Method and apparatus for contactlessly advancing substrates

Abstract

A method of contactlessly advancing a substrate (140), comprising: providing a process tunnel (102), extending in a longitudinal direction and bounded by at least a first (120) and a second (134) wall; providing first and second gas bearings (124, 134) by providing substantially laterally flowing gas alongside the first and second walls respectively; bringing about a first longitudinal division of the process tunnel into a plurality of pressure segments (116), wherein the gas bearings (124, 34) in a pressure segment have an average gas pressure that is different from an average gas pressure of the gas bearings in an adjacent pressure segment; providing a substrate (140) in between the first wall (120) and the second wall (130); and 1allowing differences in average gas pressure between adjacent pressure segments (116) to drive the substrate along the longitudinal direction of the process tunnel.

Claims

1. A method of contactlessly advancing substantially flat substrates in a transport direction, comprising: providing a process tunnel, extending from an entrance to an exit in a longitudinal direction that is parallel to the transport direction, the process tunnel being bounded by at least a first and a second wall, said walls being mutually parallel and spaced apart so as to allow the substantially flat substrates, oriented parallel to the walls, to be accommodated there between, wherein the process tunnel has two opposite lateral sides and is bounded by two lateral side walls that extend in the longitudinal direction, wherein the process tunnel defines a lateral direction that extends parallel to the first and second walls and perpendicular to the longitudinal direction, wherein both the first and the second wall comprise a plurality of gas injection channels, the process tunnel being unobstructed along the entire length thereof, wherein the first and second walls extend horizontally and the longitudinal direction of the process tunnel extends horizontally; providing at least a first precursor gas, a purge gas, and a second precursor gas; selectively supplying the first precursor gas, the purge gas and the second precursor gas to the plurality of gas injection channels of the first wall to create a plurality of atomic layer deposition (ALD)-segments in the process tunnel, wherein each ALD-segment comprises at least four laterally extending gas zones that successively contain the first precursor gas, the purge gas, the second precursor gas and the purge gas, respectively, wherein in each laterally extending gas zone the gas flows substantially laterally towards the lateral sides of the process tunnel, whereby the ALD-segments of the plurality of ALD-segments are successively arranged in the longitudinal direction of the process tunnel, and wherein each ALD-segment is provided at a substantially constant pressure; supplying a purge gas to the plurality of gas injection channels of the second wall whereby the purge gas flows substantially laterally towards the lateral sides of the process tunnel, or, alternatively, selectively supplying the first precursor gas, the purge gas and the second precursor gas to the plurality of gas injection channels of the second wall to create a plurality of ALD-segments in the process tunnel, wherein each ALD-segment comprises at least four laterally extending gas zones that successively contain the first precursor gas, the purge gas, the second precursor gas and the purge gas, respectively, wherein in each laterally extending gas zone the gas flows substantially laterally towards the lateral sides of the process tunnel, whereby the ALD-segments of the plurality of ALD-segments are successively arranged in the longitudinal direction of the process tunnel; successively supplying substrates into the process tunnel via the entrance to create a continuous stream of substrates within the process tunnel, whereby the first precursor gas, the purge gas and the second precursor gas supplied via gas injection channels of the first wall create a first gas bearing between each substrate and the first tunnel wall, wherein a stiffness of the first gas bearing is based on the substantially laterally flowing gas in the first gas bearings, whereby when purge gas is supplied via the plurality of gas injection channels of the second wall the purge gas creates a second gas bearing between each substrate and the second tunnel wall so that the substrates are floatingly supported and whereby, in the alternative when the first precursor gas, the purge gas and the second precursor gas, are supplied via the plurality of gas injection channels of the second wall the first precursor gas, the purge gas and the second precursor gas create a second gas bearing between each substrate and the second tunnel wall so that the substrates are floatingly supported, wherein a stiffness of the second gas bearing is based on the substantially laterally flowing gas in the second gas bearings; wherein with the supplying of said gases: an average gas pressure is created within both the first and the second gas bearing that, viewed in the transport direction of the process tunnel, drops monotonically along a first portion of the process tunnel thereby providing a pressure differential across each of the substrates which pressure differential drives the substrates in the transport direction, wherein said first portion in which the average pressure drops monotonically is long enough to accommodate a plurality of substrates wherein the pressure differential over each substrate is substantially constant at each longitudinal position of the substrate within said first portion of the process tunnel in which the average pressure drops monotonically so as to induce a substantial constant velocity to each substrate that is moving as part of the train of substrates within said first portion of the process tunnel, wherein said first portion of the process tunnel includes a plurality of subsequent ALD-segments, wherein within the said first portion of the process tunnel a corresponding plurality of ALD cycles is performed, wherein the average pressure in the subsequent ALD-segments in the first portion of the process tunnel at which the ALD cycle is performed monotonically drops when viewed from the entrance to the exit, and wherein the stiffness of the first gas bearing and the stiffness of the second gas bearing is independent of the longitudinal pressure drops in the average gas pressure; wherein an ALD-layer is deposited on at least a first surface and optionally on both the first surface and a second, opposite surface of each substrate during movement of each substrate through each ALD-segment of the process tunnel along the transport direction, wherein an ALD-film composed of a stack of ALD-layers is formed during movement of each substrate from the entrance to the exit.

2. The method according to claim 1, wherein an average longitudinal velocity component of the gas of the first and second gas bearings is not larger than 20% of an average lateral velocity component of said gas.

3. The method according to claim 1, wherein the pressure differential (P.sub.z) over each substrate accommodated within said first portion of the process tunnel in which the average pressure monotonically decreases is in the range of 0-100 Pa.

4. The method according to claim 1, further comprising: changing a difference in average gas pressure within said first portion of the process tunnel without altering a lateral gas flow rate (Q.sub.x) of the substantially laterally flowing gas in the first and second gas bearings, so as to change a force with which the substrate is driven without altering a stiffness of the gas bearings.

5. The method according to claim 1, further comprising: changing a lateral gas flow rate (Q.sub.x) of the substantially laterally flowing gas in the first and second gas bearings without altering a difference in average gas pressure along said first portion of the process tunnel, so as to change a stiffness of the gas bearings without altering a force with which the substrates are driven within said first portion of the process tunnel.

6. The method according to claim 1, further comprising: supplying in a second portion of the process tunnel having a second length, via the plurality of gas injection channels of the first wall and second wall, an inert purge gas or a process gas chosen from the group comprising: (i) oxygen, (ii) ammonia, (iii) hydrogen, and (iv) a phosphorus or boron comprising compound, supplying heat to the second portion of the process tunnel thereby subjecting the continuous stream of substrates moving through the second portion to an annealing treatment.

7. A method of contactlessly advancing substantially flat substrates in a transport direction during atomic layer deposition (ALD), comprising: providing a process tunnel, extending from an entrance to an exit in a longitudinal direction that is parallel to the transport direction, the process tunnel being bounded by at least a first and a second wall, said walls being mutually parallel and spaced apart so as to allow the substantially flat substrates, oriented parallel to the walls, to be accommodated there between, wherein the process tunnel has two opposite lateral sides and is bounded by two lateral side walls that extend in the longitudinal direction, wherein the process tunnel defines a lateral direction that extends parallel to the first and second walls and perpendicular to the longitudinal direction, wherein both the first and the second wall comprise a plurality of gas injection channels, the process tunnel being unobstructed along the entire length thereof, wherein the first and second walls extend horizontally and the longitudinal direction of the process tunnel extends horizontally; selectively supplying a first gas bearing by providing a first precursor gas, a purge gas and a second precursor gas to the plurality of gas injection channels of the first wall to create a plurality of ALD-segments in the process tunnel, wherein each ALD-segment comprises at least four laterally extending gas zones that successively contain the first precursor gas, the purge gas, the second precursor gas and the purge gas, respectively, wherein in each laterally extending gas zone the gas flows substantially laterally towards the lateral sides of the process tunnel, whereby the ALD-segments of the plurality of ALD-segments are successively arranged in the longitudinal direction of the process tunnel, wherein a stiffness of the first gas bearing is based on the substantially laterally flowing gas in the first gas bearings, and wherein each ALD-segment is provided at a substantially constant pressure; supplying a second gas bearing by providing at least the purge gas to the plurality of gas injection channels of the second wall whereby the purge gas flows substantially laterally towards the lateral sides of the process tunnel, wherein a stiffness of the second gas bearing is based on the substantially laterally flowing gas in the second gas bearings; successively supplying substrates into the process tunnel via the entrance to create a continuous stream of substrates within the process tunnel, whereby the first gas bearing and the second gas bearing floatingly support each substrate; wherein with the supplying of said gases: an average gas pressure is created within both the first and the second gas bearing that, viewed in the transport direction of the process tunnel, drops monotonically along a first portion of the process tunnel thereby providing a pressure differential across each of the substrates which drives the substrates in the transport direction, wherein said first portion in which the average pressure drops monotonically is configured to accommodate a plurality of substrates wherein the pressure differential over each substrate is substantially constant at each longitudinal position of the substrate within said first portion of the process tunnel in which the average pressure drops monotonically so as to induce a substantial constant velocity to each substrate that is moving as part of the train of substrates within said first portion of the process tunnel, wherein said first portion of the process tunnel includes a plurality of subsequent ALD-segments, wherein within the said first portion of the process tunnel a corresponding plurality of ALD cycles is performed, wherein the average pressure in the subsequent ALD-segments in the first portion of the process tunnel at which the ALD cycle is performed monotonically drops when viewed from the entrance to the exit, and wherein the stiffness of the first gas bearing and the stiffness of the second gas bearing is independent of the longitudinal pressure drops in the average gas pressure; wherein an ALD-layer is deposited on at least a first surface of each substrate during movement of each substrate through each ALD-segment of the process tunnel along the transport direction, wherein an ALD-film composed of a stack of ALD-layers is formed during movement of each substrate from the entrance to the exit.

8. The method of claim 7, wherein supplying the second gas bearing further comprising: selectively supplying the first precursor gas, the purge gas and the second precursor gas to the plurality of gas injection channels of the second wall to create a plurality of ALD-segments in the process tunnel, wherein each ALD-segment comprises at least four laterally extending gas zones that successively contain the first precursor gas, the purge gas, the second precursor gas and the purge gas, respectively, wherein in each laterally extending gas zone the gas flows substantially laterally towards the lateral sides of the process tunnel, whereby the ALD-segments of the plurality of ALD-segments are successively arranged in the longitudinal direction of the process tunnel, and wherein the ALD-layer is further deposited on a second surface opposite the first surface of the substrate during movement of each substrate through each ALD-segment of the process tunnel along the transport direction.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a diagrammatic longitudinal cross-sectional view of a portion of an exemplary embodiment of an apparatus according to the present invention;

(2) FIG. 2 is a diagrammatic lateral cross-sectional view of the apparatus shown in FIG. 1;

(3) FIG. 3 is a diagrammatic cross-sectional plan view of a portion of the process tunnel shown in FIGS. 1-2; and

(4) FIG. 4 is diagrammatic longitudinal cross-sectional view of a portion of a process tunnel, used to clarify a mathematical model put forward in the specification.

DETAILED DESCRIPTION

(5) An exemplary embodiment of an apparatus according to the present invention, which implements the method according to the present invention, will be described below with reference to FIGS. 1-3. The exemplary embodiment is set up as a spatial atomic layer deposition (ALD) apparatus. It is understood, however, that the scope of application of the apparatus and the method according to the present invention is not limited to the field of atomic layer deposition. The apparatus and method may be applied for the purpose of performing different substrate processing treatments, such as annealing.

(6) The disclosed apparatus 100 may include a process tunnel 102 through which a substrate 140, e.g. a silicon wafer, preferably as part of a train of substrates, may be conveyed in a linear manner. That is, the substrate 140 may be inserted into the process tunnel 102 at an entrance thereof to be uni-directionally conveyed to an exit. Alternatively, the process tunnel 102 may have a dead end and the substrate 140 may undergo a bi-directional motion from an entrance of the process tunnel, towards the dead end, and back to the entrance. Such an alternative bi-directional system may be preferred if an apparatus with a relatively small footprint is desired. Although the process tunnel 102 itself may be rectilinear, such need not necessarily be the case.

(7) The process tunnel 102 may include four walls: an upper wall 130, a lower wall 120, and two lateral or side walls 108. The upper wall 130 and the lower wall 120 may be oriented horizontally or at an angle relative to the horizontal, mutually parallel and be spaced apart slightly, e.g. 0.5-1 mm, such that a substantially flat or planar substrate 140, having a thickness of for example 0.1-1 mm and oriented parallel to the upper and lower walls 130, 120, may be accommodated there between without touching them. The lateral walls 108, which may be oriented substantially vertically and mutually parallel, may interconnect the upper wall 130 and the lower wall 120 at their lateral sides. The lateral walls 108 may be spaced apart by a distance somewhat larger than a width of a substrate 140 to be processed, e.g. its width plus 0.5-3 mm. Accordingly, the walls 108, 120, 130 of the process tunnel 102 may define and bound an elongate process tunnel space 104 having a relatively small volume per unit of tunnel length, and capable of snugly accommodating one or more substrates 140 that are successively arranged in the longitudinal direction of the tunnel.

(8) Both the upper tunnel wall 130 and the lower tunnel wall 120 may be provided with a plurality of gas injection channels 132, 122. The gas injection channels 132, 122 in either wall 130, 120 may be arranged as desired as long as at least a number of them is dispersed across the length of the tunnel 102. Gas injection channels 132, 122 may, for example, be disposed on the corners of an imaginary rectangular grid, e.g. a 25 mm25 mm grid, such that gas injection channels are regularly distributed over an entire inner surface of a respective wall, both in the longitudinal and lateral direction thereof.

(9) The gas injection channels 122, 132 may be connected to gas sources, preferably such that gas injection channels in the same tunnel wall 120, 130 and at the same longitudinal position thereof are connected to a gas source of a same gas or gas mixture. For ALD-purposes, the gas injection channels 122, 132 in at least one of the lower wall 120 and the upper wall 130 may, viewed in the transport direction T, be successively connected to a first precursor gas source, a purge gas source, a second precursor gas source and a purge gas source, so as to create a functional ALD-segment 114 thatin usewill comprise successive tunnel-wide gas zones including a first precursor gas, a purge gas, a second precursor gas and a purge gas, respectively. It is understood that one such an ALD-segment 114 corresponds to a single ALD-cycle. Accordingly, multiple ALD-segments 114 may be disposed in succession in the transport direction T to enable the deposition of a film of a desired thickness. Different ALD-segments 114 within a process tunnel 102 may, but need not, comprise the same combination of precursors. Differently composed ALD-segments 114 may for example be employed to enable the deposition of mixed films.

(10) Whether opposing gas injection channels 122, 132, which share a same longitudinal position of the process tunnel but are situated in opposite tunnel walls 120, 130, are connected to gas sources of the same gas composition may depend on the desired configuration of the apparatus 100. In case double-sided deposition is desired, i.e. ALD treatment of both the upper surface 140b and lower surface 140a of a substrate 140 travelling through the process tunnel 102, opposing gas injection channels 122, 132 may be connected to the same gas source. Alternatively, in case only single-sided deposition is desired, i.e. ALD treatment of merely one of the upper surface 140b and lower surface 140a of a substrate 140 to be processed, gas injection channels 122, 132 in the tunnel wall 120, 130 facing the substrate surface to be treated may be alternatingly connected to a reactive and an inert gas source, while gas injection channels in the other tunnel wall may all be connected to an inert gas source.

(11) In the exemplary embodiment of FIGS. 1-3, the gas injection channels 132 in the upper wall 130 are successively connected to a trimethylaluminum (Al(CH.sub.3).sub.3, TMA) source, a nitrogen (N.sub.2) source, a water (H.sub.2O) source, and a nitrogen source, so as to form a series of identical ALD-segments 114 suitable for performing aluminum oxide (Al.sub.2O.sub.3) atomic layer deposition cycles. The gas injection channels 122 in the lower tunnel wall 120, in contrast, are all connected to a nitrogen source. Accordingly, the exemplary apparatus 100 is set up to maintain an upper depositing gas bearing 134 and a lower non-depositing gas bearing 124, together configured to perform single-sided deposition on a top surface 140b of a passing, floatingly supported substrate 140.

(12) Each of the lateral walls 108 of the process tunnel 102 may, along its entire length or a portion thereof, be provided with a plurality of gas exhaust channels 110. The gas exhaust channels 110 may be spaced apartpreferably equidistantlyin the longitudinal direction of the process tunnel. The distance between two neighboring or successive gas exhaust channels 110 in a same lateral wall 108 may be related to a length of the substrates 140 to be processed (in this text, the length of a rectangular substrate 140 is to be construed as the dimension of the substrate generally extending in the longitudinal direction of the process tunnel 120). A lateral wall portion the length of a substrate 140 may preferably comprise between approximately 5 and 20, and more preferably between 8 and 15, exhaust channels 110. The center-to-center distance between two successive gas exhaust channels 110 may be in the range of approximately 10-30 mm.

(13) The gas exhaust channels 110 may be connected to and discharge into gas exhaust conduits 112 provided on the outside of the process tunnel 102. In case the apparatus 100 is set up to perform ALD, the exhaust gases may contain quantities of unreacted precursors. Accordingly, it may be undesirable to connect gas exhaust channels 110 associated with mutually different reactive gas zones to the same gas exhaust conduit 112 (which may unintentionally lead to chemical vapor deposition). Different gas exhaust conduits 112 may thus be provided for different precursors.

(14) The general operation of the apparatus 100 may be described as follows. In use, both the gas injection channels 132, 122 in the upper wall 130 and the lower wall 120 inject gas into the process tunnel space 104. Each gas injection channel 122, 132 may inject the gas provided by the gas source to which it is connected. As the apparatus 100 is capable of operating at both atmospheric and non-atmospheric pressures, gas injection may take place at any suitable pressure. However, to render vacuum pumps superfluous, and to prevent any contaminating gas flows from the process tunnel environment into the tunnel space 104 (especially at the substrate entrance and exit sections), the tunnel space may preferably be kept at a pressure slightly above atmospheric pressure. Accordingly, gas injection may take place at a pressure a little above atmospheric pressure, e.g. at an overpressure on the order of several millibars. In case a lower pressure is maintained in the gas exhaust conduits 112, for example atmospheric pressure, the gas injected into the tunnel space 104 will naturally flow sideways, transverse to the longitudinal direction of the process tunnel and towards the gas exhaust channels 110 in the side walls 108 that provide access to the exhaust conduits 112.

(15) In case a substrate 140 is present between the upper and lower walls 130, 120, the gas(es) injected into the tunnel space 104 by the gas injection channels 132 in the upper wall 130 may flow sideways between the upper wall and a top surface 140b of the substrate. These lateral gas flows across a top surface 140b of the substrate 140 effectively provide for an upper gas bearing 134. Likewise, the gas(es) injected into the tunnel space 104 by the gas injection channels 122 in the lower wall 120 will flow sideways between the lower wall and a lower surface 140a of the substrate 140. These lateral gas flows across a bottom surface 140a of the substrate 140 effectively provide for a lower gas bearing 124. The lower and upper gas bearings 124, 134 may together encompass and floatingly support the substrate 140.

(16) As the substrate 140 moves through the process tunnel 102 its upper surface 140b is strip-wise subjected to the gases present in each of the successively arranged gas zones of the upper gas bearing 134 (cf. FIG. 3). Provided that the arrangements of the zones and the respective gases are chosen properly, traversal of one ALD-segment 114 may be equivalent to subjecting the substrate 140 to one atomic layer deposition cycle. Since the tunnel 102 may comprise as many ALD-segments 114 as desired, a film of arbitrary thickness may be grown on the substrate 140 during its crossing of the tunnel. The linear nature of the process tunnel 102 further enables a continuous stream of substrates 140 to be processed, thus delivering an atomic layer deposition apparatus 100 with an appreciable throughput capacity.

(17) Now that the construction and general operation of the apparatus 100 has been described in some detail, attention is invited to the method for contactlessly advancing substrates 140 incorporated into the design thereof.

(18) As mentioned, substrates 140 may be advanced by establishing a pressure differential in the longitudinal direction of the process tunnel 102. To this end, the process tunnel 102 may be divided into a plurality of pressure segments 116. In the embodiment of FIGS. 1-3, each pressure segment 116 extends over a longitudinal portion of the process tunnel 102 that comprises to two gas zones of an ALD-segment 114, namely a precursor (TMA or H.sub.2O) gas zone and an adjacent purge gas (N.sub.2) gas zone. It is understood, however, that the division of the process tunnel 102 into pressure segments 116 may generally be independent of the division in ALD-segments 104. That is to say that the division in pressure zones 116 need not have any particular relation to the division in ALD-segments 114. A single pressure segment may, for example, coincide with one or more ALD-segments 114 or a with longitudinal fractions thereof. Different pressure segments 116 need not have an identical length.

(19) In use, each pressure segment 116 is characterized by an average gas pressure (gas pressure averaged over both gas bearings 124, 134) that differs from the average gas pressure in an adjacent pressure segment. The average gas pressure of the gas bearings 124, 134 in a pressure segment 116 may be controlled by controlling the (average) pressure at which gas is injected into the process tunnel space 104 via the gas injection channels 122, 132. To this end, the gas injection channels 122, 132 may be provided with gas pressure regulators.

(20) Each of these gas pressure regulators may be manually controllable. Such an embodiment is economical, and practical in case after setting up the apparatus 100 no further adjustments are desired. Alternatively, the gas pressure regulators may be controllable via a central controller, e.g. a CPU. The central controller may in turn may be operably connected to an input terminal that allows an operator to select the desired injection gas pressures for individual gas injections channels 122, 132 or groups thereof, so as to enable convenient control over the average pressure in different pressure segments 116 and/or to change the division of the process tunnel 102 into pressure segments. Alternatively, or in addition, the central controller may run a program that dynamically controls the gas injection pressures for different pressure segments. Such dynamic control may for example be desired when the process tunnel 102 has a dead end, which may require the pressure differential across the tunnel to be reversed once the substrate reaches the dead end. In such an embodiment, the position of the substrate 140 may be detected by one or more contactless position sensors, e.g. photo-detectors, that communicate the position of the substrate to the central controller.

(21) In the embodiment of FIGS. 1-3, the gas injection channels 122, 132 associated with a certain pressure segment 116 are statically configured to inject gas at an average gas pressure that is higher than an average gas pressure at which gas injection channels 122, 132 associated with an adjacent, downstream (as viewed in the transport direction T) pressure segment 116 are configured to inject gas. Thus, viewed in the transport direction T of the process tunnel 102, the average gas pressure of the gas bearings 124, 134 drops monotonically. This provides for a pressure differential across each of the substrates 140, which pressure differential drives them in the transport direction T.

(22) In order to provide a handle on and some insight into the different parameters that affect the velocity of a substrate 140, a basic physical model of the situation is developed below. It will be appreciated by those skilled in the art that application of the model to practical embodiments of the apparatus 100 may require adaptations to be made to compensate for non-ideal conditions or circumstances that deviate from those outlined.

(23) Referring now to FIG. 4, which shows a schematic longitudinal cross-sectional side view of a portion of a process tunnel 102. In the figure, any gas injection channels 122, 132 in the lower and upper tunnel walls 120, 130 have been omitted for reasons of drawing legibility. A substantially flat substrate 140 is located between the first, lower wall 120 and the second, upper wall 130 of the process tunnel 102. The substrate 140 is square (cf. FIG. 3) and has an edge length L and a thickness d.sub.s. The lower wall 120 and the upper wall 130 of the process tunnel are mutually parallel, and the substrate's lower and upper surfaces 140a, 140b are substantially parallel to the lower wall 120 and the upper wall 130, respectively. It is assumed that the depicted situation is symmetrical, meaning that the substrate 140 is located precisely halfway between the tunnel walls 120, 130, and that the gas bearing 124 contacting the lower surface 140a is identical to the gas bearing 134 contacting the upper surface 140b. The process tunnel 102, and hence the walls 110, 120 and the substrate 130, extend horizontally.

(24) Due to the maintenance of pressure segments (discussed above), there exists a negative pressure differential in the transport direction T of the process tunnel 102. Over the length L of the substrate 140, a gas pressure difference P.sub.z is equal to the downstream gas pressure P.sub.1 minus the upstream gas pressure P.sub.0, i.e. P=P.sub.1P.sub.0. The pressure differential drives a flow of gas bearing gas in the longitudinal or z-direction. Although this longitudinal flow is relatively small compared to the lateral flow (perpendicular to the plane of the drawing), it is most relevant to the propulsion of the substrate 140. Both above and below the substrate 140, the longitudinal flow results in a velocity profile that obeys the equation (in spatial coordinates referring to the lower gas bearing):

(25) $\begin{array}{cc}{v}_z=\frac{P_z{d}_g^2}{2L}{\left(\frac{y}{d_g}\right)}^2+\left\{v_s-\frac{P_z{d}_g^2}{2L}\right\}\left(\frac{y}{d_g}\right)& \left(1\right)\end{array}$
wherein v.sub.z denotes the gas velocity in the z-direction; d.sub.g denotes the gap or distance between the bottom and top surfaces 140a, 140b of the substrate and the first and second tunnel wall 120, 130, respectively; denotes a viscosity of the gas bearings 124, 134; y denotes the distance from the first, lower tunnel wall 120 (itself located at y=0); and v.sub.s denotes the substrate velocity in the y-direction. In practice, the viscosity may be approximated by a weighted average of the viscosities of the used purge and precursor gases, taking into account the relative lengths of the respective zones as weighting factors.

(26) The net force on the substrate 140 in the longitudinal direction of the process tunnel, denoted F.sub.n, may be said to be the resultant of two forces: a pressure force F.sub.p acting on the laterally extending leading and trailing edges of the substrate, and a viscous drag force F.sub.v acting on the bottom and top surfaces 140a, 140b of the substrate, such that
F.sub.n=F.sub.p+F.sub.v.(2)

(27) Using equation (1) the viscous drag force F.sub.v, which results from the interaction between the surfaces 140a, 140b of the substrate 140 and the gas bearings 124, 134, respectively, may be expressed as

(28) $\begin{array}{cc}{F}_v=2{A(-\frac{{\mathrm{dv}}_z}{\mathrm{dy}}.Math.}_{y=d_g})=-P_z{d}_{g}L-\frac{2v_{s}A}{d_g}& \left(3\right)\end{array}$
wherein 2A denotes the combined surface area of the bottom and top surfaces 140a, 140b of the substrate (A being equal to L.sup.2); and dv.sub.z/dy denotes a velocity gradient in either gas bearing 124, 134, which velocity gradient may be obtained by differentiating equation (1) with respect to y.

(29) The pressure force F.sub.p, which is simply equal to the pressure difference across the laterally extending trailing and leading edges of the substrate multiplied by the surface area of (a single one of) these edges, may be expressed as
F.sub.p=d.sub.sLP.sub.z.(4)

(30) Combining equations (2), (3) and (4), and setting the net force F.sub.n to zero, yields the following expression for the equilibrium velocity v.sub.s,eq of the substrate:

(31) $\begin{array}{cc}{v}_{s,\mathrm{eq}}=-\frac{d_g\left(d_s+d_g\right)P_z}{2L}& \left(5\right)\end{array}$
The equilibrium velocity as expressed by equation (5) is the velocity that a substrate 140 will assume when the abovementioned parameters are invariable along the length of the process tunnel.

(32) The equilibrium velocity v.sub.s,eq establishes itself as follows. Once the substrate 140 is inserted into the process tunnel 102, it will partly obstruct it (cf. FIG. 2) and form a flow resistance. As a result, it will experience a pressure differential P.sub.z that amounts to a force F.sub.p (see eq. (4)) acting on its laterally extending leading and trailing edges to push it in the transport direction T. Viscous forces between its main surfaces 140a, 140b and the gas bearings 124, 134 in turn, induce a velocity-dependent viscous drag F.sub.n on the substrate 140 according to equation (2). When the sum F.sub.n of the pressure force F.sub.p and the drag force F.sub.v is positive, the substrate will speed up in the transport direction T, and vice versa. A net force F.sub.n propelling the substrate 140 in the transport direction T causes the drag on the substrate to increase until the drag force F.sub.v cancels out the pressure force F.sub.p, from which point on the substrate's velocity remains constant at v.sub.s,eq. Likewise, a net force F.sub.v dragging on the substrate will cause it to slow down until the viscous force F.sub.v cancels out the pressure force F.sub.p and the substrate assumes a constant velocity v.sub.s,eq.

(33) By way of numerical example, assume that the pressure differential P.sub.z across the substrate is 100 Pa, that the substrate has an edge length of 0.156 m and a thickness d.sub.s of 200 m, and that the process tunnel has a height H of 500 m such that there exists a gap d.sub.g of 150 m on either side of the substrate. The gas bearings may be chosen to be of nitrogen (N.sub.2), and be operated at a temperature of 20 C., giving them a viscosity of 1.88.Math.10.sup.5 Pa.Math.s. Substituting these values in equation (5) yields an equilibrium substrate velocity v.sub.s,eq of 0.90 m/s.

(34) A highly practical characteristic of the method and apparatus according to the present invention is that the stiffness of the employed first and second gas bearings 124, 134 may be controlled independently of the desired (equilibrium) substrate velocity v.sub.s. This is a consequence of the fact that the stiffness of the gas bearings 124, 134, which consist of substantially laterally flowing gas, is independent of longitudinal pressure drops between adjacent pressure segments 116, 116, but is instead proportional to Q.sub.x/d.sub.g.sup.3, wherein Q.sub.x represents the lateral gas flow rate of gas flowing sideways between a substrate surface 140a, 140b and the respective adjacent tunnel wall 120, 130, and d.sub.g is the gap between the respective substrate surface 140a, 140b and the respective adjacent tunnel wall 120, 130.

(35) Accordingly, the average gas pressure of the first and second gas bearings 124, 134 within a certain pressure segment 116 may be changed, e.g. increased or decreased, by simultaneously and correspondingly altering the local pressures in both the gas injection channels 122, 132 and the gas exhaust conduits 112 of the respective segment 116 without affecting either the lateral gas flow rate Q.sub.x or the gap d.sub.g between the substrate's surfaces 140a, 140b and the tunnel walls 120, 130. Although such a change in the average pressure in the pressure segment 116 will have an effect on the longitudinal pressure drop between said pressure segment 116 and an adjacent pressure segment 116, and thus on the (equilibrium) velocity v.sub.s of a substrate passing said adjacent pressure segments 116, 116 (cf. eq. (5)), there will be no effect on a lateral pressure drop P.sub.x within the gas bearings 124, 134 of either pressure segment 116, 116, and therefore no effect on the gas flow rate Q.sub.x or the stiffness of the gas bearings therein.

(36) Alternatively, one may of course also do the opposite and change the lateral gas flow rate Q.sub.x in the first and second gas bearings 124, 134 of adjacent pressure segments 116, 116 by adjusting the lateral pressure drop P.sub.x, and thus change the stiffness of the gas bearings. If the adjustment of the lateral pressure drop P.sub.x is performed uniformly for the adjacent pressure segments 116, 116, there will be no effect on the longitudinal pressure drop between the adjacent pressure segments, and thus no effect on the (equilibrium) velocity v.sub.s of a substrate 140 passing said pressure segments.

(37) Although illustrative embodiments of the present invention have been described above, in part with reference to the accompanying drawings, it is to be understood that the invention is not limited to these embodiments. Variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. Reference throughout this specification to one embodiment or an embodiment means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrases in one embodiment or in an embodiment in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, it is noted that particular features, structures, or characteristics of one or more embodiments may be combined in any suitable manner to form new, not explicitly described embodiments.

LIST OF ELEMENTS

(38) 100 atomic layer deposition apparatus 102 process tunnel 104 process tunnel space 106 longitudinal gas channel adjacent side wall 108 lateral wall of process tunnel 110 gas exhaust channel 112 gas exhaust conduit 114 ALD-segment comprising four laterally extending gas zones 116 pressure segment 120 lower tunnel wall 122 gas injection channels in lower tunnel wall 124 lower gas bearing 130 upper tunnel wall 132 gas injection channels in upper tunnel wall 134 upper gas bearing 140 substrate 140a,b lower surface (a) or upper surface (b) of substrate T transport direction of process tunnel
Mathematical Symbols A surface area of substrate's lower/upper surface d.sub.g width of gap between substrate's surface and first/second tunnel wall d.sub.s substrate thickness H height of process tunnel, i.e. spacing between first and second process tunnel walls L edge length of (square) substrate P gas bearing pressure P.sub.z differential pressure across substrate in the longitudinal or z-direction Q.sub.x gas flow rate in gas bearing in the lateral or x-direction v.sub.s velocity of the substrate v.sub.s,eq equilibrium velocity of substrate v.sub.z velocity of gas bearing in the indicated z-direction x,y,z spatial coordinates for the coordinate system of FIG. 4 viscosity of gas bearing