Paper at
IEEE European Test Symposium (ETS'05)
Tallinn, Estonia - May 2005 (PR-MS 24.626)

Abstract

Complex SOCs are increasingly tested in a modular fashion, which enables us to record the yield-per-module. In this paper, we consider the yield-per-module as the pass probability of the module's manufacturing test. We use it to exploit the abort-on-fail feature of ATEs, in order to reduce the expected test application time. We present a model for expected test time, which obtains increasing accuracy due to decreasing granularity of the abortable test unit. For a given SOC, with a modular test architecture consisting of wrappers and disjunct TAMs, and for given pass probabilities per module test, we schedule We describe two heuristic scheduling approaches, one without and one with preemption. Experimental results for the ITC'02 SOC Test Benchmarks demonstrate the effectiveness of our approach, as we achieve up to 97% reduction in the expected test application, without any modification to the SOC or ATE.

Rapid improvements in semiconductor design and manufacturing technologies enable the creation of increasingly complex integrated circuits, often refered to as system chips or SOCs. The manufacturing test costs of these 'monster chips' threaten to increase beyond what is acceptable, if no proper countermeasures are taken. The test costs are dictated by the price of the automatic test equipment (ATE) and the time (in seconds) each SOC spends on the ATE. A reduction of the test application time directly contributes to savings in the test cost.

SOCs are increasingly designed and tested in a modular fashion. A modular test is required for non-logic embedded blocks (such as embedded memories, analog modules, embedded FPGAs, etc.) and black-boxed third-party IP cores. But also for the remainder of the SOC, modular testing has attractive benefits, in terms of 'divide-n-conquer' test generation and test re-use over multiple SOC designs [1]. A modular test requires an on-chip test infrastructure [2, 3] in the form of a wrapper per module (such as the one standardized by IEEE P1500 [4, 5]) and test access mechanisms (TAMs).

A modular test makes it possible to record the yield-per-module. This information is valuable to core providers, who can improve their product with this information, but who often had no access to statistically relevant yield numbers, as they typically do not manufacture their own products in high volumes. The yield-per-module is also relevant for SOC integrators, who will be able to better predict the yields of their next SOC product, based on historic yield data of the constituting modules.

In this paper, we consider the yield-per-module as the pass probability of a module's manufacturing test. We use it to exploit the abort-on-fail capability of ATEs, in order to reduce the expected test application time. For a given SOC, with a modular test architecture consisting of wrappers and disjunct TAMs, and for given pass probabilities per module test, we schedule the tests on each TAM such that the overall expected test application time is minimized.

The remainder of this paper is organized as follows. Section 2 reviews the prior work in this field. Section 3 presents our formal problem definition. In Section 4, we present a model for expected test application time, which obtains increasing accuracy due to decreasing granularity of the abortable test unit. Subsequently, Section 5 describes our heuristic scheduling algorithms without and with preemption. In Section 6, experimental results are given for SOC p22810 of the ITC'02 SOC Test Benchmarks [6]. They demonstrate the effectiveness of our approach, as we achieve up to 97% reduction of the expected test application time, without any modification to the SOC itself. Section 7 concludes this paper.

The idea to use pass probabilities, yield, or fault coverage of tests of (parts of) an IC to construct a schedule such that the expected test application time is minimized is not new. Lee & Krishna [7, 8] partitioned a single test in multiple abortable units of equal pass probability. As tests are typically more likely to fail in their early patterns, their test units are ordered from small in the beginning of the test to large at the end. Huss & Gyurcsik [9] presented a scheduling approach for a series of analog tests with partly overlapping test coverage. Jiang & Vinnakota [10, 11] described an efficient heuristic algorithm for the same problem. In [9, 10, 11], analog tests can only be evaluated upon completion. In the sequel of this paper, we argue that that is not necessary for digital tests. Evaluating (and, in case of failure, aborting) tests at a smaller grain size can help to significantly reduce the expected test application time.

All papers mentioned above did not consider modularly-tested (core-based) SOCs, in which multiple TAMs can operate independtly and in parallel; in fact, only few other papers do. Koranne [12] proposed a technique for test architecture (wrapper and TAM) design, in combination with test scheduling. He used average time instead of completion time of the test schedule as a heuristic to reduce an originally -hard and hence intractable problem [13] to a problem that can be solved optimally in polynomial time. Unfortunately, the paper lacks the concept of pass probability altogether. The only paper, to the best of our knowledge, that comes relatively close to our work is a paper by Larsson et al. [14]. For a modularly-tested SOC with given pass probabilities per module test, it optimizes the test architecture, such that the corresponding expected test time is minimized. Differences between [14] and our paper are the following. We assume a given test architecture with disjunct TAMs, whereas Larsson et al. design test architectures in which TAMs are allowed to fork-n-merge. For simplicity, Larsson et al. consider only entire module tests as abortable units, whereas we also allow for smaller granularities, in order to improve the accuracy of the expected test application time calculation. The two papers present different scheduling algorithms, while we also consider the case in which preemption of tests is allowed.

In this paper, a test architecture [3] is defined as a non-empty set of modules , a non-empty set of TAMs , and an assigned-modules function , in which denotes the subset of modules assigned to TAM , such that

For a given test architecture, a feasible schedule is a schedule in which tests of modules assigned to the same TAM are executed in series, whereas the sets of modules assigned to disjunct TAMs are tested in parallel. While in a test architecture the modules assigned to the same TAM form an (unordered) set , in a corresponding feasible schedule these modules for an (ordered) list. For this we introduce a function , specified by ; denotes that the test of module is ordered as item number on TAM .

A test architecture has corresponding non-delay¹ feasible schedules. In our problem at hand, we try to identify a corresponding non-delay feasible schedule which gives the minimal expected test application time.

Problem [Scheduling for Minimal Expected Test Time (SMETT)]
For an SOC is given a set of modules , and, for the test of each module , a number of test patterns and a pass probability . Also given is a test architecture with a set of TAMs , and for each TAM its width and a modules-assigned function . Finally, also given are the scan-in length and scan-out length for each module in this test architecture. Determine a corresponding feasible schedule, i.e., determine an ordered list corresponding to for each TAM , such that the overall expected test time of the SOC is minimized.

For simplicity, we assume in this paper that every module has only one test. However, our theory and results can easily be extended to cover the case in which modules have multiple tests.

The scan-in and scan-out lengths and in the above problem definition follow from (1) the test data of module [6], (2) the width of the TAM to which is assigned, and (3) the wrapper design algorithm used. For the latter, we have used the COMBINE algorithm [16]. Note that the problem discussed in this paper is also applicable to non-scan-testable modules; in those cases, the contribution of the internal scan chains to the scan-in and scan-out lengths is simply zero.

The pass probability of a test equals the yield of the corresponding module. To obtain these pass probabilities, one possible scenario is to first test a sufficient number of SOCs without abort-on-fail, just to record the yield-per-module. This could, for example, be done with a schedule that minimizes the overall test completion time [13, 2, 3, 12]. Once statistically relevant yields-per-module have been recorded, a new schedule is created that exploits the pass probabilities per test to minimize the expected test time (Problem SMETT) and applied with the ATE's abort-on-fail feature 'on' [10, 11]. An alternative scenario is to right-away start testing with the abort-on-fail feature, while initially using as pass probabilities estimates based on module type and size and experience obtained from previous SOCs. In both scenarios, it is possible to collect further yield-per-module data, even when the abort-on-fail feature is turned 'on'. In this way, we can record changes in pass probabilities (e.g., due to changing manufacturing conditions) and adjust the test schedule accordingly.

To solve Problem SMETT, calculation of the expected test time is required. In this section, we discuss the basics of expected test time calculation for a schedule of a test architecture with multiple disjunct TAMs, improvements in accuracy obtained by reducing the size of the abortable units, and the related distribution of given pass probabilities.

The test of module has pass probability ; furthermore, we assume that the test time of this test is .

(4.1)

where .

Figure 1 shows an illustrative example consisting of one TAM with three modules. Figure 1(a) shows the original schedule: . Based on this order, order function is defined: , , and . The same schedule, now with is depicted in Figure 1(b). Figure 1(c) shows the cumulative pass probability as a function of time. The test of is executed with probability 1, as it is the first test in the schedule. Only if passes its test, the test of will be executed. Hence, the expected test time after the second test is . Similarly, the test of will only be executed if the first two tests both pass, i.e., with probability . Consequently, the total expected test time is . Note that the expected test time equals the shaded area under the cumulative pass probability curve in Figure 1(c).

(a)

(b)

(c)

Figure 1: A schedule for three modules on one TAM with (a) original and (b) ordered module names, and (c) the corresponding cumulative pass-probability curve.

Next, we consider the case of a full-fledged test architecture, consisting of multiple parallel TAMs. Larsson et al. [14] described how to extend the expected test time expression of Equation 4.1 to cover multiple TAMs. Every completion of an individual test provides an opportunity to abort the test. The test completion times of the tests on the individual TAMs in a given test schedule determine a complete global ordering of all tests. This ordering is expressed by a function ; denotes that the test of module is the th test to complete in the global schedule. Now, the total expected test time for the entire test schedule can be expressed by

(4.2)

where , , and in which and are defined such that .

Figure 2 shows an illustrative example consisting of two TAMs with resp. three and two modules. Figure 2(a) shows the original schedule. The order of completion of the various tests has the following sequence: . (Actually, the tests of modules and complete simultaneously, and hence and could just as well have been swapped in this sequence.) Based on this order, function is defined: , and . This renaming is depicted in Figure 2(b). Figure 2(c) shows the corresponding cumulative pass probability as a function of time.

(a)

(b)

(c)

Figure 2: A schedule for two TAMs with resp. three and two modules with (a) original and (b) ordered module names, and (c) the corresponding cumulative pass-probability curve.

The expected test time is reduced if we reduce the size of the abortable units. Three natural abortable units are (1) module tests, (2) test patterns, and (3) clock cycles. Figure 3 illustrates this by showing the cumulative pass probability as a function of time for the three mentioned abortable unit sizes; increasing darker colors represent decreasing unit sizes. In this small example, the entire test suite consists of two module tests, each consisting of five test patterns, which in turn consist of multiple clock cycles. As discussed in Section 4.1, the expected test time equals the shaded area under the curve. As the darker curves lie strictly below the lighter curves, the corresponding expected test time is smaller.

Figure 3: Cumulative pass probability as a function of time for three abortable unit sizes: module tests, test patterns, and clock cycles.

Most ATEs can abort a digital test almost immediately; only really fast ATEs have a (negligible) small number of clock cycles pipeline delay between the occurrence of the failing response bit at the SOC pins and the actual stop of the test execution. Hence, it is fair to state that reducing the abortable unit size not only decreases the calculated expected test time , but also makes more accurate. The smallest and most accurate expected test time is calculated in a model which assumes the abortable unit to be a single clock cycle.

From Figure 3 we can also learn that the relative improvement in size and accuracy of the expected test time calculated decreases for increasingly small unit sizes. In other words: the biggest gain is obtained in going from tests to patterns, while the additional gain from going from patterns to cycles is relatively small.

Using more and smaller abortable units to calculate the expected test time requires pass probabilities for these units. In the definition of Problem SMETT, only one pass probability per module test is given. As we do not want to burden the user by providing us with more pass probabilities, we calculate those ourselves, by means of 'distributing' the pass probability of the module test over the smaller units.

We first consider the distribution of the pass probability of the test of module over the pass probabilities of the individual test patterns of . This distribution has to be such that . One way to do this is to assume a flat distribution, in which . Such a flat distribution is achieved by . However, a more realistic distribution of pass probabilities is one in which the early patterns are much more likely to fail than late test patterns. We refer to such a distribution as curved, and it is characterized by

(4.3)

Figure 4 shows for an example module with and both the pass probability and the cumulative pass probability per pattern , based on a curved distribution. The figure illustrates that by using Equation (4.3), the pass probability is at first a steeply increasing function, which soon flattens out to almost horizontal, but still increasing. This curve follows the shape of the familiar (cumulative incremental) fault coverage curves.

(a)

(b)

Figure 4: Example of (a) pass probability and (b) cumulative pass probability per pattern.

Secondly, we consider the distribution of the pass probability of an individual test pattern over the pass probabilities of its constituting clock cycles . During 'scan-in-only' clock cycles, no test responses are evaluated and thus the test cannot fail; hence, we set the corresponding pass probability to 1. Scan-in-only cycles occur (1) during scan-in of the first test pattern, and, for other patterns, (2) only if scan-in is longer than scan-out. In the latter, we assume that scan-out of a pattern takes place concurrently with scan-in of the next pattern, there are scan-in-only cycles per test pattern. During the remaining clock cycles per test pattern, test responses are evaluated and consequently the test can fail; hence, we distribute the pass probability of the test pattern over these cycles only. We assume that within one test pattern, all non-'scan-in-only' clock cycles have an equal pass probability. Then, the pass probability for a non-'scan- in-only' clock cycle of pattern of module is given by

(4.4)

Figure 5 illustrates the above for an example module , with , ,. Note that this example is chosen such that , and hence 'scan- in-only' cycles occur in every pattern. Figure 5(a) shows the pass probability per clock cycle. This pass probability is 1 for all 'scan- in-only' cycles. In all other clock cycles, the pass probabilities are such that (1) the curve between patterns is increasing (per Equation (4.3)), (2) the curve within one pattern is flat (per Equation (4.4)), and (3) the products of all pass probabilities per individual unit amount to , i.e.,

(4.5)

. Figure 5(b) shows the corresponding cumulative pass probability per clock cycle.

(a)

(b)

Figure 5: Example with (a) pass probability and (b) cumulative pass probability per clock cycle.

As mentioned in Section 3, a given test architecture has corresponding non-delay feasible schedules. Real-life test architectures typically have at least one TAM containing a large number of modules, and for these architectures, an exhaustive search over all schedules is impractical. We have implemented an efficient heuristic scheduling algorithms to address this problem.

Our overall approach is to optimize the schedule per TAM, as it is computationally straight forward, and yet results in good overall schedules. The scheduling per TAM is done such that tests that are likely to fail as well as short tests are candidates to be scheduled early.

In non-preemptive scheduling, the module tests are considered as atomic scheduling units. We assign each module a weight , and simply sort the modules in increasing weight. Weight is defined by

(5.1)

In the case of only one TAM, this scheduling algorithm gives optimal results (proof omitted due to lack of space). For the other cases, we have counter-examples that prove that results are not guaranteed to be optimal, although the algorithm turns out to be an effective heurisitc approach. The compute time for our scheduling algorithm is dominated by the time spent on sorting, viz. per TAM .

Preemption typically reduces the expected test time drastically. However, in some cases preemption also increases the test completion time slightly. In our approach, we assumed overlapped scan-out of one pattern with scan-in of the next pattern for patterns of the same test, but not for test patterns of different tests. Hence, for each preemptive cut of the test of a module , the test completion time of TAM (with ) increases with . If happens to be the TAM with dominant test time, the overall test completion time is increased due to the preemption. A (slightly) larger test completion time implies that we need a (slightly) increased ATE vector memory to store the test patterns.

In this paper, we consider a straight-forward preemption strategy, consisting of two steps. In Step 1, we divide every module test into two parts. The first part consists of 10% of the total number of test patterns for the module, while the other part consists of the remaining 90% of the test patterns. We assign them pass probabilities according to the approach of Equation (4.3). In Step 2, both parts are treated as two separate tests and scheduled with our non-preemptive scheduling algorithm, described in Section 5.1.

We obtained experimental results for the ITC'02 Test Benchmarks [6]. As the original benchmark data does not contain pass probabilities, we have added these ourselves. We have used two different sets of pass probabilities. The first set is taken from [14]; we refer to it as the set. The second set we have constructed ourselves; this so-called set takes into account the type of the module (logic or memory) and its relative size. The pass probabilities vary, for the set from 90% to 99%, and for the set from 23% to 99%; the full details can be found at [17]. Test architectures, which form the starting point of our problem definition, were generated by TR-ARCHITECT [3] for a given SOC and given maximal TAM width . We assumed that all modules are at the same level of design hierarchy, just below the SOC itself (despite what is specified in [6]), and we only considered the module-internal tests. Due to lack of space, this paper only presents results for SOC p22810, but similar results were obtained for other benchmark SOCs and published in [17].

Table 1(a) presents the expected test time results for the three different abortable units: for module tests, for patterns, and for clock cycles. For this table, no particular scheduling algorithm was used; the schedule that was analyzed is the lexicographically-sorted non-preemptive test schedule delivered by TR-ARCHITECT. Furthermore, we considered a curved pass probability distribution between patterns, and a flat pass probability distribution between clock cycles within a pattern. Column 1 lists the pass probability set used ( or ) and Column 2 lists the maximal TAM width specified (). Column 3 presents the completion time obtained by TR-ARCHITECT, i.e., without abort-on-fail. Columns 4, 6 and 8 list the expected time , and for the various abortable units. Columnts 5, 7, and 9 show the relative difference between the expected test time and the completion time .

Pass Prob. Set [3] 16 458068 24 299718 32 222471 40 190995 48 160221 56 145417 64 133405 16 458068 24 299718 32 222471 40 190995 48 160221 56 145417 64 133405

Abortable Unit Module Test Test Pattern Clock Cycle (-)/ (-)/ (-)/ 254969 -44% 230552 -50% 230487 -50% 170201 -43% 139366 -54% 139281 -54% 119506 -46% 89357 -60% 89247 -60% 87013 -54% 66517 -65% 66459 -65% 84561 -47% 61623 -62% 61553 -62% 83019 -43% 59538 -59% 59465 -59% 78705 -41% 57131 -57% 57074 -57% 160126 -65% 66983 -85% 66892 -85% 140031 -53% 14917 -95% 14808 -95% 103964 -53% 8364 -96% 8234 -96% 107216 -44% 8624 -95% 8543 -96% 103763 -35% 6588 -96% 6506 -96% 94565 -35% 4950 -97% 4851 -97% 79514 -40% 4563 -97% 4475 -97% (a)

Scheduling Non-Preemptive Preemptive (-)/ (-)/ (-)/ 135542 -41% 459860 +0.4% 123823 -9% 85983 -38% 301485 +0.6% 80582 -6% 66120 -26% 223605 +0.5% 61985 -6% 55980 -16% 190995 0.0% 52339 -7% 45891 -26% 160221 0.0% 43805 -5% 41345 -31% 145417 0.0% 39442 -5% 37694 -34% 133405 0.0% 35981 -5% 18636 -72% 459860 +0.4% 10361 -44% 11443 -23% 301485 +0.6% 6843 -40% 6422 -23% 223605 +0.5% 4860 -24% 5120 -41% 190995 0.0% 4072 -20% 4409 -33% 160221 0.0% 3479 -21% 3779 -24% 145417 0.0% 3101 -18% 3548 -22% 133405 0.0% 2813 -21% (b)

Table 1: For SOC p22810, test time results for (a) three different abortable unit sizes, and (b) non-preemptive and preemptive test scheduling.

In Table 1(a), we see that for decreasing abortable units, the expected test time decreases. For some TAM widths, the savings in test time are up to 97%. The savings obtained for set are larger than the savings for set , due to the fact that set has lower pass probabilities then set . The cycle-based calculations are the most accurate ones, but also require more compute time (up to five times more for SOC p22810) then the test- or pattern-based calculations. As the differences in expected test time for pattern- and cycle-based units are insignificantly small, we recommend to use patterns as the abortable unit.

Table 1(b) shows test time results obtained using the test scheduling algorithms presented in Section 5. Here, we used clock cycles as the abortable unit, in order to obtain the most accurate results. Column 2 lists the relative difference in expected test time between our non-preemptive scheduling algorithm and the lexicographical schedule delivered by TR-ARCHITECT . Columns 4 and 6 represent the relative differences in completion time and expected test time between our preemptive and non-preemptive scheduling algorithms. In Table 1(b), we see that our non-preemptive scheduling algorithm obtains savings in expected test time up to 41% for set and 72% for set . Our preemptive scheduling algorithm brings additional savings up to 44% in expected test time, at the (marginal) expense of <1% increase in completion time. The latter is due to the fact that at preemption boundaries in the schedule, we do not allow overlapped scan (see Section 5.2).

Modular testing, increasingly applied on complex SOCs, enables the recording of yield-per-module. In this paper, we used the yield-per-module to exploit the abort-on-fail feature of ATEs, in order to reduce the expected test application time. Working with module tests, patterns, and individual clock cycles as abortable units, we have presented a model to compute the total expected test application time. The expected test application time decreases and becomes more accurate with decreasing abortable unit sizes. Subsequently, we addressed the problem of test scheduling for a given modular test architecture consisting of wrappers and disjunct TAMs, such that the total expected test time is minimized. For this problem, we presented two heuristic scheduling algorithms, one without and one with preemption. Experimental results for the ITC'02 SOC Test Benchmarks demonstrate the effectiveness of our approach. We show that by just decreasing the abortable unit size, up to 97% reduction of the expected test time can be achieved. The use of our non-preemptive heuristic scheduling algorithm results in additional savings in expected test time up to 72%. Our preemptive scheduling algorithm brings even further additional savings in the total expected time, up to 44%, at an expense of <1% in overall completion time. All results only require rescheduling of tests, and no modifications to SOC or ATE.

Acknowledgements

We thank Jan Korst, Wil Michiels, André Nieuwland, Bart Vermeulen, and Harald Vranken of Philips Research and Julien Pouget of LIRMM for fruitful discussions during the project.

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Footnotes