Abstract
A semiconductor component that includes at least one dielectric layer and at least one first electrode and one second electrode. In addition, at least two defect types different from one another are present in the dielectric layer. These at least two defect types different from one another move along localized defect states, each at an average effective distance, in the direction of one of the two electrodes as a function of an operating voltage that is applied between the first electrode and the second electrode, and an operating temperature that is present. The average effective distance is greater than 3.2 nm.
Claims
1-7. (canceled)
8. A semiconductor component, comprising: at least one dielectric layer; and at least one first electrode and one second electrode; wherein at least two defect types different from one another being present in the dielectric layer, the at least two different defect types moving along localized defect states, each case having the same average effective distance a.sub.0, in a direction of one of the first and second electrodes, as a function of an operating voltage applied between the first electrode and the second electrode, and an operating temperature that is present, and a.sub.0>3.2 nm.
9. The semiconductor component as recited in claim 8, wherein a.sub.0>3.24 nm.
10. The semiconductor component as recited in claim 8, wherein at least three defect types different from one another are present in the dielectric layer.
11. The semiconductor component as recited in claim 8, wherein the dielectric layer is a polycrystalline oxidic high-k dielectric, the dielectric layer being a PZT layer or a KNN layer.
12. The semiconductor component as recited in claim 11, wherein the dielectric layer is a sputtered PZT layer.
13. The semiconductor component as recited in claim 12, wherein the sputtered PZT layer has a deposition temperature of less than 500° C.
14. The semiconductor component as recited in claim 12, wherein the sputtered PZT layer has a composition of Pb.sub.1.3(Zr.sub.0.52Ti.sub.0.48)O.sub.3.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0032] FIG. 1A shows the curve of a leakage current measurement for three different dielectric layers.
[0033] FIG. 1B shows the temporal profile of the effective barrier height that results from a leakage current measurement, and the subdivision into the contributions of the defect types that are present.
[0034] FIG. 2A shows the curves of four leakage current measurements and the respectively adapted model curves that are ascertained on a dielectric layer at the same operating temperature, but at different operating voltages.
[0035] FIG. 2B shows the curves of the time constants of the involved defect types as a function of the electrical field.
[0036] FIG. 3 shows the curves of the time constants of the involved defect types as a function of the electrical field for three different dielectric layers.
[0037] FIGS. 4A through 4D schematically show the movement of different defect types in a dielectric layer along localized defect states, each with an average effective distance a.sub.0.
[0038] FIG. 5 shows the change in failure times t.sub.crit as a function of average effective distance of the localized defect centers a.sub.0 for four dielectric layers and two operating conditions.
[0039] FIG. 6A shows the curve of three leakage current measurements and the respectively adapted model curves that are ascertained on Pb.sub.1.3(Zr.sub.0.52Ti.sub.0.48)O.sub.3Ni.sub.0.005 as dielectric layer at the same operating temperature, but at different operating voltages.
[0040] FIG. 6B shows the curves of the time constants of the involved defect types as a function of the electrical field.
DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS
[0041] FIG. 1A shows curve 14 of a leakage current measurement of a dielectric layer of a semiconductor component, referred to below as exemplary embodiment 1. Time is logarithmically plotted on X axis 12 in units of seconds, and the leakage current density is logarithmically plotted on Y axis 10 in units of amperes per square centimeter. Exemplary embodiment 1, provided for the leakage current measurement, encompassed a silicon substrate including dielectric passivation layers and a first electrode deposited thereon. This first electrode included a double layer made of PVD platinum 110 nm thick, which was covered by a conductive 100-nm lanthanum nickel oxide buffer layer (referred to below as an LNO layer). This LNO layer was likewise applied via PVD. The dielectric layer situated on the first electrode had a thickness of 1 μm, and was deposited in an RF PVD process at a temperature of 480° C. and with a target composition of Pb.sub.1.3(Zr.sub.0.52Ti.sub.0.48)O.sub.3. The remaining process parameters of the above-described depositions were selected in such a way that the dielectric layer had polycrystalline growth, preferably with a (100) c axis orientation. The second electrode of the semiconductor element, which represented a platinum electrode 110 nm thick, was applied to the dielectric layer via PVD. The semiconductor component corresponding to exemplary embodiment 1 was passivated, and was not subjected to thermal aftertreatment after the electrical contacting.
[0042] In addition, FIG. 1A shows curve 16 of a leakage current measurement of a dielectric layer of a further semiconductor component, referred to below as exemplary embodiment 2.
[0043] The production of exemplary embodiment 2 took place analogously to exemplary embodiment 1, except that the components were subjected to thermal aftertreatment after electrical contacting. The thermal aftertreatment was carried out at 450° C. for 40 minutes in a 60 mbar nitrogen atmosphere.
[0044] Furthermore, FIG. 1A shows curve 18 of a leakage current measurement of a dielectric layer of a further semiconductor component, referred to below as exemplary embodiment 3. The production of exemplary embodiment 3 took place analogously to exemplary embodiment 1, except that the components were subjected to thermal aftertreatment after electrical contacting. The thermal aftertreatment was carried out at 500° C. for 40 minutes in a 60 mbar nitrogen atmosphere.
[0045] Prior to the measurement of the leakage current curves, all described exemplary embodiments 1, 2, and 3 were covered with passivation layers and electrically contacted via aluminum strip conductors.
[0046] All three exemplary embodiments were measured up to the respective dielectric breakdown 15, 17, and 19. It is apparent that very different leakage current curves 14, 16, and 18 with different breakdown times 15, 17, and 19 result, depending on the production of a dielectric layer.
[0047] FIG. 1B shows an example of the extraction of model variables based on measured leakage current curve 16 for exemplary embodiment 2, based on FIG. 1A. Once again, time is logarithmically plotted on X axis 32 in units of seconds, and change in barrier height Δϕ is logarithmically plotted on Y axis 30 in units of electron volts. Curve 38 shows the ascertained curve of the change in barrier height Δϕ(t) as a function of time, starting from an output barrier height ϕ.sub.0 34.
[0048] This curve 38 of change in barrier height Δϕ(t) is ascertained by the following formula (cf. above formula 2.2):
Φ(t)=[ln(K)−ln(J.sub.TED(t))]k.sub.BT
[0049] The ascertained temporal profile of average effective barrier height ϕ(t) is subsequently numerically adapted to the formula (cf. above formula 3.2):
ϕ(t)=ϕ.sub.0+Σ.sub.iΔϕ.sub.i.sup.+(t)+Σ.sub.iΔϕ.sub.i.sup.−(t)
[0050] Correspondingly different Δϕ.sub.i.sup.+/−(t)'s which describe the curve of Δϕ(t) are obtained from this numerical fit. Thus, in the case shown, Δϕ(t) 38 is described by the curve of Δϕ.sub.a.sup.−(t) 39, the curve of Δϕ.sub.b.sup.−(t) 40, and the curve of Δϕ.sub.c.sup.−(t) 42, together with summation curve Σ.sub.i Δϕ.sub.i.sup.+36. According to the following formula (cf. above formula 5.1)
[00014]
the different τ.sub.i.sup.+/−'s may then be ascertained. In this case, for changes in barrier height Δϕ.sub.i.sup.− 39, 40, and 42 associated with the majority charge carriers, associated characteristic time constants τ.sub.a, τ.sub.b, and τ.sub.c are obtained. These time constants are characterized in FIG. 1B by 47a, 47b, and 47c, respectively, and represent the point in time at which the corresponding change in barrier height changes most greatly. In order to improve clarity, the changes in barrier height for minority charge carriers Δϕ.sub.i.sup.+ have not been explicitly individually illustrated. Only their summation curve Σ.sub.i Δϕ.sub.i.sup.+ 36 together with individual time constants τ.sub.d, τ.sub.e, and τ.sub.f 49a, 49b, and 49c are shown. A particular characteristic time constant is associated with a defect type a, b, c, d, e, and f that is present in the layer, and accordingly, six different defect types are present in this dielectric layer.
[0051] In the case illustrated in FIG. 1B, dielectric breakdown 47 of the dielectric layer takes place via tunneling majority charge carriers, corresponding to the following formula (cf. above formula 9.2):
ϕ.sub.crit.sup.−=ϕ.sub.0.sup.−+Σ.sub.iΔϕ.sub.i.sup.−(t.sub.crit)=ϕ.sub.0.sup.−+Δϕ.sub.crit.sup.− where Δϕ.sub.crit.sup.−=Σ.sub.iΔϕ.sub.i.sup.−(t.sub.crit)
[0052] The previously ascertained curves of Δϕ.sub.a.sup.−(t) 39, Δϕ.sub.b.sup.−(t) 40, and Δϕ.sub.c.sup.−(t) 42 are thus summed, resulting in changes in barrier height Σ.sub.i Δϕ.sub.i.sup.− 44, corresponding to its curve. If change in barrier height Δϕ.sub.crit.sup.− 46 of the dielectric layer, which is critical for the majority charge carriers, is reached at point in time t.sub.crit 48, this results in a local breakdown of the layer due to the different defect types a, b, and c present which have accumulated at a boundary layer between the dielectric layer and the electrode.
[0053] FIG. 2A shows the curve of the leakage current, measured for exemplary embodiment 2, at different operating voltages and a constant operating temperature of 100° C. Here as well, time is logarithmically plotted on X axis 62 in units of seconds, and the leakage current density is logarithmically plotted on Y axis 60 in units of amperes per square centimeter. Leakage current curve 100 was measured at an operating voltage of 5 volts, curve 92 was measured at an operating voltage of 10 volts, curve 76 was measured at an operating voltage of 15 volts, and curve 68 was measured at an operating voltage of 20 volts. The measurements were carried out up to a respective dielectric breakdown 66, 82, 94, and 102 of the dielectric layer. The good agreement of the applied thermionic emission diffusion theory, as well as the good agreement of an effective barrier height, which is time-variable due to mobile defects, with the measuring curves is apparent from a comparison of measured current curves 76, 92, and 100 to associated model curves 78, 90, and 104.
[0054] Points 106a, 106b, and 106c marked in leakage current curve 100 represent ascertained characteristic time constants τ.sub.a, τ.sub.b, and τ.sub.c for this curve according to the method described for FIGS. 1A and 1B. Similarly, points 98a, 98b, and 98c marked in leakage current curve 92 represent ascertained characteristic time constants τ.sub.a, τ.sub.b, and τ.sub.c for this curve. In addition, points 80a and 80b marked in leakage current curve 76 represent ascertained characteristic time constants τ.sub.a and τ.sub.b for this curve. Points 72a and 72b marked in leakage current curve 68 represent ascertained characteristic time constants τ.sub.a and τ.sub.b for this curve. For the present measurements, each characteristic time constant τ.sub.a, τ.sub.b, and τ.sub.c is respectively associated with one of defect types a, b, and c present in the dielectric layer.
[0055] FIG. 2B shows the curves of the logarithm of time constants τ.sub.i of the defect types that are present, divided by seconds, as a function of the electrical field. The electrical field is plotted on X axis 112 in units of volts per meter, and the natural logarithm of characteristic time constants τ.sub.i is plotted on Y axis 110 without units. X axis section 140 denotes the electrical field that is applied to the dielectric layer at an operating voltage of 5 volts. Characteristic time constants 106a, 106b, and 106c of leakage current curve 100 together with the particular range of measured data 107a, 107b, and 107c identified in FIG. 2A are correspondingly once again present in a vertical through this axis section 140. X axis section 142 denotes the electrical field that is applied to the dielectric layer at an operating voltage of 10 volts. Characteristic time constants 98a, 98b, and 98c of leakage current curve 92 together with the particular range of measured data 99a, 99b, and 99c identified in FIG. 2A are correspondingly once again present in a vertical through this axis section 142. X axis section 144 denotes the electrical field that is applied to the dielectric layer at an operating voltage of 15 volts. Characteristic time constants 80a and 80b of leakage current curve 76 together with the particular range of measured data 81a identified in FIG. 2A are correspondingly once again present in a vertical through this axis section 144. X axis section 146 denotes the electrical field that is applied to the dielectric layer at an operating voltage of 20 volts. Characteristic time constants 72a and 72b of leakage current curve 68 together with the particular range of measured data 73a identified in FIG. 2A are correspondingly once again present in a vertical through this axis section 146.
[0056] Corresponding to formula (10.3) derived above,
[00015]
for defect types a, b, and c, straight lines 114, 116, and 118 having slopes m.sub.a, m.sub.b, and m.sub.c are obtained, which for a constant a.sub.0 result in integral defect charges N.sub.q,a, N.sub.q,b, and N.sub.q,c. Straight lines 114, 116, and 118 are shifted along the Y axis by constants K.sub.a, K.sub.b, and K.sub.c, which are a function of a.sub.0.
[0057] FIG. 3 shows the curves of the logarithm of the time constants of the defect types that are present, as a function of the electrical field, for three dielectric layers at 100° C. The electrical field is plotted on X axis 112 in units of volts per meter, and the natural logarithm of the characteristic time constants is plotted on Y axis 170 without units. X axis section 142 denotes the electrical field that is applied to the dielectric layers at an operating voltage of 10 volts. Identified characteristic time constants τ.sub.a 98a and τ.sub.b 98b together with the associated range of measured data 99a and 99b for exemplary embodiment 2 are once again present in a vertical through this axis section 142, correspondingly found in FIG. 2B. Identified characteristic time constants τ.sub.a 128a and τ.sub.b 134a together with the associated range of measured data 135a for exemplary embodiment 3 are likewise once again present in a vertical with respect to axis section 142. In addition, identified characteristic time constants τ.sub.a 130b and τ.sub.b 136b together with the associated range of measured data 161b and 137b for exemplary embodiment 1 are once again present in a vertical through axis section 142. X axis section 144 denotes the electrical field that is applied to the dielectric layers at an operating voltage of 15 volts. Identified characteristic time constants τ.sub.a 80a and τ.sub.b 80b together with the associated range of measured data 81a for exemplary embodiment 2 are once again present in a vertical through this axis section 144, correspondingly found in FIG. 2B. Identified characteristic time constants τ.sub.a 129a and τ.sub.b 135a together with the associated range of measured data 151a and 152a for exemplary embodiment 3 are once again likewise present in a vertical with respect to axis section 144. In addition, identified characteristic time constants τ.sub.a 131b and τ.sub.b 137b together with the associated range of measured data 162b and 153b for exemplary embodiment 1 are once again present in a vertical with respect to section 144. For defect type a, straight line 120 results for exemplary embodiment 3, straight line 114 results for exemplary embodiment 2, and straight line 122 results for exemplary embodiment 1. Each of these straight lines 114, 120, and 122 has a different slope m.sub.a and a shift K.sub.a(a.sub.0) along the Y axis which results from a different average effective distance a.sub.0 in each case. For defect type b, straight line 124 results for exemplary embodiment 3, straight line 116 results for exemplary embodiment 2, and straight line 126 results for exemplary embodiment 1. Each of these straight lines 116, 124, and 126 likewise has a different slope m.sub.b and a shift K.sub.b(a.sub.0) along the Y axis which results from a different average effective distance a.sub.0 in each case.
[0058] FIG. 4A schematically shows a semiconductor component 200 at a first point in time t.sub.0. Semiconductor component 200 includes a dielectric layer 230 having a layer thickness 208. Dielectric layer 230 may be a PZT layer, for example. In addition, semiconductor component 200 includes a first electrode 202 and a second electrode 201 that are situated opposite one another. A boundary layer 203 or 204 is also situated between a particular electrode 201 or 202 and dielectric layer 230. Different defect types are present in dielectric layer 230, which are denoted here by way of example as defect type 212 with a single positive charge 214, and defect types 215 and 217 with a single negative charge 216. Indices + and − denote the number of charge carriers of a defect type in question. Defect pairs or defect accumulations are present due to the necessary charge neutrality in dielectric layer 230. This means that when defects with a negative charge 215 and 217 occur, defects with a positive charge 212 also exist in the material. The different defect types 212, 215, and 217 are situated on localized anomalies 235. At first point in time t.sub.0 illustrated in FIG. 4A, no voltage between the electrodes 201 and 202, and thus also no electrical field, has yet been applied.
[0059] FIG. 4B shows semiconductor component 200 at a second point in time t.sub.1 subsequent to first point in time t.sub.0. A voltage is applied between first electrode 202 and second electrode 201, and thus an electrical field 220 is generated in the dielectric layer 230, at this point in time t.sub.1. The different defect types 212, 215, and 217 now vary as a function of the operating voltage applied between first electrode 201 and second electrode 202 and an operating temperature that is present along localized defect states 235. This movement state of defect types 212, 215, and 217 is also referred to as “hopping.” Localized defect states 235 each have same average effective distance a.sub.0 210. In this case, average effective distance a.sub.0 210 is greater than 3.2 nm. Defect types 212 with a positive charge 214 migrate to the electrode having a negative potential (in this case, first electrode 202) and accumulate in boundary layer 203 there. In contrast, defect types 215 and 217 with negative charge 216 move toward the electrode having a positive potential (in this case, second electrode 201) and accumulate in boundary layer 204 there. Charge carriers of leakage current J.sub.TED, which seek to move from one electrode to the other, must overcome Schottky barriers ϕ(t), which are influenced by boundary layers 203 and 204. These barriers have an output barrier height ϕ.sub.0, and undergo changes in barrier height Δϕ.sub.i due to the defect types that accumulate there.
[0060] FIG. 4C shows semiconductor component 200 at a third point in time t.sub.2 subsequent to second point in time t.sub.1. A plurality of the different defect types 212, 215, and 217 have already accumulated at boundary layers 202 and 203 of dielectric layer 230 and resulted in changes in barrier height Δϕ.sub.i there. A critical barrier height ϕ.sub.crit is reached at one of boundary layers 202 or 203 at a fourth point in time t.sub.3 subsequent to the third point in time. As is apparent from FIG. 4D, this now results in a local dielectric breakdown 225 of dielectric layer 230. A semiconductor component 200, which is locally destroyed on a limited surface, remains after t.sub.crit is exceeded. This is followed by even further local dielectric breakdowns 225 under continuing load at t>t.sub.crit, which ultimately results in complete destruction of semiconductor component 200.
[0061] FIG. 5 shows the change in failure times t.sub.crit as a function of average effective distance a.sub.0 of localized defect centers for three dielectric layers and three operating conditions. Failure time t.sub.crit is exponentially plotted on Y axis 300 in units of hours (h), and average effective distance a.sub.0 is linearly plotted on the X axis in units of nanometers (nm). Marking 335 denotes ascertained failure time t.sub.crit=46 s for exemplary embodiment 3 for an a.sub.0 of 3.24 nm and an operating voltage of −20 volts that are present, and an operating temperature of 150° C. Marking 336 denotes ascertained failure time t.sub.crit=192 s for exemplary embodiment 2 for an a.sub.0 of 3.49 nm and an operating voltage of −20 volts that are present, and an operating temperature of 150° C. Marking 337 denotes ascertained failure time t.sub.crit=305 s for exemplary embodiment 1 for an a.sub.0 of 3.65 nm and an operating voltage of −20 volts that are present, and an operating temperature of 150° C.
[0062] Connecting markings 335, 336, and 337 results in a straight line 340 that indicates how average effective distance a.sub.0 may be changed by a correspondingly different thermal treatment of the exemplary embodiments, and that a greater average effective distance a.sub.0 also results in greater failure times t.sub.crit.
[0063] Marking 345 denotes ascertained failure time t.sub.crit=2.95*10.sup.4 s for exemplary embodiment 3 for an a.sub.0 of 3.24 nm and an operating voltage of −2.5 volts that are present, and an operating temperature of 175° C. Marking 346 denotes ascertained failure time t.sub.crit=1.11*10.sup.5 s for exemplary embodiment 2 for an a.sub.0 of 3.49 nm and an operating voltage of −2.5 volts that are present, and an operating temperature of 175° C. Marking 347 denotes ascertained failure time t.sub.crit=3.99*10.sup.5 s for exemplary embodiment 1 for an a.sub.0 of 3.65 nm and an operating voltage of −2.5 volts that are present, and an operating temperature of 175° C.
[0064] Markings 345, 346, and 347 have significantly greater failure times due to the different operating conditions compared to 335, 336, and 337. However, here as well, connecting markings 345, 346, and 347 results in a straight line 350 that confirms the above-described relationship and thus shows that the relationship between average effective distance a.sub.0 and failure time t.sub.crit is valid, regardless of the operating conditions that are present.
[0065] Marking 365 denotes ascertained failure time t.sub.crit=5.25*10.sup.4 s for exemplary embodiment 3 for an a.sub.0 of 3.24 nm and an operating voltage of −10 volts that are present, and an operating temperature of 100° C. Marking 366 denotes ascertained failure time t.sub.crit=1.1*10.sup.5 s for exemplary embodiment 2 for an a.sub.0 of 3.49 nm and an operating voltage of −10 volts that are present, and an operating temperature of 100° C. Marking 367 denotes ascertained failure time t.sub.crit=2.42*10.sup.5 s for exemplary embodiment 1 for an a.sub.0 of 3.65 nm and an operating voltage of −10 volts that are present, and an operating temperature of 100° C.
[0066] After being connected, markings 365, 366, and 367 result in a straight line 370 that once again confirms the above-described relationship and thus shows that the relationship between average effective distance a.sub.0 and failure time t.sub.crit is valid, regardless of the operating conditions that are present. For a.sub.0=3.2 nm, a failure time of 12 hours results with regard to straight line 370. For the design of a PZT actuator, continuous operation over a period of 12 hours at a maximum voltage of 10 V and a maximum operating temperature of 100° C. is a practical requirement for a consumer electronics product (a micromirror, for example).
[0067] For examined exemplary embodiments 1, 2, and 3, it was possible to identify in each case three different defect types a, b, and c that are responsible for contributions Σ.sub.i Δϕ.sub.i.sup.−. On the one hand, this includes defect type a having a charge of 1 e and a true activation energy of 0.92 eV that are present. In the present exemplary embodiments, this defect type may be associated with hydrogen or OH groups within the dielectric layer. On the other hand, this includes defect type b having a charge of 3 e and a true activation energy of 0.95 eV that are present. In the present exemplary embodiments, this defect type may be associated with lead and/or titanium within the dielectric layer. Defect type c has a charge of 4 e and a true activation energy 0.855 eV that are present. In the present exemplary embodiments, this defect type may be associated with lead, titanium, and/or zirconium within the dielectric layer.
[0068] For examined exemplary embodiments 1, 2, and 3, it was also possible to identify in each case three different defect types d, e, and f that are responsible for contributions Σ.sub.iΔϕ.sub.i.sup.+. On the one hand, this includes defect type d having a charge of 1 e and a true activation energy of less than 0.8 eV that are present. In the present exemplary embodiments, this defect type may be associated with hydrogen within the dielectric layer. On the other hand, this includes defect type e having a charge of 2 e and a true activation energy of 1.04 eV that are present. In the present exemplary embodiments, this defect type may be associated with oxygen or lead within the dielectric layer. Defect type e has a charge of 2 e and a true activation energy 1.22 eV that are present. In the present exemplary embodiments, this defect type may be associated with lead within the dielectric layer.
[0069] FIG. 6A shows curves 404, 406, and 408 of leakage current measurements on Pb.sub.1.3(Zr.sub.0.52Ti.sub.0.48)O.sub.3Ni.sub.0.005 as dielectric layer of a semiconductor element, referred to as exemplary embodiment 4. The production of exemplary embodiment 4 took place analogously to exemplary embodiment 1, except that the dielectric layer was deposited with a target composition of Pb.sub.1.3(Zr.sub.0.52Ti.sub.0.48)O.sub.3Ni.sub.0.005.
[0070] The curves of the leakage current shown in FIG. 6A were measured at different operating voltages and a constant operating temperature of 150° C. Time is logarithmically plotted on X axis 402 in units of seconds, and the leakage current is logarithmically plotted on Y axis 400 in units of amperes. Leakage current curve 408 was measured at an operating voltage of 5 volts, curve 406 was measured at an operating voltage of 10 volts, and curve 404 was measured at an operating voltage of 15 volts. The measurements were carried out up to a respective dielectric breakdown 410, 412, and 414 of the dielectric layer. The good agreement of the applied thermionic emission diffusion theory, as well as the good agreement of an effective barrier height, which is time-variable due to mobile defects, with the measuring curves is apparent from a comparison of measured current curves 404, 406, and 408 to associated model curves 422, 430, and 438.
[0071] Points 432, 434, and 436 marked in leakage current curve 408 represent characteristic time constants τ.sub.g, τ.sub.h, and τ.sub.j for this curve, ascertained analogously according to the method described for FIGS. 1A and 1B for exemplary embodiments 1 through 3. Similarly, points 424, 426, and 428 marked in leakage current curve 406 represent ascertained characteristic time constants τ.sub.g, τ.sub.h, and τ.sub.j for this curve. In addition, points 416, 418, and 420 marked in leakage current curve 404 represent ascertained characteristic time constants τ.sub.g, τ.sub.h, and τ.sub.j for this curve. For the present measurements, each characteristic time constant τ.sub.g, τ.sub.h, and τ.sub.j is respectively associated with one of defect types type g, h, and j present in the dielectric layer.
[0072] FIG. 6B shows the curves of the logarithm of time constants τ.sub.i of the defect types that are present, divided by seconds, as a function of the electrical field. The electrical field is plotted on X axis 451 in units of volts per meter, and the natural logarithm of characteristic time constants τ.sub.i is plotted on Y axis 450 without units. X axis section 455 denotes the electrical field that is applied to the dielectric layer at an operating voltage of 5 volts. Characteristic time constants 432, 434 and 436 of leakage current curve 408 together with the particular range of measured data 481, 484, and 508 identified in FIG. 6A are correspondingly once again present in a vertical through this axis section 455. X axis section 460 denotes the electrical field that is applied to the dielectric layer at an operating voltage of 10 volts. Characteristic time constants 424, 426, and 428 of leakage current curve 406 together with the particular range of measured data 488, 498, and 512 identified in FIG. 6A are correspondingly once again present in a vertical through this axis section 460. X axis section 465 denotes the electrical field that is applied to the dielectric layer at an operating voltage of 15 volts. Characteristic time constants 416, 418, and 420 of leakage current curve 404 together with the particular range of measured data 492, 482, and 516 identified in FIG. 6A are correspondingly once again present in a vertical through this axis section 465.
[0073] Corresponding to formula (10.3), for defect types g, h, and j, straight lines 480, 494, and 504 having slopes m.sub.g, m.sub.h, and m.sub.j are obtained, which for a constant a.sub.0=3.1 nm result in integral defect charges N.sub.q,g=2, N.sub.q,h=3, and N.sub.q,j=4. Straight lines 480, 494, and 504 are shifted along the Y axis by constants K.sub.g, K.sub.h, and K.sub.j, which are a function of a.sub.0.
