Patent Publication Number: US-7719403-B2

Title: Film resistor and a method for forming and trimming a film resistor

Description:
RELATED APPLICATION 
   This application is a divisional (DIV) of U.S. patent application Ser. No. 11/231,054, entitled “FILM RESISTOR AND A METHOD FOR FORMING AND TRIMMING A FILM RESISTOR,” filed on Sep. 20, 2005, which is herein incorporated by reference in its entirety. 

   FIELD OF THE INVENTION 
   The present invention relates to a film resistor, and in particular, though not limited to a thin film resistor. The invention also relates to an integrated circuit comprising a plurality of the film resistors, and the invention further relates to a method for forming and trimming a film resistor, and in particular, though not limited to a method for forming and trimming a thin film resistor on an integrated circuit. 
   BACKGROUND TO THE INVENTION 
   Thin film resistors are commonly used in integrated circuits. Typically, a plurality of thin film resistors are formed on an electrically insulating substrate layer, which typically is an oxide layer formed on the integrated circuit chip. The thin film resistors, in general are formed in a specific area on the substrate layer to, in general, extend parallel to each other. It is desirable that the thin film resistors be located relatively close to each other for two important reasons, firstly, to minimise the area occupied by the thin film resistors on the integrated circuit chip, in order to minimise the overall die area required, and secondly, to minimise the effect of process variations on the thin film resistors, which can result in mismatch and other related problems. 
   However, even locating the thin film resistors close to each other does not completely avoid the effects of process variation, which can result in mismatch of the resistors on the same chip, and from chip to chip. Thus, trimming of the resistance of thin film resistors must be carried out after the film resistors have been formed on the integrated circuit chip. This, thus, requires that provision must be made during the formation of the thin film resistors for facilitating subsequent trimming of the resistance of the film resistors. 
   One method for forming thin film resistors which lends itself to subsequent trimming requires that the thin film resistors be formed with a sidewardly projecting tab which is subsequently trimmed for increasing the resistance of the resistors. Such prior art thin film resistors are illustrated in  FIG. 1  and are indicated by the reference numeral  100 . Each thin film resistor  100  is formed on an electrically insulating substrate  101 , which typically is of an oxide material, such as silicon dioxide. The thin film resistors may be of any suitable material, for example, silicon chrome, which may be doped or otherwise. The thin film resistors are typically formed by physical vapour deposition (PVD), by chemical vapour deposition (CVD) or by sputtering, and are deposited to a depth, which is maintained constant and depends on the process. The length and width of the thin film resistors are dictated by the desired resistance values of the resistors. Typically, such thin film resistors are deposited to a depth of up to 100 Angstroms. The thin film resistors  100  extend between respective pairs of electrical contact pads  102  and  103 , and each thin film resistor  100  is provided with a sidewardly extending tab  104  for facilitating trimming of the resistance of the thin film resistor  100 . In order to minimise the spacing between the thin film resistors  100 , the thin film resistors  100  are arranged in pairs with the tabs  104  of adjacent pairs facing each other and being staggered along the respective lengths of the thin film resistors  100 . 
   The effect of the tabs  104  on the thin film resistors  100  is to reduce the current density of current flowing through the thin film resistors  100  adjacent the area of the tabs  104 , and thus trimming of the tabs  104  provides relatively high resolution trimming. 
   Trimming of each thin film resistor  100  is generally carried out by progressively extending a trimming slot  105  into the tab  104  of the thin film resistor  100  being trimmed. The trimming slots  105  are formed by a laser light beam, and in general are formed to extend parallel to the thin film resistors  100 . By virtue of the fact that the current density is reduced in the thin film resistors  100  adjacent the area of the tabs  104 , a relatively wide resistance value trim range is achievable, as well as relatively high trim resolution. 
   While alignment techniques for aligning a laser light beam with a tab  104  to be trimmed have been improved over the years, the size of the active high energy spot of the laser light beam which actually forms the trimming slot  105  is still relatively large, and accordingly, it is essential that the spacing between the tabs  104  of adjacent thin film resistors  100  must be sufficient to avoid any danger of the laser light beam as it is forming a trimming slot  105  in the tab  104  of one of the thin film resistors  100  damaging the adjacent thin film resistor  100 . Typically, the high energy laser spot is of diameter of the order of three microns to five microns. Thus, while the spacing between the thin film resistors can be reduced somewhat by arranging the thin film resistors  100  with the tabs  104  of adjacent pairs of resistors facing each other, nonetheless, the thin film resistors  100  must be spaced apart a sufficient distance to avoid unintentional trimming of a thin film resistor  100  adjacent another thin film resistor  100  the tab  104  of which is being trimmed. 
   Typically, the transverse distance A between the tab  104  of one thin film resistor  100  and the adjacent thin film resistor  100  should be at least nine microns, while the longitudinal distance B between the tabs  104  of adjacent thin film resistors  100  should be of the order of ten microns. Additionally, the tab  104  of each thin film resistor  100  should be a longitudinal distance C from the closest electrical contact pad  102  or  103  of at least nine microns. 
   Accordingly, while this prior art method of forming and trimming thin film resistors provides a relatively wide trim range as well as relatively high trim resolution, nonetheless, it still requires a relatively large spacing between the thin film resistors, which in turn results in a relatively large die area to accommodate the thin film resistors, and potential mismatch between the thin film resistors. 
   There is therefore a need for a film resistor which addresses this problem. 
   The present invention is directed towards providing a film resistor which can be located relatively close to an adjacent film resistor, and which can be subsequently trimmed. The invention is also directed towards a method for forming and trimming such a film resistor, and the invention is also directed towards providing an integrated circuit comprising a plurality of film resistors formed thereon. 
   SUMMARY OF THE INVENTION 
   According to the invention there is provided a film resistor comprising:
         a resistive film of electrically resistive material extending longitudinally between a first end and a spaced apart second end, and having opposite spaced apart first and second major surfaces extending between opposite spaced apart first and second side edges, the resistive film being adapted to accommodate current flow between the first and second ends, and   a low impedance element electrically coupled to the resistive film adjacent an intermediate portion of the resistive film disposed intermediate the first and second ends for conducting current in parallel with the intermediate portion of the resistive film for reducing current density of current flow in the intermediate portion for facilitating trimming of the resistance of the film resistor in the intermediate portion thereof.       

   In one embodiment of the invention the low impedance element is electrically coupled to the resistive film along the length of the intermediate portion in a direction between the first and second ends of the resistive film. Preferably, the low impedance element abuts and is electrically coupled to the first major surface of the resistive film along the intermediate portion. Advantageously, the low impedance element is laminated with the resistive film adjacent the intermediate portion. 
   Ideally, the low impedance element overlays the first major surface of the resistive film adjacent the intermediate portion, and is electrically coupled to the resistive film throughout the area thereof overlaid by the low impedance element. 
   In one embodiment of the invention the low impedance element is electrically coupled to the resistive film adjacent the second side edge thereof. 
   Preferably, the low impedance element is electrically coupled to the resistive film at a location spaced apart from the first side edge thereof and defines a trimmable portion in the intermediate portion between the low impedance element and the first side edge. 
   Advantageously, the resistance of the film resistor is trimmable by progressively extending a trimming slot in the trimmable portion. 
   In one embodiment of the invention a first transverse edge extends in the intermediate portion in a general direction from the first side edge of the resistive film to the low impedance element, the first transverse edge defining with the first side edge and the low impedance element a first trimmable area in the trimmable portion. Preferably, the resistance of the film resistor is trimmable by progressively extending a first trimming slot in the first trimmable area. Advantageously, the first trimming slot is extended into the first trimmable area from the first transverse edge. 
   In another embodiment of the invention a second transverse edge spaced apart from the first transverse edge extends in the intermediate portion in a general direction from the first side edge of the resistive film to the low impedance element, the second transverse edge defining with the first side edge and the low impedance element a second trimmable area in the trimmable portion. Preferably, the second transverse edge is disposed between the first transverse edge and the second end of the resistive film. Advantageously, the resistance of the film resistor is trimmable by progressively extending a second trimming slot in the second trimmable area. Preferably, the second trimmable slot is extended into the second trimmable area from the second transverse edge. 
   Ideally, one of the first and second trimming slots is extended into the corresponding one of the first and second trimmable areas for coarse trimming the resistance of the film resistor, and the other one of the first and second trimming slots is extended into the corresponding one of the first and second trimmable areas for fine trimming of the resistance of the film resistor. 
   In one embodiment of the invention the current density progressively reduces in the respective first and second trimmable areas towards the first side edge of the resistive film and the corresponding one of the first and second transverse edges. 
   Preferably, the resistive film is an elongated resistive film extending longitudinally between the first and second ends thereof. 
   In one embodiment of the invention the low impedance element is an elongated low impedance element extending longitudinally in a general direction parallel to the resistive film. Advantageously, the respective opposite ends of the low impedance element are shaped to minimise current crowding adjacent the ends thereof. 
   In one embodiment of the invention the respective opposite ends of the low impedance element are chamfered such that a side edge of the low impedance element disposed adjacent the second side edge of the resistive film is longer than an opposite side edge thereof disposed remote of the second side edge of the resistive film. 
   In another embodiment of the invention the low impedance element is more tolerant of the cutting effect of a laser light trimming beam than the resistive film. 
   In a further embodiment of the invention the low impedance element is of electrical resistance which is lower than the electrical resistance of the resistive film. 
   In one embodiment of the invention the resistive film is a thin film resistor. 
   In another embodiment of the invention a pair of low impedance elements are electrically coupled to the resistive film adjacent corresponding spaced part intermediate portions of the resistive film. Preferably, one of the low impedance elements and the corresponding intermediate portion is located adjacent on of the first and second ends of the resistive film, and the other one of the low impedance elements and the corresponding one of the intermediate portions is located adjacent the other one of the first and second ends of the resistive film. 
   The invention also provides a compound film resistor comprising a pair of film resistors according to the invention electrically coupled in series by the low impedance elements of the respective film resistor. 
   Additionally, the invention provides an integrated circuit comprising an electrically insulating substrate layer and a film resistor according to the invention formed on the substrate layer. 
   Further the invention provides an integrated circuit comprising an electrically insulating substrate, and a plurality of spaced apart film resistors according to the invention formed on the substrate layer with the second major surfaces of the resistive films abutting the substrate layer, and the resistive films extending parallel to each other with the first side edge of each resistive film lying adjacent but spaced apart from the second side edge of the adjacent resistive film. 
   The invention also provides a method for forming and trimming a film resistor, the method comprising the steps of:
         forming a resistive film of electrically resistive material on an electrically insulating substrate, the resistive film extending between a first end and a spaced apart second end, and having opposite spaced apart first and second major surfaces extending between opposite spaced apart first and second side edges, the resistive film being adapted to accommodate current flow between the first and second ends,   electrically coupling a low impedance element to the resistive film adjacent an intermediate portion of the resistive film disposed intermediate the first and second ends for conducting current in parallel with the intermediate portion of the resistive film for reducing current density of current flow in the intermediate portion for facilitating trimming of the resistance of the film resistor in the intermediate portion thereof, and   trimming the resistance of the film resistor by progressively extending a trimming slot into the intermediate portion of the resistive film.       

   In one embodiment of the invention the low impedance element is electrically coupled to the resistive film at a location spaced apart from the first side edge thereof and defines a trimmable portion in the intermediate portion between the low impedance element and the first side edge. 
   In another embodiment of the invention a first transverse edge is formed in the intermediate portion extending in a general direction from the first side edge of the resistive film to the low impedance element, the first transverse edge defining with the first side edge and the low impedance element a first trimmable area in the trimmable portion. Preferably, the first trimmable area is trimmed by progressively extending a first trimming slot in the first trimmable area. Advantageously, the first trimming slot is extended into the first trimmable area from the first transverse edge. Ideally, the first trimming slot is progressively extended in the first trimmable area parallel to the first side edge of the resistive film. 
   In another embodiment of the invention a second transverse edge spaced apart from the first transverse edge is formed in the intermediate portion extending in a general direction from the first side edge of the resistive film to the low impedance element, the second transverse edge defining with the first side edge and the low impedance element a second trimmable area in the trimmable portion. Preferably, the second trimmable area is trimmed by progressively extending a second trimming slot in the second trimmable area. Advantageously, the second trimming slot is extended into the first trimmable area from the second transverse edge. Ideally, the second trimming slot is progressively extended in the second trimmable area parallel to the first side edge of the resistive film. 
   Ideally, one of the first and second trimming slots is extended into the corresponding one of the first and second trimmable areas for coarse trimming the resistance of the film resistor, and the other one of the first and second trimming slots is extended into the corresponding one of the first and second trimmable areas for fine trimming of the resistance of the film resistor. 
   ADVANTAGES OF THE INVENTION 
   The advantages of the invention are many. However, one of the most important advantages of the invention is that the invention provides film resistors, and in particular thin film resistors, which can be located on an integrated circuit considerably more closely together than known thin film resistors can be located heretofore, without any loss in the resolution at which the resistors can be trimmed. Indeed, many of the configurations of the film resistor according to the invention facilitate higher resolution trimming than can be achieved with film resistors known heretofore, and where the film resistors are configured for facilitating separate coarse and fine trimming, particularly high resolution trimming can be achieved. The film resistors according to the invention also have a relatively wide trim range of resistance values, and this is particularly so in the film resistors which are configured to facilitate separate coarse and fine trimming. 
   By virtue of the fact that the thin film resistors can be located significantly more closely together than many prior art thin film resistors, a significant reduction in die area is achieved. Where the low impedance elements overlay the resistive film of the film resistors, a particularly large reduction in the die area requirement is achieved. Furthermore, where the low impedance elements overlay the resistive film of the thin film resistors, and the low impedance elements are of material which is more tolerant of the cutting effect of a laser light trimming beam than the resistive film, the thin film resistors can be located more closely to each other than would otherwise be possible. This is achievable by locating the thin film resistors so that the low impedance elements of the respective thin film resistors are adjacent but spaced apart from the intermediate portion, namely, the trimmable area of the adjacent thin film resistor. Thus, as each thin film resistor is being trimmed, there is little danger of damage being caused to the adjacent thin film resistor, even if the laser light trimming beam is not entirely accurately aligned during trimming, since the part of the adjacent thin film resistor which is adjacent the trimmable area being trimmed is the low impedance element, which is more tolerant of the laser light trimming beam than the resistive film. Thus, by providing the low impedance element to be of material which is more tolerant of the laser light beam than the resistive film, a further reduction in the die area is achieved. 
   Additionally, by virtue of the fact that the thin film resistors can be located particularly closely together, mismatch between the thin film resistors prior to trimming resulting from process variations is significantly reduced, thereby minimising the subsequent trimming requirements. 
   A further advantage which is achievable by the invention is that the thin film resistors can be more accurately matched, since they can be located in similar orientations. In other words, the respective thin film resistors can be, and are preferably located with the low impedance element of each thin film resistor adjacent the intermediate portion of the adjacent thin film resistor. Additionally, by so locating the thin film resistors relative to each other, setting up of the laser trim apparatus for trimming the thin film resistors is significantly simplified, since by locating the thin film resistors in the same orientation relative to each other, and spacing the thin film resistors at a constant pitch, the setting up of the laser trimming apparatus to sequentially thin the thin film resistors merely requires indexing the laser light trimming beam in steps of constant pitch from one thin film resistor to the next. 
   The invention and its many advantages will be readily apparent to those skilled in the art from the following description of some preferred embodiments thereof, which are given by way of example only, with reference to the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a top plan view of prior art thin film resistors on a portion of an integrated circuit chip, 
       FIG. 2  is a top plan view of a portion of an integrated circuit according to the invention comprising a plurality of thin film resistors also according to the invention, 
       FIG. 3  is a transverse cross-sectional side elevational view of the portion of the integrated circuit of  FIG. 2  on the line III-III of  FIG. 2 , is  FIG. 4  is a transverse cross-sectional end view of a portion of the portion of the integrated circuit of  FIG. 2  on the line IV-IV of  FIG. 2 , 
       FIG. 5  is a top plan view of one of the thin film resistors according to the invention of the integrated circuit of  FIG. 2 , 
       FIG. 6  is a top plan view of the portion of the integrated circuit of  FIG. 2  illustrating trimming of the resistance of one of the thin film resistors of the integrated circuit of  FIG. 2 , 
       FIG. 7  is a top plan view of one of the thin film resistors of the integrated circuit of  FIG. 2  after the resistance of the thin film resistor has been trimmed, 
       FIG. 8  is a waveform illustrating how the resistance of one of the thin film resistors of the integrated circuit of  FIG. 2  increases as trimming of the thin film resistor progresses, 
       FIG. 9  is a waveform illustrating the increase in resistance of one of the thin film resistors of the integrated circuit of  FIG. 2  during a typical trimming of the resistance of the thin film resistor, 
       FIG. 10  is a top plan view of a thin film resistor according to another embodiment of the invention, 
       FIG. 11  is a transverse cross-sectional side elevational view of the thin film resistor of  FIG. 10  illustrated on a portion of an integrated circuit, 
       FIG. 12  is a top plan view similar to  FIG. 2  of a portion of an integrated circuit according to another embodiment of the invention comprising a plurality of compound thin film resistors also according to the invention, 
       FIG. 13  is a transverse cross-sectional side elevational view of the integrated circuit of  FIG. 12  on the line XIII-XIII of  FIG. 12 , 
       FIG. 14  is a transverse cross-sectional end elevational view of a portion of the portion of the integrated circuit of  FIG. 12  on the line XIV-XIV of  FIG. 12 , 
       FIG. 15  is a top plan view of one of the thin film resistors of the integrated circuit of  FIG. 12 , 
       FIG. 16  is a top plan view of a thin film resistor according to a further embodiment of the invention, 
       FIG. 17  is a side elevational view of the thin film resistor of  FIG. 16  illustrated on a portion of an integrated circuit, and 
       FIG. 18  is a top plan view of a thin film resistor according to another embodiment of the invention. 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION 
   Referring to the drawings, which are not to scale, and initially to  FIGS. 2 to 7 , there is illustrated a portion of an integrated circuit according to the invention, indicated generally by the reference numeral  1  which comprises a substrate  3  of silicon within which components (not shown) of the integrated circuit  1  are formed. An electrically insulating layer  4  of silicon dioxide is formed on the substrate  3 , and a plurality of thin film resistors also according to the invention, indicated generally by the reference numeral  5 , are formed on the insulating layer  4 , and extend parallel to each other. Since the invention relates to the thin film resistors  5 , other components of the integrated circuit  1  will not be described, however, such components will be well known to those skilled in the art, and will be appropriate to the particular integrated circuit. 
   Each thin film resistor  5  comprises an elongate resistive film  7  of an electrically resistive material which will be described in more detail below, and which extends longitudinally between a first end  8  and a second end  9 . The first end  8  and the second end  9  of each resistive film  7  are electrically coupled to first and second electrical contact pads  10  and  11 , respectively, and each resistive film  7  accommodates flow of electrical current between the corresponding pair of first and second contact pads  10  and  11 . Each resistive film  7  has a first or top major surface  14  and an opposite spaced apart second or bottom major surface  15  which extend between opposite spaced apart first and second side edges  16  and  17 , respectively. 
   An elongate low impedance element  20  is formed on and electrically coupled to the top major surface  14  of the resistive film  7  of each thin film resistor  5  intermediate the first and second ends  8  and  9 . Each low impedance element  20  extends along and defines an intermediate portion  22  of the resistive film  7  and conducts current in parallel with the corresponding intermediate portion  22  for reducing the current density of current flow in the intermediate portion  22  for facilitating trimming of the resistance of the thin film resistor  5  in the intermediate portion  22 , as will be described in more detail below. The low impedance element  20  of each thin film resistor  5  extends the length of the corresponding intermediate portion  22 , and extends longitudinally along and parallel to the second side edge  17  of the corresponding resistive film  7  with a first side edge  21  of the low impedance element  20  coinciding with the second side edge  17  of the resistive film  7 . Each low impedance element  20  is located on the corresponding resistive film  7  with a second side edge  23  thereof spaced apart from the first side edge  16  of the resistive film  7  for defining a trimmable portion in the intermediate portion  22 , as will be described below between the second side edge  23  of the low impedance element  20  and the first side edge  16  of the resistive film  7 . Each low impedance element  20  is essentially laminated with the corresponding resistive film  7 , and is in electrical contact with the resistive film  7  over the entire area of the resistive film  7  overlaid by the low impedance element  20 . Thus, the majority of the current being conducted through each resistive film  7  is carried by the corresponding low impedance element  20  in the area of the intermediate portion  22 , and the current density in the intermediate portion  22  is significantly less than in first and second portions  24  and  25 , respectively, of the resistive film  7 , which extend between the intermediate portion  22  and the first and second ends  8  and  9 , respectively. 
   Spaced apart first and second transverse edge forming slots  26  and  27 , respectively, extend inwardly into the resistive film  7  in the intermediate portion  22  of each thin film resistor  5  perpendicularly from the first side edge  16  towards the second side edge  17 , and terminate adjacent the second side edge  23  of the corresponding low impedance element  20 . The first and second transverse edge forming slots  26  and  27  form first and second transverse edges  28  and  29 , respectively, in the resistive films  7 . The first transverse edge  28  of each resistive film  7  defines with the first side edge  16  of the resistive film  7  and the second side edge  23  of the corresponding low impedance element  20  a first trimmable area  30  in the trimmable portion of the intermediate portion  22 . The second transverse edge  29  of each resistive film  7  defines with the first side edge  16  of the resistive film  7  and the second side edge  23  of the corresponding low impedance element  20  a second trimmable area  31  also in the trimmable portion of the intermediate portion  22 . The first and second trimmable areas  30  and  31  are of reduced current density for facilitating coarse and fine trimming of the thin film resistors  5 . Current density lines  32  in  FIGS. 5 and 7  illustrate the variation in current density in the first and second trimmable areas  30  and  31 . The current density progressively decreases in each of the first and second trimmable areas  30  and  31  from the corresponding low impedance element  20  to the first side edge  16  of the resistive film  7  in the intermediate portion  22 , and towards the corresponding one of the first and second transverse edges  28  and  29 . 
   In this embodiment of the invention coarse trimming is carried out in the first trimmable area  30 , and fine trimming is carried out in the second trimmable area  31 . The trimming is carried out by progressively extending first and second trimming slots  34  and  35  parallel to and spaced apart from the first side edge  16  into the first and second trimmable areas  30  and  31 , respectively, from the respective first and second transverse edges  28  and  29 , see  FIG. 7 . The trimming, in this embodiment of the invention, is carried out with a laser light trimming beam. Initially, the first trimming slot  34  is progressively extended from the first transverse edge  28  of the intermediate portion  22  of the thin film resistor  5  being trimmed into the first trimmable area  30  for coarse trimming of the thin film resistor  5 . The trimming of the first trimmable area  30  continues by progressively extending the first trimming slot  34  into the first trimmable area  30  until the resistance of the thin film resistor  5  is increased to a level just below the desired resistance. Thereafter, fine trimming is carried out by progressively extending the second trimming slot  35  into the second trimmable area  31  from the second transverse edge  29 . The second trimming slot  35  is progressively extended into the second trimmable area  31  until the resistance of the thin film resistor  5  is at the desired resistance value. 
   In this embodiment of the invention, since the fine trimming is carried out in the second trimmable area  31  of each thin film resistor  5 , the length of each second trimmable area  31  from the second transverse edge  29  in a direction towards the second end  9 , which is determined by the length l 2  of the corresponding low impedance element  20  from the second transverse edge  29  in the direction towards the second end  91  is longer than the length of the first trimmable area  30  from the first transverse edge  28  in a direction towards the first end  8 , which is determined by the length l 1  of the low impedance element  20  from the first transverse edge  28  in the direction towards the first end  8 . This, as will be described below, provides for higher resolution trimming in the second trimmable area  31  than in the first trimmable area  30 . 
   By virtue of the fact that each low impedance element  20  is electrically coupled to the corresponding resistive film  7  along the length of the intermediate portion  22 , the current density in the first and second trimmable areas  30  and  31  progressively decreases towards the corresponding first and second transverse edges  28  and  29 . Thus, as the first trimming slot  34  is progressively extended into the first trimmable area  30 , the increase in resistance of the thin film resistor  5  obtained per unit increase in the length of the first trimming slot  34  increases as the length of the first trimming slot  34  increases. Thus, the resolution of the trimming as the first trimming slot  34  is progressively extended into the first trimmable area  30  reduces. However by continuing the coarse trim in the first trimmable area  30  until the resistance of the thin film resistor  5  is increased to a value just below the desired resistance value, fine trimming can then be carried out in the second trimmable area  31  in the area towards the second transverse edge  29  where the current density is lowest, since only a small increase in the resistance of the thin film resistor  5  will be required from the fine trimming. Once the second trimming slot  35  extending into the second trimmable area  31  is relatively short relative to the length l 2  of the low impedance element  20  from the second transverse edge  29 , trimming in the second trimmable area  31  is carried out where the current density is relatively low, and thus the resolution of the fine trimming will be relatively high. This is described in more detail below with reference to  FIGS. 8 and 9 . 
   The longer the low impedance element  20  extends along the corresponding resistive film  7  from the first and second transverse edges  28  and  29  towards the first and second ends  8  and  9 , respectively, the lower will be the current density in the first and second trimmable areas  30  and  31  adjacent the first and second transverse edges  28  and  29 , and thus the higher will be the achievable trim resolution in the first and second trimmable areas  30  and  31  in the areas adjacent the first and second transverse edges  28  and  29 , respectively. However, before describing trimming of the thin film resistors  5  in further detail, the resistive films  7  and the low impedance elements  20  of the thin film resistors  5  will first be described in more detail. 
   The resistive film  7  of each thin film resistor  5 , as discussed above, is of an electrically resistive material, which in general will be determined by the desired resistance value of the thin film resistor  5 . However, typical electrically resistive materials are silicon-chrome, nickel-chrome and titanium-silicon, which may or may not be doped, and typically are deposited on the insulating layer  4  by a PVD or a CVD process. The material which is to form the resistive films  7  is deposited to a constant depth t 1  which is determined by the deposition process. Typically, the material is deposited to a depth to form the resistive films  7  of depth t 1  of up to 100 Angstroms, and more typically, of depth t 1  in the range of 20 to 50 Angstroms. Each resistive film  7  is of length L and width w 1 , both of which are largely dictated by the desired resistance value of the thin film resistors  5 . The width w 1  of such resistive films can vary anywhere from 0.1 micron to 36 microns, and even greater, although, more typically the width w 1  of such resistive films lies in the range of 1 micron to 36 microns. 
   The material of the low impedance element  20  of each thin film resistor  5  is of relatively high conductivity, and typically, of a few orders of magnitude higher than the conductivity of the material of the resistive film  7 , so that most of the current flowing through the thin film resistor  5  is conducted through the corresponding low impedance element  20 . In a typical preferred case the conductivity of the low impedance element  20  of each thin film resistor  5  is two orders of magnitude greater than the conductivity of the resistive film  7 . Additionally, the material of the low impedance elements  20  may have a higher resistance to the cutting effect of a laser light trimming beam than that of the resistive films  7 , in order to permit the thin film resistors  5  to be located more closely to each other, as will be described below. Materials with greater resistance to the cutting effect of a laser light trimming beam than the materials of the resistive films, which are suitable for the low impedance elements  20  are titanium-tungsten, titanium-nitride, tungsten, aluminium-silicon-copper, aluminium-silicon, aluminium-copper and aluminium. The material forming the low impedance elements  20  is deposited directly onto the top major surface  14  of the resistive films  7  of the thin film resistors  5  by a PVD or a CVD process. By forming the low impedance elements  20  directly onto the corresponding resistive films  7 , electrical contact is ensured between each low impedance element  20  and the corresponding resistive film  7  over the entire area of the resistive film  7  overlaid by the low impedance element  20 . 
   The low impedance elements  20  are deposited to a constant depth t 2 , which is determined by the deposition process. Each low impedance element  20  is of length l and width w 2 . The width w 2  of each low impedance element  20  is dictated by the conductivity required, as well as by the width w 1  of the corresponding resistive film  7 , in order that the corresponding first and second trimmable areas  30  and  31  are of width w 3 , which is sufficient to allow for trimming. Indeed, it is desirable that the width w 2  of each low impedance element is considerably less than the width w 1  of the corresponding resistive film  7  in order to form the first and second trimmable areas  30  and  31  to be of sufficient width w 3  to facilitate trimming of the first and second trimmable areas  30  and  31 . Additionally, by minimising the width w 2  of each low impedance element  20 , the overall width w 1  of the corresponding resistive film  7  can be minimised. The length l of each low impedance element  20  is dictated by the trimming resolution required and the spacing between the first and second trim slots  34  and  35 . The length l 1  of each low impedance element  20  from the first transverse edge  28  along the first trimmable area  30 , and the length l 2  of each low impedance element  20  from the second transverse edge  29  along the second trimmable area  31  are dictated by the trim resolution required, the longer the lengths l 1  and l 2  of the low impedance element  20 , the higher will be the trim resolution and the greater will be the trim range. In this embodiment of the invention as discussed above, since coarse trimming is being carried out in the first trimmable area  30  of each thin film resistor  5 , and fine trimming is being carried out in the second trimmable area  31  of each thin film resistor  5 , the length l 2  of each low impedance element  20  is longer than its length l 1 . 
   Ends  33  of each low impedance element  20  are shaped in order to minimise current crowding in the corresponding resistive film  7  adjacent the ends  33 . In this embodiment of the invention the shaping is carried out by chamfering the ends  33  of each low impedance element  20  inwardly towards each other from the first side edge  21  of the low impedance element  20 , which is adjacent the second side edge  17  of the corresponding resistive film  7  towards the second side edge  23  of the low impedance element  20  at an angle relative to the first side edge  21  of the low impedance element  20  of approximately 45°, although the chamfer angle may lie in the range from just greater than 0° to just less than 90°. 
   The first and second transverse edge forming slots  26  and  27  are etched in the resistive films  7  of the thin film resistors  5  at a suitable time in the forming process of the thin film resistors  5  by a suitable etching process, which will be well known to those skilled in the art. 
   Referring now in particular to  FIG. 6 , a representation of the trim spot  36  of a laser light beam directed onto the intermediate portion  22  of the resistive film  7  of one of the thin film resistors  5  for trimming thereof is illustrated. The trim spot  36  has a high energy centre spot  371  which is the active part of the trim spot  36  for cutting the respective first and second trim slots  34  and  35 , and an outer low energy halo  38  extending around the high energy centre spot  37 . Typically, the high energy centre spot  37  is of diameter in the range 3 microns to 5 microns and the outer diameter of the halo  38  of the trim spot  36  is approximately 7.5 microns. The width w 4  of the first and second trimming slots  34  and  35  formed by the high energy centre spot  37  is approximately 3 microns to 5 microns also. The trimming is carried out in the first and second trimmable areas  30  and  31  by progressively extending the first and second trimming slots  34  and  35  into the first and second trimmable areas  30  and  31 , respectively, in incremental steps of 0.1 microns in a general longitudinal direction from the corresponding first and second transverse edges  28  and  29  substantially parallel to the first side edge  16  of the resistive film  7 . By extending the first and second trimming slots  34  and  35  into the first and second trimmable areas  30  and  31  parallel to the first side edge  16  of the corresponding resistive film  7 , the width w 3  of the first and second trimmable areas  30  and  31  can be minimised, and in turn the overall width w 1  of the resistive film  7  can be minimised. 
   The first and second transverse edge forming slots  26  and  27  form therebetween a focusing area  40  in the intermediate portion  22  of each of the thin film resistors  5 , within which the high energy centre spot  37  of the laser light trimming beam can be focused and aligned prior to forming the first and second trimming slots  34  and  35  in the first and second trimmable areas  30  and  31 , respectively, of the thin film resistor  5  to be trimmed. The first and second transverse edge forming slots  26  and  27  should be sufficiently spaced apart so that the distance between the first and second transverse edges  28  and  29  is sufficient for facilitating focusing of the laser light trimming beam in the focusing area  40  and alignment of laser light trimming beam with the first and second trimmable areas  30  and  31  prior to commencement of cutting of the first and second trimming slots  34  and  35 . The focusing area  40  has little or no effect on the resistance of the thin film resistor  5 , and thus may be burned off during focusing of the laser light trimming beam. 
   Where the low impedance elements  20  are of a material which is more tolerant of the cutting effect of the laser light trimming beam than the material of the resistive films  7 , and the thin film resistors  5  are located and oriented with the low impedance elements  20  of each thin film resistor  5  adjacent the first and second trimmable areas  30  and  31  of the adjacent thin film resistor  5 , the thin film resistors  5  can be located particularly closely together without risk of damaging a thin film resistor while an adjacent thin film resistor is being trimmed. Even if the laser light trimming beam is not altogether accurately aligned with the first and second trimmable areas  30  and  31  of the thin film resistor  5  being trimmed, and the laser light trimming beam were to encroach on the adjacent thin film resistor  5 , the laser light trimming beam would fall on an adjacent portion of the low impedance element  20  of the adjacent thin film resistor  5 , and since the low impedance element  20  is more tolerant of the cutting effect of the laser light trimming beam than the material of the resistive film  7 , no damage would result to the thin film resistor  5  adjacent the first and second trimmable areas  30  and  31  of the adjacent thin film resistor  5  being trimmed. Accordingly, by forming the low impedance elements  20  of material of greater resistance to the cutting effect of the laser light trimming beam than that of the material of the resistive films  7 , the thin film resistors  5  can be located relatively closely together, and closer together than if the low impedance elements  20  were of a material which was not more tolerant of the cutting effect of the laser light trimming beam than that of the material of the resistive films  7 . However, even where the low impedance elements  20  are not of a material which is more tolerant of the cutting effect of the laser light trimming beam than that of the material of the resistive films  7 , the thin film resistors according to the invention can still be located considerably more closely together than many thin film resistors known heretofore. 
   In fact, in practice it has been found that in an integrated circuit having a fourteen-bit, seven-segment DAC implemented in R2R configuration where the resistors are implemented as thin film resistors according to the invention with the low impedance elements being of a material not being more tolerant of the cutting effect of the laser light trimming beam than the resistive films, the die area requirement for the thin film resistors is 400 microns by 273 microns. This compares with a die area requirement of 1,100 microns by 400 microns using prior art tab type thin film resistors of the type illustrated in  FIG. 1 . However, by implementing the DAC with thin film resistors according to the invention with the low impedance elements of material which is more tolerant of the cutting effect of the laser light trimming beam than the material of the resistive films, the die area requirement for the thin film resistors is further reduced to an area of 224 microns by 181 microns. Thus, the die area reduction achieved by using the thin film resistors according to the invention with the low impedance elements of material which is more tolerant of the cutting effect of the laser light trimming beam than the material of the resistive films, results in a very significant 91% reduction in the die area requirement. Even when the low impedance elements are of a material which is not more tolerant of the cutting effect of the laser light trimming beam than the material of the resistive films, the thin film resistors according to the invention result in a significant 75% reduction in the die area requirement. 
   Referring now to  FIG. 8 , there is illustrated a waveform A showing how the resistance of one of the thin film resistors  5  progressively increases per unit increase in the length of the first trimming slot  34  as the length of the first trimming slot  34  is progressively increased in the first trimmable area  30 . Resistance in ohms is plotted on the Y-axis, while the length of the first trimming slot  34  from the first transverse edge  28  into the first trimmable area  30  in microns is plotted on the X-axis. Initially, the increase in resistance of the thin film resistor  5  per unit increase in the length of the first trimming slot  34  is relatively low for the first 4 microns, approximately, of the first trimming slot  34  from the first transverse edge  28 . However, thereafter the increase in the resistance obtained from each unit increase in the length of the first trimming slot  34  progressively increases as the length of the first trimming slot  34  increases at a considerably more rapid rate. Thus, as the length of the first trimming slot  34  increases from the first transverse edge  28 , the resolution of the trim decreases per unit increase in the length of the first trimming slot  34 . However, while the trim resolution decreases per unit increase in the length of the first trimming slot  34 , the trim resolution is relatively high for the first 4 microns approximately of the first trimming slot  34 . Thereafter, however, the rate of decrease in the trim resolution is more rapid as the length of the first trimming slot  34  is increased. 
   Since the length l 2  of the portion of the low impedance element  20  extending along the second trimmable area  31  of each thin film resistor  5  is greater than the length l 1  of the portion of the low impedance element  20  extending along the first trimmable area  30 , the trim resolution achievable by the second trimming slot  35  in the second trimmable area  31  is higher per unit length of the second trimming slot  35  from the second transverse edge  29 , micron for micron, compared with the trim resolution achievable by the first trimming slot  34  in the first trimmable area  30  from the first transverse edge of each thin film resistor  5 . 
   Accordingly, by using the first trimming slot  34  to coarse trim each thin film resistor  5  by extending the first trimming slot  34  into the first trimmable area  30  to a length which raises the resistance of the thin film resistor  5  to a level just below the desired resistance value, even if the coarse trimming requires extending the first trimming slot  34  to a length greater than 6 microns, coarse trimming can still be achieved by extending the first trimming slot  34  to a length up to approximately 9 microns to 10 microns from the first transverse edge  28 , see  FIG. 8 . Thereafter, fine trimming can then be carried out by extending the second trimming slot  35  into the second trimmable area  31  from the second transverse edge  29 . If the coarse trimming has raised the resistance of the thin film resistor  5  to just below the desired resistance value, fine trimming in the second trimmable area  31  should be achieved within the first 5 microns of length of the second trimming slot  35 , thereby permitting the fine trimming to be carried out with relatively high resolution. 
   Referring now to  FIG. 9 , a waveform B illustrates the increase in the resistance during trimming of a typical one of the thin film resistors  5 . The portion B 1  of the waveform B represents the coarse trimming, while the portion B 2  of the waveform B represents the fine trimming. Initially coarse trimming of the thin film resistor  5  is carried out in the first trimmable area  30  by progressively extending the first trimming slot  34  into the first trimmable area  30  until the resistance of the thin film resistor  5  is just below the desired resistance value. In this case, the first trimming slot  34  is extended into the first trimmable area  30  for a length of almost 8 microns. Fine trimming is then carried out in order to bring the resistance value of the thin film resistor  5  up to the desired resistance value. This is carried out by extending the second trimming slot  35  into the second trimmable area  31  until the resistance value of the thin film resistor  5  is of the desired value. In this particular case, the second trimming slot is extended into the second trimmable area  31  a distance of approximately 4 microns. 
   As can be seen from the portion B 2  of the waveform B, the increase in the resistance of the thin film resistor  5  obtained per unit increase in the length of the second trimming slot  35  progressively increases as the length of the second trimming slot  35  is increased. However, the rate of increase in the resistance of the thin film resistor  5  obtained per unit increase in the length of the second trimming slot  35  as the length of the second trimming slot  35  is increased, is considerably less than the rate of increase in the resistance of the thin film resistor  5  obtained per unit increase in the length of the first trimming slot  34  as the first trimming slot  34  is increased. This results from the fact that the length l 2  of the low impedance element  20  extending from the second transverse edge  29  along the second trimmable area  31  is greater than the length l 1  of the low impedance element  20  extending from the first transverse edge  28  along the first trimmable area  30 . By virtue of the fact that the rate of increase in the resistance of the thin film resistor  5  obtained per unit increase in the length of the second trimming slot  35  as the length of the second trimming slot  35  is increased, is less than the corresponding rate of increase in the resistance of the thin film resistor  5  as the length of the first trimming slot  34  is increased, higher trim resolution is provided in the second trimmable area  31  than in the first trimmable area  30 . 
   Referring now to  FIGS. 10 and 11 , there is illustrated a thin film resistor according to another embodiment of the invention, indicated generally by the reference numeral  50 . The thin film resistor  50  is substantially similar to the thin film resistor  5  described with reference to  FIGS. 2 to 9 , and similar components are identified by the same reference numerals. The thin film resistor  50  is illustrated in  FIG. 11  on an insulating layer  4  similar to that of the integrated circuit  1  of  FIGS. 2 to 7 . The main difference between the thin film resistor  50  and the thin film resistors  5  is that the width of the resistive film  7  over its length from the first end  8  to the second end  9  is not constant. The first portion  24  of the resistive film  7  which extends from the intermediate portion  22  to the first end  8  comprises an elongated first narrow strip  51  of width w′ 1  which extends from the first end  8  to a first wider portion  52  also of the first portion  24 , which in turn terminates in the intermediate portion  22 . The first wider portion  52  is of width w 1  which is similar to the width of the intermediate portion  22 . Similarly, the second portion  25  of the resistive film  7  comprises a second narrow strip  53  extending from the second end  9  to a second wider portion  54  which terminates in the intermediate portion  22 . The widths w′ 1  of the first and second narrow strips  51  and  53  are similar, and increase progressively towards the corresponding first and second wider portions  52  and  54  at  55  and  56 , respectively, in order to prevent current crowding as the current passes between the first and second narrow strips  51  and  53  and the corresponding first and second wider portions  52  and  54 . The lengths of the narrow strips  51  and  53  may be any desired length, and may be longer or shorter, but typically longer than the corresponding wider portions  52  and  54 , and both the length and the width w′ 1  of the first and second narrow strips  51  and  53  will be dictated by the desired resistance value of the thin film resistor  50 . 
   The first and second narrow strips  51  and  53  and the first and second wider portions  52  and  54 , as well as the intermediate portion  22  of the resistive film  7 , are formed simultaneously by a PVD or CVD process as a single one-piece resistive film  7  of constant depth t 1 . The low impedance element  20  is deposited by a PVD or CVD process on top of the resistive film  7  and extends between the first and second portions  24  and  25  of the resistive film  7  to define the intermediate portion  22 , and is electrically coupled over its entire area with the top major surface  14  of the resistive film  7  as already described with reference to the thin film resistors  5  of  FIGS. 2 to 9 . 
   Otherwise, the thin film resistor  50  is similar to the thin film resistor  5 , and trimming of the thin film resistor  50  is likewise similar, whereby coarse trimming is carried out by extending a first trimming slot into the first trimmable area  30  from the first transverse edge  28 , and fine trimming is carried out by extending a second trimming slot into the second trimmable area  31  from the second transverse edge  29 . 
   Referring now to  FIGS. 12 to 15 , there is illustrated a portion of an integrated circuit also according to the invention, indicated generally by the reference numeral  60 . The integrated circuit  60  comprises a silicon substrate  61 , a portion of which is illustrated in  FIG. 13 , and an electrically insulating layer  62  of silicon dioxide on top of the silicon substrate  61 . A plurality of compound thin film resistors also according to the invention, indicated generally by the reference numeral  65 , are formed on the insulating layer  62 , three of which compound thin film resistors  65  are illustrated in  FIG. 12 . Each compound thin film resistor  65  is formed by a pair of thin film resistors  66   a  and  66   b  also according to the invention, which are electrically coupled in series between corresponding first and second electrical contact pads  67  and  68 . The thin film resistors  66  are somewhat similar to the thin film resistors  5  of  FIGS. 2 to 7 , and similar components are identified by the same reference numerals. The thin film resistors  66  of each compound thin film resistor  65  are electrically coupled in series between the corresponding first and second electrical contact pads  67  and  68  by a low impedance element  70 , which forms the low impedance elements  20  of the thin film resistors  66  of each compound thin film resistor  65 . 
   The main difference between the thin film resistors  66  and the thin film resistors  5  of  FIGS. 2 to 7  is that the low impedance element  20  of each thin film resistor  66 , while located intermediate the first and second ends  8  and  9  of the resistive film  7 , is located adjacent the second end  9  of the resistive film  7  rather than being spaced apart from the second end  9 , as in the case of the thin film resistors  5 . Thus, in this embodiment of the invention the second end  9  of the resistive film  7  of each thin film resistor  66  forms the first transverse edge  28  of the intermediate portion  22 . The intermediate portion  22  of each thin film resistor  66 , while being located intermediate the first and second ends  8  and  9  of the corresponding resistive film  7 , is located adjacent the second end  9  of the resistive film  7 . Accordingly, each thin film resistor  66  is provided with only one trimmable area, namely, a first trimmable area  71 , which is similar to the first trimmable area  30  of the thin film resistors  5 , and which is defined between the first side edge  16  of the resistive film  7 , the first transverse edge  28  and the second side edge  23  of the corresponding low impedance element  20  in the corresponding intermediate portion  22 . 
   In this case, the first end  8  of the thin film resistor  66   a  of each compound thin film resistor  65  is coupled to the corresponding first electrical contact pad  67 , while the first end  8  of the thin film resistor  66   b  of each compound thin film resistor  65  is coupled to the corresponding second electrical contact pad  68 . 
   Accordingly, since the thin film resistors  66   a  and  66   b  of each compound thin film resistor  65  each comprises a first trimmable area  71 , the compound thin film resistors  65  can be subjected to coarse and fine trimming by carrying out coarse trimming in the first trimmable area  71  of the thin film resistor  66   a  and fine trimming in the first trimmable area  71  of the thin film resistor  66   b , or vice versa. Trimming of the first trimmable areas  71  is carried out in similar fashion to that described with reference to the thin film resistor  5  of  FIGS. 2 to 7 . Where the first trimmable area  71  of the thin film resistor  66   a  is to be provided for coarse trimming, and the first trimmable area  71  of the thin film resistor  66   b  is to be provided for fine trimming, in general, the length l 2  of the low impedance element  20  extending from the second end  9  of the thin film resistor  66   b  along the first trimmable area  71  thereof will be longer than the length l 1  of the low impedance element  20  extending from the second end  9  of the thin film resistor  66   a  along the first trimmable area  71  thereof, in order to provide higher trim resolution in the thin film resistor  66   b.    
   While the thin film resistors  66  have been described as forming compound thin film resistors  65 , it will be readily apparent to those skilled in the art that each thin film resistor  66  could form a single thin film resistor in its own right, and in which case, it is envisaged that the first end of the thin film resistor  66  would be electrically coupled to a first contact pad, and the second end of the thin film resistor  66  would be coupled to a second contact pad by a portion of the low impedance element  20  extending beyond the second end of the thin film resistor  66 . 
   Referring now to  FIGS. 16 and 17 , there is illustrated a thin film resistor  80  according to another embodiment of the invention. The thin film resistor  80  is substantially similar to the thin film resistor  5  of  FIGS. 2 to 7 , and similar components are identified by the same reference numerals. The thin film resistor  80  is illustrated in  FIG. 17  on an insulating layer  4 , which is similar to that the integrated circuit  1  of  FIGS. 2 to 7 . In this embodiment of the invention, the thin film resistor  80  is provided with two low impedance elements, namely, a first low impedance element  81  and a second low impedance element  82 , both of which are located on the resistive film  7  intermediate the first and second ends  8  and  9 , respectively, thereof. The first low impedance element  81  is located adjacent the first end  8  of the resistive film  7 , and defines a first intermediate portion  83  of the resistive film  7 , which is similar to the intermediate portion  22  of the thin film resistor  5 . The second low impedance element  82  is located adjacent the second end  9  of the resistive film  7 , and defines a second intermediate portion  84  of the resistive film  7 , which is also similar to the intermediate portion  22  of the thin film resistor  5 . 
   A first transverse edge forming slot  85  similar to the first transverse edge forming slot  26  extends into the first intermediate portion  83  for forming a first transverse edge  28 . A second transverse edge forming slot  86  extends into the second intermediate portion  84  for forming a second transverse edge  29 . The first transverse edge  28  defines with the first side edge  16  of the resistive film  7  and the second side edge  23  of the first low impedance element  81  a first trimmable area  87 , while the second transverse edge  29  defines with the first side edge  16  of the resistive film  7  and the second side edge  23  of the second low impedance element  82 , a second trimmable area  88 . The first and second trimmable areas  87  and  88  are substantially similar to the first and second trimmable areas  30  and  31  of the thin film resistor  5 , and in this embodiment of the invention, the first low impedance element  81  extends for a length l 1  from the first transverse edge  28  along the first trimmable area  87 , which is shorter than the length l 2  that the second low impedance element  82  extends from the second transverse edge  29  along the second trimmable area  88 . Accordingly, the first trimmable area  87  is suitable for coarse trimming the resistance of the thin film resistor  80 , while the second trimmable area  88  is suitable for fine trimming the resistance of the thin film resistor  80 . 
   The first and second transverse edge forming slots  85  and  86  define with the adjacent first and second ends  8  and  9 , respectively, first and second focus areas  90  and  91 , respectively, for facilitating focusing of the laser light trimming beam prior to forming the first and second trimming slots  34  and  35  in the first and second trimmable areas  87  and  88 , respectively. 
   The thin film resistor  80  is electrically coupled to the first and second contact pads  10  and  11  by the first and second low impedance elements  81  and  82 , respectively. 
   The resistive film  7  and the first and second low impedance elements  81  and  82  are of similar materials and are formed by similar processes to those of the resistive film  7  and the low impedance element  20  of the thin film resistor  5 . The first and second low impedance elements  81  and  82  are deposited directly onto the resistive film  7  and are in direct electrical contact with the resistive film  7  in the area of the resistive film  7  overlaid by the respective first and second low impedance elements  81  and  82 . 
   Otherwise, the thin film resistor  80  is similar to the thin film resistor  5 , and trimming of the resistance of the thin film resistor  80  is carried out in similar fashion to that described with reference to  FIGS. 2 to 9 . Coarse trimming of the thin film resistor  80  is carried out by progressively extending the first trimming slot  34  from the first transverse edge  28  into the first trimmable area  87  until the resistance value of the thin film resistor  80  is just below the desired value, and then fine trimming is carried out by progressively extending the second trimming slot  35  from the second transverse edge  29  into the second trimmable area  88  until the resistance of the thin film resistor  80  is at the desired value. 
   Referring now to  FIG. 18 , there is illustrated a thin film resistor  95  according to another embodiment of the invention. The thin film resistor  95  is substantially similar to the thin film resistor  5  described with reference to  FIGS. 2 to 7 , and similar components are identified by the same reference numerals. The only difference between the thin film resistor  95  and the thin film resistor  5  is in the intermediate portion  22 . In this embodiment of the invention, the first and second transverse edge forming slots  26  and  27  in the intermediate portion  22  which form the transverse edges  28  and  29  have been omitted. Accordingly, the low impedance element  20  defines with the first side edge  16  of the resistive film  7  a single trimmable area  96  in the intermediate portion  22 . 
   Trimming of the thin film resistor  95  is carried out by initially focusing the laser light trimming beam in the trimmable area  96  at a position intermediate the ends  33  of the low impedance element  20 . In order to facilitate coarse and fine trimming of the thin film resistor  95 , the focusing of the laser light trimming beam should be carried out at a position offset from the midpoint of the low impedance element  20  between the ends  33  thereof. For example, at a position represented by the chain line  97 , which is closer to the end  33   a  of the low impedance element  20  than to the end  33   b  of the low impedance element  20 . Coarse trimming is then carried out by advancing the first trimming slot  34  from the chain line  97  in the direction of the arrow D in the trimmable area  96  towards the end  33   a , until the resistance of the thin film resistor  95  is just below the desired resistance value. Fine trimming of the thin film resistor  95  is carried out by advancing the second trimming slot  35  from the chain line  97  in the direction of the arrow E in the trimmable area  96  towards the end  33   b  until the resistance value of the thin film resistor  95  is at the desired value. 
   Otherwise, the thin film resistor  95  and its trimming is similar to that of the thin film resistor  5  described with reference to  FIGS. 2 to 9 . 
   While the low impedance elements of the thin film resistors described with reference to  FIGS. 2 to 9 ,  FIGS. 10 and 11 ,  FIGS. 12 to 15 ,  FIGS. 16 and 17 , and  FIG. 18  have been described as overlaying the corresponding resistive film or films, in certain cases, it is envisaged that the low impedance elements may be located to one side of the resistive film or films and adjacent thereto, although an advantage of overlaying the low impedance elements on the resistive film or films is that the die area required for the thin film resistors is minimised. Additionally, where the low impedance elements are of a material which is more tolerant of the cutting effect of the laser light trimming beam than the material of the resistive film, a further reduction in die area can be achieved, since the thin film resistors can be located more closely to each other. 
   While the thin film resistors described with reference to  FIGS. 2 to 9 ,  FIGS. 10 and 11 , and  FIGS. 16 and 17  have been described as having the first and second transverse edges being formed by respective first and second transverse edge forming slots extending from the first side edge into the resistive film, in certain cases, it is envisaged that the entire area of the resistive film bounded by the first and second transverse edge forming slots and the low impedance element may be removed by etching or otherwise. However, an advantage of forming the first and second transverse edges by the first and second transverse edge forming slots is that a more accurate and true transverse edge is obtained when the first and second transverse edges are formed by corresponding first and second transverse edge forming slots, rather than by completely removing the portion of the resistive film bounded by the first and second transverse edge forming slots and the low impedance element. 
   While the thin film resistors according to the invention have been described as being formed on integrated circuits of particular materials, the thin film resistors may be formed on any integrated circuit, or indeed any other suitable substrate. Needless to say, while particular ranges of widths and thicknesses and types of materials of the resistive films and the low impedance elements have been described, any other suitable widths, thicknesses and materials may be selected in the formation of the resistive films and the low impedance elements. 
   Additionally, while the film resistors according to the invention have been described as being thin film resistors, the film resistors may be thick film resistors, which may be formed on integrated circuits, or indeed may be of the type formed on printed circuit boards, or on other substrates. 
   While the ends of the low impedance elements have been described as being chamfered for avoiding current crowding adjacent the ends of the low impedance elements, while this is desirable, it is not essential, and furthermore, the ends of the low impedance elements may be otherwise shaped for avoiding current crowding, for example, they may be rounded by radiusing, or the like. 
   Needless to say, coarse trimming of each thin film resistor described with reference to  FIGS. 2 to 9 ,  FIGS. 10 and 11 , and  FIGS. 16 and 17  could be carried out in the second trimmable area and fine trimming could be carried out in the first trimmable area. 
   While the low impedance elements have been described as being located on the resistive films with the first side edge of each low impedance element coinciding with the second side edge of the corresponding resistive film, while this is preferable, it is not essential. For example, the low impedance elements may be located or the resistive films with the first side edge of each low impedance element spaced apart from the second side edge of the corresponding resistive film. However, by locating the low impedance elements with the first side edge of each low impedance element coinciding with the second side edge of the corresponding resistive film, the width of the trimmable area or areas defined between the first side edge of the resistive film and the second side edge of the low impedance element is maximised, thereby minimising the width of the resistive films required at the intermediate portion or portions thereof. However, it is envisaged in certain cases that the low impedance element of each thin film resistor may be located intermediate the first and second side edges of the corresponding resistive film. In which case, trimmable areas may be provided on the respective opposite sides of the low impedance element between the low impedance element and the first side edge of the corresponding resistive film, and the low impedance element and the second side edge of the corresponding resistive film. 
   While the low impedance element of the thin film resistors described with reference to  FIGS. 2 to 7  and  FIGS. 10 and 11  have been described with the portion of the low impedance element extending along the first trimmable area being of length less than the length of the portion of the low impedance element extending along the second trimmable area, in certain cases, it is envisaged that the length of the portion of the low impedance element extending along the first trimmable area may be of similar length to the length of the portion of the low impedance element extending along the second trimmable area. In which case, the trim resolution which would be achievable in each of the first and second trimmable areas would be substantially similar. However, by raising the resistance of the thin film resistor to a level just below the desired resistance during coarse trimming in the first trimmable area, a relatively short second trimming slot in the second trimmable area should be sufficient in order to raise the resistance of the thin film resistor to the desired level, and thus fine trimming in the second trimmable area would be carried out in an area adjacent the second transverse edge with relatively high resolution. Similarly, in the thin film resistors described with reference to  FIGS. 12 to 15  and  FIGS. 16 and 17 , the length of the respective low impedance elements could be substantially similar.