Abstract:
A method implemented by one or more processors, including receiving first information relating a plurality of flow rates of a species to corresponding concentrations of the species within films generated using the flow rates; receiving a desired concentration profile of the species within a desired film; and generating a plurality of process steps that, when performed, would form the desired film with the desired concentration profile by controlling the flow rate of the species based, in part, on the first information and the desired concentration profile, wherein a first concentration of the species at a first point in the desired concentration profile differs from a second concentration of the species at a second point in the desired concentration profile. A computer-readable medium, system and apparatus are also disclosed.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS  
       [0001]    The application is a divisional of co-pending U.S. patent application Ser. No. 09/974,951, filed Oct. 10, 2001, which is a divisional of U.S. patent application Ser. No. 09/454,423, filed Dec. 3, 1999, now U.S. Pat. No. 6,342,453 B 1 . 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The invention relates to semiconductor processing techniques, more particularly, to controlling constituents of a film introduced onto a substrate.  
           [0004]    2. Description of Related Art  
           [0005]    In the formation of modern integrated circuit devices, many constituents are introduced to a substrate such as a wafer to form films. Typical films include dielectric material films, such as transistor gate oxide or interconnect isolation films, as well as conductive material or semiconducting material films. Interconnect metal films and polysilicon electrode films, respectively, are examples of conductive and semiconducting material films.  
           [0006]    In addition to the above-noted material films, other constituents are often introduced onto a substrate such as a wafer or a structure on a substrate to change the chemical or conductive properties of the substrate or the structure. Examples of this type of constituent introduction includes, for example, the deposition of a refractory metal onto an electrode or junction to form a silicide and the deposition of germane onto a substrate to form a silicon germanium junction in a bipolar transistor. The introduction of constituents onto a substrate or structure on a substrate such as described is referred to herein as a subset of film formation.  
           [0007]    One way to enhance the performance of integrated circuit devices is to improve control of the introduction of the constituents, such as improved control of the introduction of process gas species in deposition introduction. Many wafer process chambers, including the EPI Centura system, commercially available from Applied Materials, Inc. of Sunnyvale, Calif., utilize mass flow controllers to introduce process gas species. In general, a mass flow controller functions by permitting a desired flow rate of a gas species based on an input signal to the mass flow controller demanding the flow rate. The concentration profile of a species constituent within a film deposited on a substrate is then a function of the mass flow rate of species introduced. In general, the relationship between a species concentration profile or gradient introduced into or onto a substrate, for example a wafer, and the mass flow rate of the species introduced is not necessarily linear.  
           [0008]    In general, mass flow controllers are used to either supply a constant flow rate or a variable flow rate from a first flow set point to a second flow set point over a period of time. One common flow ramp between a first set point and a second set point is a linear flow ramp. A linear ramp, however, does not necessarily produce a desired concentration profile, e.g., a linear profile, of the species in the introduced film. In the example of a species of germane (GeH 4 ) introduced to form a silicon-germanium film, a graded film is desirable in many situations. The desired graded profile in the film, for example germanium concentration profile, may be linear or non-linear. The method to control a mass flow controller to precisely control the amount of flow and produce the desired germanium concentration profile in the junction, whether it is linear or non-linear, is of significant importance. In commercial use, targeting a desired concentration profile, for example a linear profile, has generally not proved possible through a linearly increasing or decreasing constant flow introduction of the germanium species by a mass flow controller.  
           [0009]    What is needed is a way to control the introduction of a species to form a film having a desired concentration profile of the species in the film. The ability to quantitatively control the introduction of a species through a mass flow controller to form a film with a specific film thickness is also desirable. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]    [0010]FIG. 1 schematically illustrates a side view of a portion of a substrate having a film with a graded concentration profile introduced according to an embodiment of the invention.  
         [0011]    [0011]FIG. 2 illustrates the concentration gradient of a germanium species in a film according to an embodiment of the invention.  
         [0012]    [0012]FIG. 3 illustrates a schematic view of an embodiment of a system for introducing a species to a substrate according to the invention.  
         [0013]    [0013]FIG. 4 illustrates a curve fit of the experimentally-determined concentration of germanium of a film introduced according to six discrete germane flow rates and a constant silane flow rate.  
         [0014]    [0014]FIG. 5 illustrates the experimentally-determined growth rate of silicon germanium in a film introduced on a substrate for six discrete germane flow rates and a constant silane flow rate.  
         [0015]    [0015]FIG. 6 illustrates a block diagram for the introduction of a germanium species to a substrate in accordance with an embodiment of the invention.  
         [0016]    [0016]FIG. 7 is a Secondary Ion Mass Spectroscopy (SIMS) profile of an epitaxial silicon-germanium film introduced according to the invention to have a linearly graded profile of germanium.  
         [0017]    [0017]FIG. 8 is the flow rate of germane (GeH 4 ) per unit time to produce the graded profile of FIG. 7.  
         [0018]    [0018]FIG. 9 is a SIMS profile of an epitaxial silicon-germanium film introduced according to the invention to have a concave graded profile of germanium.  
         [0019]    [0019]FIG. 10 is the flow rate of GeH 4  per unit time to produce the graded profile of FIG. 9.  
         [0020]    [0020]FIG. 11 schematically illustrates a heterojunction bipolar transistor formed according to an embodiment of the invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0021]    A method and a system for the controlled introduction of a species to a substrate are disclosed. In one embodiment, the method includes controlling the flow rate of a species into a chamber according to determined concentration and introduction rate profiles to introduce (e.g., deposit) a film on a substrate in the chamber. The determined concentration and introduction rate profiles may be established through experimental data related to a concentration of a species in a formed film according to a plurality of selected flow rates of the species constituent (hereinafter “species”) into the chamber. This information is utilized to adjust the introduction rate of a species per unit time to form a film having a desired concentration profile as well as a desired thickness.  
         [0022]    [0022]FIG. 1 shows a side view of a portion of a semiconductor substrate having a silicon germanium (Si 1-x Ge x ) epitaxially-introduced film thereon. Structure  10  includes substrate  25  that is, for example, a silicon semiconductor wafer with  
         [0023]    Si 1-x Ge x  film  30  introduced on a surface thereof Si 1-x Ge x  film  30 , in this embodiment, has a graded concentration profile of germanium (Ge), represented by concentration points  35  and  40 . Concentration points  35  and  40  represent, for example, two of many concentration points. In one example, the concentration profile from concentration point  35  to concentration point  40  is desired to be linear with the highest concentration of Ge present at concentration point  40  and the lowest concentration at concentration point  35 . In one example, the concentration profile of Ge in Si 1-x Ge x  film  30  varies linearly from a concentration of approximately zero percent Ge at concentration point  35  to a concentration of 20 percent Ge at concentration point  40 .  
         [0024]    [0024]FIG. 2 graphically represents the concentration profile of germanium in Si 1-x Ge x  film  30  of FIG. 1. In this representation, the concentration profile is measured from the surface of the film (represented by concentration point  35 ) to the silicon-Si 1-x Ge x  film interface (represented by concentration point  40 ). Thus, the film thickness is measured from the surface of film  30  to the interface of film  30  and substrate  25 . In one example, denoted by the solid line, the concentration profile varies in a linear fashion through the film. It is to be appreciated that the invention method and system is capable of producing a variety of concentration profiles, including non-linear profiles such as profile  210  and profile  220  in FIG. 2.  
         [0025]    [0025]FIG. 3 is an example of a process environment utilizing a system of the invention to introduce a species to form a film such as film  30  on substrate  25  of FIG. 1. In this embodiment, an EPI Centura system, commercially available from Applied Materials, Inc. of Sunnyvale, Calif., modified according to the invention is described. It is to be appreciated that the system is not limited to an EPI Centura system but can be accommodated in other systems, particularly where a mass flow controller is utilized to introduce a species into a reaction chamber. A Si 1-x Ge x  chemical vapor deposition (CVD) film formation process is also described. Similarly, it is to be appreciated that the invention is not limited to CVD Si 1-x Ge x  film formation systems but will apply to other systems and methods, particularly where a species is introduced into a chamber to form a film.  
         [0026]    Referring to FIG. 3, the system includes chamber  100  that accommodates substrate  25 , such as a semiconductor wafer, for processing. Substrate  25  is seated on stage  125  that is, in one embodiment, a susceptor plate. Heating lamps  102  and  104  are used to heat substrate  25 . Processor  110  controls the temperature and pressure inside chamber  100 . The temperature is measured via, for example, pyrometers  106  and  108  coupled to the chamber. Similarly, the pressure may be monitored by one or more pressure sensors, such as BARATRON® pressure sensors, commercially available from MKS Instruments of Andover, Mass., and regulated by a pressure control value. In the schematic illustration shown in FIG. 3, pyrometer  106  and pyrometer  108  are coupled to processor  110  through signal line  115 . Processor  110  uses received information about the substrate temperature to control heat lamps  102  and  104 . The one or more pressure sensors are coupled to processor  110  through signal line 135. Processor  110  uses received information about the chamber pressure to control the pressure through, for example, controlling a vacuum source and a pressure control value coupled to the chamber.  
         [0027]    Processor  110  also controls the entry of constituents into chamber  100 . In one embodiment, the system includes at least two source gases  120  and  130  coupled to manifold  105 . Processor  110  controls the introduction of each of source gas  120  and source gas  130 , as desired, through manifold  105  and controls the flow of the source gas or gases through mass flow controllers  160  and  162 , respectively. For use in a Si 1-x Ge x  film formation process, mass flow controller  160  is, for example, a one standard liter per minute (SLM) of silane (SiH 4 ) unit and mass flow controller  162  is a  150  standard cubic centimeters per minute (sccm) of germane (GeH 4 ) unit. Processor  110  also controls the introduction of a process gas (source gas  180 ), such as for example, nitrogen (N2) or hydrogen (H 2 ), through mass flow controller  168  as known in the art. Each mass flow controller is, for example, a unit commercially available from UNIT Instruments, Inc. of Yorba Linda, Calif.  
         [0028]    In one embodiment, processor  110  controls the introduction of a source gas to form a Si 1-x Ge x  film on substrate  25 , such as Si 1-x Ge x  film  30  in FIG. 1. Source gas  120  is, for example, the constituent silane (SiH 4 ) and source gas  130  is, for example, the constituent germane (GeH 4 ). In this embodiment, one goal is to introduce a film having a concentration gradient of the species germanium (Ge) through the thickness of the Si 1-x Ge x  film. Still further, this gradient is desired, in one embodiment, to be linear between a concentration of Ge at a surface of the film (concentration point  35  of FIG. 1) of zero percent and a maximum at an interface between the silicon wafer and the film (concentration point  40  of FIG. 1).  
         [0029]    In general, mass flow controllers, such as mass flow controller  160  and mass flow controller  162 , can vary (e.g., increase or decrease) the flow rate change of a species introduced into a chamber. The concentration change of a species such as Ge over a thickness of a film may be accomplished at the mass flow controller by changing the flow rate of the source gas into chamber  100 . For any measurable control, this flow rate change is generally linear. However, a linear flow rate change, for example, from higher to lower mass flow and thus lower introduction amount of species, does not necessarily produce a linear concentration gradient of the species in the formed film. This is particularly the case with the constituent GeH 4 , where a linear increase or decrease of flow rate does not generally result in a linear change in concentration of the species constituent Ge in the formed film. Instead, a concentration profile of Ge in a formed film generally more closely resembles the convex profile represented by dashed line  210 . According to the invention, however, a concentration profile such as represented by line  200  may be obtained by controlling mass flow controller  162  to introduce source gas  130  at a non-linear rate.  
         [0030]    In an embodiment of the invention, a method is presented wherein a desired concentration profile of the species, including the linear concentration profile illustrated in FIG. 2 (line  200 ), is produced. According to this method, experimental determinations of the concentration of a species such as Ge is measured in a film formed according to a plurality of flow rates of the constituent GeH 4  through mass flow controller  162  on a sacrificial wafer. In one embodiment, the concentration of Ge in a film formed on a wafer is measured for six discrete flow rates of GeH 4  through mass flow controller  162 . Each experimental measurement corresponds to a single unit of film introduced on a wafer by introducing a constant flow rate of GeH 4  through mass flow controller  162 . In one embodiment, six concentrations of Ge in six discrete films introduced by six discrete GeH 4  flow rates through mass flow controller  162  on six wafers are measured. Each film is analyzed for species Ge concentration through analytical methods such as Secondary Ion Mass Spectroscopy (SIMS), x-ray diffraction, or ellipsometry. The six discrete flow rates are plotted versus the Ge concentration in a corresponding film as illustrated in FIG. 4. In this example, a single experimental measurement is obtained from a film on a single wafer by placing a sacrificial wafer in chamber  100  and the reaction conditions of the chamber established. In one embodiment, a film is formed at a chamber pressure of  100  Torr and a temperature of 680° C. In one example, process gas is introduced in chamber  100  according to the following flow rate recipe:  
                                       Source Gas   Constituent   Flow Rate                   120   SiH 4      1 SLM       130   GeH 4     varied       180   H 2     30 SLM                  
 
         [0031]    It is to be appreciated, that other recipes may be utilized to introduce the films on the wafers. Such recipes will generally depend on the desired process parameters. For example, in the introduction of a Si 1-x Ge x  film, additional constituents such as hydrochloric acid (HCl), may be added to modify the properties of the film. One objective in collecting the experimental data is to mimic the desired process conditions as closely as possible.  
         [0032]    According to the above recipe, six flow rates of source gas  130  of the constituent GeH 4  are selected between 0 and 300 sccm. It is to be appreciated that GeH 4  flow rates higher than 300 sccm can be selected. One limit of GeH 4  flow may be considered as one beyond which the Ge concentration in the introduced film will not further increase for an increase in the GeH 4  flow rate. A corresponding concentration of Ge is measured in a film formed on the sacrificial wafer. Once the data is collected, a curve is established through a curve fit algorithm such as a Gauss-Jordan algorithm. FIG. 4 illustrates the curve fit for six points. In one example, a Gauss-Jordan numerical algorithm is used to calculate the coefficients of a third order polynomial that best fits the six experimental measurements. This method of curve fitting is known as the Least Square Fit (LSF) method of curve fit. It is to be appreciated that the Gauss-Jordan numerical algorithm is not the only method to calculate coefficients of an LSF polynomial. Similarly, the LSF method as well as the Gauss-Jordan method are not limited to six data points out may be used, for example, with as few as three data points or more than six data points.  
         [0033]    According to an embodiment of the invention, the flow rate of GeH 4  (e.g., six discrete flow rate measurements) is also measured against the introduction rate, e.g., growth rate, of the Si 1-x Ge x  film introduced on the sacrificial wafer. It is to be appreciated that the same six flow rates as utilized in FIG. 4 may be utilized to compare the growth rate of Si 1-x Ge x . In one embodiment, the experimentally-obtained Si 1-x G e  growth rates are measured from the same film grown on the same six sacrificial wafers used to measure Ge concentration. FIG. 5 shows a plot of GeH 4  flow rate versus Si x Ge 1-x  growth rate and a curve fit through the plotted points. The same numerical method of LSF is used to determine the best curve fit to the experimentally- obtained growth rate measurements. The coefficients of the third order polynomial are calculated using, for example, the Gauss-Jordan method noted above with respect to FIG. 4.  
         [0034]    The experimentally-determined data for concentration of a species as a function of flow rate and the experimentally-determined data for growth rate as a function of flow rate is input into processor  100 . Also, a desired Ge concentration profile as a function of the Si 1-x Ge x  film thickness is input into processor  110 . For example, Si 1-x Ge x  film  30  in FIG. I is formed for input germanium concentrations of 20% at point  40  and 0% at point  35  having a linear change in concentration from point  40  to point  35  over a 500 Angstroms Si 1-x Ge x  input film thickness identified as film  30 .  
         [0035]    When wafer  10  is placed in processor  110 , processor  110  first calculates the curves of FIGS. 4 and 5 using the six experimentally determined measures for concentration and growth rate. Processor  110  next uses the desired input concentration profile over the desired growth thickness as a guide to calculate the set points for GeH 4  mass flow controller  162 . For a desired Ge concentration, the corresponding GeH 4  flow rate is calculated from FIG. 4. This flow rate is then used to calculate the Si 1-x Ge x  growth rate, from FIG. 5. The corresponding growth rate used along with a selected time interval (Δt) establishes the desired growth thickness of a portion of Si 1-x Ge x  film for the time interval. The thickness of the Si 1-x Ge x  grown within a selected time interval is subtracted from the total desired film thickness to establish the thickness left to be grown. Using the new thickness that yet needs to be grown, the desired input concentration profile as a function of thickness is used to calculate a corresponding new Si 1-x Ge x  concentration value. Using the new concentration value, the above process of using the data from FIGS. 4 and 5 will be repeated to calculate a new thickness of Si 1-x Ge x  grown for a second time interval, Δt. This iterative process will continue until the total desired thickness of Si 1-x Ge x  is on wafer  10 .  
         [0036]    In one example, a Si 1-x G x  film has a Ge concentration of 20 percent at the wafer film interface (concentration point  40 ) and zero at the film surface (concentration point  35 ). In this example, a linear concentration profile is desired. Given the desired concentration (e.g., 20 percent), the data obtained from FIG. 4 is queried to obtain the desired flow rate of GeH 4  species through mass flow controller  162  (flow as a function of concentration). Once the flow is established, the data collected and represented by FIG. 5 is utilized to calculate a growth rate for the desired flow (growth rate as a function of flow rate). For a predetermined time interval (e.g., 0.2 seconds), the amount of film  30  introduced on substrate  25  during a time interval of 0.2 seconds may be determined for the desired concentration. Thus, by using the experimental data and a predetermined time interval, the concentration in a Si 1-x Ge x  film and a film thickness is known.  
         [0037]    In the example where a linear variance in concentration is desired, such as illustrated by line  200  in FIG. 2, a corresponding concentration is determined for a second time interval. Thus, in reference to FIG. 2, knowing the concentration profile as a function of film thickness and starting from a desired concentration point of film  30 , subsequent concentration points along the path of line  200  may be calculated for time intervals, At. In one embodiment, a time interval of 0.2 seconds is used to control mass flow controller  162  and the corresponding GeH 4  flow rate (FIG. 4) as well as growth rate (FIG. 5) is calculated to obtain a linear profile (line  200 ). The process continues until a desired film thickness of film  30  is formed.  
         [0038]    Processor  110  contains, in one embodiment, a suitable algorithm to calculate the desired flow rate of a constituent to mass flow controller  162  as a function of concentration. Processor  110  also contains, in this embodiment, a suitable algorithm to calculate a growth rate as a function of flow rate. For example, processor  110  is supplied with software instruction logic that is a computer program stored in a computer-readable medium such as memory in processor  110 . The memory is, for example, a hard disk drive. Additional memory associated with processor  110  stores, among another items, the experimentally determined data of concentration of the constituent species over a desired flow rate spectrum (FIG. 4), and experimentally-determined data related to the growth rate of the constituent species over the desired flow rate spectrum (FIG. 5) as well as the corresponding curve fit algorithms.  
         [0039]    [0039]FIG. 6 shows an illustrative block diagram of the hierarchical structure of system logic according to one embodiment of the invention for forming a film having a desired concentration profile and thickness on a substrate which is a wafer. Such control logic would constitute a program to be run on processor  110 . A suitable programming language for such a program includes, but is not limited to, C, C ++ , and other languages. The program may be supplied directly on processor  110  or to processor  110  by way of an outside device, such as a computer.  
         [0040]    As a first operation, certain user inputs are supplied to processor  110  and stored in the form of either internal or external memory. The information supplied to processor  110  for the system logic includes experimental data for introduction rate, e.g., concentration of a species such as Ge concentration as a function of mass flow rate (block  310 ), experimental data for growth rate of an introduced film, such as Si 1-x Ge x , as a function of mass flow rate (block  320 ), the desired thickness of a film on a substrate, such as a Si x Ge 1-x  film on a wafer (block  330 ), and the desired concentration profile of a film formed on a substrate such as a wafer (block  340 ).  
         [0041]    Once the above-described data is supplied to processor  110 , the system logic calculates a flow rate of a species, such as GeH 4 , for a value of concentration desired by the user (block  350 ) for a predetermined time interval. System logic is then used to control mass flow controller  162  to regulate the corresponding flow rate of source gas  130  of GeH 4.    
         [0042]    In addition to calculating a corresponding flow rate of a species for a desired concentration, the system logic calculates an introduction rate, e.g., a growth rate, of a corresponding film on a substrate, such as a wafer for the calculated flow rate (block  360 ). For a calculated growth rate of film, an amount of film can further be calculated for a given time interval (block  370 ). This information is used by processor  110  to introduce a constituent, such as GeH 4 , through mass flow controller  162  to introduce a film on substrate  25  for a selected time interval. 0.2 seconds is an example of a desired time interval as 0.2 seconds represents the time interval utilized for ramp-up or ramp-down of flow through a mass flow controller, for example, a UNIT mass flow controller used in an EPI Centura system.  
         [0043]    Once a constituent is introduced into chamber  100  to form a portion of film  30  according to the method described herein for a predetermined time interval, the system logic determines whether the desired film thickness is achieved by comparing the calculated film thickness with the desired film thickness (block  380 ). If the desired input film thickness with the desired input concentration profile has not been achieved, the system logic of processor  110  calculates a new value for film thickness representing the additional thickness amount needed to obtain the total desired input thickness (block  390 ), and calculates the corresponding desired input concentration value for the newly calculated thickness (block  395 ). Processor  110  returns to block  350  and uses the newly calculated value of desired concentration to calculate a corresponding flow rate. Processor  110  continues this process until a desired film thickness is achieved. Once a desired film thickness is achieved, the system logic discontinues the loop and completes the film formation (block  396 ). It is to be appreciated that calculations of flow rates and film growth may precede the introduction of a constituent into the chamber.  
         [0044]    According to the method and system described, a film-forming constituent can be controlled, through control of a mass flow controller, to achieve a desired concentration profile of a species in a film and a desired film thickness introduced on a substrate, such as a wafer. In the above embodiment, a method of achieving a linear concentration profile is described. FIG. 7 shows a SIMS profile of a epitaxially grown Si 1-x Ge x  film on a silicon substrate having a linear concentration profile of Ge introduced according to a method of the invention. The SIMS profile illustrates the atomic profile of Ge from the surface (0 depth) to the interface of the Si I-Ge x  and the silicon substrate. Thus, the depth represents the depth into the Si 1-x Ge x  film.  
         [0045]    In FIG. 7, the thickness of the Si 1-x Ge x  film is approximately 1000Å. The concentration at the surface of the film is zero (represented as beginning at a depth of approximately 500Å to account for a cap on the SIMS system). The concentration profile through the film is linear to a Ge concentration of 16 percent at the Si 1-x Ge x  /silicon interface.  
         [0046]    [0046]FIG. 8 shows a plot of the flow rate of GeH 4  introduced to produce the linear Ge profile illustrated in FIG. 7. FIG. 8 illustrates that a linear concentration profile is formed but the flow rate of GeH 4  that produced the profile is varied in a non- linear fashion.  
         [0047]    It is to be appreciated that the principles of the invention are not limited to a method and system for introducing a film having a linear concentration profile of a species constituent, but are equally applicable to situations where a non-linear concentration profile is desired. For example, a profile such as illustrated by lines  210  and  220  in FIG. 2 or other profile may be desired. In one aspect, the invention provides a technique for controlling a mass flow controller to achieve a desired concentration profile in a film introduced on a substrate.  
         [0048]    [0048]FIG. 9 shows a film profile of epitaxially grown silicon-germanium film on a silicon substrate having a concave concentration profile of Ge formed according to a method of the invention. Similar to FIG. 7, the film&#39;s profile illustrates the atomic profile of Ge from the surface (zero depth) to the interface of the Si 1-x Ge x  and the silicon substrate. The thickness of the silicon-germanium film is approximately 1000Å. The concentration profile adapts a concave representation from a Ge concentration of zero percent at the surface of the film to a concentration of 15 percent at the interface.  
         [0049]    [0049]FIG. 10 shows a plot of the flowchart of GeH 4  introduced to produce the profile illustrated in FIG. 9. FIG. 10 illustrates that the concave profile produced in FIG. 9 is not the result of a linear change in the flow rate of GeH 4 .  
         [0050]    In addition to providing the ability to establish a desired concentration profile of a film introduced on a substrate, such as a wafer, the invention offers a method and system for defining the thickness of a film introduced on a wafer. Accordingly, the invention may be practiced so as to achieve a desired concentration profile of a species, introduced by mass flow meter, having a desired concentration profile and a desired film thickness.  
         [0051]    One application of controlling the introduction of constituents onto a semiconductor substrate to yield a graded film is in the formation of heterojunction bipolar transistors (HBTs). Bipolar transistors are utilized in a variety of applications including as amplifying and switching devices. HBTs generally offer improved performance over traditional bipolar transistors and metal oxide semiconductor (MOS) transistors in high frequency applications, particularly applications approaching 50 gigahertz (gHz). As higher frequency applications (e.g., 50 gHz or greater) become desirable, a need for improved HBTs exist. The invention contemplates improved performance of HBTs by utilizing Si 1-x Ge x  graded junctions having optimized concentration profiles.  
         [0052]    [0052]FIG. 11 shows a representative example of an HBT according to the invention. HBT 400 includes emitter region 410, base region 420 and collector region 430. Emitter-base (E-B) spacer 435 is positioned between emitter region 410 and base region 420. Base-collection (B-C) spacer 445 is positioned between base region 420 and collector region 430. HBT 400 is characterized by base region 420 of an epitaxially formed Si 1-x Ge x  film as are E-B spacer 435 and B-C spacer 445. The bipolar transistor, in this embodiment, comprises N-type emitter region 410, P-type base region 420, and N-type collector region 430 (a NPN transistor). FIG. 11 illustrates the movement of electrons through transistor 400 in response to a voltage applied through electrode 450. In one example that follows, at least E-B spacer 435 will be formed with concentration gradient analagous to that shown in FIG. 9 (i.e., profile).  
         [0053]    The use of Si 1-x Ge x  in an HBT generally enables high-frequency performance. One of the major advantages of Si 1-x Ge x  is a smaller energy gap than that of silicon. In unstrained bulk Si 1-x Ge x  the energy gap drops from approximately 1.1 electron-volts (eV) in silicon to 1.0 eV for Si 0.8 Ge 0.2.  The lattice constant of Si 1-x Ge x  is also larger than the lattice constant in silicon. If the thickness of the Si 1-x Ge x  alloy is below a critical value, the mismatch in lattice constant is accommodated elastically, no dislocations are formed, and the Si 1-x Ge x  film is strained. Strain lifts the degeneracy of both valence and conduction bands. As a result, the energy gap of strained Si 1-x Ge x  decreases even more than unstrained Si 1 -xGe x  to approximately 0.9 eV for strained Si 0.8 Ge 0.2 .  
         [0054]    The change in the energy gap in strained Si 1-x Ge x  film, Å, allows for a fast transmit of charge carriers in the base region (e.g., base region  420 ) of HBTs under the action of the drift electric field, E:  
         E=-dΔ/d 1 ,  (1) 
         [0055]    where 1 is the distance across the base region. For example, the band gap reduction of 0.2 eV across a 500Å base region, translates to a drift electric field of  40  kV/cm.  
         [0056]    Charge carrier drift mobility, μ, through the base region of an HBT is proportional to the scattering time, τ, and inversely proportional to the effective mass of the carrier, m*:  
         μ˜τ/m*.  (2) 
         [0057]    The scattering time diminishes with increasing Ge concentration because of alloy scattering. The effective mass, m*, becomes anisotropic between “in-plane” and “perpendicular to the junction” directions of motion because of strain. For the perpendicular direction, the effective mass of holes is significantly smaller than Si 1-x   x Ge x  due to valence band offset. The resulting hole mobility augments with the increase of x, from 450 cm 2 NVs for x=0 to 1 cm 2 /Vs for x=0.2 in Si 1-x Ge x  with low dopant (i.e., P-type, N-type) concentration. The opposite trend takes place for electrons: their perpendicular mobility drops from 1400 cm 2  vs for x=0 to 750 cm 2 /vs for x=0.2. Despite the decrease in the electron mobility with increasing x, the electron mobility is larger than the hole mobility over the majority of the practically useful range of the Ge concentration (i.e., x between 0 and 0.2). Accordingly, the transistor configuration of choice for high-speed applications is generally the NPN transistor because the species travelling from the emitter region to the collector region are electrons.  
         [0058]    Typical P-type doping levels for Si 1-x Ge x  base region 420 of NPN transistor 400 are in the 10 18 cMr 3  - 10 19 cm- 3  range. In one aspect, this choice is generally determined by the requirement of having fairly low sheet (i.e., in-plane) resistance of base region 420. When the dopant concentration becomes large, two effects are generally thought to occur: first, the carrier perpendicular mobility is significantly reduced. For instance, for electrons, the perpendicular mobility is approximately  250  cm 2 NVs and  120  cm 2  vs for doping levels of 10 18 cm −3  and 10 18 cm −3 , respectively. Second, the mobility dependence on the Ge concentration is reduced: carrier mobility, μ, is almost x-independent for doping levels in the  10   18 cm −3  - 101 9 cm- 3  range. The effects of dopant concentration is presented in detail in the treatise Semiconductors and Semimetals, Vol. 56, “Germanium Silicon: Physics and Materials,”edited by R. Hull and J. C. Bean, in the article by S. A. Ringel and P. N. Grillot, “Electronic Properties and Deep Levels in Ge-Si,” at pages 293-346 (1999). The significant reduction in carrier mobility can be counterweighted by reducing the perpendicular size of the base (to  200Å- 300Å or thinner) and by the drift electric field (i.e., built-in potential) (see Equation 1).  
         [0059]    The small size of base region  420  generally results in degraded overall performance of devices because of low leakage currents and reduced breakdown voltages. In order to overcome this problem, it has been suggested to use lightly doped spacers at the emitter-base and collector-base regions, e.g., E-B spacer 435 and C-B spacer  445 . See Meyerson, B. S., et al., “Silicon: Germanium Heterojunction Bipolar Transistors; from Experiment to Technology,” Selected Topics in Electronics and Systems, Vol. 2, “Current Trends in Heterojunction Bipolar Transistors,” edited by M. F. Chang. E-B spacer  435  and C-B spacer  445  may be intrinsic (i.e., no doping) or lightly N-type doped (e.g., typically below 10 17 cm −3 ). As for lightly doped Si 1-x Ge x  the electron perpendicular mobility generally depends on the Ge concentration.  
         [0060]    If the band energy gap changes linearly, the built-in electric field is constant across the junction (Equation 1). This means that passing through the spacers, electrons spend significantly more time in the high Ge concentration regions (where their mobility is lower) than they do in the regions where the Ge concentration is lower. The invention recognizes that the overall transient time can be substantially reduced by creating a Ge concentration profile in such a way that the electric field would be higher in the regions where mobility is lower. In other words, the electric field changes in an opposite way to that of the mobility change (i.e., the electric field increases through the heterojunction if carrier mobility decreases and vice versa) to enhance the cut-off frequency of the transistor.  
         [0061]    In one example, the transient time, τ, through E-B spacer  435  is determined for the following two profiles of Ge concentration: Profile A is a linear grade, and Profile B where the electric field is inversely proportional to the electron perpendicular mobility to yield a concave gradient. As a simplification, a linear relationship between the electron drift velocity, v, and the electric field is assumed:  
         v=μE.  (3) 
         [0062]    In this example, E-B spacer  435  has a thickness, W, in which the Ge concentration changes from 0 to x 1 . The corresponding changes in the band gap and in the mobility are from Δ 0 =1. eV to Å 1  and from go=14 cm 2Vs to μ 1 . The transient time is given by the integration across base region  420  from 0 to W:  
         τ=∫dl/v[x(l)].  (4) 
         [0063]    Note that the velocity is a function of x which in turn is a function of the distance, 1, across base region  420 .  
         [0064]    Literature data on the band gap and mobility for x=0-0.2 can be closely approximated by the following linear relations:  
         Δ=Δ 0  - αx, μ=μ 0 -βx,  (5) 
         [0065]    respectively, with a=l eV and  3 =3250 cm 2 NVs. For Profile A, the electric field is constant: E=axl/W, mobility is p=,o-(  3 x,[W)l, and Equation 4 is reduced to  
         μ=(W/a x 1 ) |dl/(μ 0 - 1 β1),  (6) 
         [0066]    with [*=[x,/W. Integrating Equation 6, the transient time of electron carriers through E-B spacer  435  for Profile A becomes:  
         τ A =(W 2 ,/αx 1   2 ) ln(μ 0 /μ 1 ).  (7) 
         [0067]    For Profile B, the velocity is constant: v=vo, and therefore  
         τ B =W/v 0 .  (8) 
         [0068]    From Eqs. 1 and 5, we have for the electric field:  
         E=αdx/dl.  (9) 
         [0069]    Using Eqs. 3, 5 and 9, we obtain:  
         αdx/dl(μ 0 - β x )=v 0 .  (10) 
         [0070]    After integration Equation 9 and substitution for the transient time of electron carriers through E-B spacer  435  in Profile B becomes:  
         [0071]    Ts =W 2 /(aOSx 1  - (αμ 0 x 1   2 /2).  (11) 
         [0072]    From Eqs. 9 and 11, we finally have:  
         τ A /τ B =[(μ 0 /β-x 1   2 / 2 )ln(μ 0 /μ 1 )]/x 1   (12) 
         [0073]    Substituting data for x 1 =0.15, Equation 12 becomes: τ A/τB= 1.5.  
         [0074]    According to the above analysis, the transient time for a concentration profile according to Profile B is shorter than for the linear profile of Profile A. For Profile B, the electric field is smaller near emitter region  410  and increases towards base region  420 . This change in electric field may be attributed to the band gap changing more slowly near emitter region  410  than it does near base region  420  (see Equation 1). According to Equation 5, this in turn means that for Profile B, the Ge concentration changes more slowly near emitter region  410  and faster near base region  420 . In other words, moving across E-B spacer  435 , the Ge profile has a concave curvature (similar to line  220  in FIG. 2) with the Ge concentration being smaller on the emitter side of E-B spacer  435  and increasing to a maximum at the interface between E-B spacer  435  and the base region.  
         [0075]    In the above example, a NPN HBT transistor was described having a Si 1-x Ge x  base region with an E-B spacer and a B-C spacer. The specific example described the E-B spacer. It is to be appreciated that similar beneficial results may be obtained with a similarly optimized B-C spacer, as well as an optimized base region. It is also to be appreciated that hole mobility generally increases with increasing Ge concentration (a behavior opposite to that of the electron mobility). Therefore, in the case of a PNP HBT, a convex profile (similar to line  210  of FIG. 2) of Ge concentration in a spacer will generally result in the shortest transient time and the highest cut-off frequency of PNP HBTs.  00851  In the preceding detailed description, the invention is described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention as set forth in the claims. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.