from the binary iodides and sulphur can be represented as AGI = AG~ + R T I n K p l with pl(12) 2
KPl
pl(Cul)pl(lnl3)pl(S2 )
The following relationships are evident from stoichiometry of eqn. (1): pl(S2) =
pI(Cul) = pl(Inl 3)
(4)
Therefore pl(12) 2
Kpl - pl(Cul)3 At equilibrium AG1 = 0 and
-AG'; = RTlnKpl = RTln~ - AG~ = RT{2 In p l ( I 2 )
--
pl(I2) 2
3 In pt(Cui)}
(5)
Similarly, the A G 2 function for eqn. (2) is given by AG 2 =
AG'~+ R
T In ~p2(CuI)p2(S2)0"5} ~ p2(i2)0, s
(6)
The values of the partial pressures from eqn. (4) are introduced into eqn. (6): PE(CUI) =
pl(Cul)
p2(52) = Pt(S2) =
pl(Cul)
P2(12) = p l ( I 2 )
~, (p,(CuI)pl(CuI)°5) AG2 = AG'j + a t , n ] ~ (
AG'~+RTIn[ p,(12)o. 5 j AG2 = AG'2+ RT{I.5 In pt(Cul)-0.5 In p~(I2)}
(7)
K. BAI.AKRISHNAN e l al.
946
C o m b i n a t i o n ofeqns. (5)and (7)gives the tinal result: A(; 2 = AG 2 +0.5A(/I-f 0.5RTInpI(12)
(8)
Similar calculations for eqn. 13) result in AG.~ = A G . ~ + 0 . 5 A G I 0 . 5 R ' l ' l n p l [ 1 2 l
(91
For any spontaneous reaction, AG should be negative. The ternary c o m p o u n d CulnS2 will be deposited at the deposition end only when AG z and AGs values are negative. The corresponding AG values arc calculated by substituting the values of A l l and AS AG 2 = +19461
19.8T (-0.5RTInp(I 2)
(10)
A G e = - 86 082 + 23.4T-- 0.5R T In p(I 2)
(I I)
A ( ; 2 becomes negative at any temperature higher than 1025 K for an iodine concentration of 5 m g c m 3, whereas A(/3 is negative at any temperature below 3990 K ff)r an iodine concentration of 5 mg cm ~. Hence, if the source temperature is kept below 1025 K, Cul will not be transported. This leads to an incongruent ( ' V T ofCulnS2. ForcongruentCV'lofCulnSewithl 2 { S m g c m b at the transportmg agent, the source temperature must be kept above 1025 K. The same procedure has been applied to predict the m i n i m u m source temperature of CulnS2 with H1 and ('ulnSe2 with 12 and HI as the transporting agents ('Fable I).
IA BI.II 1 PRII)I(lhl)
("~*mpoulld
VA[ U I ' S ()1 M I N I M U M
.%'ollrc("
5a)tR,t I AND
I)1 ['(15,1111Vx,
II MI'I~RAItIRI5~,
1)anv).rt
/5"cdt( led
f'rcd, h'd
tl~( "111
DIDIIIIIIttll
/tIHIIIIII,fDI
I'.(K)
II~IK)
(.'ul nS., ('ulnS,
('u:ln:N ('u:ln:S
1, Ill
1025 1640
S44 1480
('ulnSe, ('ulnSe.,
('u:ln:Sc Cu:ln:Se
1, III
901 1250
S35 I I(R)
3.2. P r e d i c t i o n o[dcf)oA'ilioII t(,mt)('rdlurc
The constituent elements react with the iodine to form gaseous binary halides and sulphur according to tile equation Cu(s) + Inls) + 2S(s)+ 212(81 ~- C u l ( g ) + Inl 3(g)+ S2(g)
t 121
These gaseous binary iodides and sulphur diffuse to the colder deposition zone owing to the temperature gradient. At the colder deposition zone, two reactions are possible: ( ' u l ( g ] + I n l s ( g ) + S,(g)~--~C'u(s) ~ In(s) ~ 2S(s)+212(g)
(13)
Cul(g) + lnl 3(g) + S2(g) . : ('ulnS2(s) + 212(g)
(14)
CHEMICAL VAPOUR TRANSPORT OF TERNARY SEMICONDUCTORS
947
The estimated value of the free energy change for reactions (13) and (14) assuming Kp = 1 for the effective transport are AGI4 (cal m o l - 1) = - 3 4 0 3 4 + 4 0 . 3 T
(15)
AGI5 (cal m o l - 1) = _ 100474+43.9T
(16)
and
As shown by eqn. (15), AG 14 becomes negative at any temperature below 844 K and the deposition of the elements is possible. However, if the ternary compound is to be effectively transported, the formation of the elements can be avoided by maintaining the deposition zone temperature Td above 844 K. In the present experimental investigation Td is maintained at 1048 K and the corresponding AG values at 1048 K are AGt4 = + 8200 cal m o l - 1 AG 15 = - 54 467 cal mol - t
(17)
From these values it is very clear that reaction (13) is not feasible but reaction (14) is spontaneous at 1008 K. Hence the ternary compound is formed at 1048K in preference to the constituent elements. Thus the proposed model is able to fix the minimum deposition temperature Td as 844 K in the case o f C V T of CulnS2 with 12 (5 mg cm - 3) as the transporting agent. In the CVT of CulnSe2 using iodine as the transporting agent, the formation of elements can be avoided by maintaining the deposition zone temperature Td above 835 K. The results are presented in Table I. 4.
RESULTS AND DISCUSSION
4.1. Criteria to f i x the source temperature
From thermodynamical calculations, the feasibility of any chemical reaction can be predicted. A reaction is feasible only if the AG value for that reaction is negative. The transport of the ternary compound is feasible only if AG values of all the reactions are negative. Thus, in the case of transport of CulnS 2, even though AG 3 is negative at normal experimental temperatures, AG2 becomes negative at a source temperature of 1025 K at the iodine concentration of 5 mg cm 3. Thus the transport of CulnS 2 is possible only if the source temperature is maintained above a minimum value of 1025 K. Hence this model enables prediction of the essential criteria to fix the source temperature of the CVT technique. This model also explains the incongruent CVT of CulnS2 below 1025 K. Paorici et al. 3 have grown CulnS2 single crystals by taking elements in stoichiometric ratio as the source material together with iodine as the transporting agent at the minimum source temperature of I I 3 0 K . However, in the present investigation, the platelets have been deposited at a lower temperature of 1073 K. According to this theoretical model, it is possible to deposit CulnS2 platelets at any source temperature higher than 1025 K. Present experimental results confirm that
948
g,. B A I . A K R I S I ' I N A N t't
~;1[.
CulnS2 can be successfully deposited at any appreciable transport rate even at a source temperature of 1073 K. The experimental details are discussed in Seclion 5. it is not necessary to go for a higher temperature range to carr) out the transport. Thus the proposed theoretical model enables the minimum source temperature for the CVT of ternary chalcogenides to be lixed. 4.Q. Iodilt~'." lhc hc.st lratl.s]~orlitl L, ~l.~Oll t#ttotl.ff halos, on.s /or the ~/lemi~~l/ tal)ottr tran.v~ort ~ff ternary ('hah'o~eni(k,.~ In the literature several transporting agents such as (_'1,, Br 2, I,, HCI. HBr and HI have been reported for the transport of binary and ternary compounds~:
A(s)+ B(sj4 2Y(s) q- 2X2(g)-:=: AX(g) + BX ~(g)+ Y,(g) A BY2(s)+ 2Xz(g)
(IN)
w h e r e A B Y , i s a l - I l l Vl compound and X is the halogen. For a better transport of the ternary chalcogenidcs the following t~vo stages are important: (a) the conversion of the elements into volatile halide and chalcogen at the source zone: (b) the formation of the ternary compound from the ,, olatile halides and chalcogen at the deposition zone. l-he tirst stage involves the tission of the bonds in elements and I,. When the same elements are transported using different transporting agents, the elticiencv of the transport reaction depends on the X--X bond energy of the transporting agent. The halogen with the It, west bond energy will easily form the gaseous halides and is a more efficient transporting agent. From the bond energy values (I--l, 36 kcal tool ~: CI--CI. 58 kcal tool ~ Br--Br. 46 kcal mol 115,it is clear that I,. which has the lowest bond energy, will undergo tission easily and will form the binary iodides much more easily. During the formation of binary halides such as Cui and Inl.~, heat energ.~ is released owing to the bond formation. From the bond energy values (Cu-- 1.76 kcal tool ~: Cu--Br, 84 kcal tool ~: ( ' u - CI. 92 kcal tool ~1~"'. it is clear that the formation of iodides, which have low bond energies, involves the release of low heat energy compared with the corresponding bromides and chlorides. Hence iodides are comparatively less stable and require lower heat energy to be dissociated with the tission of the (_'u--I bond. In the second stage, the tormation of the ternary compound in the deposition zone involves the tission of A--X, B - X . Y - Y bonds. Once again the halides with the lowest bond energies will undergo easier fission, i.e. a lower energy is required tO effect the bond fission; on comparing the bond energies of the different halides, iodides (Cu--I, 76 kcal tool ~: In--I, 82 kcal tool ~ have the lowest bond energies. They will easily undergo tission at ,'t much lower temperature than the corresponding chlorides and bromides. Thus the formation of a ternary cornpound is feasible at a much lower energy only in the case of iodides. Since the formation of halides in the tirst stage and dissociation of halides leading to the formation of ternary compound in the second s t a g e a r e feasible at a much lower temperature only in the case of iodides, iodine is the best transporting agent among the halogens for the CVT of ternary compounds.
C H E M I C A L V A P O U R T R A N S P O R T OF T E R N A R Y S E M I C O N D U C T O R S
949
4.3. Effect of source temperature and transporting agent concentration The values of AGz and AG 3 depend on the partial pressure of iodine and temperature as represented in eqns. (10) and (1 I). The dependence of AG2 on the amount of iodine at any constant temperature and on the temperature for a fixed iodine concentration is represented in Fig. 1. The transport of the ternary compound is more feasible at a lower concentration of the transporting agent, as revealed by the negative AG2 value even at the much lower temperature of 1025 K. The partial pressure of iodine depends on the temperature. Since the partial pressure is in the logarithmic term, the influence of the partial pressure of iodine is comparatively less than that of temperature. AG2 is initially positive and becomes negative when the temperature is above a particular value. As revealed by the graph, this temperature depends on the amount of iodine taken in the ampoule. For the iodine concentration of 5 mg cm - 3, AG2 becomes negative at any temperature above 1025 K for CulnS2. Thus the formation of CuI is spontaneous only above the temperature of 1025 K in the case of transport of CulnS2 with iodine. Since the formation of Inl 3 is spontaneous under normal experimental conditions, the transport reaction depends only on the formation of gaseous CuI. Similar calculations for the transport of CulnSc2 show that the effect of source temperature and transporting agent concentration are similar to those for CulnS2. IODINE I
i
CONCENTRATION ( mg/cm 3 ) 2
3
!
!
4
5
i
6
i
i
Iodine concentration roll / crn3
200~
A -1 B -2 C -3 O-4 E -S
1SOC lOOC
gg5 K
E o
0 d
10~15K
-500
!
-1000 -I 500 -2000
A
gg5
l 1005
1 101S
I 1025
i
TEMPERATURE ( K )
Fig. I. The variation in AG2with temperatureand iodineconcentration(CuinS2).
950
K. BAI.AKRISHNAN ~'/' a/.
It was found that the minimum source temperature for the transport of ('ulnSce is 901 K at the iodine concentration of 5 mg cm ~ 5. EXPERIMI'ZNI'AL I)ETAII.S
Platelets of CulnS, and ('ulnSe 2 have been deposited by the CVT technique using iodine as the transporting agent. F'or the deposition of ('ulnSe, the high purity elements copper, indium and sulphur in stoichiometric ratio and trace amounts of iodine have been placed in a quartz tube. The quartz tube was evacuated to a vacuum of 10 5 Torr and then sealed off and then placed in a horizontal kanthal coiled double-zone furnace. Zone temperatures were maintained correct to + I (" by' means of t~.o Masibus temperature controllers. The deposition zone was cleaned initially by keeping the temperature higher than the source zone temperature for 24 h. After this the temperature gradient was reversed, and the source temperature and deposition temperature were kept constant at 830 C and 800 (" respectively. Platelets of C u l n S : were formed on the colder tip of the ampoule after 100 h. Ct, lnSce was deposited in the same way. from the elements together with iodine as the transporting agent, keeping the source temperature and deposition temperature at 810 C a n d 7 7 0 ('respectively. 6. ( ' ( ) N ( ' I . t l S I ( I N
The proposed general thcrmodynamic model helps to tix the minimum source temperature and minimum dcposition temperature for the effective transport of ternary compounds. The experimental results for the transport of ('ulnS2 and CulnSe 2 are in good accordance with the predictions of the proposed model. The influence of temperature is much more critical than that of the transporting agent concentration. The theoretical considerations on the basis of bond energy values predict that iodine is the best transporting agent among halogens for the transport of ternary chalcogcnides. A( ' K N O W I . I ! I ) G M I i N T
One of the authors {K.B.) is grateful to the University Grants ('ommission for the award of a Junior Research Fellowship. RH-I!RI-N('I!S
I 2 3 4 5 6 7
I".l!mmcncggcr,.I.('rv',l, Grnulh.,¢ 4(196~1135. l . . & . ~Vchmcir, ,I. ('r.1 ~I. O'ro~t III,/5 (I~)7~) 341. ('. Paorici. I.. Z a n o t t i and M . ( ' u r t h . / . ('r~l. Rr.~. ]~'clmM., 17i 19S2~ql7 II. Schafer. ('lwmi(,gtl Trun.sp~*rt Reucli, m.~. A c a d e m i c Press. Nev, h'ork. I q 6 4 l I. J. Emeleus and A. (}. Sharpe, .'!,lodern ..I.Vwct~ ,!I luorganic ('hcmt.~tr~. ELI:IS, I.ondon. 197"~ A . D . John. Lau~c'.~ tlumlbook ,*1 (']wnli.~trl. Mc(-ira~,~,-I till. New York. I I th cdn.. I C)71. P. 1.. S,.mi. "l'extb¢~ok ,{llm,r~amc ('lwnli.~lrt. Sultan ( ' h a n d . New Delhi. 19g5