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Modeling and Experiments of Waveform Effects on Oxide Charging in Plasma Immersion Ion Implantation William G. En, Member, IEEE, and Nathan W. Cheung, Member, IEEE Abstract—An analytical model of the time-dependent currents of a plasma allows the determination of the physical mechanisms and dependencies of charging damage in Plasma Immersion Ion Implantation (PIII). From the model, we determine that the plasma requires several ms to equilibrate after the application of an implantation voltage pulse. Although the individual pulses only change the surface potential by a fraction of a volt, the long equilibration time means that the pulse repetition rate perturbs the time-averaged surface potential. A physical relation describing the dependence of the time-averaged surface potential on plasma and voltage bias parameters predicts that a shorter pulse width, lower electron temperature, and rectangular pulse shape maximizes the allowable implantation rate and minimizes the charging damage. For a given pulse shape and plasma condition, a maximum pulse repetition rate exists. Beyond this threshold frequency. the oxide fails because the oxide field exceeds its breakdown value. Experimental results corroborate the simulation’s predictions, showing the dependence of the pulsing repetition rate on charging damage.

I. INTRODUCTION

O

XIDE CHARGING continues to be a concern in conventional ion implantation [1] as well as plasma processing [2], [3]. For current MOS IC processes, which use gate oxide thicknesses around 7 nm, voltage drops of only 6–7 V degrade the long-term reliability of the oxide and 10 V cause complete oxide failure. During conventional ion implantation the incident ion beam induces large quantities of charge which must be neutralized by electron or plasma flood guns. In plasma processing, the plasma deposits charge through a variety of processes [4], [5]. As future generations of MOS IC’s require thinner gate oxide thicknesses, more stringent control of wafer charging will be needed. We are studying oxide charging effects in an emerging process called Plasma Immersion Ion Implantation (PIII). In the PIII process, a target immerses in a plasma containing the ion species to be implanted. Before any implantation takes place, the plasma forms a small ion sheath around the target maintaining a steady-state equilibrium with no net charge flow Manuscript received February 22, 1996; revised August 26, 1996. The review of this paper was arranged by Editor J. M. Vasi. This work was supported by SEMATECH under the National Science Foundation Grant ECS9202993, and Advanced Micro Devices. W. G. En is with Advanced Micro Devices, Sunnyvale, CA 94088-3453 USA. N. W. Cheung is with the Plasma Assisted Materials Processing Laboratory, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720 USA. Publisher Item Identifier S 0018-9383(97)01480-9.

Fig. 1. Schematic of plasma immersion ion implantation showing conformity of the plasma sheath to the wafer surface. Ions from the plasma accelerate across the sheath and implant.

to the target. When a hi;gh-voltage negative pulse is applied to the target, the sheath to expands rapidly, the uncovered ions accelerate, and then implant into the target (Fig. 1). After the voltage pulse is turned off, the plasma returns to the initial equilibrium after several milliseconds. To implant the required dose, the pulse is repeated. PIII is an economical alternative for many implantation applications [6]. Some of its advantages include high dose rate, large area implantation, and cluster-tool compatibility. PIII’s ability to implant at high dose rates at low ion energies (below 1 kV) allow faster implantation of ultra shallow junctions. Shallow junctions are made using a two-step implantation process: first ions from a SiF plasma amorphize the surface, and then without breaking vacuum BF ions are implanted. Sub 100 nm p /n junctions have been formed with diode ideality of 1.05 and total leakage less than 2 nA/cm at 5 V [7], [8]. The uniformity of the PIII implant has achieved a standard deviation better than 1.3% for sheet resistance measurements with a mean value of 350 /sq. [9]. PIII can also conformally implant high aspect ratio trenches (12:1, 1- m opening) through the use of higher feed gas pressure (5–10 mtorr) [10], [11]. Using a triode configuration, PIII can implant a Pd seeding layer for electroless copper plating [12]. The triode configuration consists of a RF-powered Pd electrode sputtered by an argon plasma with PIII. Since PIII can implant very high doses (10 cm ) in very short periods of time ( 3 min), buried oxide layer (SIMOX) formation has recently been demonstrated [13].

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discussed later in the paper are valid for the typical operating conditions within which PIII runs. First, the model requires determination of the ion current. The analytical relations used to find the ion current are based on an analytical model by Lieberman and Stewart, which determines the time-varying ion currents induced in the plasma during an applied voltage waveform [15], [16]. The Lieberman and Stewart model uses the Child Law [17] to determine the current density for an instantaneous voltage across a collision-less sheath of thickness (1) Fig. 2. Schematic of the four current components modeled (plasma ion, secondary electron, plasma electron, and displacement currents).

In all of these PIII processes devices on the Si wafers are exposed to both a plasma and ion implantation, resulting in potential oxide charging effects. Though plasma electrons are able to neutralize accumulated positive surface charge, charging damage can still be induced in certain cases [14]. In this paper, an analytical model of the total charge currents generated during PIII is implemented and tested. The model provides a physical description of the mechanisms of oxide charging. The model provides a physical description of each plasma current component, which correlates with experimental results. Next, the mechanisms of charging damage are derived from the plasma relations, which determine the plasma equilibration time after an implantation pulse, and the dependence of the gate oxide voltage drop on PIII plasma and bias parameters. Finally, experimental data supports the simulator’s description of the dependence of charging damage on implantation pulsing.

II. ANALYTICAL PLASMA MODEL This physical model determines the total plasma currents during PIII from a set of analytical relations that describe all of the current sources. The plasma consists of four current sources: the plasma ion, plasma electron, secondary electron, and displacement currents, as illustrated in Fig. 2. The physical relations requires only measured plasma characteristics [ion density ( ), electron temperature ( ), plasma potential ( ), and floating potential ( )] which can all be measured using a single Langmuir probe measurement. Thus we can describe all of the charging currents with physical relations, providing some insight into the physical mechanisms of charging damage. The model uses several assumptions of the plasma condition. First, the plasma ions are assumed to respond fully to the variations of the applied bias. Since the ions respond on the order of many MHz for the plasma conditions of interest, the voltage variation on the order of milliseconds is slow enough for the ions to respond. Also, the ion motion across the sheath region is assumed to be collision-less. For typical plasma feed gas pressures in the mtorr range, the ion mean free path is several cm, much larger than the typical sheath thickness of several mm. These assumptions and a few additional ones

, and are the free-space permittivity, ion charge, where and ion mass, respectively. The ion current can also be described by the uncovering of ions by the sheath motion ( ) and by the ion motion toward the sheath boundary ( ) from the bulk plasma (2) is the ion density of the plasma. Equating these two where relations generates a first-order differential equation which can be solved for the sheath thickness. Once the sheath thickness is known, the ion current is calculated from the Child Law. In addition to the ion current, three other currents must be modeled to complete the simulation. One is the secondary electron current, produced by the bombarding ions. This current is equal to the ion current times the secondary electron yield ( ) (3) The secondary electron yield has been measured in the literature as a function of the ion energy for targets processed in a glow discharge [18], under conditions similar to PIII. This data has been included in the model. The plasma electrons are assumed to have a Boltzmann distribution, resulting in an exponential dependence on the sheath potential (4) where

and

are the average electron velocity [ ] and electron temperature in volts, respectively. The last term is the displacement current due to the change in capacitance of the plasma sheath surrounding the wafer ( ) and the change in the sheath voltage ( ) (5)

In each region of operation, before during and after the applied waveform, various parts of this model dominate. However, this model uses all of these relations in every region to determine the total charging current, making this model continuous for all conditions under consideration. Previous experimental work has shown that the model can accurately predict the total currents generated in PIII (Fig. 3) [19], [20]. The plasma currents are implemented within the circuit simulator SPICE [21], which allows a modular approach. In addition, we have used the device models in SPICE to

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(a)

Fig. 3. Comparison of measured total current and simulated total current for a 5 kV pulse applied to a planar aluminum target. Insert shows the applied voltage wave form which is used in the simulation. The plasma conditions measured using a Langmuir probe and used in the model are: ion density (no ) 4 1010 cm03 , electron temperature (Te in units of V) 4 V, plasma potential (Vp ) 18 V, and floating potential (Vf ) 6 V.

2

0

(b)

(c) Fig. 5. Pictorial illustration showing the evolution of oxide charges in PIII: (a) from the initial equilibrium with a net negative charge, (b) to implantation that reduces the net negative charge, and (c) to finally surface equilibration where the surface returns to the initial equilibrium. Fig. 4. Schematic of example charging scenario used throughout the paper. On the left, is a schematic of the structure modeled by the circuit diagram on the right.

accurately determine the time-varying currents and potentials generated by the plasma in devices during PIII. This allows us to quantify the charging effects of PIII on the devices present [22]. Use of SPICE allows the interacting system of the plasma, device structure, and applied bias waveform to be simulated simultaneously. Oxide charging mechanisms in PIII can be modeled or measured using area capacitor test devices. The plasma model previously described, the thin oxide capacitor, and the applied voltage bias are placed in placed in series in the simulation, as shown in Fig. 4. We will use this system throughout the paper to explain various aspects of charging in PIII. III. THEORY

OF

OXIDE CHARGING

IN

PIII

Since the plasma model can determine all of the current components generated in PIII, the evolution of the currents during the first applied voltage pulse can be studied carefully.

The time-varying bias can be separated into three distinct regimes: before, during, and after the pulse, as shown in Fig. 5. In each regime different currents dominate and different potentials are generated. Before the voltage pulse begins [Fig. 5(a)], the plasma brings the floating surface of the thin gate oxide to the floating potential. Since the plasma electrons are faster than the ions, a net charge must be setup on the surface to retard the electrons and balance the fluxes. This surface voltage in equilibrium is called the floating potential ( ). When the hi;gh-voltage pulse turns on [Fig. 5(b)], with a peak voltage from a few hundred volts to one hundred kilovolts, ions implant into the surface. The plasma electrons are repelled away from the surface by the negative bias, and the plasma ions are accelerated to the surface. Since the capacitance of the sheath ( ) is extremely low, all of the applied bias drops across the sheath, providing the accelerating potential for the implanting ions. The implanting ions generate secondary electrons which increase the net positive charge on the surface as the secondary electrons accelerate away. The combined ion and secondary electron currents induce a

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Hertz, the surface does not have time to fully equilibrate and the surface charge accumulates from multiple pulses. V. OXIDE VOLTAGE VARIATION DUE

Fig. 6. Simulation showing the variation of the voltage drop across a 10-nm gate oxide for a single 10-kV voltage pulse caused by the implanted charge and the secondary electrons.

small perturbation in the oxide voltage ( ) as shown in Fig. 6. After the applied bias is turned off [Fig. 5(c)], plasma electrons bring the surface back to equilibrium at the floating potential. Since the potential barrier by the applied bias is gone, the positive shift of the oxide voltage increases the electron current over the ion current, generating a net negative current to remove the charge deposited during the implantation. Depending on the plasma condition, many milliseconds may be required for the plasma electrons to return the surface back to the floating potential. IV. EQUILIBRATION TIME

IN

PIII

Using the analytical relations in the model, the equilibration time can be determined for a floating surface after an implantation pulse. For the positive charge generated in a PIII pulse, the equilibration time is independent of the charge per pulse because of the exponential dependence of the electron current. If the charge deposited increases. the neutralizing electron current increases too. However, the equilibration time does depend on the plasma condition and oxide thickness. The equilibration time due to a voltage pulse derives from the net current after the pulse due to the charge deposited (derivation in Appendix A) (6) is a unitless number less than one representing a where fraction of . As shown in Appendix A, when the charge does not depend on the deposited deposited is positive, charge ( ), to the first order. For PIII, the implant pulses deposit positive charge on the surface, resulting in a fixed equilibration time. Using typical values of oxide thickness ( nm), electron temperature ( V), ion density ( cm ), ion velocity ( cm/s), and constant ( ); the time required to equilibrate is 17.3 ms. For any given pulse waveform, the plasma requires a much longer time to equilibrate than the typical pulse repetition rate of several kHz allows. Thus for pulse repetition rates above a few tens of

TO

PIII

Since the wafer surface requires such a long time to equilibrate, the charge deposited during PIII can accumulate over many pulses if the pulse repetition rate is more than a few tens of Hertz. This accumulation of charge causes the dc surface potential to shift away from the floating potential. It will equilibrate to a new potential based on the PIII implantation conditions. Since each individual pulse on causes a small variation in the surface potential, the new equilibrium after many pulses can be considered to be effectively dc. Using this approximation and the analytical relations of the model, a simple calculation shows the dependence of the new dc oxide voltage on the applied voltage pulsing (derivation in Appendix B) (7) where , and , are the pulse on time, pulse repetition frequency, ion charge deposited per pulse, and the effective is secondary electron yield for the pulse ( the total secondary electron charge generated by the pulse), respectively. Several observations can now be made with respect to the effects of pulsing on the surface potential. The term is the duty factor of the pulsing. To minimize the change in , (9) requires that the duty factor be minimized. Also, the third term in (7) contains the term ( ) which is the fraction of the total flux of ions reaching the wafer that implants, the efficiency of the implant. Ions continually bombard the wafer surface while it is exposed to the plasma; however, only the ions that are accelerated during the pulse on time get implanted. To maximize the implant rate, the efficiency of the implant must be maximized. Using (7), we can maximize the efficiency of the implant and minimize the charging damage. Minimizing the electron temperature directly reduces the effect of the duty factor and implantation efficiency. Also, reducing the secondary electron yield ( ) allows a higher efficiency for the same change in surface potential. Unfortunately, the secondary electron yield is a function of the target material and the impinging ion which are factors not easily changed for a given implant. Through the simulator, the effects seen in these hand calculations are shown. With a simple square pulse waveform, Fig. 7 illustrates the change of for a 10-nm thick oxide from its initial equilibrium to a new steady-state for several pulse repetition rates. The charge balance due to the plasma charge flux generates the initial equilibrium . As the repetition rate increases, the charge builds up with multiple pulses shifting . For the 1 kHz case only a small voltage variation occurs because the plasma has almost enough time to equilibrate between pulses. In support of this simulation result, previous experimental work has shown that low repetition rates does not affect the charging damage to thin oxides [14].

EN AND CHEUNG: MODELING AND EXPERIMENTS OF WAVEFORM EFFECTS ON OXIDE CHARGING

Fig. 7. Multiple pulse effect for three different pulse repetition rates (1, 5, and 10 kHz) using an ideal square pulse shape. Initially all three conditions are at the same equilibrium, but after several ms of pulsing, they shift to three different steady-states.

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Fig. 9. Frequency dependence of the steady-state time-averaged oxide voltage (hVox i) for a 10-nm oxide for a waveform containing a fall time tail. The shape of the waveform is shown in the insert.

this rapid increase in voltage occurs is defined as the threshold frequency. Thus charging during PIII limits the maximum pulse repetition rate allowed. VI. PULSE SHAPE EFFECTS

Fig. 8. Frequency dependence of the steady-state time-averaged oxide voltage (hVox i) for a 10-nm oxide with an ideal square waveform. The shape of the waveform is shown in the insert. The threshold frequency (ft ) is defined as the frequency where hVox i reaches zero, as shown.

As the pulse repetition rate increases the plasma no longer fully equilibrates between pulses. As a result, charge from the implantation pulses accumulates over multiple pulses, shifting until the plasma electron current increases enough to discharge the increased positive current. Thus, the voltage pulsing can significantly alter , changing the charging damage that occurs. Another way to look at the charging effect is to plot as a function of the pulsing repetition rate for an ideal square pulse shape (Fig. 8). Initially the floating potential sets up a negative , as electrons accumulate on the surface. The magnitude of the voltage drop across the oxide decreases initially as the repetition rate of the pulses increases because the average positive current increases due to the secondary electrons and the average negative electron current decreases. Eventually, the sign of the accumulated charge on the surface changes from negative charge to positive charge, and the magnitude of the voltage drop across the oxide increases rapidly, exceeding the breakdown voltage of the oxide. The frequency at which

As the previous calculations show, the millisecond timescale that the plasma requires to equilibrate after an implantation pulse affects the wafer surface potential during PIII. If the voltage pulses are too close together then the charge builds up, and a new equilibrium surface potential is reached. The shape of the pulse, which affects the pulse on time and the implant charge per pulse, changes the parameters in (7) changing the charging behavior. The effect of the pulse shape on charging is shown by examining the general dependencies of charging on two control parameters (the fall time and the pulse width) of the pulse shape. The fall time of the voltage pulse begins when the applied voltage drops from the peak voltage. When the implantation voltage drops, the ion and secondary electron currents decrease significantly, while the electron current remains negligible since the bias is still negative. Therefore, during the fall time little net current flows. In (7), the fall time causes an increase in the pulse width ( ) and little change in the total charge per pulse. As Fig. 9 illustrates, the oxide voltage drops at an earlier frequency, and the threshold frequency decreases from that of the ideal square waveform. With larger fall times the threshold frequency decreases, reducing the maximum allowable implantation rate (Fig. 10). Thus for an optimized implantation pulse, the fall time should be minimized. The pulse width of the applied bias also affects charging. A longer pulse width increases both the charge implanted per pulse ( ) and . A larger decreases the threshold increases the dose rate at frequency; however, a larger lower repetition rates. The best measure of the optimal pulse width is the average dose rate which is the dose rate averaged over one pulse cycle ( ). Fig. 11 shows the normalized time -averaged implantation current as a function of the repetition rate for three pulse widths: 10 ms, 100, and 2 s. As the pulse width decreases, higher pulse repetition rates are needed

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TABLE I EXPERIMENTAL PLASMA PARAMETERS FROM LANGMUIR PROBE MEASUREMENTS

Fig. 10. Variation of threshold frequency (ft ) as a function of the fall time tail (Tf ).

Fig. 11. Normalized, steady-state, and time-averaged implant current as a function of repetition rate for three different pulse widths. All pulses are ideal with no fall time tail. The threshold frequency (ft ) of each pulse waveform is plotted as a threshold boundary for severe oxide damage.

to generate the same implant current because shorter pulse widths generate less charge per pulse. However, the threshold frequency for each of these pulse widths shows that the maximum implantation rate, without exceeding the threshold frequency, occurs with shorter pulse widths. To minimize the implantation time for a given implant dose, shorter pulse widths are necessary. VII. COMPARISON BETWEEN SIMULATION AND EXPERIMENT Using test capacitors, experiments confirmed the predicted dependence of charging damage on pulsing repetition rate. For a set of six samples, the repetition rate of the PIII pulse waveform was varied from 0 to 10 kHz, under identical argon plasma conditions for 5 min. The argon plasma was generated by an ECR source, with the wafer placed 44 cm downstream from the plasma generation, decoupling the wafer bias from the plasma generation. The plasma conditions were measured near the wafer surface using a Langmuir probe which are listed in Table I. For each pulse frequency, we determined the damage induced by measuring the interface trap density using – techniques. The test capacitors consist of 10-nm thick gate oxide with 500-nm LOCOS (local oxidation) field oxide. The

gate electrode is made of evaporated aluminum with an area of m m. Aluminum was chosen over a more typical doped polysilicon gate due to the need for secondary electron yield data. First, the secondary electron yield of aluminum in an argon plasma environment for argon ions has been well characterized, but polysilicon has not. The simulator used measured plasma parameters and voltage waveform to determine the oxide voltage ( ) generated by each process run. Without any implantation pulsing, the simulator predicted that was 6 V, which is enough to generate a small quantity of tunneling charge through the oxide and damage the devices. As Fig. 12 shows, the simulator predicts that the magnitude of decreases with increasing repetition rate until the threshold frequency of about 8 kHz. As the pulse repetition rate increases beyond the threshold frequency, the magnitude of increases rapidly beyond the oxide breakdown voltage. Experimentally, the samples showed a decrease in the interface trap density ( ) up to the threshold frequency. Beyond the threshold frequency, the rapid increase in the oxide voltage caused complete oxide failure in the samples. Thus the experimental results showed the same charging damage trend as predicted by simulation, demonstrating that the simulator can predict charging damage trends in PIII. These results are useful for more typical polysilicon gated devices as well. The model results are independent of the gate material except for the secondary electron yield data, which can be measured for the particular doped polysilicon used. For future polysilicon gate devices with thinner gate oxides the model of the gate capacitor may need to be modified to take into account poly depletion, which would modify the exact numbers of the charging damage trends predicted by the model, but the overall mechanisms of charging damage illustrated by the model would remain unchanged. VIII. CONCLUSIONS The time-dependent charging damage in PIII is accurately simulated using basic plasma relations for the relevant plasma current components. Due to the finite plasma currents, the plasma is shown to require many ms to re-equilibrate a floating surface after a voltage pulse. This equilibration time is not dependent on the charge deposited. The long time required

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used in the model can be solved using a few additional approximations. In the actual model implementation these additional approximations are not used. Determination of the equilibration time for the floating surface of a thin gate oxide begins with the plasma equilibrium. In equilibrium, no net current flows to the floating electrode. Also, the only current components present are the plasma electron and ion currents because secondary electrons are not generated without the accelerating bias. Thus the net current to the surface is

(A1) Fig. 12. Comparison between simulation and experiment for the dependence of oxide charging damage on pulse repetition rate. Simulation curve shows relation of hVox i for a 10-nm gate oxide as a function of pulse repetition rate, and the experimental curve of the interface trap density ( it ) for six different pulse repetition rates correlates qualitatively with the simulation results.

Q

to equilibrate causes the charging potential to depend on the pulse repetition rate above several Hz. Simulation results showing the dependence of on pulsing repetition rate were correlated with experimental data. In addition, the simulation predicts that lower electron temperature, short pulse widths around 2 s, and rectangular pulse shape will minimize the charging damage and maximize the allowable implantation rate for PIII processing.

DERIVATION

APPENDIX A EQUILIBRATION TIME

This equilibrium is disturbed when a small quantity of charge is deposited on the surface, due to the implantation , perturbs the voltage pulse. When a quantity of charge, equilibrated electrode, the voltage on the surface changes by , using where is the capacitance of the thin gate oxide. This change in surface potential causes a change in the plasma electron current (A2) In this case, a net current from the plasma neutralizes the nonequilibrium charge. Rearranging (A1) and substituting it into (A2), the expression for the net current generated by the nonequilibrium charge simplifies to (A3)

OF

A. List of Variables: Net current flowing from the plasma to the oxide surface. Ion current flowing from the plasma to the oxide surface. Electron current flowing from the plasma to the oxide surface. Unit charge. Ion density of the plasma. Sheath edge ion velocity. Average electron velocity [ ]. Plasma potential. Voltage drop across the oxide. Change in oxide voltage drop due to deposition of net charge . Electron temperature in units of V. Net charge on oxide surface. Change in oxide surface charge. Capacitance of the thin gate oxide. Unitless constant representing the fraction of the surface equilibrates to. Equilibration time of the gate oxide after deposition of net charge . To acquire a better understanding of the physical dependencies of the equilibration time ( ), the analytical equations

Since the net current equals the derivative of the surface charge with respect to time, the equilibration time for the gate electrode ( ) can be found

(A4) (A5) If the limits of integration are from to zero the integral becomes infinite. To get a practical estimate of the time to , is used equilibrate a fraction of the electron temperature, in place of the lower limit of zero, where is much less than one. was chosen because it represents a minimal variation away from the equilibrium voltage. Solving for the integral, the relation for the equilibration time is determined

(A6) This relation can be simplified further by considering two cases. In first case the charge deposited on the wafer surface and are negative. Since is small, is negative. So can be approximated by , and since is large in

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magnitude compared to for typical charging damage cases, is approximated as zero. Thus (A6) simplifies to (A7) In this expression, the first term relates the equilibration time to the change in surface potential, and the second term is a constant with respect to the surface charge. The reason is dependent on the surface potential is because a negative surface charge repels the electrons and attracts a constant ion current. Thus with a constant discharge current, the equilibration time is proportional to . In the second case, when a positive charge is deposited on and positive ), still simthe surface (positive plifies to but now simplifies to . Thus a different result occurs (A8) For this positive potential variation, the time to equilibrate does not vary with the deposited positive charge. The exponential dependence of the electron current on the surface potential causes the current induced to increase with the increase in , negating any dependence on deposited charge to first order. In addition, the arbitrary constant does not affect the equilibration time very much because of the natural log term. APPENDIX B DERIVATION OF OXIDE VOLTAGE DEPENDENCE ON PIII A. List of Variables: Steady-state time-averaged ion current. Steady-state time-averaged electron current. Steady-state time-averaged secondary electron current. Steady-state time-averaged oxide voltage. Pulsing repetition rate. Pulse on time. Effective secondary electron yield ( ). Ion charge implanted per pulse. Secondary electron charge generated per pulse. ) in steady-state derives The average oxide voltage ( from the time averaged currents. Three current components determine the new equilibrium, which are the plasma ion current, plasma electron current, and secondary electron current. The time-averaged sum of these three currents in steady-state is zero

On the other hand, the time averaged plasma electron current changes with the implantation pulsing. Two effects change the plasma electron current. First, the plasma electron current falls to zero during the implantation pulse, allowing electrons only during the off cycle. Second, surface voltage variations affect the plasma electron current by modulating the barrier height to electrons. So the time average plasma electron current comes out of the time integral of the electron current over one period divided by the period (B3) where is the repetition rate of the pulses. To understand the implications of this result, (B3) can be greatly simplified. Since the surface voltage does not vary much due to a single implantation pulse, the plasma electron current reduces to a function of the time-averaged surface potential rather than the instantaneous surface potential. In addition, the plasma electron current remains off during the pulse, simplifying the relation further. Using these two approximations, a simplified relation for the time averaged plasma electron current results (B4) The implantation pulsing adds an additional current component: the secondary electron current. The implantation of the ions generates a large number of secondary electrons which accelerate away from the surface. These secondaries leave behind positive charges on the floating surface. The time averaged secondary electron current can then be found from the total number of secondaries generated per pulse averaged over one period

(B5) where , and are the total secondary electron charge produced per pulse, the total implanted charge, the effective secondary electron yield, and the frequency of the pulses, respectively. Substituting (B2)–(B5) into (B1) and solving for the time averaged oxide voltage yields an expression that shows the dependence of the oxide voltage on the pulsing and plasma conditions

(B6)

(B1) REFERENCES The time-averaged ion current does not change due to the implantation pulsing. Since, the implantation pulsing does not perturb the bulk plasma, the flux of charge from the bulk of the plasma to the surface remains unchanged. Therefore by charge conservation, the time averaged ion current remains constant for any implantation pulsing (B2)

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[4] S. Fang, S. Murakawa, and J. P. McVittie, “Modeling of oxide breakdown from gate charging during resist ashing,” IEEE Trans. Electron Devices, vol. 41, pp. 1848–1855, Oct. 1994. [5] S. Fang and J. P. McVittie, “Model for oxide damage from gate charging during magnetron etching,” Appl. Phys. Lett., vol. 62, no. 13, pp. 1507–1509, 1993. [6] N. W. Cheung, W. En, E. C. Jones, and C. Yu, “Plasma immersion ion implantation of semiconductors,” in Beam Solid Interactions: Fundamentals and Applications, 1993, pp. 297–306. [7] E. C. Jones and N. W. Cheung, “Characteristics of sub-100-nm p+ /n junctions fabricated by plasma immersion ion implantation,” Electron Device Lett., vol. 14, pp. 444–446, Sept. 993. [8] X. Y. Qian, N. W Cheung, M. A. Lieberman, S. B. Felch, R. Brennan, and M. I. Current, “Plasma immersion ion implantation of SiF4 and BF3 for sub-100 nm p+ /n junction fabrication,” Appl. Phys. Lett., vol. 59, no. 3, pp. 348–350, 1991. [9] S. B. Felch, D. P. Brunco, A. Ahmad, K. Prall, and D. L. Chapek, “Formation of deep sub-micron buried channel pMOSFET’s with plasma doping (PLAD),” in Nikkei Microdevelopment Seminar, 1995, pp. 21–24. [10] B. Mizuno, I. Nakayama, N. Aoi, M. Kubota, and T. Komeda, “New doping method for subhalf micron trench sidewalls by using an electron cyclotron resonance plasma,” Appl. Phys. Lett., vol. 53, no. 21, pp. 2059–2061, 1988. [11] C. Yu and N. W. Cheung, “Trench doping conformality by plasma immersion ion implantation (PIII),” IEEE Electron Device Lett., vol. 15, pp. 196–198, June 1994. [12] M. H. Kiang, M. A. Lieberman, N. W. Cheung, and X. Y. Qian, “Pd/Si plasma immersion ion implantation for selective electroless copper plating on SiO2 ,” Appl. Phys. Lett., vol. 60, no. 22, pp. 2267–2269, 1992. [13] J. Liu, S. S. K. Iyer, C. Hu, N. W Cheung, R. Gronsky, J. Min, and P. Chu, “Formation of buried oxide in silicon using separation by plasma implantation of oxygen,” Appl. Phys. Lett., vol. 67, no. 16, pp. 2361–2363, 1995. [14] W. En and N. W. Cheung, “Wafer charging monitored by hi;ghfrequency and quasistatic C –V measurements,” Nucl. Instr. Meth. Phys. Res., vol. B74, pp. 311–313, 1993. [15] M. A. Lieberman, “Model of plasma immersion ion implantation,” J. Appl. Phys., vol. 66, no. 7, pp. 2926–2929, 1989. [16] R. A. Stewart and M. A. Lieberman, “Model of plasma immersion ion implantation for voltage pulses with finite rise and fall times,” J. Appl. Phys., vol. 70, no. 7, pp. 3481–3487, 1991. [17] C. D. Child, “Discharge from hot CaO,” Phys. Rev., vol. 32, pp. 492–511, 1911. [18] B. Szapiro and J. J. Rocca, “Electron emission from glow-discharge cathode materials due to neon and argon ion bombardment,” J. Appl. Phys., vol. 65, no. 9, pp. 3713–3716, 1989.

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[19] W. En and N. W. Cheung, “Analytical modeling of plasma immersion ion implantation target current using the SPICE circuit simulator,” J. Vac. Sci. Technol. B, vol. 12, no. 2, pp. 833–837, 1994. [20] , “Comparison of experimental target currents with analytical model results for plasma immersion ion implantation,” IEEE Trans. Plasma Sci., vol. 23, no. 3, pp. 415–421, 1995. [21] P. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE, 1st ed. New York: McGraw-Hill, 1988. [22] W. En, B. P. Linder, and N. W. Cheung, “Modeling of oxide charging effects in plasma processing,” to be published in J. Vac. Sci. Technol. B, Jan./Feb. 1996.

William G. En (M’93) received the B.S., M.S., and Ph.D. degrees from the University of California, Berkeley, all in electrical engineering, in 1991, 1994, and 1996, respectively. Since 1996, he has been with Advanced Micro Devices, Sunnyvale, CA, working as a Senior Process Development Engineer. His research interests cover ion implantation and plasma processes, thin-film technologies, plasma diagnostics, and processing of electronic materials. Dr. En is a recipient of the Robert Noyce Memorial Intel Graduate Fellowship. He is a member of the Plasma Sciences Society and the American Vacuum Society.

Nathan W. Cheung (M’96) is a Professor in the Department of Electrical Engineering and Computer Sciences, the University of California, Berkeley, and an Associate Faculty of Lawrence Berkeley Laboratory. Prior to that, he had performed research with Exxon Research Laboratory, Linden, NJ, and Bell Telephone Laboratories, Murray Hill, NJ , and was a Visiting Faculty at the National Research Resources for Submicron Structure, Cornell University, Ithaca, NY. His research interests include ion and plasma assisted materials processing, electronic and optical materials, integrated circuit processing, integrated circuit reliability, and thinfilm technologies. Dr. Cheung is a member of the American Electrochemical Society, American Vacuum Society, Materials Research Society, and the Bohmische Physical Society.