Abstract:
A self-reparable semiconductor comprises M functional units each including N sub-functional units. Corresponding ones of the N sub-functional units in each of the M functional units perform the same function. At least two of the N sub-functional units in one of the M functional units perform different functions. A first spare functional unit includes X sub-functional units, wherein X is greater than or equal to one and less than or equal to N and wherein the X sub-functional units of. the first spare functional unit are functionally interchangeable with corresponding sub-functional units of the M functional units and wherein the X sub-functional units are provided for the at least two of the N sub-functional units. A plurality of switching devices replace at least one of the N sub-functional units with at least one of the X sub-functional units when the at least one of the N sub-functional units is non-operable.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is a divisional of U.S. patent application Ser. No. 10/358,709 filed on Feb. 5, 2003, which application claims the benefit of U.S. Provisional Application No. 60/430,199, filed on Dec. 2, 2002. The disclosures of the above applications are incorporated herein by reference. 

   FIELD OF THE INVENTION 
   The present invention relates to semiconductors, and more particularly to a self-reparable semiconductor with multiple functional units that perform the same function. 
   BACKGROUND OF THE INVENTION 
   An increasing trend in the semiconductor industry is to highly integrate an integrated circuit multiple times. For example, the semiconductor may include multiple generally independent functional units that perform the same function. Each functional unit has the same sub-functional units. 
   Referring now to  FIG. 1 , a semiconductor  8  includes M generally independent functional units  10 - 1 ,  10 - 2 , . . . , and  10 -M (collectively referred to as functional units  10 ) that perform the same high level function. Each functional unit  10  includes the same N sub-functional units. For example, the functional unit  10 - 1  includes sub-functional units  11 ,  21 ,  31 , . . . , and N 1 . The functional unit  10 - 2  includes sub-functional units  12 ,  22 ,  32 , . . . , and N 2 . The functional unit  10 -M includes sub-functional units  1 M,  2 M,  3 M, . . . , and NM. The sub-functional units in a row perform the same low level function. Typically, there are no connections between the functional units other than ground and power. There are, however, connections between the sub-functional units in a functional unit. The connections may be one-way or two-way and may include one or more connecting wires. 
   Referring now to  FIG. 2 , an exemplary functional unit may be a Gigabit physical layer device  70 . For example, four or eight Gigabit physical layer devices may be fabricated on the semiconductor. The physical layer device  70  includes a first sub-functional unit  74  that performs physical coding sub-layer (PCS), Flow Control Token (FCT), and Decision Feedback Sequence Estimation (DFSE) functions. A second sub-functional unit  76  implements a finite impulse response (FIR) filter function. A third sub-functional unit  78  performs echo and near end crosstalk (NEXT) functions. Fourth and fifth sub-functional units  80  and  84  implement digital and analog front end (AFE) functions, respectively. 
   If the yield for each individual functional unit is 90%, then the yield for the semiconductor with x identical functional units is (0.9) x . For example, if a semiconductor includes eight functional units each having a yield of 90%, the yield of the semiconductor is 43%, which is not an acceptable yield. 
   SUMMARY OF THE INVENTION 
   A self-reparable semiconductor according to the invention includes a first functional unit with first and second sub-functional units that cooperate to perform a first function. A second functional unit includes first and second sub-functional units that also cooperate to perform the first function. A first spare functional unit includes first and second sub-functional units. The first sub-functional units of the first, second and first spare functional units are functionally interchangeable. The second sub-functional units of the first, second and first spare functional units are functionally interchangeable. Switching devices communicate with the first and second sub-functional units of the first, second and first spare functional units and replace at least one of the first and second sub-functional units of at least one of the first and second functional units with at least one of the first and second sub-functional units of the first spare functional unit when the at least one of the first and second sub-functional units is non-operable. 
   In other features, a controller identifies non-operable sub-functional units and operates the switching devices to replace the non-operable sub-functional units. 
   In still other features, the first and second functional units are laid out in one of columns and rows and the first and second sub-functional units of the first and second functional units are laid out in the other of columns and rows. 
   In other features, the spare functional unit is located one of between the first and second functional units and next to one of the first and the second functional units. 
   In yet other features, a second spare functional unit includes first and second sub-functional units. The first sub-functional units of the first, second, first spare and second spare functional units are functionally interchangeable. The second sub-functional units of the first, second, first spare and second spare functional units are functionally interchangeable. 
   In still other features, the first, second, first spare and second spare functional units are laid out in one of columns and rows and the first and second sub-functional units of the first, second, first spare and second spare functional units are laid out in the other of columns and rows. The first and second sub-functional units of the first and second spare functional units and the switching devices are capable of replacing two non-operable sub-functional units that perform the same function and that are located in one of the same row and the same column. 
   In yet other features, at least one of the switching devices includes a multiplexer that receives p inputs and outputs q outputs where q is less than p. A demultiplexer receives q inputs and outputs p outputs. A switch selectively connects the q outputs of the multiplexer to the p inputs of the demultiplexer. 
   Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein: 
       FIG. 1  is a functional block diagram of a semiconductor including multiple functional units each with sub-functional units according to the prior art; 
       FIG. 2  is a functional block diagram of an exemplary functional unit for a Gigabit physical layer device according to the prior art; 
       FIG. 3A  is a functional block diagram of an on-chip controller that commands the switching devices and optionally includes a test/fault detection circuit; 
       FIG. 3B  is a functional block diagram of an off-chip controller that commands the switching devices and optionally includes a test/fault detection circuit; 
       FIG. 4  is a functional block diagram of a first exemplary self-reparable semiconductor including a spare functional unit that replaces a non-operable functional unit according to the present invention; 
       FIG. 5  is a functional block diagram of a second exemplary self-reparable semiconductor with a spare functional unit that replaces one or more non-operable sub-functional units according to the present invention; 
       FIG. 6  is a functional block diagram of a third exemplary self-reparable semiconductor including a spare functional unit located at one end according to the present invention; 
       FIG. 7  is a functional block diagram of a fourth exemplary self-reparable semiconductor including a partial spare functional unit according to the present invention; 
       FIG. 8  is a functional block diagram of a fifth exemplary self-reparable semiconductor including two partial spare functional units located in the middle according to the present invention; 
       FIG. 9  is a functional block diagram of a sixth exemplary self-reparable semiconductor including two partial spare functional units located at one end according to the present invention; 
       FIG. 10  is a functional block diagram of a seventh exemplary self-reparable semiconductor including a partial spare functional unit and multiplexed switching devices according to the present invention; 
       FIG. 11  is a functional block diagram of an eighth exemplary self-reparable semiconductor including multiple functional units each with sub-functional units, two partial spare functional units and multiplexed switching devices according to the present invention; and 
       FIG. 12  is a flowchart illustrating steps for replacing non-operable sub-functional units with sub-functional units in a single spare functional unit. 
       FIG. 13  is an example of a summing node switch. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. For purposes of clarity, the same reference numbers will be used in the drawings to identify similar elements. 
   A self-reparable semiconductor according to the present invention includes one or more full or partial spare functional units. If a defect in a functional unit or a sub-functional unit is detected, then that functional unit or sub-functional unit is switched out and replaced with a functional unit or sub-functional unit in the full or partial spare functional unit. The reconfiguration is realized with switching devices that may be integrated with or separate from the functional or sub-functional units. 
   Defective functional or sub-functional units can be detected after assembly, during power up, periodically during operation, and/or manually. While the present invention will be described in conjunction with specific examples, skilled artisans will appreciate that each semiconductor may include any number of functional units that perform the same high-level function. The functional units may include any number of common sub-functional units. 
   In addition, while specific switching devices and arrangements are shown, the specific switching devices and arrangements that will be used will depend upon the particular implementation, details of the particular functional and/or sub-functional units and other normal design criteria. Similar or different types of switching devices may be used on the same semiconductor to replace the non-operable functional and/or sub-functional units. When the connecting wires between subfunctional units carry analog signals, analog switching is performed which preferably employs current-switching devices, generally for analog output signals and summing node switching for analog input signals. Such switching devices have several advantages over voltage-based switching devices such as reduced attenuation, lower impedance and lower distortion.  FIG. 13  shows an example of summing node switching. Summing node switching provides for input analog signals, which may be greater than Vdd or negative. In contrast to voltage mode switching, voltage signals greater than Vdd or negative may cause the switching transistor to become forward biased. A further explanation of active summing devices may be found in commonly assigned application Ser. No. 09/629,092, filed Jul. 31, 2000 and entitled “Active Resistance Summer For A Transformer Hybrid”, the contents of which are incorporated herein by reference. 
   Digital switching devices may be employed for connecting wires carrying digital signals. These type of switches include for example, standard logic devices, gates, muxes, transistors and the like. 
   Referring now to  FIG. 3A , a semiconductor  86  of each of the embodiments can include a controller  88  that is located on-chip and that communicates with the switching devices  90  and the sub-functional units  92 . A test or fault identification circuit  94  identifies non-operable sub-functional units  92  and generates configuration data. The controller  88  commands the switching devices  90  to replace the non-operable sub-functional units  92  as previously described. The controller  88  may execute a built-in self test mode after assembly, during power up, periodically during operation, and/or manually. 
   Referring now to  FIG. 3B , a semiconductor  86  of each of the embodiments can include a controller  96  that is located off-chip and that is removably connected to on-chip memory  98 , such as non-volatile memory. The memory  98  stores configuration data defining switch positions for the switching devices  90 . The controller  96  is connected to the sub-functional units  92  and detects and/or tests for failures. The controller  96  uses the test results to define the configuration data that is then stored in the memory  98 . When powered on, the configuration data is used to configure the sub-functional units  92 . As can be appreciated, there are a variety of other ways to implement the switching devices. For example, fuses, such as laser fuses or anti-fuses, can be used to make and/or break connections to replace functional units and/or sub-functional units. External pins or dip switches can also be used. 
   Referring now to  FIG. 4 , a spare functional unit  10 -S is fabricated on a semiconductor  90  in addition to the functional units  10 - 1 ,  10 - 2 , . . . , and  10 - 6 . In addition, switching devices  94  are located at inputs and outputs of some or all of the sub-functional units. In the exemplary embodiment illustrated in  FIG. 3 , the spare functional unit  10 -S is located between the functional units  10 . As can be appreciated, however, the spare functional unit  10 -S can be located in any position on the semiconductor  100 . For example, the spare functional unit  10 -S can be located to the left or right of any of the functional units  10 . 
   The switching devices  94  and the spare functional unit  10 -S allow the semiconductor  90  to replace non-operable functional units  10 - 1 ,  10 - 2 ,  10 - 3 ,  10 - 4 ,  10 - 5  and/or  10 - 6 . In the example in  FIG. 4 , the spare functional unit  10 -S allows any number of sub-functional units in one functional unit to fail. By allowing the replacement of non-operable functional units, the yield of the semiconductor  90  is significantly improved. If one or any combination of the sub-functional units  11 ,  21 ,  31 , and/or  41  in the functional unit  10 - 1  fail (as shown by cross-hatched shading), the switches  94  are reconfigured to replace the non-operable sub-functional units  11 ,  21 ,  31 , and  41  with the sub-functional units in the spare functional unit  10 -S. 
   For example, if the sub-functional unit  11  is non-operable, the inputs  92 - 1 ,  92 - 2 , and  92 - 3  to the sub-functional units  11 ,  12 , and  13  are shifted one functional unit to the right by switches  94 - 1 ,  94 - 2 ,  94 - 3 , and  944 . The outputs  92 - 4 ,  92 - 5 , and  92 - 6  of the sub-functional units  42 ,  43 , and  4 S are shifted one functional unit to the left by switches  94 - 5 ,  94 - 6 ,  94 - 7 , and  94 - 8 . 
   After reconfiguration, the first functional unit  10 - 1  includes sub-functional units  12 ,  22 ,  32 , and  42 . The second functional unit  10 - 2  includes sub-functional units  13 ,  23 ,  33 , and  43 . The third functional unit  10 - 3  includes sub-functional units  1 S,  2 S,  3 S, and  4 S. The fourth functional unit  10 - 4  includes sub-functional units  14 ,  24 ,  34 , and  44 . The fifth functional unit  10 - 5  includes sub-functional units  15 ,  25 ,  35 , and  45 . The sixth functional unit  10 - 6  includes sub-functional units  16 ,  26 ,  36 , and  46 . This exemplary embodiment allows replacement on a functional unit basis only. 
   Referring now to  FIG. 5 , a spare functional unit  10 -S is fabricated on a semiconductor  100  in addition to the functional units  10 - 1 ,  10 - 2 , . . . , and  10 - 6 . In addition, switching devices  104  are located at inputs and outputs of the sub-functional units. In the exemplary embodiment illustrated in  FIG. 5 , the spare functional unit  10 -S is located between the functional units  10 . 
   The switching devices  104  and the spare functional unit  10 -S allow the semiconductor  100  to replace non-operable sub-functional units in the functional units  10 - 1 ,  10 - 2 ,  10 - 3 ,  10 - 4 ,  10 - 5  and/or  10 - 6 . In the example in  FIG. 5 , the spare functional unit  10 -S allows one sub-functional unit in each row to fail. By allowing the replacement of non-operable sub-functional units, the yield of the semiconductor  100  is significantly improved. This exemplary embodiment allows replacement on a functional unit or a sub-functional unit basis and/or replacement of multiple sub-functional units in different functional units. 
   If the sub-functional units  11 ,  31  and  26  fail (as shown in shading), the switches  104  are reconfigured to replace the non-operable sub-functional units  11 ,  31  and  26  with sub-functional units  15 ,  35  and  25 , respectively, in the spare functional unit  10 -S. 
   The non-operable sub-functional unit  11  is replaced as follows: The inputs  106 - 1 ,  106 - 2 , and  106 - 3  to the sub-functional units  11 ,  12 , and  13  are shifted one functional unit to the right by switches  104 - 1 ,  104 - 2 ,  104 - 3 , and  104 - 4 . The outputs  106 - 4 ,  106 - 5 , and  106 - 6  of the sub-functional units  12 ,  13 , and  1 S are shifted one functional unit to the left by switches  104 - 5 ,  104 - 6 ,  104 - 7 , and  104 - 8 . The non-operable sub-functional unit  13  is replaced in a similar manner. 
   The non-operable sub-functional unit  26  is replaced as follows: The outputs  106 - 7 ,  106 - 8 , and  106 - 9  of the sub-functional units  14 ,  15 , and  16  are shifted one functional unit to the left by switches  104 - 8 ,  104 - 9 ,  104 - 10 , and  104 - 11 . The outputs  106 - 10 ,  106 - 11 , and  106 - 12  of the sub-functional units  2 S,  24 , and  25  are shifted one functional unit to the right by switches  104 - 12 ,  104 - 13 ,  104 - 14 , and  104 - 15 . 
   After reconfiguration, the first functional unit  10 - 1  includes sub-functional units  12 ,  21 ,  32 , and  41 . The second functional unit  10 - 2  includes sub-functional units  13 ,  22 ,  33 , and  42 . The third functional unit  10 - 3  includes sub-functional units  1 S,  23 ,  3 S, and  43 . The fourth functional unit  10 - 4  includes sub-functional units  14 ,  2 S,  34 , and  44 . The fifth functional unit  10 - 5  includes sub-functional units  15 ,  24 ,  35 , and  45 . The sixth functional unit  10 - 6  includes sub-functional units  16 ,  25 ,  36 , and  46 . 
   Referring now to  FIG. 6 , a semiconductor  150  includes the spare sub-functional unit  10 -S that is located at one end. If the sub-functional unit  21  fails (as shown in shading), the inputs  120 - 1 ,  120 - 2 , . . . , and  120 - 6  to the sub-functional units  21 ,  22 , . . . , and  26  are shifted one functional unit to the right by switches  124 - 1 ,  124 - 2 , . . . , and  124 - 7 . The outputs  120 - 7 ,  120 - 8 , . . . , and  120 - 12  of the sub-functional units  22 ,  23 , . . . and  2 S are shifted one functional unit to the left by switches  124 - 8 ,  124 - 9 , . . . , and  124 - 14 . 
   After reconfiguration, the first functional unit  10 - 1  includes sub-functional units  11 ,  22 ,  31 , and  41 . The second functional unit  10 - 2  includes sub-functional units  12 ,  23 ,  32 , and  42 . The third functional unit  10 - 3  includes sub-functional units  13 ,  24 ,  33 , and  43 . The fourth functional unit  10 - 4  includes sub-functional units  14 ,  25 ,  34 , and  44 . The fifth functional unit  10 - 5  includes sub-functional units  15 ,  26 ,  35 , and  45 . The sixth functional unit  10 - 6  includes sub-functional units  16 ,  2 S,  36 , and  46 . 
   Referring now to  FIG. 7 , a semiconductor  160  includes a partial spare sub-functional unit  10 -PS that is located at one end. The partial spare sub-functional unit  10 -PS includes one or more sub-functional units (for some but not all of the sub-functional units). For example, the partial sub-functional unit  10 -PS includes sub-functional units  2 S and  3 S but not  1 S or  4 S. The partial sub-functional units that are provided may be associated with sub-functional units that are more likely to have a lower yield. By not fabricating the other sub-functional units and switches, the cost of the semiconductor  160  may be reduced. 
   If the sub-functional unit  21  fails (as shown in shading), the inputs  120 - 1 ,  120 - 2 , . . . , and  120 - 6  to the sub-functional units  21 ,  22 , . . . , and  26  are shifted one functional unit to the right by switches  124 - 1 ,  124 - 2 , . . . , and  124 - 13   6 . The outputs  120 - 7 ,  120 - 8 , . . . , and  120 - 12  of the sub-functional units  22 ,  23 , . . . and  2 S are shifted one functional unit to the left by switches  124 - 8 ,  124 - 9 , . . . , and  124 - 13 . 
   After reconfiguration, the first functional unit  10 - 1  includes sub-functional units  11 ,  22 ,  31 , and  41 . The second functional unit  10 - 2  includes sub-functional units  12 ,  23 ,  32 , and  42 . The third functional unit  10 - 3  includes sub-functional units  13 ,  24 ,  33 , and  43 . The fourth functional unit  10 - 4  includes sub-functional units  14 ,  25 ,  34 , and  44 . The fifth functional unit  10 - 5  includes sub-functional units  15 ,  26 ,  35 , and  45 . The sixth functional unit  10 - 6  includes sub-functional units  16 ,  2 S,  36 , and  46 . 
   Referring now to  FIG. 8 , additional full and/or partial spare functional units can be provided. For example, a semiconductor  170  in  FIG. 8  includes two partial spare sub-functional units  10 -PS 1  and  10 -PS 2 . The full and/or partial spare sub-functional units  10 -PS 1  and  10 -PS 2  can be located adjacent to each other (as shown) or in non-adjacent positions. If the full or partial sub-functional units are located adjacent to each other, switches  172  switch inputs and/or outputs between two adjacent switches. For example, the switch  174 - 1  can switch inputs and/or outputs from sub-functional unit  11  to either sub-functional unit  22  or  23 . 
   If the sub-functional units  21  and  22  fail (as shown in shading), the inputs  172 - 1 ,  172 - 2 ,  172 - 3 , and  172 - 4  to the sub-functional units  21 ,  22 ,  23  and  24  are shifted two functional units to the right by switches  174 - 1 ,  174 - 2 , . . . , and  174 - 6 . The outputs  172 - 5 ,  172 - 6 , . . . , and  172 - 8  of the sub-functional units  23 ,  24 ,  2 S 1  and  2 S 2  are shifted two functional units to the left by switches  174 - 7 ,  174 - 8 , . . . , and  174 - 12 . 
   If the sub-functional unit  37  fails, the inputs  172 - 9 ,  172 - 10 , and  172 - 11  to the sub-functional units  35 ,  36 , and  37  are shifted one functional unit to the left by switches  174 - 12 ,  174 - 13 ,  174 - 14 , and  174 - 15 . The outputs  172 - 12 ,  172 - 13 , and  172 - 14  of the sub-functional units  3 S 2 ,  35 , and  36  are shifted one functional unit to the right by switches  174 - 16 ,  174 - 17 ,  174 - 18 , and  174 - 19 . 
   After reconfiguration, the first functional unit  10 - 1  includes sub-functional units  11 ,  23 ,  31 , and  41 . The second functional unit  10 - 2  includes sub-functional units  12 ,  24 ,  32 , and  42 . The third functional unit  10 - 3  includes sub-functional units  13 ,  2 S,  33 , and  43 . The fourth functional unit  10 - 4  includes sub-functional units  14 ,  2 S 2 ,  34 , and  44 . The fifth functional unit  10 - 5  includes sub-functional units  15 ,  25 ,  3 S 2 , and  45 . The sixth functional unit  10 - 6  includes sub-functional units  16 ,  26 ,  35 , and  46 . The seventh functional unit  10 - 7  includes sub-functional units  17 ,  27 ,  36 , and  47 . 
   The semiconductor can also include two or more full and/or partial functional units that are located at one end or in any other position. In  FIG. 9 , two partial spare functional units  10 -PS 1  and  10 -PS 2  are located at one end of a semiconductor  180 . If sub-functional units  21  and  24  fail (as shown in shading), the switching devices  182  replace them with sub-functional units  2 S 1  and  2 S 2  in the spare functional units  10 -PS 1  and  10 PS 2 . 
   After reconfiguration, the first functional unit  10 - 1  includes sub-functional units  11 ,  22 ,  31 , and  41 . The second functional unit  10 - 2  includes sub-functional units  12 ,  23 ,  32 , and  42 . The third functional unit  10 - 3  includes sub-functional units  13 ,  25 ,  33 , and  43 . The fourth functional unit  10 - 4  includes sub-functional units  14 ,  26 ,  34 , and  44 . The fifth functional unit  10 - 5  includes sub-functional units  15 ,  27 ,  35 , and  45 . The sixth functional unit  10 - 6  includes sub-functional units  16 ,  2 S 1 ,  36 , and  46 . The seventh functional unit  10 - 7  includes sub-functional units  17 ,  2 S 2 ,  37 , and  47 . 
   Referring now to  FIG. 10 , to reduce the complexity of the switching devices, the semiconductor  190  includes multiplexed switching devices that include multiplexers (M)  192  that receive p input signals and that output  1  to q output signals, where q is less than p. For example, p input signals can be multiplexed into one output signal. 
   Alternately, the p input signals can be multiplexed into two or more output signals. For example, eight input signals can be multiplexed into three output signals. In this example, one input signal is not multiplexed, for example a high speed signal such as data signals in the Gigabit physical layer device. Two medium speed signals can be multiplexed into one output signal. The remaining five input signals, which are preferably “slow” signals such as control signals in the Gigabit PHY, can be multiplexed into one output signal. 
   Demultiplexers (D)  194  receive  1  to q input signals and generate p output signals. The number of inputs and outputs that are multiplexed and demultiplexed will depend upon the particular sub-functional units that communicate with the multiplexers  192  and demultiplexers  194 . By decreasing the number of connecting wires that need to be switched, the switching devices can be simplified. The exemplary embodiments shown in  FIGS. 10 and 11  show multiple inputs that are multiplexed to a single output. Based on the preceding discussion, however, skilled artisans will appreciate that the output of the multiplexer may include one or more outputs that may be multiplexed or not multiplexed. 
   For example, if the sub-functional unit  21  fails, the switching devices  196 - 1  and  196 - 2  connect the multiplexer  192 - 1  with the demultiplexer  192 - 3 . This establishes a forward path for signals being sent from the sub-functional unit  11  to the sub-functional unit  22  (which replaces non-operable sub-functional unit  21 ). The demultiplexer  192 - 3  communicates with the sub-functional unit  22 . Likewise, a reverse path can be established if needed. The switching devices  196 - 1  and  196 - 2  connect the multiplexer  192 - 4  to the demultiplexer  194 - 1 , which communicates with the sub-functional unit  11 . As can be appreciated, while forward and reverse signal paths are shown, forward and/or reverse paths may be used between the sub-functional units as needed. Some of the multiplexers and demultiplexers can be omitted if both forward and reverse paths are not used between sub-functional units. 
   After failure and reconfiguration, the first functional unit  10 - 1  includes sub-functional units  11 ,  22 ,  31 , and  41 . The second functional unit  10 - 2  includes sub-functional units  12 ,  23 ,  32 , and  42 . The third functional unit  10 - 3  includes sub-functional units  13 ,  2 S,  33 , and  43 . The fourth functional unit  10 - 4  includes sub-functional units  14 ,  24 ,  3 S, and  44 . The fifth functional unit  10 - 5  includes sub-functional units  15 ,  25 ,  34 , and  45 . The sixth functional unit  10 - 6  includes sub-functional units  16 ,  26 ,  35 , and  46 . 
   The semiconductor with multiplexed switching devices can include multiple full or partial spare sub-functional units. Referring now to  FIG. 11 , a semiconductor  200  includes two partial spare sub-functional units  10 -PS 1  and  1 OPS 2 . The multiple full or partial spare sub-functional units need not be located adjacent to each other. Switching devices  204  connect to at least two adjacent switches. For example, the switching device  204 - 1  communicates with the switching devices  204 - 2  and  204 - 3 . Likewise, the switching device  204 - 2  communicates with the switching devices  204 - 3  and  204 - 4 . The semiconductor  200  is capable of replacing two failures in the same row. 
   For example, if sub-functional units  31  and  33  fail (as shown in shading), the switches  204  are reconfigured. The first functional unit  10 - 1  includes sub-functional units  11 ,  21 ,  32 , and  41 . The second functional unit  10 - 2  includes sub-functional units  12 ,  22 ,  34 , and  42 . The third functional unit  10 - 3  includes sub-functional units  13 ,  23 ,  35 , and  43 . The fourth functional unit  10 - 4  includes sub-functional units  14 ,  24 ,  3 S 1 , and  44 . The fifth functional unit  10 - 5  includes sub-functional units  15 ,  25 ,  3 S 2 , and  45 . 
   Assuming that defects are uniformly and independently distributed on the semiconductor (which may or may not be true), if the yield for a single functional unit is P S , then the yield for a first sub-functional unit is P sub1 =P S ((area of sub-functional unit)/area of functional unit)). The yield P S  of the functional unit is equal to the product of the yields for each sub-functional unit. 
   If p is the yield of the functional units, m is the minimum number of working functional units and n is equal to m plus the number of spare functional units, the yield is defined as follows: 
   
     
       
         
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           For example, a semiconductor with 8 functional units each having a uniform yield of 90% (and spare functional units) would have a yield of 43%. Assume that the functional units have four sub-functional blocks A, B, C, and D. All of the sub-functional blocks are swapped out as a group if A, B, C and/or D experience a fault. With one spare functional unit, the yield increases to 77.5%. 
         
       
     
  
   If the functional blocks can be swapped out in two groups (A and B) and/or (C and D), the yield is equal to:
 
yield= f ( p   A   ×p   B   ,m,n )× f ( p   C   ×p   D   ,m,n )
         In this example, the yield increases to 85.6%.       

   If the functional blocks can be swapped out in three groups (A and B), C and/or D, the yield is equal to:
 
yield= f ( p   A   ×p   B   ,m,n )× f ( p   C   ,m,n )× f ( p   D   ,m,n )
         In this example, the yield increases to 88.6%.       

   If the functional blocks can be swapped out in four groups A, B, C and/or D, the yield is equal to:
 
yield= f ( p   A   ,m,n )× f ( p   B   ,m,n )× f ( p   C   ,m,n )× f ( p   D   ,m,n )
         In this example, the yield increases to 91.7%.       

   As can be appreciated, providing one spare functional unit increase yield dramatically. Splitting the functional units into two or more sub-functional units that can be individually swapped out further increases yield. At some point, the tradeoff between improved yield is offset by increased design complexity. 
   Referring now to  FIG. 12 , steps of a method for replacing non-operable sub-functional units using a single full or partial functional unit is shown. Control begins with step  240 . In step  242 , control identifies rows and columns of non-operable sub-functional units. In step  244 , control sets N equal to the number of rows in the functional units and sets R equal to one. In step  246 , control determines whether R is equal to N+1. If true, control ends in step  248 . If false, control continues with step  250  where control determines if row R has greater than or equal to one non-operable (N.O.) sub-functional unit (SFU). If false, control increments R in step  252  and control returns to step  246 . If true, control continues with step  254  where control determines if row R includes greater than or equal to two non-operable (N.O.) sub-functional units (SFU). Since only one spare full or partial sub-functional unit is provided, an error is signaled in step  256  if two or more non-operable sub-functional units are in the same row. 
   In step  258 , control sets m equal to the column number of the full or partial spare functional unit and z equal to the column of the non-operable sub-functional unit. In step  262 , control sets i=z. In step  270 , control determines whether z&gt;m. If false, control continues with step  274  and shifts the i th  sub-functional unit to column (i+1) using the switching devices. In step  276 , control determines whether (i+1)=m. If not, control increments i in step  278  and continues with step  274 . Otherwise, control increments R in step  280  and control continues with step  254 . 
   If z is greater than m in step  270 , control continues with step  284  and shifts the i th  sub-functional unit to column (i−1) using the switching devices. In step  286 , control determines whether (i−1) is equal to m. If not, control decrements i in step  288  and continues with step  284 . Otherwise, control continues with step  280 . 
   As can be appreciated by skilled artisans, similar algorithms for replacing non-operable functional units and/or sub-functional units can be performed for semiconductors including two or more full or partial spare functional units and/or sub-functional units. In addition, while specific switching arrangements are shown, the specific switching devices that will be used will depend upon the particular implementation, details of the particular functional and/or sub-functional units and other normal design criteria. Various different types of switching devices may also be used on the same semiconductor. 
   Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present invention can be implemented in a variety of forms. Therefore, while this invention has been described in connection with particular examples thereof, the true scope of the invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, the specification and the following claims.