DETERMINING AN OPTIMAL ION ENERGY FOR PLASMA PROCESSING OF A DIELECTRIC SUBSTRATE

Abstract

An ion energy for plasma processing of a dielectric substrate is determined by exposing the dielectric substrate to a plasma discharge and applying a pulsed voltage waveform. This waveform includes a sequence of pulses, each having a higher voltage interval and a lower voltage interval having a voltage slope. First pulses of the sequence having differing voltage slopes are generated and applied to the dielectric substrate. For each first pulse, the voltage slope and a corresponding output current are determined. For each first pulse, at least one coefficient of a mathematical relation between the voltage slope and the corresponding output current based solely on the voltage slope and the output current determined for one or more of the first pulses is determined. A test function is applied and an optimal voltage slope value corresponding to the at least one coefficient making the test function true is selected.

Claims

1. A method of determining an ion energy for plasma processing of a dielectric substrate, the method comprising: exposing the dielectric substrate to a plasma discharge, applying a pulsed voltage waveform generated by a power supply to the dielectric substrate, wherein the pulsed voltage waveform comprises a sequence of pulses, each pulse comprising a higher voltage interval and a lower voltage interval, wherein the lower voltage interval comprises a voltage slope, generating first pulses of the sequence having differing voltage slopes between one another and applying the first pulses to the dielectric substrate, for each one of the first pulses, determining the voltage slope and an output current corresponding to the voltage slope at an output of the power supply, for each one of the first pulses, determining at least one coefficient of a mathematical relation between the voltage slope and the corresponding output current based solely on the voltage slope and the output current determined for one or more of the first pulses, applying a test function to the at least one coefficient and selecting an optimal voltage slope value corresponding to the at least one coefficient making the test function true.

2. The method of claim 1, wherein the at least one coefficient is an expression consisting of: one or more mathematical operators, one or more values of the voltage slopes and one or more values of the output current.

3. The method of claim 1, wherein the mathematical relation is a polynomial function between the output current and the voltage slope.

4. The method of claim 3, wherein the polynomial function is a first degree polynomial I.sub.P=kS+b, wherein I.sub.P represents output current, S represents voltage slope and wherein the at least one coefficient is at least one of k and b.

5. The method of claim 1, wherein the at least one coefficient is representative of one or more capacitances of an interaction between the plasma discharge and the dielectric substrate, the at least one coefficient being resolved based solely on the voltage slope and output current determined for one or more of the first pulses.

6. The method of claim 1, wherein the first pulses have monotonically increasing voltage slopes.

7. The method of claim 1, comprising measuring, for each of the first pulses, at least one of: the respective voltage slope and the output current corresponding to the voltage slope.

8. The method of claim 1, wherein the test function is configured to determine an extremum of the at least one coefficient.

9. The method of claim 1, further comprising generating second pulses of the sequence, the second pulses having a voltage slope corresponding to the optimal voltage slope value and applying the second pulses to the dielectric substrate to perform plasma processing.

10. The method of claim 1, wherein plasma processing is selected from one or a combination of: plasma-assisted etching and plasma-assisted deposition.

11. An apparatus for plasma processing of a dielectric substrate, comprising: a plasma reactor configured to generate a plasma, a processing platform for supporting the dielectric substrate, a power supply comprising an output coupled to the processing platform, at least one of: a voltage measurement unit and a current measurement unit coupled to the output, and a control unit coupled to the power supply, wherein the control unit and the power supply are jointly configured to generate a pulsed voltage waveform, wherein the pulsed voltage waveform comprises a sequence of pulses, each pulse comprising a higher voltage interval and a lower voltage interval, wherein the lower voltage interval comprises a voltage slope, wherein the control unit and the power supply are jointly configured to generate first pulses of the sequence having differing voltage slopes between one another, wherein for each one of the first pulses, the control unit is configured to determine the voltage slope and a corresponding output current at the output, and to evaluate at least one coefficient of a mathematical relation between the voltage slope and the output current based solely on the voltage slope and the output current determined for one or more of the first pulses, wherein the control unit is further configured to apply a test function to the at least one coefficient.

12. The apparatus of claim 11, wherein the control unit and the power supply are jointly configured to generate second pulses of the sequence, the second pulses having a voltage slope representative of the at least one coefficient making the test function true.

13-14. (canceled)

15. The apparatus of claim 11, wherein the power supply is a hybrid converter comprising a switch mode power supply and an adjustable current source.

16. An apparatus for plasma processing of a dielectric substrate, comprising: a plasma reactor configured to generate a plasma, a processing platform for supporting the dielectric substrate, a power supply comprising an output coupled to the processing platform, at least one of: a voltage measurement unit and a current measurement unit coupled to the output, and a control unit coupled to the power supply, wherein the control unit and the power supply are jointly configured to generate a pulsed voltage waveform, wherein the pulsed voltage waveform comprises a sequence of pulses, each pulse comprising a higher voltage interval and a lower voltage interval, wherein the lower voltage interval comprises a voltage slope, wherein the control unit and the power supply are jointly configured to generate first pulses of the sequence having differing voltage slopes between one another, wherein for each one of the first pulses, the control unit is configured to determine the voltage slope and a corresponding output current at the output, and to evaluate at least one coefficient of a mathematical relation between the voltage slope and the output current based solely on the voltage slope and the output current determined for one or more of the first pulses, wherein the control unit is further configured to apply a test function to the at least one coefficient; wherein the control unit is configured to determine an ion energy for plasma processing of the dielectric substrate by: exposing the dielectric substrate to a plasma discharge, and selecting an optimal voltage slope value corresponding to the at least one coefficient making the test function true.

17. The apparatus of claim 16, wherein the power supply is a hybrid converter comprising a switch mode power supply and an adjustable current source.

18. The apparatus of claim 16, wherein the mathematical relation is a polynomial function between the output current and the voltage slope.

19. The apparatus of claim 16, wherein the first pulses have monotonically increasing voltage slopes.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Aspects of the present disclosure will now be described in more detail with reference to the appended drawings, wherein same reference numerals illustrate same features and wherein:

[0028] FIG. 1 illustrates the block diagram of an apparatus for plasma processing according to the present disclosure;

[0029] FIG. 2 represents a simplified electric model of the system of FIG. 1;

[0030] FIG. 3 depicts a typical waveform of the output voltage, the output current and the substrate voltage potential;

[0031] FIG. 4 illustrates a possible implementation of the auto-tuning method according to the present disclosure, comprising applying a sequence of first pulses having different voltage slopes;

[0032] FIG. 5 represents a possible realization of the power supply for use in the apparatus of FIG. 1;

[0033] FIG. 6 shows graphs of output voltage output current and calculated coefficient values for an experimental setup of the method of the present disclosure;

[0034] FIG. 7 shows the measured ion energy distribution corresponding to different voltage slopes of FIG. 6.

DETAILED DESCRIPTION

[0035] An apparatus for plasma processing a dielectric substrate, such as a semiconductor substrate, is shown in FIG. 1. Gas is infused to the reactor 110. The plasma is ignited in the reactor 110 with an external power supply 101, which is coupled with the gas by a matching network 105 and a coil 108 outside the chamber. The power supply is connected to the matching network 105 and the matching network is connected to the coil 108. The power supply 101 can be any suitable power source including radio-frequency (RF), microwave-frequency (MF) and pulsed dc power sources. Although the plasma source as shown in FIG. 1 is inductively coupled, it can be of any other variety, such as capacitively coupled plasma source and helicon type plasma source.

[0036] The apparatus of FIG. 1 can be used for plasma etching or deposition. Therefore, a dielectric substrate material 109 is placed on the table 111 inside the reactor 110. The pressure in the reactor is kept low (i.e. below atmospheric pressure) by a (vacuum) pump depicted in FIG. 1. A power amplifier 114 is connected to the table 111 through electrical connection 113.

[0037] A voltage measurement unit 116 can be connected to the power amplifier 114, measuring the output voltage of the amplifier. The voltage measurement unit 116 is coupled to controller 115 through (data) connection 117 for sending measured results to the controller 115.

[0038] A current measurement unit 119 can be provided to measure the output current of the power amplifier 114, e.g. through an interface 112 connected to electrical connection 113 and/or table 111. The current measurement unit 119 is coupled to controller 115 through (data) connection 120 for sending measured results to the controller 115.

[0039] The controller 115 implements an automatic control algorithm according to the present disclosure, which is based on the measured voltage and/or current values. The controller 115 is coupled to the power amplifier 114 through (data) connection 118 for sending control signals to the power amplifier 114 to adjust the output (voltage) waveform. The automatic control algorithm is configured to control ion energy in order to obtain a narrowest IED. Advantageously, the control algorithm is implemented as a real-time control system with a voltage and/or current feedback.

[0040] A basic equivalent electric model of the system of FIG. 1 is depicted in FIG. 2. During etching or deposition phase, the plasma can be assumed to be a constant voltage source V.sub.p. An ion sheath is formed between the plasma and the surface of the material. The ion sheath is equivalent to a dc current source I.sub.I in parallel with a sheath capacitance C.sub.sh and a diode D.sub.1. The substrate is equivalent to a capacitor C.sub.sub. For a conductive substrate, C.sub.sub is infinitely large, which can be treated as an ideal wire. For a dielectric substrate, C.sub.sub has a finite value. There are parasitic capacitances between the table and other components, including the plasma and the reactor wall, which is defined by the table capacitance C.sub.t. The table is conductive and connected to the output of the power amplifier.

[0041] For a conductive substrate, the output voltage V.sub.out is a constant dc value. The sheath voltage V sh is then defined by V.sub.sh=V.sub.out. The voltage and current measurement unit are used to monitor the dc value. V.sub.out is regulated by the feedback controller.

[0042] As depicted in FIG. 3, for a dielectric substrate, the waveform of V.sub.out is of a tailored pulse-shape, which can be divided into 2 phases, including a discharge phase and an etching or deposition phase. The discharge phase consists of a positive pulse V.sub.0 lasting for T.sub.1, used to attract electrons and discharge the substrate periodically. T.sub.1 should be as short as possible only if the substrate surface gets fully discharged. The etching or deposition phase consists of a negative slope defined by V.sub.1, V.sub.2 and T.sub.2. A negative voltage V.sub.1 is applied to the table after the substrate is fully discharged. The voltage potential V e on the substrate surface during etching or deposition is approximated by

V.sub.e?V.sub.1?V.sub.0.

[0043] To compensate the ion accumulation on the substrate surface, a negative voltage slope should be applied to the table. The voltage slope is defined by 3 portions V.sub.1, V.sub.2 and T.sub.2. The slope rate S is defined by

[00001]$S=\frac{V_2-V_1}{T_2}.$

[0044] In order to obtain a constant negative voltage on the substrate during etching or deposition phase, the voltage slope rate should be tuned to an exact value, which is equivalent to

[00002]$S=-\frac{I_i}{C_{sub}}.$

[0045] However, in practice, I.sub.I and C.sub.sub are unknown. In the prior arts, it is tuned either by hand or by theoretical calculation. Both tuning methods result in a deviation with the optimal voltage slope. In addition, the hand-tuning method requires a lot of time and an additional retarding field energy analyzer or equivalent. Furthermore, the above theoretical calculation method is based on an over-simplified model and relies on the pre-measured substrate capacitance, which might vary in the process.

[0046] Referring to FIG. 4, an algorithm to auto-tune the output voltage slope according to the present disclosure, works based only on output voltage and output current. Either one can be set, e.g. by controller 115 and the other one can be measured, e.g. by voltage measurement unit 116 and/or current measurement unit 119. The tuning algorithm according to the present disclosure can be implemented by the controller 115 in a fully automatic way and discards the need for any manual intervention or additional measurement (e.g. measurement of capacitance values).

[0047] During the etching or deposition phase, the output current is a negative dc value and equal to ?I.sub.P. The value of I.sub.P is given by

[00003]$I_P=-\left(\frac{C_{sh}{C}_{sub}}{C_{sh}+C_{sub}}+C_t\right)S+\frac{C_{sub}}{C_{sh}+C_{sub}}{I}_i.$

[0048] If all the capacitances and the ion current are constant and independent of the sheath voltage, I.sub.P has a linear relation with the voltage slope rate S. However, in practice, the sheath capacitance C.sub.sh is dependent on the sheath voltage thus changing with the voltage slope rate S. I.sub.P can then be described as

I.sub.P=k(S)S+b(S),

Where k(S) and b(S) are a function of the voltage slope rate S and given by

[00004]$k\left(S\right)=-\left(\frac{C_{sh}{C}_{sub}}{C_{sh}+C_{sub}}+C_t\right)$$\mathrm{and}$$b\left(S\right)=\frac{C_{sub}}{C_{sh}+C_{sub}}{I}_i.$

respectively. When the voltage slope rate S is tuned to the optimal value, with which the narrowest IED is obtained, V sh turns to be constant. I.sub.P is then given by

I.sub.P=?C.sub.tS+I.sub.i.

[0049] Since the capacitance C.sub.sh, C.sub.sub, C.sub.t are all positive, function k(S) and b(S) both reach their maximum values when the narrowest IED is achieved. When varying the voltage slope S, by finding the maximum value of k(S) or b(S), the IED can be tuned to be the narrowest.

[0050] In order to find the optimal voltage slope S, a series of voltage slopes S.sub.n (n=1, 2, 3 . . . ) are applied to the table in different switching cycles. The current measurement unit 119 then records the corresponding dc current values I.sub.n (n=1, 2, 3 . . . ) during etching or deposition phase. Alternatively, a series of output current values I.sub.n (n=1, 2, 3 . . . ) are set by the power amplifier 114, and the corresponding voltage slopes S.sub.n (n=1, 2, 3 . . . ) can be measured by voltage measurement unit 116.

[0051] The value of k(S) or b(S) can be calculated based on the real-time measurement results of the output voltage and current. k(S) is approximated by

[00005]$k\left(S_n\right)=\frac{I_n-I_{n-1}}{S_n-S_{n-1}}.$

b(S) is approximated by

[00006]$b\left(S_n\right)=\frac{S_n{I}_{n-1}-S_{n-1}{I}_n}{S_n-S_{n-1}}.$

[0052] The approximation is accurate if the step value of S.sub.n?S.sub.n?1 is sufficiently small. As depicted by FIG. 4, when k(S.sub.n) reaches its maximum value at S.sub.n=S.sub.m, the optimal output voltage slope is found to be S.sub.m. The corresponding output current is equivalent to be I.sub.m. The maximum value of b (S.sub.n) can also be used to find the optimal voltage slope.

[0053] The above method can be also used to calculate the unknown parameters. The table capacitance is found to be

C.sub.t=k(S.sub.m).

The ion current is found to be

I.sub.i=b(S.sub.m).

The substrate capacitance is found to be

[00007]$C_{sub}=-\frac{b\left(S_m\right)}{S_m}.$

[0054] It should be noted that the power amplifier 114 can be any variety of suitable power amplifiers. In one embodiment, it can be a voltage-source amplifier, including a switched-mode voltage amplifier, a linear amplifier or any combination of them. In another embodiment, the power amplifier can be realized by a hybrid converter.

[0055] As depicted in FIG. 5, the hybrid converter comprises two adjustable dc voltage-source amplifiers V.sub.0 and V.sub.1, two switches S.sub.1 and S.sub.2 and an adjustable dc current-source amplifier I.sub.p. The positive pulse V.sub.0 can be obtained by turning on S.sub.1. After the discharge phase, by turning off S.sub.1 and turning on S.sub.2 synchronously the output voltage v.sub.out turns to be V.sub.1. By turning off S.sub.2, a negative voltage slope is obtained since the current source is sinking current from the capacitive load. The output voltage slope rate is determined by the magnitude of the I.sub.P. Such a hybrid converter is suitable for carrying out the tuning methods described herein. By varying the magnitude of the I.sub.P, the maximum value of k(S) or b(S) can be found as described above, allowing to obtain the narrowest IED.

[0056] Methods of the present disclosure are not limited to find the maximum value of k(S) or b(S). In other embodiments, the structure of a reactor might be different, resulting in a different equivalent electric model. Since the sheath capacitance is virtually removed from the electric model when the narrowest IED is obtained, an exceptional behavior is introduced to the mathematic relations, such as an extremum, a singularity, etc. Such a behavior can be found by applying a dedicated test function, e.g. finding the maximum of coefficients k(S) or b(S), by varying the output voltage slope.

[0057] Referring to FIG. 6, the above auto-tuning method was implemented in an experiment. By varying the voltage slope S.sub.m?1, S.sub.m, S.sub.m+1 of consecutive pulses and measuring corresponding output current I.sub.m?1, I.sub.m, I.sub.m+1, the coefficient k(S.sub.m?1), k(S.sub.m), k(S.sub.m+1) could be determined and a maximum k(S) was found to be k(S.sub.m). In FIG. 6, the dc current was changed in small steps and therefore the voltage slope difference between consecutive pulses is very small and hard to recognize from the figure. Therefore, the optimum voltage slope is S.sub.m. The ion energy distribution was measured for the different voltage slopes, as depicted in FIG. 7. The IED corresponding to S.sub.m effectively yielded the narrowest width, thereby proving the reliability of the method of the present disclosure.