Method and apparatus to calibrate a semi-empirical process simulator

Abstract

A method and apparatus for calibrating a semi-empirical process simulator used to determine process values in a plasma process for creating a desired surface profile on a process substrate includes providing a test model which captures all mechanisms responsible for profile evolution in terms of a set of unknown surface parameters. A set Sets of test conditions processes is are derived for which the profile evolution is governed by only a limited number of parameters. For each set of test conditions process, model test values are selected and a test substrate is substrates are actually subjected to a the test process processes defined by the test values , thereby creating a test surface profile profiles. The test values are used to generate an approximate profile prediction predictions and are adjusted to minimize the discrepancy between the test surface profile profiles and the approximate profile prediction predictions, thereby providing a final model of the profile evolution in terms of the process values.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation-in-part of U.S. patent application Ser. No. 09/033,997, now U.S. Pat. No. 6,151,532 filed Mar. 3, 1998 in the names of inventors Maria E. Barone, Richard A. Gottscho, and Vahid Vahedi and commonly assigned herewith. It is also related to Applications of a semi-empirical physically based profile simulator, Enhanced process and profile simulator algorithms filed in common date herewith.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to plasma processing of semiconductor devices. In particular, this invention provides a method and apparatus to calibrate a semi-empirical process simulator for predicting the surface profile and the etch or deposition rates that a given plasma process will create.

2. Background Art

Various forms of processing with ionized gases, such as plasma etching and reactive ion etching, are increasing in importance particularly in the area of semiconductor device manufacturing. Of particular interest are the devices used in the etching process. FIG. 1A illustrates a conventional inductively coupled plasma etching system 100 that may be used in the processing and fabrication of semiconductor devices. Inductively coupled plasma processing system 100 includes a plasma reactor 102 having a plasma chamber 104 therein. A transformer coupled power (TCP) controller 106 and a bias power controller 108 respectively control a TCP power supply 110 and a bias power supply 112 influencing the plasma created within plasma chamber 104.

TCP power controller 106 sets a set point for TCP power supply 110 configured to supply a radio frequency (RF) signal, tuned by a TCP match network 114, in a TCP coil 116 located near plasma chamber 104. A RF transparent window 118 is typically provided to separate TCP coil 116 from plasma chamber 104 while allowing energy to pass from TCP coil 116 to plasma chamber 104.

Bias power controller 108 sets a set point for bias power supply 112 configured to supply a RF signal, tuned by a bias match network 120, to an electrode 122 located within the plasma reactor 104 creating a direct current (DC) bias above electrode 122 which is adapted to receive a substrate 124, such as a semi-conductor wafer, being processed.

A gas supply mechanism 126, such as a pendulum control valve, typically supplies the proper chemistry required for the manufacturing process to the interior of plasma reactor 104. A gas exhaust mechanism 128 removes particles from within plasma chamber 104 and maintains a particular pressure within plasma chamber 104. A pressure controller 130 controls both gas supply mechanism 126 and gas exhaust mechanism 128.

A temperature controller 134 controls the temperature of plasma chamber 104 to a selected temperature setpoint using heaters 136, such as heating cartridges, around plasma chamber 104.

In plasma chamber 104, substrate etching is achieved by exposing substrate A set1process
o_ddθ_e/dt=Γ_dS_d(1−θ_d−θ_e−θ_dK_s1Γ_1e=_s
Wherein k_e1, k_s1, and k_th are coefficients, generally of unknown value, associated with the ion-enhanced, physical sputtering and thermal etching mechanisms, respectively. The parameters Γ_re and Γ_is are products of ion-enhanced etching and physical sputtering yields, respectively, with ion flux integrated over incident ion energies greater than respective threshold energies, expressed respectively as E_th and E_th, and over all angles,
Γ_ie=∫∫Y_irφF)Γ₁(φ, F_e=∫dF.(F.^1/2E_sh,s^1/2)∫dφY_e(φ,Γ_e)∫(φ, E) and
Γ_is=∫∫Y_is(φ,E)Γ₁(φ,E)dφdE=∫dE(E^1/2−E_th,s^1/2)∫dφY_s(φ,E)₁(φ,E)

This model assumes that the etch yields are products of angular functions and the square root of ion energy, which dependence has been observed experimentally. However, other scaling laws could be used instead. The yield functions only represent functional dependencies, the absolute magnitudes being lumped into the coefficients k's along with other constants.

Expressions for θ_e and θ_d can be derived from the steady-state site balance equation on each type of surface present on the substrate, for example the substrate top and trench bottoms and sidewalls. At each point on the surface, the etch rate, ER, can be written:
ER=k_s2β_1s+θ_ek_e2Γ_te+k_shΓ_e−k_dθ_dS_d(1−0_e)

The coefficients k_e2, k_s2, k_d and k_th are yield constants associated with physical sputtering, ion-enhanced etching, thermal etching and ion-induced deposition, respectively. Incorporating the expressions for θ_e, θ_d, Γ_1s and Γ_ie renders the etch rate in terms of the plasma characteristics and the coefficients k, each of which is in principle an adjustable parameter that can be determined by the calibration.

It is also preferred to employ an analytic scheme for surface advancement so that the fine features can be resolved more accurately. One such scheme known in the art and capable of modeling fine feature aspects, such as sharp corners, is the method of characteristics, also known as the shock-front-tracking algorithm. (See, e.g., S. Hamaguchi, “Modeling of Film Deposition for Microelectronic Applications”, Thin Films, vol. 22, p. 81, S. Rossnagel, ed. Academic Press, San Diego, 1996). Another is the level set approach. (See, e.g., J. A. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press 1996). The shock-front-tracking approach models the surface (i.e., the interface layer between vacuum and solid) as a collection of piecewise continuous line segments, for each of which a rate of movement is calculated. The possibility of each segment's advancing or receding along its normal independently of the movement of the other segments allows for multiple potential solutions for the resulting surface. In order to avoid multiple solutions, these analytic schemes model the points between the line segments as shocks (i.e., discontinuities in the slope), and properly track the movement of the shocks.

Thus, the cumulative output of blocks 104 through 112, particularly of the operation of the plasma model in block 108 and the profile simulator in block 112, which together comprise an initial mathematical surface profile model as specified above, generates a quantitative but approximate prediction of the etch or deposition rates and surface profile(s) created by the test process processes.

In block 114, the test values of the input parameters the test process(es) provided in block 104 are used to provide a test surface profile profiles, created experimentally by subjecting a test substrate substrate(s) to a test process processes, in the reactor of interest, defined by the test values of the input parameters. The etch or deposition rates and surface profile(s) of the test substrate substrates are then measured. In block 116, the etch or deposition rates and surface profile(s) of the test substrate substrates are quantitatively compared with the quantitative approximate prediction predictions resulting from block 112. The difference between the test surface profile(s) and/or etch/deposition rates and the approximate prediction(s) is evaluated according to some criterion, such as an accuracy of range of 10%, applied in block 116.

In general, on the first pass, in which the approximate prediction(s) is computed using preliminary test values of unknown surface parameters, the residual is not sufficiently small to satisfy the criterion, and the calibration procedure advances to block 118, in which the values of the unknown surface parameters are adjusted so as to minimize the discrepancy. The adjusted values are then resubmitted to the profile simulator of block 112 and the plasma model of block 108, for another iteration that render the approximate profile prediction(s) and of the comparison in block 116. Iteration continues until the discrepancy between the test surface profile(s) and the approximate prediction(s) is adequately minimized.

Thus, both block 116 and block 118 effect a calculation of optimum values of the unknown surface parameters test values appearing in the initial mathematical surface profile model. After the surface parameters suitable for the current set of conditions test process(es) are determined, a different set of conditions test process(es) in block 104 is selected from block 102 and its respective surface parameters are determined using the same process of block 104 through block 120 until all surface parameters are determined.

For example, physical sputtering yield, energy scaling, and energy threshold coefficients may be obtained by fitting to etch rate data and final profile SEM (Scanning Electron Micrograph) data collected after wafer processing in a chemically inert plasma such as an argon discharge with the ion flux and energy distribution to the separately measured or modeled. Coefficients representing thermal etch rate may be obtained by best fit to etch rate data collected under conditions for which there is no energetic ion bombardment. If sufficient gas phase reactant density can be achieve the surface will saturate and the dependence of etch rate on adsorption probability can be eliminated leaving saturated etch rate as the only unknown parameter. Patterned features including overhang structures may be etched in order to isolate surface reaction probabilities which determine transport throughout the feature. In order to calibrate models for deposited material, deposition and etch rates on blanket or patterned wafers processed under conditions favoring deposition may be collected. Incomplete film stacks may be used to isolate the mechanisms leading to redeposition. For chemically assisted sputtering, also referred to as ion-neutral synergy etching, data may be collected from wafers processed under conditions where the ratio of ion energy flux to etchant neutral flux is varied. For large (small) enough ion energy flux to etchant neutral flux ratios the etch rate is dependent only on the etchant flux (incident ion energy flux). Model fits to this etch rate and profile data combined with ion and/or neutral flux measurements and/or models can be used to determine unknown coefficients including neutral sticking coefficient, neutral desorption and/or recombination rates, average etch product stoichiometry, and yield per incident ion as a function of energy and angle. For all the sets of experiments above subsets of the complete process chemistry may be used to further isolate and calibrate specific reactions.

In one presently alternative specific embodiment, the approximate profile prediction generated by the profile simulator in block 112 comprises a series of frames, each computed after a sufficiently small time increment, and block 114 only compares frames of the approximate profile prediction that correspond to cumulative exposure times roughly equal to the time of the snapshots in the test surface profile. If the test profile includes multiple snapshots at different exposure times and/or at a different test value of one or more input parameters other than time, block 116 compares each test snapshot with the appropriate frame of the profile prediction and the system operates to minimize the residual over the entire pairwise comparison.

As will now be evident to those of ordinary skill in the art, many configurations departing from the procedure shown in FIG. 1 1B fall within the scope of the invention. For example, FIG. 2 illustrates another specific embodiment in which block 206 combines the plasma model with the unknown parameter test values and the substrate parameters in a single module. The entire initial mathematical surface profile model may reside in a single module, block 206, rather than being divided into distinct parts 108 (FIG. 1 1B) and 112 (FIG. 1 1B) to deal separately with phenomena acting over different length scales. Alternatively, depending on the nature of the initial mathematical surface profile model and comparison algorithm used, insertion of the test values and preliminary surface parameters into the initial mathematical surface profile model may be delayed until the comparison block.

Turning to FIG. 4, which illustrates, in block-diagram form, a hardware system incorporating the invention. As indicated therein, the system includes a system bus 400, over which all system components communicate, a mass storage device (such as a hard disk or optical storage unit) 402 as well as a main system memory 404.

The operation of the illustrated system is directed by a central-processing unit (“CPU”) 406. The user interacts with the system using a keyboard 408 and a position-sensing device (e.g., a mouse) 410. The output of either device can be used to designate information or select particular areas of a screen display 412 to direct functions to be performed by the system.

The main memory 404 contains a group of modules that control the operation of CPU 406 and its interaction with the other hardware components. An operating system 414 directs the execution of low-level, basic system functions such as memory allocation, file management and operation of mass storage devices 402. At a higher level, an analysis module 416, implemented as a series of stored instructions, directs execution of the primary functions performed by the invention, as discussed below. Instructions defining a user interface 418 allow straightforward interaction over screen display 412. User interface 418 generates words or graphical images on display 412 to prompt action by the user, and accepts user commands from keyboard 408 and/or position-sensing device 410. The main memory 404 also includes one or more database 420, in general containing any of the test or process values of input parameters including input variables, the desired profile, the test surface profile and rough preliminary test values in the plasma model and profile simulator.

It must be understood that although the modules of main memory 404 have been described separately, this is for clarity of presentation only; so long as the system performs all necessary functions, it is immaterial how they are distributed within the system and its programming architecture.

The test surface profile(s) is produced experimentally, as is well known in the art, by subjecting one or more test substrates to a test process(es) in a plasma reactor and measuring the resulting surface profile using, for example, scanning electron microscopy. The desired and test surface profiles may be supplied to the hardware system in electronic format or as graphic hardcopy, in which case the image(s) is processed by a digitizer 398 before numerical comparison with the approximate prediction. The digitized profile is sent as bitstreams on the bus 400 to a database 420 of the main memory 404. The test surface profile may be stored in the mass storage device 402 as well as in database 420.

As noted above, execution of the key tasks associated with the present invention is directed by analysis module 416, which governs the operation of CPU 406 and controls its interaction with main memory 404 in performing the blocks necessary to provide a final mathematical surface profile model including calibrated optimum test values in the initial surface profile model; and, by further processing based on the final surface profile model and a desired surface profile, to determine process values of one or more input variables governing a plasma process sequence appropriates appropriate for creating the desired profile on a process substrate; or, by inserting process values of the input variables into the final mathematical model, to predictively calculate a process surface profile to be created on a process substrate by a plasma process sequence defined by the process values.

In particular, the hardware system depicted in FIG. 3 may be used to implement the calibration procedure illustrated by FIG. 1 1B as follows. The input variable test values selected in block 104, the test values of any fixed input parameter, and the test surface profile created in block 114 and, as needed, the desired surface profile and/or process values of interest are provided to the database 420 so that they are available to the analysis module 416. Alternatively, the module 416 may retrieve any of the test values, rough preliminary values and test surface profile data from the mass storage device 402 or user interface 418 in response to a user command. Or, the rough preliminary values may be determined by the module 416, based on the input variable test values, according to a predetermined algorithm.

Turning now to FIG. 1 1B, by executing the plasma modeling and profile simulation of blocks 108 and 112, respectively, the module 416 establishes the initial mathematical surface model predicting the profile created by the test process. In block 116, the module 416 (FIG. 4) accesses the test surface profile and compares it with the initial mathematical surface profile model and evaluates the residual according to some predetermined criterion. If the residual is not sufficiently small, the analysis module 416 uses the results of the comparison to adjust the test values of the plasma model and profile simulator in block 118. The new test values are retained in the database 420 for another iteration of the modeling/simulation and comparison blocks. When the test surface profile and approximate prediction are sufficiently similar, the test values used in that final iteration are stored in the database 420 as the optimum values.

The analysis module uses these optimum values of the input variables for computation of process values, which can be loaded into a plasma reactor for production of a device including the desired profile, or for profile prediction as described above.

It will therefore be seen that the foregoing represents a highly extensible and advantageous approach to plasma processing of semiconductor devices. The terms and expressions employed herein are used as terms of description and not of limitations, and there is no intention, in the use of such terms and expressions, of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. For example, the various modules of the invention can be implemented on a general-purpose computer using appropriate software instructions, or on a network of computers, or a multiprocessor computer or as hardware circuits, or as mixed hardware-software combinations (wherein, for example, plasma modeling and profile simulation are performed by dedicated hardware components).

While embodiments and applications of this invention have been shown and described, it would be apparent to those skilled in the art having the benefit of this disclosure that many more modifications than mentioned above are possible without departing from the inventive concepts herein. The invention, therefore, is not to be restricted except in the spirit of the appended claims.

Claims

1. A method for calibrating a semi-empirical process simulator, said method comprising:

performing test processes under conditions where only a limited number of parameters contribute to a profile evolution;

deriving a set of test conditions for which a the profile evolution is governed only by a the limited number of parameters;

selecting a plurality of test values for each said set of test conditions;

subjecting a test substrate to a test process defined by said plurality of test values, thereby creating a test surface profile;

generating an approximate profile prediction from said plurality of test values;

adjusting said plurality of test values to minimize a discrepancy between said test surface profile and said approximate profile prediction, thereby solving for said limited number of parameters; and

repeating said selecting, subjecting, generating, and adjusting for another said set of test conditions until said plurality of parameters is determined, thereby providing a final model of said profile evolution in terms said plurality of parameters.

2. The method of claim 1, wherein said profile evolution comprises an etch rate, a deposition rate, and a surface profile.

3. The method of claim 1, wherein generating said approximate profile prediction includes using a plurality of preliminary test values.

4. The method of claim 3, wherein said adjusting said plurality of test values includes changing at least one preliminary test value.

5. The method of claim 4, further comprising comparing said test surface profile and said approximate profile prediction.

6. The method of claim 5, further comprising incorporating at least one changed preliminary test value.

7. The method of claim 1, wherein said semi-empirical process simulator is used to determine a plurality of parameters governing a plasma process for creating a desired surface profile on a process substrate.

8. The method of claim 7, further comprising generating a plurality of parameters from said final model and said desired surface profile.

9. The method of claim 8, further comprising generating a prediction of said surface profile from said final model and said plurality of parameters.

10. The method of claim 1, wherein said semi-empirical process simulator is used to predict a surface profile to be created on a process substrate by a plasma process defined by a plurality of parameters.

11. The method of claim 1, wherein said plurality of parameters comprises: a plurality of unknown substrate parameters and a plurality of unknown reactor parameters.

12. The method of claim 11, wherein said plurality of unknown substrate parameters comprises: a dimension of a substrate, a substrate composition, and a distribution of a feature on a surface substrate.

13. The method of claim 11, wherein said plurality of unknown reactor parameters comprises: a power level, a gas temperature, a gas pressure, a gas flow, and a gas composition.

14. The method of claim 1, wherein said plurality of parameters varies with time.

15. A method for configuring an apparatus for calibrating a semi-empirical process simulator, the method comprising the steps of:

performing test processes under conditions where only a limited number of parameters contribute to a profile evolution;

deriving a set of test conditions for which a the profile evolution is governed only by a the limited number of parameters;

selecting a plurality of test values for each said set of test conditions;

subjecting a test substrate to a test process defined by said plurality of test values, thereby creating a test surface profile;

generating an approximate profile prediction from said plurality of test values;

adjusting said plurality of test values to minimize a discrepancy between said test surface profile and said approximate profile prediction, thereby solving for said limited number of parameters; and

repeating said selecting, subjecting, generating, and revising for another said set of test conditions until said plurality of parameters is determined, thereby providing a final model of said profile evolution in terms said plurality of parameters.

16. An apparatus for calibrating a semi-empirical process simulator, the apparatus comprising:

a computer memory for storing a desired surface profile;

a the computer memory for storing a test surface profile, created by subjecting a test substrate to a test process defined by a respective plurality of parameters;

means for performing test processes under conditions where only a limited number of parameters contribute to a profile evolution;

means for deriving a set of test conditions for which a the profile evolution is governed only by a the limited number of parameters;

means for selecting a plurality of test values for each said set of test conditions;

means for subjecting a test substrate to a test process defined by said plurality of test values, thereby creating a test surface profile;

means for generating an approximate profile prediction from said plurality of test values;

means for revising said plurality of test values to minimize a discrepancy between said test surface profile and said approximate profile prediction, thereby solving for said limited number of parameters; and

means for repeating said selecting, subjecting, generating, and revising for another said set of test conditions until said plurality of parameters is determined, thereby providing a final model of said profile evolution in terms said plurality of parameters.

17. The apparatus of claim 16, further comprising a computer memory for storing a preliminary test value, the means for generating an approximate profile description from the initial surface profile model and the respective test value employing the preliminary test value.

18. A program storage device readable by a machine, tangibly embodying a program of instructions readable by the machine to perform a method for calibrating a semi-empirical process simulator, the method comprising:

performing test processes under conditions where only a limited number of parameters contribute to a profile evolution;

deriving a set of test conditions for which a the profile evolution is governed only by a the limited number of parameters;

selecting a plurality of test values for each said set of test conditions;

subjecting a test substrate to a test process defined by said plurality of test values, thereby creating a test surface profile;

generating an approximate profile prediction from said plurality of test values;

adjusting said plurality of test values to minimize a discrepancy between said test surface profile and said approximate profile prediction, thereby solving for said limited number of parameters; and

repeating said selecting, subjecting, generating and adjusting for another said set of test conditions until said plurality of parameters is determined, thereby providing a final model of said profile evolution in terms said plurality of parameters.