Apparatus and method for depositing silicon germanium films

• US 20070155138A1
• Filed: 05/23/2006
• Published: 07/05/2007
• Est. Priority Date: 05/24/2005
• Status: Abandoned Application

• Current Assignee: ASM America Incorporated (ASM International NV)
• Original Assignee: ASM America Incorporated (ASM International NV)
• Inventors: Bauer, Matthias, Tomasini, Pierre, Cody, Nyles
• Application Number:
  US11/439,688
• Publication Number:
  US 20070155138A1
• Time in Patent Office: Days
• US Class Current: 438/483
• CPC Class Codes: C23C 16/30 Deposition of compounds, mixtures or solid solutions, e.g. borides, carbides, nitrides
• CPC Class Codes: C23C 16/45523 Pulsed gas flow or change of composition over time
• CPC Class Codes: C23C 16/52 Controlling or regulating the coating process C23C16/45557, C23C16/279 take precedence
• CPC Class Codes: C30B 25/02 Epitaxial-layer growth
• CPC Class Codes: C30B 29/52 Alloys
• CPC Class Codes: H01L 21/02381 Silicon, silicon germanium, germanium
• CPC Class Codes: H01L 21/02422 Non-crystalline insulating materials, e.g. glass, polymers
• CPC Class Codes: H01L 21/02532 Silicon, silicon germanium, germanium
• CPC Class Codes: H01L 21/0262 Reduction or decomposition of gaseous compounds, e.g. CVD
• CPC Class Codes: H01L 21/02639 Preparation of substrate for selective deposition

Abstract

A new model is provided for the CVD growth of silicon germanium from silicon-containing and germanium-containing precursors. According to the new model, the germanium concentration x is related to the gas phase ratio according to the equation [x/(1−x)]²=mP_Ge/P_Si, and m=Ae^−E/(RT), where P_Si is the partial pressure of the silicon-containing precursor, P_Ge is the partial pressure of the germanium-containing precursor, A is a constant, R is the universal gas constant, and T is the temperature. Methods and apparatuses are described for controlling CVD process parameters, associated with a series of reactions at constant or varied temperature, to achieve targeted germanium concentrations in silicon germanium films deposited onto semiconductor substrates. In particular, the new model can be used to calculate the resultant germanium concentration for selected precursor flow rates. The new model can also be used to control a precursor injection apparatus to achieve a desired germanium concentration.

Claims

1. A method of depositing a silicon germanium layer with a targeted composition onto a substrate, comprising:

injecting a silicon-containing precursor gas at a flow rate F_1Si and a germanium-containing precursor gas at a flow rate F_1Ge into a reaction chamber toward a substrate at a selected processing temperature with the chamber at a selected processing pressure, the precursor gases reacting to deposit a first silicon germanium layer with composition Si<sub>1−

x</sub>Ge_x onto the substrate;

measuring x;

injecting a silicon-containing precursor gas at a flow rate F_2Si and a germanium-containing precursor gas at a flow rate F_2Ge into the reaction chamber toward a substrate at the selected processing temperature with the chamber at the selected processing pressure, the precursor gases reacting to deposit a second silicon germanium layer with composition Si<sub>1−

y</sub>Ge_y onto the substrate, wherein y is a targeted value, the ratio F_2Si/F_2Ge substantially satisfying the equation

$\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Ge}}}={\left(\frac{x}{1-x}\right)}^2<br><br>{\left(\frac{1-y}{y}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Ge}}}\right).$

2. The method of claim 1, wherein the silicon-containing precursor gases comprise silane gas with molecular formula Si_nH_2n+2 and the germanium-containing precursor gases comprise germane gas with molecular formula Ge_mH_2m+2, wherein n and m are whole numbers.

3. The method of claim 1, wherein each of the injecting steps includes injecting a chlorinated precursor into the reaction chamber toward the substrate along with the silicon-containing and germanium-containing precursor gases.

4. The method of claim 2, wherein injecting germane gas comprises injecting a mixture of germane gas and a carrier gas.

5. The method of claim 1, wherein the first and second silicon germanium layers are deposited onto first and second substrates, respectively.

6. The method of claim 1, wherein n equals 1.

7. The method of claim 1, wherein n equals 2.

8. The method of claim 1, wherein n equals 3.

9. The method of claim 1, wherein m equals 1.

10. The method of claim 1, wherein m equals 2.

11. The method of claim 1, wherein m equals 3.

12. A method of depositing a silicon germanium layer with a targeted composition onto a substrate, comprising:

providing a first substrate at a selected processing temperature in a reaction chamber at a selected processing pressure;

injecting SiH₄ gas at a flow rate F_1Si and GeH₄ gas at a flow rate F_1Ge into the reaction chamber toward the first substrate, the SiH₄ and GeH₄ gases reacting to deposit silicon germanium with composition Si<sub>1−

x</sub>Ge_x onto the first substrate;

measuring x;

providing a second substrate at the selected processing temperature in the reaction chamber at the selected processing pressure; and

injecting SiH₄ gas at a flow rate F_2Si and GeH₄ gas at a flow rate F_2Ge into the reaction chamber toward the second substrate, the ratio F_2Si/F_2Ge substantially satisfying the equation

$\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Gm}}}={\left(\frac{x}{1-x}\right)}^2<br><br>{\left(\frac{1-y}{y}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Gm}}}\right).$

wherein y is a targeted value of a composition Si<sub>1−

y</sub>Ge_y of a silicon germanium layer deposited onto the second substrate by a reaction of the SiH₄ and GeH₄ gases.

13. A method of calculating a parameter associated with a deposition process of a silicon germanium layer, comprising:

providing a substrate in a reaction chamber;

injecting a silane gas with a molecular formula Si_nH_2n+2 at a flow rate F_1Si and a mixture of a germane gas and a carrier gas at a flow rate F_1Gm into the reaction chamber toward the substrate, the silane and germane gases reacting to deposit silicon germanium with composition Si<sub>1−

x</sub>Ge_x onto the substrate, the germane gas having a molecular formula Ge_mH_2m+2, the mixture having a dilution d₁, wherein n and m are whole numbers;

measuring x;

selecting two parameters from the set comprising (1) a flow rate F_2Si of a silane gas with a molecular formula Si_nH_2n+2, (2) a flow rate F_2Gm of a mixture of a carrier gas and a germane gas with a molecular formula Ge_mH_2m+2 and dilution d₂, and (3) a concentration y in a silicon germanium composition Si<sub>1−

y</sub>Ge_y;

assigning values to the two selected parameters; and

calculating the unselected parameter of said set from the equation

$\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Gm}}}={\left(\frac{x}{1-x}\right)}^2<br><br>{\left(\frac{1-y}{y}\right)}^2<br><br>\left(\frac{d_2}{d_1}\right)<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Gm}}}\right)$

or from one or more equations that are collectively mathematically equivalent to the above equation.

14. The method of claim 13, wherein n and m are equal to 1.

15. The method of claim 13, further comprising performing at least one action from the set comprising (1) storing the calculated parameter in a storage, (2) displaying the calculated parameter, and (3) using the calculated parameter as a process parameter in depositing a silicon germanium layer with composition Si₁₋

yGe_y onto a substrate.

16. A method of depositing a silicon germanium film with a targeted composition onto a substrate, comprising:

injecting SiH₄ gas at a flow rate F_1Si and GeH₄ gas at a flow rate F_1Ge into the reaction chamber toward a substrate at a first temperature T₁ (in Kelvin), the SiH₄ and GeH₄ gases reacting to deposit a first silicon germanium film with composition Si<sub>1−

x</sub>Ge_x onto the substrate;

measuring x;

injecting SiH₄ gas at a flow rate F_2Si and GeH₄ gas at a flow rate F_2Ge into the reaction chamber toward a substrate at a second temperature T₂ (in Kelvin), the SiH₄ and GeH₄ gases reacting to deposit a second silicon germanium film with composition Si<sub>1−

y</sub>Ge_y onto the substrate;

measuring y;

injecting SiH₄ gas at a flow rate F_3Si and GeH₄ gas at a flow rate F_3Ge into the reaction chamber toward a substrate at a third temperature T3 (in Kelvin), the ratio F_3Si/F_3Ge substantially satisfying the equation

$\frac{F_{3<br><br>\mathrm{Si}}}{F_{3<br><br>\mathrm{Ge}}}={\left(\frac{1-z}{z}\right)}^2<br><br>{\left(\frac{x}{1-x}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Ge}}}\right)<br><br>{\mathrm{e<br><br>}}^{\left(\frac{E}{R}\right)<br><br>\left(\frac{1}{T_1}-\frac{1}{T_3}\right)}$

wherein z is a targeted value of a composition Si<sub>1−

z</sub>Ge_z of a third silicon germanium film deposited onto a substrate at a temperature T₃ (in Kelvin) by a reaction of SiH₄ and GeH₄ gases, wherein

$\frac{E}{R}=\frac{\ln <br><br>\left[{\left(\frac{1-x}{x}\right)}^2<br><br>{\left(\frac{y}{1-y}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Ge}}}{F_{1<br><br>\mathrm{Si}}}\right)<br><br>\left(\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Ge}}}\right)\right]}{\frac{1}{T_1}-\frac{1}{T_2}}.$

17. The method of claim 16, wherein the first, second, and third silicon germanium films are deposited onto first, second₁ and third substrates, respectively.

18. A method of calculating a parameter associated with a deposition process of a silicon germanium film, comprising:

injecting silane gas at a flow rate F_1Si and a mixture of a carrier gas and germane gas with a dilution d₁ at a flow rate F_1Gm into a reaction chamber toward a substrate at a first temperature T₁ (in Kelvin), the silane and germane gases reacting to deposit a first silicon germanium film with composition Si<sub>1−

x</sub>Ge_x onto the substrate, the silane and germane gases having molecular formulas Si_nH_2n+2 and Ge_mH_2m+2, respectively, wherein n and m are whole numbers;

measuring x;

injecting silane gas with a molecular formula Si_nH_2n+2 at a flow rate F_2Si and a mixture of a carrier gas and germane gas with a dilution d₂ at a flow rate F_2Gm into the reaction chamber toward a substrate at a second temperature T₂ (in Kelvin), the silane and germane gases reacting to deposit a second silicon germanium film with composition Si<sub>1−

y</sub>Ge_y onto the substrate, the germane gas having a molecular formula Ge_mH_2m+2;

measuring y;

selecting three parameters from the set comprising (1) a flow rate F_3Si of a silane gas with a molecular formula Si_nH_2n+2, (2) a flow rate F_3Gm of a mixture of a carrier gas and germane gas with a dilution d₃, the germane gas having a molecular formula Ge_mH_2m+2, (3) a temperature T₃ (in Kelvin), and (4) a concentration z in a silicon germanium composition Si<sub>1−

z</sub>Ge_z;

assigning values to the three selected parameters; and

calculating the unselected parameter of said set from one of the two equations

$\frac{F_{3<br><br>\mathrm{Si}}}{F_{3<br><br>\mathrm{Gm}}}={\left(\frac{1-z}{z}\right)}^2<br><br>{\left(\frac{x}{1-x}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Gm}}}\right)<br><br>\left(\frac{d_3}{d_1}\right)<br><br>{\mathrm{e<br><br>}}^{\left(\frac{E}{R}\right)<br><br>\left(\frac{1}{T_1}-\frac{1}{T_3}\right)}$$\mathrm{and}$$\frac{F_{3<br><br>\mathrm{Si}}}{F_{3<br><br>\mathrm{Gm}}}={\left(\frac{1-z}{z}\right)}^2<br><br>{\left(\frac{y}{1-y}\right)}^2<br><br>\left(\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Gm}}}\right)<br><br>\left(\frac{d_3}{d_2}\right)<br><br>{\mathrm{e<br><br>}}^{\left(\frac{E}{R}\right)<br><br>\left(\frac{1}{T_2}-\frac{1}{T_3}\right)}$

or from one or more equations that are collectively mathematically equivalent to either of the above equations, wherein

$\frac{E}{R}<br><br>\frac{\ln <br><br>\left[{\left(\frac{1-x}{x}\right)}^2<br><br>{\left(\frac{y}{1-y}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Gm}}}{F_{1<br><br>\mathrm{Si}}}\right)<br><br>\left(\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Gm}}}\right)<br><br>\left(\frac{d_1}{d_2}\right)\right]}{\frac{1}{T_1}-\frac{1}{T_2}}.$

19. The method of claim 18, wherein n and m are equal to 1.

20. The method of claim 19, further comprising performing at least one action from the set comprising (1) storing the calculated parameter in a storage, (2) displaying the calculated parameter, and (3) using the calculated parameter as a process parameter in depositing a third silicon germanium film with composition Si₁₋

yGe_y onto a substrate.

21. An apparatus for depositing a silicon germanium layer with a targeted composition onto a substrate, comprising:

a reaction chamber containing a substrate support structure;

a source of a silicon-containing precursor gas;

a source of a germanium-containing precursor gas;

an injector assembly connected to the gas sources for injecting the silicon-containing and germanium-containing gases at controllable flow rates into the reaction chamber toward a substrate supported by the substrate support structure; and

a computer unit configured to store information associated with a first reaction of the silicon-containing precursor gas injected into the chamber at a flow rate F_1Si and the germanium-containing precursor gas injected into the chamber at a flow rate F_1Ge by the injector assembly to deposit a first silicon germanium layer with composition Si<sub>1−

x</sub>Ge_x onto a substrate supported by the substrate support structure, the stored information from the first reaction comprising F_1Si, F_1Ge, and x, the computer unit also configured to store information associated with a second reaction of a silicon-containing precursor gas at a flow rate F_2Si and a germanium-containing precursor gas at a flow rate F_2Ge to deposit a second silicon germanium layer with composition Si<sub>1−

y</sub>Ge_y, the stored information from the second reaction comprising only two parameters of the set consisting of F_2Si, F_2Ge, and y;

wherein the computer unit is additionally configured to calculate the unstored parameter of the set consisting of F_2Si, F_2Ge, and y from the equation

$\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Ge}}}={\left(\frac{x}{1-x}\right)}^2<br><br>{\left(\frac{1-y}{y}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Ge}}}\right).$

22. The apparatus of claim 21, wherein the silicon-containing precursor gas comprises silane gas with molecular formula Si_nH_2n+2 and the germanium-containing precursor gas comprises germane gas with molecular formula Ge_mH_2m+2, wherein n and m are whole numbers.

23. The apparatus of claim 21, further comprising a source of a chlorinated precursor gas connected to the injector assembly for injecting the chlorinated precursor gas into the reaction chamber toward a substrate supported by the substrate support structure.

24. The apparatus of claim 21, wherein the computer unit is configured to control the injector assembly to inject the silicon-containing and germanium-containing gases into the reaction chamber substantially at the flow rates F_2Si and F_2Ge, respectively, toward a substrate supported by the substrate support structure.

25. An apparatus for depositing a silicon germanium layer with a targeted composition onto a substrate, comprising:

a reaction chamber containing a substrate support structure;

a source of SiH₄ gas;

a source of GeH₄ gas;

an injector assembly connected to the SiH₄ and GeH₄ gas sources for injecting SiH₄ gas and GeH₄ gas at controllable flow rates into the reaction chamber toward a substrate supported by the substrate support structure; and

a computer unit configured to store information associated with a first reaction of SiH₄ gas injected into the chamber at a flow rate F_1Si and GeH₄ gas injected into the chamber at a flow rate F_1Ge by the injector assembly to deposit a first silicon germanium layer with composition Si<sub>1−

x</sub>Ge_x onto a first substrate supported by the substrate support structure, the stored information from the first reaction comprising F_1Si, F_1Ge, and x, the computer unit also configured to store information associated with a second reaction of SiH₄ gas at a flow rate F_2Si and GeH₄ gas at a flow rate F_2Ge to deposit a second silicon germanium layer with composition Si<sub>1−

y</sub>Ge_y, the stored information from the second reaction comprising only two parameters of the set consisting of F_2Si, F_2Ge, and y;

wherein the computer unit is additionally configured to calculate the unstored parameter of the set consisting of F_2Si, F_2Ge, and y from the equation

$\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Ge}}}={\left(\frac{x}{1-x}\right)}^2<br><br>{\left(\frac{1-y}{y}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Ge}}}\right).$

26. The apparatus of claim 25, wherein the computer unit is configured to control the injector assembly to inject the SiH₄ and GeH₄ gases into the reaction chamber substantially at the flow rates F_2Si and F_2Ge, respectively, toward a substrate supported by the substrate support structure.

27. An apparatus for calculating a parameter associated with a deposition process of a silicon germanium layer, comprising:

a reaction chamber containing a substrate support structure;

a source of silane gas having a molecular formula Si_nH_2n+2, wherein n is a whole number;

a source of a mixture of a carrier gas and a germane gas with a dilution d₁, the germane gas having a molecular formula Ge_mH_2m+2, wherein m is a whole number;

an injector assembly connected to the gas sources for injecting the silane gas and the mixture of carrier and germane gas at controllable flow rates into the reaction chamber toward a substrate supported by the substrate support structure; and

a control system configured to store information associated with a reaction of the silane gas injected into the chamber at a flow rate F_1Si and the carrier/germane gas mixture injected into the chamber at a flow rate F_1Gm by the injector assembly to deposit a silicon germanium layer with composition Si<sub>1−

x</sub>Ge_x onto a substrate supported by the substrate support structure, the stored information comprising F_1Si, F_1Gm, and x;

wherein the control system is additionally configured to store assigned values of two selected parameters from the set comprising (1) a flow rate F_2Si of a silane gas with a molecular formula Si_nH_2n+2, (2) a flow rate F_2Gm of a mixture of a carrier gas and a germane gas with a molecular formula Ge_mH_2m+2 and dilution d₂, and (3) a concentration y in a silicon germanium composition Si<sub>1−

y</sub>Ge_y, the control system configured to calculate the unselected parameter of said set from the equation

$\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Gm}}}={\left(\frac{x}{1-x}\right)}^2<br><br>{\left(\frac{1-y}{y}\right)}^2<br><br>\left(\frac{d_2}{d_1}\right)<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Gm}}}\right)$

or from one or more equations that are collectively mathematically equivalent to the above equation.

28. The apparatus of claim 27, wherein n and m are equal to 1.

29. The apparatus of claim 27, wherein the control system is configured to perform at least one action from the set comprising (1) storing the calculated parameter in a storage, (2) displaying the calculated parameter, and (3) using the calculated parameter as a process parameter in depositing a silicon germanium layer with composition Si₁₋

yGe_y onto a substrate.

30. An apparatus for depositing a silicon germanium layer with a targeted composition onto a substrate, comprising:

a reaction chamber containing a substrate support structure;

a source of silane gas with a molecular formula Si_nH_2n+2, wherein n is a whole number;

a source of germane gas with a molecular formula Ge_mH_2m+2, wherein m is a whole number;

a gas injector assembly connected to the gas sources for injecting the silane and germane gases at controllable flow rates into the reaction chamber toward a substrate supported by the substrate support structure;

a control system configured to store information associated with a first reaction of the silane gas injected into the chamber at a flow rate F_1Si and the germane gas injected into the chamber at a flow rate F_1Ge by the gas injector assembly to deposit a first silicon germanium layer with composition Si<sub>1−

x</sub>Ge_x onto a substrate supported by the substrate support structure at a first substrate temperature T₁ (in Kelvin), the control system also configured to store information associated with a second reaction of the silane gas injected into the chamber at a flow rate F_2Si and the germane gas injected into the chamber at a flow rate F_2Ge by the gas injector assembly to deposit a second silicon germanium layer with composition Si<sub>1−

y</sub>Ge_y onto a substrate supported by the substrate support structure at a second substrate temperature T₂ (in Kelvin), the stored information of the first and second reactions comprising F_1Si, F_1Ge, T₁, x, F_2Si, F_2Ge, T₂, and y, the control system being configured to store information associated with a third reaction of silane gas at a flow rate F_3Si and germane gas at flow rate F_3Ge to deposit a third silicon germanium layer with composition Si<sub>1−

z</sub>Ge_z onto a substrate at a third substrate temperature T₃ (in Kelvin), the stored information of the third reaction comprising only two parameters of the set consisting of F_3Si, F_3Ge, and z;

wherein the control system is additionally configured to calculate the unstored parameter of the set consisting of F_3Si, F_3Ge, and z from the equations

$\frac{F_{3<br><br>\mathrm{Si}}}{F_{3<br><br>\mathrm{Ge}}}={\left(\frac{1-z}{z}\right)}^2<br><br>{\left(\frac{x}{1-x}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Ge}}}\right)<br><br>{\mathrm{e<br><br>}}^{\left(\frac{E}{R}\right)<br><br>\left(\frac{1}{T_1}-\frac{1}{T_3}\right)}$$\mathrm{and}$$\frac{E}{R}=\frac{\ln <br><br>\left[{\left(\frac{1-x}{x}\right)}^2<br><br>{\left(\frac{y}{1-y}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Ge}}}{F_{1<br><br>\mathrm{Si}}}\right)<br><br>\left(\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Ge}}}\right)\right]}{\frac{1}{T_1}-\frac{1}{T_2}}.$

31. The apparatus of claim 30, wherein the control system is configured to control the gas injector assembly to inject the silane and germane gases substantially at the flow rates F_3Si and F_3Ge, respectively, toward a substrate supported by the substrate support structure at the third substrate temperature T₃.

32. The apparatus of claim 30, wherein n equals 1.

33. The apparatus of claim 30, wherein n equals 2.

34. The apparatus of claim 30, wherein n equals 3.

35. The apparatus of claim 30, wherein m equals 1.

36. The apparatus of claim 30, wherein m equals 2.

37. The apparatus of claim 30, wherein m equals 3.

38. The apparatus of claim 30, wherein the control system is configured to store the information for a case in which the first silicon germanium layer is deposited onto a first substrate and the second silicon germanium layer is deposited onto a second substrate, the control system being configured to control the gas injector assembly to deposit the third silicon germanium layer onto a third substrate.

39. The apparatus of claim 38, wherein n and m equal 1.

40. An apparatus for calculating a parameter associated with a deposition process of a silicon germanium film, comprising:

a reaction chamber containing a substrate support structure;

a source of silane gas having a molecular formula Si_nH_2n+2, wherein n is a whole number;

a source of a mixture of a carrier gas and germane gas with a dilution d, the germane gas having a molecular formula Ge_mH_2m+2, wherein m is a whole number;

a gas injector assembly connected to the gas sources for injecting the silane gas and the carrier/germane gas mixture at controllable flow rates into the reaction chamber toward a substrate supported by the substrate support structure;

a control system configured to store information associated with a first reaction of the silane gas injected into the chamber at a flow rate F_1Si and the carrier/germane gas mixture injected into the chamber at a flow rate F_1Gm by the gas injector assembly to deposit a silicon germanium film with composition Si<sub>1−

x</sub>Ge_x onto a substrate supported by the substrate support structure at a first substrate temperature T₁, the control system also configured to store information associated with a second reaction of the silane gas injected into the chamber at a flow rate F_2Si and the carrier/germane gas mixture injected into the chamber at a flow rate F_2Gm by the gas injector assembly to deposit a silicon germanium film with composition Si<sub>1−

y</sub>Ge_y onto a substrate supported by the substrate support structure at a second substrate temperature T₂, the stored information comprising F_1Si, F_1Gm, T₁, x, F_2Si, F_2Gm, T₂, and y;

wherein the control system is additionally configured to store assigned values of three selected parameters from the set comprising (1) a flow rate F_3Si of silane gas with a molecular formula Si_nH_2n+2, (2) a flow rate F_3Gm of a mixture of a carrier gas and germane gas with a dilution d₃, the germane gas having a molecular formula Ge_mH_2m+2, (3) a temperature T₃ (in Kelvin), and (4) a concentration z in a silicon germanium composition Si<sub>1−

z</sub>Ge_z, the control system configured to calculate the unselected parameter of said set from one of the two equations

$\frac{F_{3<br><br>\mathrm{Si}}}{F_{3<br><br>\mathrm{Gm}}}={\left(\frac{1-z}{z}\right)}^2<br><br>{\left(\frac{x}{1-x}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Si}}}{F_{1<br><br>\mathrm{Gm}}}\right)<br><br>\left(\frac{d_3}{d}\right)<br><br>{\mathrm{e<br><br>}}^{\left(\frac{E}{R}\right)<br><br>\left(\frac{1}{T_1}-\frac{1}{T_3}\right)}$$\mathrm{and}$$\frac{F_{3<br><br>\mathrm{Si}}}{F_{3<br><br>\mathrm{Gm}}}={\left(\frac{1-z}{z}\right)}^2<br><br>{\left(\frac{y}{1-y}\right)}^2<br><br>\left(\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Gm}}}\right)<br><br>\left(\frac{d_3}{d}\right)<br><br>{\mathrm{e<br><br>}}^{\left(\frac{E}{R}\right)<br><br>\left(\frac{1}{T_2}-\frac{1}{T_3}\right)}$

or from one or more equations that are collectively mathematically equivalent to either of the above equations, wherein

$\frac{E}{R}=\frac{\ln <br><br>\left[{\left(\frac{1-x}{x}\right)}^2<br><br>{\left(\frac{y}{1-y}\right)}^2<br><br>\left(\frac{F_{1<br><br>\mathrm{Gm}}}{F_{1<br><br>\mathrm{Si}}}\right)<br><br>\left(\frac{F_{2<br><br>\mathrm{Si}}}{F_{2<br><br>\mathrm{Gm}}}\right)\right]}{\frac{1}{T_1}-\frac{1}{T_2}}.$

41. The apparatus of claim 40, wherein n and m equal 1.