Corresponding author: Svetlana P. Kobeleva (kob@misis.ru)

A method has been suggested for determining stoichiometry deviation in cadmium and zinc chalcogenides based on the temperature dependence of the ratio of components partial pressures during evaporation of solid compounds in a limited volume. The new method differs from methods implying the collection of excessive component during evaporation in large volumes. The method includes measuring the partial pressures of vapor phase components during material heating to above 800 K, solving a set of material balance equations and the electric neutrality equation, and calculating the stoichiometry deviation in the initial compound at room temperature. Intrinsic point defect concentrations are calculated using the method of quasichemical reactions. The independent variables in the set of material balance equations are the sought stoichiometry deviation, the partial pressure of the metal and the concentration of free electrons. We show that the parameter of the material balance equation which determines the method’s sensitivity to stoichiometry deviation, i.e., the volume ratio of vapor and solid phases, can be considered constant during heating and evaporation if this parameter does not exceed 50. If the partial pressure is measured based on the optical density of the vapors, then the sensitivity of the method can be increased to not worse than 10^{–6} at.%.

II–VI group semiconductors, including cadmium and zinc chalcogenides, are used for visible and IR range receivers and emitters [

Intrinsic point defects in II–VI compounds are electrically active and critically affect the electrical conductivity and the optical properties of the compounds [^{–4} at.%, methods of analytical chemistry are not applicable. Nor is secondary ion mass spectroscopy ^{–4} at.%. Therefore all the methods of determining δ are based on the specific features of the evaporation of these compounds.

II–VI compounds decompose completely in the vapor phase into metal atoms and diatomic (tetra- or hexa-atomic) chalcogen molecules [_{A}_{B}_{2} are correlated by the evaporation constant _{AB}

where the indices S and V denote the solid and the vapor phases, respectively,

Despite the relatively small component excess in the solid state, the thermodynamically equilibrium vapor phase consists mainly of metal atoms during material evaporation with an excess of the metal or diatomic chalcogen molecules if there is an excess of the chalcogen. This is illustrated in Fig. _{Cd}) and tellurium (_{Te2}) partial pressures γ = _{Cd}/_{Te2} in CdTe at 900 K. In a wide temperature range the equilibrium partial pressures of the components are similar to the equilibrium saturated vapor pressures at each specific temperature and are set by the respective equations [

The partial pressure of the second component can be calculated based on the evaporation constant (Eq. (1)).

Most of δ measurement methods imply analysis of the material condensing at the cold end of the measuring system [

The aim of this work is to derive a material balance equation describing the composition of equilibrium vapor and solid phases at the evaporation temperature

Ratio of partial pressures as a function of δ for CdTe at 900 K.

During evaporation of II–VI compounds in a reactor having the volume _{0s} + _{0g}, the number of atoms in the reactor does not change, i.e.:

where _{A}_{B}

The stoichiometry deviation is δ = _{s} – _{s} < 10^{–4} at.fractions.

Therefore

At a vapor pressure of less than 1 atm, gas can be considered ideal, and therefore

where _{B} is the Boltzmann constant and

Accepting that the solid phase is homogeneous, the component concentration in the solid phase can be expressed via the concentration of intrinsic point defects:

_{A}_{S} = _{AA}_{AB}_{Ai}

_{B}_{S} = _{BB}_{BA}_{Bi}

where _{A}_{B}_{B}_{A}_{i}_{i}

Taking into account Eqs. (6)–(8) one can rewrite Eq. (5) as follows:

where α = _{g}/_{s}.

Here we take into account that

This is the sought material balance equation which correlates, via the partial pressures of the components, the vapor phase composition, having current thermodynamically equilibrium composition of the evaporating compound δ for the volume ratio of the vapor and solid phases α, with the sought stoichiometry deviation at room temperature δ_{0}. The concentration of intrinsic point defects will be expressed via the constants of the quasichemical reactions of their formation [

where

Taking into account earlier results [_{A}_{0}. One more equation which contains the independent variables _{A}

_{i}^{2}, _{i}

If the volume of the vapor phase is sufficiently large, the parameter α depends on the evaporation temperature and the parameter δ_{0}. Let us determine the conditions under which α can be considered constant.

If the change in the volumes of the solid and vapor phases is Δ_{s} = –Δ_{g}, then

The sought condition is satisfied if

and

Let us determine the limits of _{g0}/Δ

At the metal excess side:

and at the chalcogen excess side:

Based on the _{Cd} for CdTe is about 5 atm at 1250 K, the concentration of Cd and Te atoms is about 10^{22} cm^{–3} and _{g0}/Δ_{g0}/Δ_{g0}/Δ

We will now assess the validity range of the condition expressed by Eq. (14).

If metal is in excess in the vapor phase, then

If chalcogen is in excess in the vapor phase, then

The condition of Eq. (14) is satisfied if:

– for metal excess

– for chalcogen excess

Figure _{min}.

Temperature dependence of critical ratio of vapor and solid phase volumes for CdTe: (_{min}.

It can be seen from Fig. _{0}.

This is illustrated by Fig. _{min} contains an excess of chalcogen (example is the CdTe compound) for three initial δ_{0} (_{min} and

The solid lines in Fig. _{min} are the temperature dependences for the case when charged defects are predominant, and the dotted lines show the dependence of vapor composition at above _{P}_{min} for the case of predominantly electrically neutral defects. The vapor composition for γ = 2 corresponds to congruent evaporation of the compound.

Thus, the sets of Eqs. (9) and (12) contain three independent variables. If during heating of the reactor with the material to the temperature _{0}.

However there is currently no authentic information on the composition and formation parameters of intrinsic point defects in II–VI compounds. Even for the best studied material CdTe there are at least 6 defect formation models suggesting different compositions and formation reaction parameters [

Temperature dependences of γ = _{A}_{B}_{2}: (_{0} < 0; (_{0} > 0 (_{min} at the temperature _{min};

The optimum implementation of the suggested method for determining stoichiometry deviation is the partial pressure measurement approach put forward by R.F. Brebrick, based on the optical density of the vapor phase at the specific wavelength [^{–4} mol.% [

Another reactor design option was suggested [_{0} calculation over a wide range (up to 10^{–6} at.% of excessive component). This reactor design option for measurement of equilibrium partial component pressures of cadmium and zinc chalcogenides allows one to reduce the parameter a and hence to increase the stoichiometry deviation sensitivity of the method.

It was suggested to analyze the composition of equilibrium vapor phase using the material balance equation

where the parameter α = _{g}/_{s} determines the sensitivity of the method to δ_{0}. Conditions were assessed under which the parameter α can be considered constant for δ_{0} calculation simplicity. Coupled with the solution of the electrical neutrality equation, this provides for the completeness of the set of two equations with two variables, i.e., δ_{0} and the concentration of conduction electrons. Partial pressure measurements on the basis of the optical density of vapors are the most suitable variant. Taking into account the sensitivity of pressure measurements based on the optical density of vapors, one can calculate δ_{0} in the range of up to 10^{–6} at.%.