Patent Publication Number: US-2022238791-A1

Title: Semiconductor component including a dielectric layer

Description:
FIELD 
     The present invention relates to a semiconductor component. 
     BACKGROUND INFORMATION 
     The “hopping” of a defect type, for example oxygen vacancies, present in a dielectric layer is described in “Improved reliability predictions in high permittivity dielectric oxide capacitors under high dc electric fields with oxygen vacancy induced electromigration” by C. A. Randall, R. Maier, W. Qu, K. Kobayashi, K. Morita, Y. Mizuno, N. Inoue, and T. Oguni, Journal of Applied Physics 113, 014101 (2013), as the reason for breakdown in a dielectric layer. The key model parameters are physically motivated, but are empirically ascertained by fitting to the failure time, assuming only one active defect type. A description of how these parameters correlate more closely with the material is not provided. Complex failure mechanisms, for which multiple defect types are present in the semiconductor layer, are mapped incompletely or not at all. The service life prediction described therein is valid only when, for a load case in question having a certain temperature and a certain electrical field, one defect type dominates, and in addition the failure is caused solely by the accumulation of this one defect type at a boundary layer. 
     Furthermore, in “Highly accelerated lifetime testing of potassium sodium niobate thin films” by Wanlin Zhu, Betul Akkopru-Akgun, and Susan Trolier-McKinstry, Applied Physics Letters 111, 212903 (2017), typical failure frequencies over the operating period are determined for various operating conditions. It is clear therefrom that the failure mechanism in the material differs within a sample group over the tested operating conditions or even for one particular operating condition. However, it is also not possible, based on the empirical model, to derive links to physical, electrical, or chemical processes in the material. 
     An object of the present invention is to optimize the service life of a semiconductor component having more than one active defect type, as a function of the provided main operating voltage and main operating temperature of the semiconductor component. 
     SUMMARY 
     The object may be achieved by providing a semiconductor component according to an example embodiment of the present invention. Such a semiconductor component is produced on silicon substrates with the aid of thin-film technologies, and may be used, for example, as a piezoelectric actuator for MEMS components such as micromirrors. In accordance with an example embodiment of the present invention, the semiconductor component includes at least one dielectric layer. In addition, the semiconductor component includes at least one first electrode and one second electrode via which a main operating voltage is applied to the dielectric layer. The main operating voltage is the highest allowable potential difference at the two electrodes of the semiconductor component during active operation, according to the specification of the semiconductor component. Furthermore, at least two different defect types are also present in the dielectric layer. These defect types may be vacancies (oxygen or lead vacancies, for example), lattice distortion due to occupied interstices (occupied by hydrogen, for example), Frenkel defects, or also substitutional defects (due to intentionally or unintentionally introduced foreign atoms, for example). These defect types differ from one another with respect to their electrical charge number, for example. A first electrical charge N q,1  and a first material- and defect-dependent true activation energy E A,0,1  are associated with a first defect type. A second electrical charge N q,2  and a second true activation energy E A,0,2  are associated with a second defect type. The at least two different defect types accumulate at characteristic times τ 1  and τ 2  at a boundary layer of the two electrodes as a function of a main operating voltage that is applied between the first electrode and the second electrode, and a main operating temperature that is present, and generate maximum changes in barrier height δΦ 1  and δΦ 2  at the electrodes. The main operating temperature is the highest allowable temperature during active operation, according to the specification of the semiconductor component. τ 1  and δΦ 1  are associated with the first defect type, and τ 2  and δΦ 2  are associated with the second defect type. The greater the maximum change in barrier height δΦ 1  and δΦ 2  and the smaller τ 1  and τ 2  of the corresponding defect type are, the more quickly critical change in barrier height Δϕ crit   +/−  is reached at one of the boundary layers between the dielectric layer and the electrodes, resulting in a dielectric breakdown. For the semiconductor component according to an example embodiment of the present invention, τ 2  is greater than τ 1 . This means that the second defect type basically requires more time in comparison to the first defect type to move within the dielectric layer toward an electrode and accumulate at a boundary layer of the electrode. However, δΦ 1 &lt;δΦ 2  also applies, and therefore maximum change in barrier height δΦ 2  generated by the second defect type is greater than maximum change in barrier height δΦ 1  generated by the first defect type. Thus, a defect type that has comparatively less influence on the electrical breakdown of the dielectric layer initially reaches the boundary layer. The resulting effect is that critical change in barrier height Δϕ crit   +/−  of the electrode is reached only at a later time, and thus a longer service life is achieved under the operating conditions for which the semiconductor component has been designed. 
     Maximum changes in barrier height δΦ i  may be influenced, for example, via the selection of the starting materials during the deposition process for the dielectric layer. For example, in the case of a PZT layer, a lead, zirconium, and/or titanium deficit or excess may be set via the composition in the starting material. This means that for the case of a sputter deposition the selection of the target material, and for the case of sol-gel depositions the selection of the precursor sols, may be of importance. Thus, for example, δΦ i &#39;s associated with lead vacancies may be decreased beyond a stoichiometric composition by increasing the lead content in the target or in the precursor sols. In contrast, for example δΦ i &#39;s associated with a lead excess may be decreased by reducing the lead content in the target or in the precursor sols. 
     Furthermore, maximum changes in barrier height δΦ i  may be changed, for example, via process parameters during the deposition. Thus, for example, elevated temperatures in the PZT sputtering process may result in outgassings of lead, resulting in a reduction of the lead content in the layer. Thus, δΦ i &#39;s associated with lead vacancies could be decreased by reducing the process temperature in the PZT sputtering process. 
     The involved process gases may also be utilized to influence defect species. Oxygen vacancies, for example, are a known defect type in PZT layers. The quantity of oxygen vacancies present in the material may be influenced, among other ways, by changing the oxygen partial pressure during a PZT sputter deposition. Thus, for example, δΦi&#39;s associated with oxygen vacancies could be decreased by adding an oxygen flow. 
     Follow-up processes are often necessary for the passivation and contacting of a semiconductor component. In addition, follow-up processes are often necessary for the production of other components on the same substrate. These follow-up processes may have a very great influence on the electrical service life of a semiconductor component. If hydrogen from follow-up processes penetrates into the lead oxide structure of the PZT, the oxygen may reduce the lead oxide. This creates an oxygen vacancy together with outgassing of H 2 O or OH sites, or mobile hydrogen ions result in the structure. The reduction of the hydrogen content in follow-up processes, such as the deposition of passivations in hydrogen-containing plasma processes, results in a reduction of δΦ i &#39;s associated with the oxygen vacancies or hydrogen ions. In such processes, for example the hydrogen content may be reduced by using a lower-hydrogen precursor, for example by using N 2  instead of NH 3  as a nitrogen source in the deposition of a PECVD SiN passivation. For example, a further option for reducing hydrogen in the deposition of PECVD passivations is to reduce the gas flows of a hydrogen-containing precursor in order to achieve a reduction in δΦ i &#39;s associated with the oxygen vacancies or hydrogen ions. 
     The quantity of defects and/or δΦ i &#39;s associated with the oxygen vacancies or hydrogen ions may be influenced via a suitable selection of the follow-up processes and/or also by use of hydrogen barriers that envelop the dielectric. Enveloping the PZT with a hydrogen barrier (for example, sputtered metal oxides: RuO, TiO, AlO x ) likewise results in a reduction in δΦ i &#39;s associated with the oxygen vacancies or hydrogen ions. A further option for reducing material damage caused by hydrogen is to reduce the temperatures and/or the duration of thermal steps in the follow-up processes in order to provide less energy for the reaction with the dielectric layer. This results in a reduction in δΦ i &#39;s associated with the oxygen vacancies or hydrogen ions. 
     In a further example embodiment of the present invention, for known dominant oxygen vacancies in the dielectric material, thermal steps in an oxygen atmosphere may be provided. The subsequent introduction of oxygen into a structure with oxygen vacancies results in a reduction of δΦ i &#39;s associated with the oxygen vacancies. 
     For example, the criterion according to which τ 1 &lt;τ 2  and δΦ 1 &lt;δΦ 2  may be achieved by doping the dielectric layer with at least one further defect type in such a way that δΦ 1 &lt;δΦ 2  applies for the maximum changes in barrier height at the contact between the dielectric layer and the electrode. The energetic structure in the material interior may be changed in this way. Thus, for example, for an existing interfering defect type a, having a comparably small τ 1  and a large δΦ 1 , new deeper, localized defect centers not previously present, i.e., having a lower local minimum of the potential energy, are created. The mobility of interfering defect type a may thus be reduced. Introducing the further defect type may in fact result in a further large maximum barrier height decrease δΦ 3 . However, this decrease for the corresponding main operating condition preferably only takes place at a point in time after the electrical failure of the dielectric layer at point in time t crit  The reason is that the involved further defect type has a characteristic time constant τ 3  that is so large that, up to the failure of the component, the further defect type cannot accumulate at a boundary layer of the electrodes. 
     Defects may also be unintentionally introduced into the starting materials due to contaminations, which may be reduced by increasing the degree of purity of the starting materials, for example of the target for sputtering, or of the precursor sols in the sol-gel process. The reduction of foreign substances (iron, chlorine, for example) in the structure of the dielectric layer thus reduces δΦ i &#39;s associated with these defects. 
     When field-activated defects dominate over thermally activated defects, increasing the thickness of the dielectric layer is a further option for changing the sequence in the defect structure. Increasing the thickness of the dielectric layer, for example for the case of piezoelectric actuators with PZT in particular, is an option for increasing the service life with the actuator force unchanged, since a small electrical field increases all time constants τ i  of the involved i defect types. 
     Over the load period up to dielectric failure, a semiconductor component in accordance with an example embodiment of the present invention shows a temporal profile of leakage current density J TED , which is described by the equation of thermionic emission diffusion theory according to Crowell and Sze: 
     
       
         
           
             
               
                 
                   
                     J 
                     TED 
                   
                   = 
                   
                     
                       
                         q 
                         · 
                         
                           N 
                           C 
                         
                         · 
                         
                           v 
                           R 
                         
                       
                       
                         1 
                         + 
                         
                           
                             v 
                             R 
                           
                           
                             v 
                             D 
                           
                         
                       
                     
                     · 
                     
                       e 
                       
                         - 
                         
                           
                             Φ 
                             B 
                             eff 
                           
                           
                             
                               k 
                               B 
                             
                             · 
                             T 
                           
                         
                       
                     
                     · 
                     
                       [ 
                       
                         
                           e 
                           
                             
                               q 
                               · 
                               U 
                             
                             
                               
                                 k 
                                 B 
                               
                               · 
                               T 
                             
                           
                         
                         - 
                         1 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where q is the unit charge, N C  is the effective density of states in the conduction band, v R  is the effective recombination velocity, v D  is the effective diffusion velocity, ϕ B   eff  is the effective Schottky barrier, k B  is the Boltzmann constant, T is the ambient temperature, and U is the potential difference across the dielectric layer. In this regard, U means the main operating voltage that is applied to the two electrodes of the semiconductor component. 
     The temporal profile of the leakage current density results from the change in effective Schottky barrier ϕ B   eff (t). This change or Schottky barrier ϕ B   eff (t) characterizes the influence of the two boundary layers, situated between the two electrodes and the dielectric layer, on the leakage current density. The effective Schottky barrier is also referred to below as ϕ(t) for short, and encompasses all components of semiconductor-electrode material transfer, changes due to the applied main operating voltage, and changes due to the accumulation of defects. The logarithm of the leakage current density reduces equation (1) to a time constant K and a time-variable term, which reflects the processes in the material interior that are caused by the movements of all mobile defects contained in the material: 
     
       
         
           
             
               
                 
                   
                     ln 
                     ⁡ 
                     
                       ( 
                       
                         
                           J 
                           
                             T 
                             ⁢ 
                             E 
                             ⁢ 
                             D 
                           
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ln 
                         ⁡ 
                         
                           ( 
                           K 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             
                               Φ 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             
                               
                                 k 
                                 B 
                               
                               · 
                               T 
                             
                           
                           . 
                           
                               
                           
                           ⁢ 
                           where 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         K 
                       
                     
                     = 
                     
                       
                         
                           q 
                           · 
                           
                             N 
                             C 
                           
                           · 
                           
                             v 
                             R 
                           
                         
                         
                           1 
                           + 
                           
                             
                               v 
                               R 
                             
                             
                               v 
                               D 
                             
                           
                         
                       
                       · 
                       
                         [ 
                         
                           
                             e 
                             
                               
                                 q 
                                 · 
                                 U 
                               
                               
                                 
                                   k 
                                   B 
                                 
                                 · 
                                 T 
                               
                             
                           
                           - 
                           1 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2.1 
                   ) 
                 
               
             
           
         
       
     
     The term “defect” also encompasses structural changes in the structure. 
     The displacement of the defects upon approach to the electrodes results in defect accumulations in the dielectric layer which result in changes in the effective barrier height. Solving equation 2.1 for ϕ results in 
     
       
         
           
             
               
                 
                   
                     Φ 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           ln 
                           ⁡ 
                           
                             ( 
                             K 
                             ) 
                           
                         
                         - 
                         
                           ln 
                           ⁡ 
                           
                             ( 
                             
                               
                                 J 
                                 
                                   T 
                                   ⁢ 
                                   E 
                                   ⁢ 
                                   D 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     ⁢ 
                     
                       k 
                       B 
                     
                     ⁢ 
                     T 
                   
                 
               
               
                 
                   ( 
                   2.2 
                   ) 
                 
               
             
           
         
       
     
     This temporal profile of the effective barrier height due to the accumulation of defects is described by the approach 
     
       
         
           
             
               
                 
                   
                     ϕ 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           ϕ 
                           + 
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       + 
                       
                         
                           ϕ 
                           - 
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                     = 
                     
                       
                         ϕ 
                         0 
                         + 
                       
                       + 
                       
                         
                           ∑ 
                           i 
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                             
                               ϕ 
                               i 
                               + 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       + 
                       
                         ϕ 
                         0 
                         - 
                       
                       + 
                       
                         
                           ∑ 
                           i 
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                             
                               ϕ 
                               i 
                               - 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3.1 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ϕ 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         ϕ 
                         0 
                       
                       + 
                       
                         
                           ∑ 
                           i 
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                             
                               ϕ 
                               i 
                               + 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       + 
                       
                         
                           ∑ 
                           i 
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                             
                               ϕ 
                               i 
                               - 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
                       where 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ϕ 
                         0 
                       
                     
                     = 
                     
                       
                         ϕ 
                         0 
                         + 
                       
                       + 
                       
                         ϕ 
                         0 
                         - 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3.2 
                   ) 
                 
               
             
           
         
       
     
     In general, accumulations and associated changes in the effective Schottky barrier occur at both boundary layers ϕ + (t) and ϕ − (t). Indices + and − each denote the changes at the boundary layer, which characterizes the transition from minority charge carriers or majority charge carriers in the dielectric layer. The boundary layers have an output barrier height ϕ 0 , and experience changes in barrier height Δϕ i  caused by a defect type i. Defect pairs or defect accumulations must always be present due to the necessary charge neutrality. This means that when defects with a negative charge occur, defects with a positive charge also exist in the material. The effects of these defects are respectively denoted by indices + and −. The individual defects move in the opposite direction in the applied electrical field of the main operating voltage, depending on their charge. Defects with a positive charge migrate to the electrode having a negative potential, and accumulate in the vicinity thereof in the dielectric layer. Defects with a negative charge move to the electrode having a positive potential, and in turn accumulate in the vicinity thereof. 
     Change in barrier height Δϕ i , which is brought about by defect type i, is characterized by its maximum height δϕ i  and a characteristic time constant τ i  in which the change in barrier height changes most greatly: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       
                         ϕ 
                         i 
                         
                           + 
                           
                             / 
                             - 
                           
                         
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                   
                   = 
                   
                     δ 
                     ⁢ 
                     
                       
                         ϕ 
                         i 
                         
                           + 
                           
                             / 
                             - 
                           
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             e 
                             
                               τ 
                               i 
                               
                                 t 
                                 
                                   + 
                                   
                                     / 
                                     - 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In general, δϕ i  is a function of defect number Z i , but is additionally a function of the type of boundary layer. The effect of the defect number cannot be generalized, since a significant change in barrier height Δϕ i  may already result due to accumulation of a monolayer. Therefore, for materials according to an example embodiment of the present invention, Z i &gt;0 alone is crucial. The term 
     
       
         
           
             ( 
             
               1 
               - 
               
                 e 
                 
                   τ 
                   i 
                   
                     t 
                     
                       + 
                       
                         / 
                         - 
                       
                     
                   
                 
               
             
             ) 
           
         
       
     
     in the above formula represents an approximation of the statistical accumulation of a defect distribution that is present in the material. The positive and negative maximum heights of barrier change δϕ +  and δϕ −  and associated time constants τ i   +  and τ i   +  have different magnitudes, since different defects and different boundary layers are involved. Together with formula (3.2), this results in 
     
       
         
           
             
               
                 
                   
                     
                       ϕ 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         ϕ 
                         0 
                       
                       + 
                       
                         
                           ∑ 
                           i 
                         
                         ⁢ 
                         
                           δ 
                           ⁢ 
                           
                             
                               ϕ 
                               i 
                               
                                 + 
                                 
                                   / 
                                   - 
                                 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   e 
                                   
                                     t 
                                     
                                       τ 
                                       i 
                                       
                                         + 
                                         
                                           / 
                                           - 
                                         
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     and for the time-variable portion of the barrier change, results in 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       ϕ 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       ∑ 
                       i 
                     
                     ⁢ 
                     
                       δ 
                       ⁢ 
                       
                         
                           ϕ 
                           i 
                           
                             + 
                             
                               / 
                               - 
                             
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               e 
                               
                                 t 
                                 
                                   τ 
                                   i 
                                   
                                     + 
                                     
                                       / 
                                       - 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.1 
                   ) 
                 
               
             
           
         
       
     
     Time constant τ i   +/−  is defined by the mobility of the defects in the dielectric layer and the distance to be covered in this layer. During the displacement within the dielectric layer, defect type i must cover distance d i  of the center of gravity of its distribution with respect to the boundary layer. Together with velocity v i , the characteristic time constant for the accumulation process of defect type i results in 
     
       
         
           
             
               
                 
                   
                     τ 
                     i 
                   
                   = 
                   
                     
                       d 
                       i 
                     
                     
                       v 
                       i 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Semiconductor components according to an example embodiment of the present invention are characterized by a displacement of the defects in the applied electrical field of the main operating voltage via hopping. Defect type i moves along localized defect states having an average effective distance a i . This results in a hopping velocity v i , which is described via the known approach of variable range hopping: 
     
       
         
           
             
               
                 
                   
                     
                       v 
                       i 
                     
                     = 
                     
                       
                         
                           C 
                           
                             0 
                             , 
                             i 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             a 
                             i 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           - 
                           
                             
                               E 
                               
                                 A 
                                 , 
                                 0 
                                 , 
                                 i 
                               
                             
                             
                               
                                 k 
                                 B 
                               
                               ⁢ 
                               T 
                             
                           
                         
                       
                       ⁢ 
                       
                         sinh 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 N 
                                 
                                   q 
                                   , 
                                   i 
                                 
                               
                               ⁢ 
                               
                                 a 
                                 i 
                               
                               ⁢ 
                               E 
                             
                             
                               
                                 k 
                                 B 
                               
                               ⁢ 
                               T 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
                       where 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       E 
                     
                     = 
                     
                       U 
                       d 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       C 
                       
                         0 
                         , 
                         i 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         a 
                         i 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ν 
                       0 
                     
                     ⁢ 
                     
                       a 
                       i 
                     
                     ⁢ 
                     
                       e 
                       
                         - 
                         
                           
                             2 
                             ⁢ 
                             
                               a 
                               i 
                             
                           
                           α 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7.1 
                   ) 
                 
               
             
           
         
       
     
     C 0,i (a i ) represents a function that describes the influence of the local defect distribution. As is customary for variable range hopping, hopping attempt frequency v i  refers to the frequency with which a defect runs up against potential barriers that are present. In addition, the hopping likelihood of the defect is proportional to overlap integral 
     
       
         
           
             e 
             
               - 
               
                 
                   2 
                   ⁢ 
                   
                     a 
                     i 
                   
                 
                 α 
               
             
           
         
       
     
     of the wave functions of two hydrogen-like localized defects having decay length α at distance a i  of the localized defect states. C 0,i (a i ) represents a function that describes the influence of the local defect distribution. The hopping likelihood, which increases with the operating temperature, is taken into account via the exponential term containing material- and defect-dependent true activation energy E A,0,i . True activation energy E A,0,i  refers to an activation energy that is independent of the operating voltage and operating temperature. The term exp (−E A,0,i /(k B T)) becomes dominant as the main operating temperature increases and the main operating voltage at the same time decreases. This means that under these operating conditions, defect types with high true activation energy and low charge contribute to the electrical failure of the semiconductor component. The hyperbolic sine, which contains the product of charge N q,i  associated with defect i, average localized defect center distance a i , and electrical field E, describes the targeted lowering of the energy barriers in the hopping process. Electrical field E results from applied main operating voltage U and thickness d of the dielectric layer. The term sink (N q,i  a i  E/(k B T)) gains in influence with increasing main operating voltages and decreasing main operating temperatures. In this case, defect types with a high charge number and at the same time with low true activation energy contribute to the electrical failure of the semiconductor component. 
     For a semiconductor component, the n defect types contained in the dielectric layer move across localized defect states having same average distance a 0 , so that the following applies: 
     
       
         
           
             
               
                 
                   
                     a 
                     1 
                   
                   = 
                   
                     
                       
                         a 
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       … 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         a 
                         n 
                       
                     
                     = 
                     
                       a 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     This distance of the localized defect states may be extracted from leakage current data J TED  with knowledge of the physical modeling described above. The average effective distance a 0  represents a key material property for the dielectric failure under thermal load and voltage load. This material property is independent of the operating voltage and the operating temperature, and may be influenced via the manufacturing process. 
     With knowledge of the physical modeling described above, for involved i defect types, charge N q,i  and true activation energy E a,0,i  may be determined from leakage current data J TED  In addition, for an operating state the associated temporal profile of barrier decrease Δϕ i  may be ascertained. This temporal profile of barrier decrease Δϕ i  is described by characteristic time constant τ i , in which change in barrier height Δϕ i  changes most greatly, and by its maximum decrease in barrier height δϕ i . With knowledge of charge N q,i  and true activation energy E a,0,i , the defect types may be identified over various operating states and associated with their effect Δϕ i , which differs according to the operating state. Thus, for semiconductor components it is possible to identify the operating state via which a long service life may be achieved. This operating state is characterized in that faster defect types with time constants τ i  less than failure time t crit  have comparably small maximum decreases in barrier height δϕ i . 
     For semiconductor components, critical changes in barrier heights Δϕ crit   +/−  exist for the two boundary layers. If one of these critical changes in barrier heights Δϕ crit   +/−  is reached or exceeded locally at point in time t crit , the dielectric breakdown takes place locally. This means that when Δϕ crit   +  is reached, the breakdown takes place via tunneling minority charge carriers (case 1): 
     
       
         
           
             
               
                 
                   
                     
                       ϕ 
                       crit 
                       + 
                     
                     = 
                     
                       
                         
                           ϕ 
                           0 
                           + 
                         
                         + 
                         
                           
                             ∑ 
                             i 
                           
                           ⁢ 
                           
                             
                               Δϕ 
                               i 
                               + 
                             
                             ⁡ 
                             
                               ( 
                               
                                 t 
                                 crit 
                               
                               ) 
                             
                           
                         
                       
                       = 
                       
                         
                           ϕ 
                           0 
                           + 
                         
                         + 
                         
                           Δϕ 
                           crit 
                           + 
                         
                       
                     
                   
                   , 
                   
                     
                       where 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Δϕ 
                         crit 
                         + 
                       
                     
                     = 
                     
                       
                         ∑ 
                         i 
                       
                       ⁢ 
                       
                         
                           Δϕ 
                           i 
                           + 
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             crit 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9.1 
                   ) 
                 
               
             
           
         
       
     
     In contrast, when ϕ crit   −  is reached, the breakdown takes place via tunneling majority charge carriers (case 2): 
     
       
         
           
             
               
                 
                   
                     
                       
                         ϕ 
                         crit 
                       
                       - 
                     
                     = 
                     
                       
                         
                           ϕ 
                           
                             0 
                             - 
                           
                         
                         + 
                         
                           
                             Σ 
                             i 
                           
                           ⁢ 
                           
                             
                               Δϕ 
                               
                                 i 
                                 - 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 t 
                                 crit 
                               
                               ) 
                             
                           
                         
                       
                       = 
                       
                         
                           ϕ 
                           
                             0 
                             - 
                           
                         
                         + 
                         
                           Δϕ 
                           
                             crit 
                             - 
                           
                         
                       
                     
                   
                   , 
                   
                     
                       where 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Δϕ 
                         
                           crit 
                           - 
                         
                       
                     
                     = 
                     
                       
                         Σ 
                         i 
                       
                       ⁢ 
                       
                         
                           Δϕ 
                           
                             i 
                             - 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             t 
                             crit 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9.2 
                   ) 
                 
               
             
           
         
       
     
     When Δϕ crit  is locally reached, a local increase in the current density up to the local destruction of the semiconductor element takes place. In the curve of leakage current density J TED  at point in time t=t crit , this is apparent either via a brief rise, followed by a direct reversion to the J TED  value prior to the increase, or via a continuous jump. In the first case, the conduction path itself is thermally destroyed. In the second case, the supplied electrical power is not sufficient to completely destroy the conduction path. After t crit  is exceeded, a semiconductor component remains which is locally destroyed on a limited surface. Increasing load with t&gt;t crit  results in even further local dielectric breakdowns, which ultimately results in complete destruction of the semiconductor component. The first local breakdown thus represents a relevant measure for the service life of the semiconductor component. 
     By use of the physical description of the change in barrier height (5) via hopping transport of the n defect types (6) and (7), charge N q,i , true activation energy E a,0,i , the level of maximum barrier changes δϕ i , and characteristic time constant τ i  may thus be ascertained from temporal profiles of the leakage current density (1). Semiconductor components may be improved in a targeted manner by this measurement before and after a variation in the manufacturing process. 
     For this purpose, leakage current curves J TED  up to the dielectric breakdown at point in time t crit  are initially measured at a semiconductor component at at least two operating voltages U 1  and U 2  and at least two main operating temperatures T 1  and T 2 . Equations (2.2) and (5) described above are subsequently set equal to one another, and the temporal profile of change in barrier height Δϕ, individual variables δϕ i , and τ i  as a function of the operating voltage result from a numerical fit, based on the temporal profile of J TED . By use of (9.1) or (9.2), critical barrier decrease Δϕ crit  as a function of the main operating voltage and main operating temperature is also obtained. 
     τ i  is obtained as a function of electrical field E and the main operating temperature according to formulas (6), (7), and (8) described above: 
     
       
         
           
             
               
                 
                   
                     
                       τ 
                       i 
                     
                     ⁡ 
                     
                       ( 
                       
                         E 
                         ; 
                         T 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           d 
                           i 
                         
                         
                           
                             
                               C 
                               
                                 0 
                                 , 
                                 i 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 a 
                                 0 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             e 
                             
                               - 
                               
                                 
                                   E 
                                   
                                     A 
                                     , 
                                     o 
                                     , 
                                     i 
                                   
                                 
                                 
                                   
                                     k 
                                     B 
                                   
                                   ⁢ 
                                   T 
                                 
                               
                             
                           
                         
                       
                       ⁢ 
                       
                         1 
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             h 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       N 
                                       
                                         q 
                                         , 
                                         i 
                                       
                                     
                                     ⁢ 
                                     
                                       a 
                                       0 
                                     
                                   
                                   
                                     
                                       k 
                                       B 
                                     
                                     ⁢ 
                                     T 
                                   
                                 
                                 ⁢ 
                                 E 
                               
                               ) 
                             
                           
                         
                       
                     
                     = 
                     
                       
                         
                           
                             K 
                             ~ 
                           
                           i 
                         
                         ⁡ 
                         
                           ( 
                           
                             a 
                             0 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         1 
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             h 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       N 
                                       
                                         q 
                                         , 
                                         i 
                                       
                                     
                                     ⁢ 
                                     
                                       a 
                                       0 
                                     
                                   
                                   
                                     
                                       k 
                                       B 
                                     
                                     ⁢ 
                                     T 
                                   
                                 
                                 ⁢ 
                                 E 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10.1 
                   ) 
                 
               
             
           
         
       
     
     When n&gt;1 defects are present, variables N q,i , E a,0,i , and a 0  may be determined from equation (10.1), based on τ i  thus ascertained, at at least two main operating temperatures T 1  and T 2 , and at least two main operating voltages U 1 =E 1 /d and U 2 =E 2 /d, by mathematical fitting. The measured J TED  curves are subject to manufacturing variations and tolerances which result from the measuring technique used. The accuracy of material properties a 0 , C 0,i (a 0 ), N q,i , and E A,0,i , determined from these measurements, may thus be improved by increasing the number of samples, and also by additional measured data for more than two voltages and/or more than two temperatures. 
     After a change in the process conditions, the determination of δϕ i  and τ i  is repeated and unequivocally associated with a defect type via variables N q,i  and E a,0,i . The physical influence of the process change on the involved i defects is thus shown. 
     At least one further, third defect type is preferably present in the dielectric layer. The third defect type is designed to accumulate at one of the two electrodes as a function of the main operating voltage that is applied between the first electrode and the second electrode and of the main operating temperature that is present at a characteristic time τ 3 , and to generate a maximum change in barrier height δΦ 3  at the electrodes. τ 1 &lt;τ 2 &lt;τ 3  applies, the sequence of maximum changes in barrier height differing from sequence δΦ 1 &gt;δΦ 2 &gt;δΦ 3 . This means that, for example, δΦ 3 &gt;δΦ 2 &gt;δΦ 1  or δΦ 2 &gt;δΦ 1 &gt;δΦ 3  applies. Dielectric layers in which more than only two different defect types are present occur more frequently. In the case of a PZT layer, for example at least local excesses or deficits of the atoms Pb, Ti, and Zr are present in the dielectric layer. In addition, in practice, operating states occur in which more than two defects make a relevant contribution to the electrical failure of the dielectric layer. 
     The dielectric layer is preferably designed as a polycrystalline oxidic high-k dielectric and in particular as a Pb[Zr x Ti 1-x ]O 3  (PZT), doped Pb[Zr x Ti 1-x-y ]O 3 Ni y  (PZT), [K x Na 1-x ]NbO 3  (KNN), HfO 2 , ZrO 2 , or SrTiO 3  layer. 
     The dielectric layer is preferably designed as a sputtered PZT layer. The so-called target material is deposited in a plasma on a substrate. PZT, for example, is used as target material. In this regard, the sputtered PZT layer preferably has a deposition temperature of less than 500° C. Such a dielectric layer demonstrably results in the effect that more than two defect types actively contribute to the dielectric failure as a function of the selected main operating voltage and main operating temperature. 
     The sputtered PZT layer preferably has a composition of Pb x (Zr 0.52 Ti 0.48 )O 3 . The following applies for x: 1.2≤x≤1.3, so that the composition may be made up of Pb 1.2 (Zr 0.52 Ti 0.48 )O 3  or Pb 1.3 (Zr 0.52 Ti 0.48 )O 3 . Alternatively, the sputtered PZT layer of the semiconductor component has a nickel content between 0.1 and 1 atom percent. Furthermore, additional defects may preferably be introduced into the high-k dielectrics via dopings in order to influence maximum changes in barrier height δΦ and time constants τ. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  shows the curve of a leakage current measurement for five different dielectric layers. 
         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. 
         FIG. 2A  shows the maximum changes in barrier height and characteristic time constants of three exemplary embodiments for the operating state 175° C./−2.5 V by way of example. 
         FIG. 2B  shows the maximum changes in barrier height and characteristic time constants for one exemplary embodiment for two operating states 175° C./−2.5 V and 100° C./−10 V by way of example. 
         FIG. 2C  shows the maximum changes in barrier height and characteristic time constants of two exemplary embodiments for the operating state 175° C./−2.5 V by way of example. 
         FIG. 2D  shows the maximum changes in barrier height and characteristic time constants of two exemplary embodiments for the operating state 175° C./−2.5 V by way of example. 
         FIG. 2E  shows the maximum changes in barrier height and characteristic time constants of two exemplary embodiments for the operating state 100° C./−10 V by way of example. 
         FIGS. 3A through 3D  schematically show the movement of different defect types in a dielectric layer along localized defect states, each with an average effective distance a 0 . 
     
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
       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 1.3 (Zr 0.52 Ti 0.48 )O 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 passivation and the electrical contacting. 
     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. 
     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. 
     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. 
     Moreover,  FIG. 1A  shows curve  20  of a leakage current measurement of a dielectric layer of a further semiconductor component, referred to below 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 1.2 (Zr 0.52 Ti 0.48 )O 3 . 
     Furthermore,  FIG. 1A  shows curve  22  of a leakage current measurement of a dielectric layer of a further semiconductor component, referred to below as exemplary embodiment 5. The production of exemplary embodiment 5 took place analogously to exemplary embodiment 1, except that the dielectric layer was deposited with a target composition of Pb 1.3 (Zr 0.52 Ti 0.48 )O 3 Ni 0.005 . 
     Prior to the measurement of the leakage current curves, all described exemplary embodiments 1, 2, 3, 4, and 5 were covered with passivation layers and electrically contacted via aluminum strip conductors. 
     Four of the five exemplary embodiments were measured up to the respective dielectric breakdown  15 ,  17 ,  19 , and  24 . It is apparent that very different leakage current curves  14 ,  16 ,  18 ,  20 , and  22  with different breakdown times  17 ,  15 ,  19 , and  24  result, depending on the production and the composition of a dielectric layer. 
       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 0 . 
     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 
                           
                             T 
                             ⁢ 
                             E 
                             ⁢ 
                             D 
                           
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ) 
                     
                   
                 
                 ] 
               
               ⁢ 
               
                 k 
                 B 
               
               ⁢ 
               T 
             
           
         
       
     
     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 
                 0 
               
               + 
               
                 
                   ∑ 
                   i 
                 
                 ⁢ 
                 
                   Δ 
                   ⁢ 
                   
                     
                       ϕ 
                       i 
                       + 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                 
               
               + 
               
                 
                   ∑ 
                   i 
                 
                 ⁢ 
                 
                   Δ 
                   ⁢ 
                   
                     
                       ϕ 
                       i 
                       - 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                 
               
             
           
         
       
     
     Correspondingly different Δϕ i   +/− (t)&#39;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 a   − (t)  39 , the curve of Δϕ b   − (t)  40 , and the curve of Δϕ c   − (t)  42 , together with summation curve Σ i Δϕ i   +   36 . According to the following formula (cf. above formula 5.1) 
     
       
         
           
             
               Δ 
               ⁢ 
               
                 ϕ 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
             
             = 
             
               
                 ∑ 
                 i 
               
               ⁢ 
               
                 δ 
                 ⁢ 
                 
                   
                     ϕ 
                     i 
                     
                       + 
                       
                         / 
                         - 
                       
                     
                   
                   ⁡ 
                   
                     ( 
                     
                       1 
                       - 
                       
                         e 
                         
                           t 
                           
                             τ 
                             i 
                             
                               + 
                               
                                 / 
                                 - 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     the different τ i   +/− &#39;s and δϕ i   +/− &#39;s may then be ascertained. In this case, for changes in barrier height Δϕ i   −    39 ,  40 , and  42  associated with the majority charge carriers, associated characteristic time constants τ a , τ b , and τ c  are obtained. These time constants are characterized in  FIG. 1B  by  47   a ,  47   b , and  47   c , respectively, and represent the point in time at which the corresponding change in barrier height changes most greatly. Associated maximum barrier decreases δϕ i   −  for curves Δϕ i   −    39 ,  40  are denoted by reference numerals  50  and  51  by way of example. In order to improve clarity, the changes in barrier height for minority charge carriers Δϕ +  have not been explicitly individually illustrated. Only their summation curve Σ i Δϕ i   +   36  together with individual time constants τ d , τ e , and τ f    49   a ,  49   b , and  49   c  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. Accordingly, six different defect types are thus present in this dielectric layer. 
     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 
                 crit 
                 - 
               
               = 
               
                 
                   
                     ϕ 
                     0 
                     - 
                   
                   + 
                   
                     
                       ∑ 
                       i 
                     
                     ⁢ 
                     
                       
                         Δϕ 
                         i 
                         - 
                       
                       ⁡ 
                       
                         ( 
                         
                           t 
                           crit 
                         
                         ) 
                       
                     
                   
                 
                 = 
                 
                   
                     ϕ 
                     0 
                     - 
                   
                   + 
                   
                     Δϕ 
                     crit 
                     - 
                   
                 
               
             
             , 
             
               
                 where 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   Δϕ 
                   crit 
                   - 
                 
               
               = 
               
                 
                   ∑ 
                   i 
                 
                 ⁢ 
                 
                   
                     Δϕ 
                     i 
                     - 
                   
                   ⁡ 
                   
                     ( 
                     
                       t 
                       crit 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     The previously ascertained curves of Δϕ a   − (t)  39 , Δϕ b   − (t)  40 , and Δϕ c   − (t)  42  are thus summed, resulting in changes in barrier height Σ i  Δϕ −    44 , corresponding to its curve. If change in barrier height Δϕ crit   −   52  of the dielectric layer, which is critical for the majority charge carriers, is reached at point in time t 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. 
       FIG. 2A  shows the measured curves of changes in barrier height Δϕ(t) ±  for the three exemplary embodiments 1, 2, and 3, together with respective characteristic time constants τ i   +/−  and maximum changes in barrier height δϕ +/−  at a main operating temperature of 175° C. and a main operating voltage of −2.5 V. Time is logarithmically plotted on X axis  62  in units of seconds, and the change in barrier height divided by critical change in barrier height Δϕ crit   −  of the particular exemplary embodiment 1, 2, and 3 is plotted on Y axis  60  without units. 
     The curves of Δϕ(t) −   63 ,  64 ,  65  for exemplary embodiments 3, 2, and 1 as well as the associated curves of Δϕ(t) +   66 ,  67 ,  68  of exemplary embodiments 3, 2, and 1 are illustrated. The electrical failure of the dielectric layers in the exemplary embodiments takes place in each case at associated points in time  94 ,  96 , and  98  at which the critical decrease in barrier height is reached. 
     The defect structure for exemplary embodiment 1 is made up of defect types a, b, c, d, e, and f together with their associated time constants τ a    72   a, τ   b    72   b , T c    72   c, τ   d    90   a, τ   e    70   b , and τ f    70   c . Resulting maximum decreases in barrier height δϕ b   −   72   c, δϕ   c   −   73   c, δϕ   d   +   91   a, δϕ   e   +   71   b , and δϕ f   +   71   c  are associated with the different defect types. 
     The defect structure for exemplary embodiment 2 is made up of defect types a, b, c, d, e, and f together with their associated time constants τ a    82   a, τ   b    82   b, τ   c    82   c, τ   d    80   a, τ   e    80   b , and τ f    80   c . In addition, resulting maximum decreases in barrier height δϕ a   −   83   a, δϕ   b   −   83   b, δϕ   c   −   83   c, δϕ   d   +   81   a, δϕ   e   +   81   b , and δϕ f   +   81   c  are associated with the different defect types. 
     The defect structure for exemplary embodiment 3 is made up of defect types a, b, c, d, e, and f together with their associated time constants τ a    92   a, τ   b    92   b, τ   c    92   c, τ   d    70   a, τ   e    90   b , and τ f    90   c . Once again, resulting maximum decreases in barrier height δϕ a   −   93   a, δϕ   b   −   93   b, δϕ   c   −   93   c, δϕ   d   +   71   a, δϕ   e   +   91   b , and δϕ f   +   91   c  are associated with the different defect types. 
     True activation energies E A,0,i  and charges N q,i  may be ascertained for the different defect types by mathematical fitting to the above-described model and the following equation (cf. above equation 10.1). 
     
       
         
           
             
               
                 τ 
                 i 
               
               ⁡ 
               
                 ( 
                 
                   E 
                   ; 
                   T 
                 
                 ) 
               
             
             = 
             
               
                 
                   d 
                   i 
                 
                 
                   
                     
                       C 
                       
                         0 
                         , 
                         i 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         a 
                         0 
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     e 
                     
                       - 
                       
                         
                           E 
                           
                             A 
                             , 
                             o 
                             , 
                             i 
                           
                         
                         
                           
                             k 
                             B 
                           
                           ⁢ 
                           T 
                         
                       
                     
                   
                 
               
               ⁢ 
               
                 1 
                 
                   sin 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     h 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               N 
                               
                                 q 
                                 , 
                                 i 
                               
                             
                             ⁢ 
                             
                               a 
                               0 
                             
                           
                           
                             
                               k 
                               B 
                             
                             ⁢ 
                             T 
                           
                         
                         ⁢ 
                         E 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     A true activation energy of 0.92 eV with a charge of 1 e results for defect type a. A true activation energy of 0.95 eV with a charge of 3 e results for defect type b. A true activation energy of 0.855 eV with a charge of 4 e results for defect type c. A true activation energy of &lt;0.8 eV with a charge of 1 e results for defect type d. A true activation energy of 1.04 eV with a charge of 2 e results for defect type e. A true activation energy of 1.22 eV with a charge of 2 e results for defect type f. In this way, for example defect type a may be physically joined to hydrogen and/or OH groups, and defect type e may be physically joined to oxygen vacancies and/or lead within the dielectric layer. Due to the different types of production of exemplary embodiments 1, 2, and 3, the maximum decreases in barrier height of defect types a and e, δϕ a   −  and δϕ e   + , respectively, are changed. For the main operating conditions selected here by way of example, τ a &lt;τ b  and δϕ a   − &lt;δϕ b   −  apply for exemplary embodiments 1 and 2 of the semiconductor component. Barrier curve  63  of exemplary embodiment 3 is influenced by relatively large barrier decrease  93   a  of exemplary embodiment 3, which takes place at a relatively early point in time  92   a . This results in an earlier electrical failure at point in time t crit    98  in comparison to failure points in time t crit    94  or  96  of exemplary embodiments 1 or 2. To achieve a longer service life of the semiconductor component, barrier decreases that take place early should be correspondingly small. For exemplary embodiments 1 and 2, it is also shown that τ a &lt;τ b &lt;τ c  and δϕ a   − &lt;δϕ b   − &lt;δϕ c   − . 
       FIG. 2B  shows a comparison of the curves of changes in barrier height Δϕ(t) ±  for exemplary embodiment 2 for two different operating conditions, together with particular characteristic time constants τ i   +/−  and maximum changes in barrier height δϕ i   +/− . Time is logarithmically plotted on X axis  62  in units of seconds, and the change in barrier height divided by critical change in barrier height Δϕ crit   −  of the particular operating state is plotted on Y axis  60  without units. 
     This results in curve Δϕ(t) −   64  for the main operating temperature 175° C. and a main operating voltage of −2.5 V (referred to below as operating condition a), and curve Δϕ(t) −   110  for the main operating temperature 100° C. and a main operating voltage of −10 V (referred to below as operating condition b). Associated curve Δϕ(t) +   67  for operating condition a and curve Δϕ(t) +   100  for operating condition b are likewise illustrated. 
     The electrical failure of the dielectric layer takes place for operating conditions a and b at points in time  96  and  97 , respectively. The defect structure for exemplary embodiment 2 for operating condition a is formed by active defect types a, b, c, d, e, and f together with their associated time constants τ a    82   a, τ   b    82   b, τ   c    82   c, τ   d    80   a, τ   e    80   b , and τ f    80   c  up to electrical failure, and maximum decreases in barrier height δϕ a   −   83   a, δϕ   b   −   83   b, δϕ   c   −   83   c, δϕ   d   +   81   a, δϕ   e   +   81   b , and δϕ f   +   81   c  caused by these defect types. 
     The defect structure for exemplary embodiment 2 for operating condition b is formed by active defect types a, b, d, and e together with their associated time constants τ a    170   a, τ   b    170   b , T d    101   a , and τ e    101   b  up to electrical failure, and maximum decreases in barrier height δϕ a   −   171   a, δϕ   b   −   171   b, δϕ   d   +   102   a , and δϕ e   +   102   b  caused by these defect types. 
     It is apparent that the defect structure and the active defects in a semiconductor component up to electrical breakdown are a function of the selected operating condition. Time shifts  106  result from the main operating temperature and term 
     
       
         
           
             e 
             
               - 
               
                 
                   E 
                   
                     A 
                     , 
                     0 
                     , 
                     i 
                   
                 
                 
                   
                     k 
                     B 
                   
                   ⁢ 
                   T 
                 
               
             
           
         
       
     
     in equation (10.1). Changes  105  in the maximum decreases in barrier height result from changes in the main operating voltage and accompanying changes in Δϕ crit   ± . 
     For exemplary embodiment 2, τ a &lt;τ b &lt;τ c  and δϕ a   − &lt;δϕ b   − &lt;δϕ c   − , and τ d &lt;τ e &lt;τ f  and δϕ d   + &lt;δϕ e   + &lt;δϕ f   + , apply for operating conditions a. In addition, for exemplary embodiment 2 τ a &lt;τ b  and δϕ a   − &lt;δϕ b   − , and τ d &lt;τ e  and δϕ d   + &lt;δϕ e   + , apply for operating conditions b. 
       FIG. 2C  shows a comparison of the curves of changes in barrier height Δϕ(t) ±  for the two exemplary embodiments 2 and 4 together with their particular characteristic time constants τ i   +/−  and maximum changes in barrier height δϕ i   +/−  at a main operating temperature of 175° C. and a main operating voltage of −2.5 V. Time is logarithmically plotted on X axis  62  in units of seconds, and the change in barrier height divided by critical change in barrier height Δϕ crit  of exemplary embodiment 2 is plotted on Y axis  60  without units. The change in barrier height in exemplary embodiment 4 has been normalized in such a way that maximum changes in barrier height δϕ a   −   132   a  and δϕ a   −   83   a  are identical. 
     Curve Δϕ(t) −   64  of exemplary embodiment 2 and curve Δϕ(t) −   130  of exemplary embodiment 4 are illustrated. Curve Δϕ(t) +    67  of exemplary embodiment 2 and curve Δϕ(t) +   120  of exemplary embodiment 4 are also illustrated. The electrical failure of the dielectric layer of exemplary embodiment 2 takes place at point in time  96  when the critical decrease in barrier height is reached. During the test period it was not possible to subject exemplary embodiment 4 to load to the point of failure, and therefore curve  130  does not reach the value −1. 
     The defect structure for exemplary embodiment 2 is formed by defect types a, b, c, d, e, and f together with their associated time constants τ a    82   a, τ   b    82   b, τ   c    82   c, τ   d    80   a, τ   e    80   b , and τ f    80   c , and maximum decreases in barrier height δϕ a   −   83   a, δϕ   b   −   83   b, δϕ   c   −   83   c, δϕ   d   +   81   a, δϕ   e   +   81   b , and δϕ f   +   81   c  caused by these defect types. 
     The defect structure for exemplary embodiment 4 is formed by defect types a, c, d, and e together with their associated time constants τ a    131   a, τ   c    131   b, τ   d    121   a , and τ e    121   b , and maximum decreases in barrier height δϕ a   −   132   a, δϕ   c   −   132   b , and δϕ d   +   122   a  caused by these defect types. 
     A true activation energy of 0.92 eV with a charge of 1 e results for defect type a. A true activation energy of 0.95 eV with a charge of 3 e results for defect type b. A true activation energy of 0.855 eV with a charge of 4 e results for defect type c. A true activation energy of &lt;0.8 eV with a charge of 1 e results for defect type d. A true activation energy of 1.04 eV with a charge of 2 e results for defect type e. A true activation energy of 1.22 eV with a charge of 2 e results for defect type f. Due to the reduction of the lead content in the sputtered PZT layer of exemplary embodiment 4, it was possible to reduce maximum decreases in barrier height δϕ b   − , δϕ c   − , and δϕ f   +  of defect types b, c, and f associated with lead, in comparison to exemplary embodiment 2. This reduction is denoted by reference numeral  115  by way of example for δϕ c   −   132   b . Maximum decreases in barrier height δϕ b   −  and δϕ f   +  are so small that they are no longer discernibly present due to the numerical fit to the model. Since τ a &lt;τ b &lt;τ c  for defect type b, it may be deduced that τ b &lt;τ c  and δϕ b   − &lt;&lt;δϕ c   − . 
       FIG. 2D  shows a comparison of the curves of changes in barrier height Δϕ(t) ±  for the two exemplary embodiments 2 and 5 together with their particular characteristic time constants τ i   +/−  and maximum changes in barrier height δϕ i   +/−  at a main operating temperature of 175° C. and a main operating voltage of −2.5 V. Time is logarithmically plotted on X axis  62  in units of seconds, and the change in barrier height divided by critical change in barrier height Δϕ crit  of particular exemplary embodiment 2 and 5 is plotted on Y axis  60  without units. 
     Curve Δϕ(t) −   64  of exemplary embodiment 2 and curve Δϕ(t) −   150  of exemplary embodiment 5 are illustrated. Associated curve Δϕ(t) +   67  of exemplary embodiment 2 and curve Δϕ(t) +   140  of exemplary embodiment 5 are also illustrated. The electrical failure of the dielectric layer of exemplary embodiment 2 takes place at point in time  96 , and for exemplary embodiment 5 takes place at point in time  99 . 
     The defect structure for exemplary embodiment 2 is formed by defect types a, b, c, d, e, and f together with their associated time constants τ a    82   a, τ   b    82   b, τ   c    82   c, τ   d    80   a, τ   e    80   b , and τ f    80   c , and maximum decreases in barrier height δϕ a   −   83   a, δϕ   b   −   83   b, δϕ   c   −   83   c, δϕ   d   +   81   a, δϕ   e   +   81   b , and δϕ f   +   81   c  caused by these defect types. The defect structure for exemplary embodiment 5 is formed by defect types a, b, and d together with their associated time constants τ a    148   a, τ   b    148   b , and τ d    145   a , and maximum decreases in barrier height δϕ a   −   149   a, δϕ   b   −   149   b , and δϕ d   +   146   a  caused by these defect types. 
     A true activation energy of 0.92 eV with a charge of 1 e results for defect type a. A true activation energy of 0.95 eV with a charge of 3 e results for defect type b. A true activation energy of 0.855 eV with a charge of 4 e results for defect type c. A true activation energy of &lt;0.8 eV with a charge of 1 e results for defect type d. A true activation energy of 1.04 eV with a charge of 2 e results for defect type e. A true activation energy of 1.22 eV with a charge of 2 e results for defect type f. Due to the additional nickel content in the sputtered PZT layer of exemplary embodiment 5, it was possible to significantly influence maximum decreases in barrier height δϕ a   −  and δϕ b   − . In addition, it was possible to reduce maximum decreases in barrier height δϕ e   +  and δϕ f   +  to the extent that they are no longer discernibly present due to the numerical fit to the model. For the operating conditions 175° C. and −2.5 V, τ a &lt;τ b  and δϕ a   − &lt;δϕ b   −  apply for exemplary embodiment 5. 
       FIG. 2E  shows a comparison of the curves of changes in barrier height Δϕ(t) ±  for the two exemplary embodiments 2 and 5 at a main operating temperature of 100° C. and a main operating voltage of −10 V, together with particular characteristic time constants τ i   +/−  and maximum changes in barrier height δϕ i   +/− . Time is logarithmically plotted on X axis  155  in units of seconds, and the change in barrier height divided by critical change in barrier height Δϕ crit   −  of particular exemplary embodiment 2 and 5 is plotted on Y axis  156  without units. 
     Curve Δϕ(t) −   110  of exemplary embodiment 2 and curve Δϕ(t) −   169  of exemplary embodiment 5 are illustrated. Associated curve Δϕ(t) +   100  of exemplary embodiment 2 and curve Δϕ(t) +   165  of exemplary embodiment 5 are also illustrated. The electrical failure of the dielectric layer of exemplary embodiment 2 takes place at point in time  96   c , and for exemplary embodiment 5 takes place at point in time  96   d.    
     The defect structure for exemplary embodiment 2 is formed by active defect types a, b, d, and e together with their associated time constants τ a    170   a, τ   b    170   b, τ   d    161   a , and τ e    161   b , and maximum decreases in barrier height δϕ a   −   171   a, δϕ   b   −   171   b, δϕ   d   +   162   a , and δϕ e   +   162   b  caused by these defect types. 
     The defect structure for exemplary embodiment 5 is formed by defect types a and d together with their associated time constants τ a    175   a  and τ d    158   a , and maximum decreases in barrier height δϕ a   −   176   a  and δϕ d   +   159   a  caused by these defect types. 
     A true activation energy of 0.92 eV with a charge of 1 e results for defect type a. A true activation energy of 0.95 eV with a charge of 3 e results for defect type b. A true activation energy of &lt;0.8 eV with a charge of 1 e results for defect type d. A true activation energy of 1.04 eV with a charge of 2 e results for defect type e. Due to the additional nickel content in the sputtered PZT layer of exemplary embodiment 5, it was possible to significantly influence maximum decrease in barrier height δϕ a   −   176   a . In addition, it was possible to reduce maximum decrease in barrier height W to the extent that it is no longer discernibly present due to the numerical fit to the model. 
     For exemplary embodiment 2, τ a &lt;τ b  and δϕ a   − &lt;δϕ b   − , and τ d &lt;τ e  and δϕ d   + &lt;δϕ e   + , apply for the operating conditions 100° C. and −10 V. 
       FIG. 3A  schematically shows a semiconductor component  200  at a first point in time t 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 an 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 0  illustrated in  FIG. 3A , no voltage between the electrodes  201  and  202 , and thus also no electrical field, has yet been applied. 
       FIG. 3B  shows semiconductor component  200  at a second point in time t 1  subsequent to first point in time t 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 1 . The different defect types  212 ,  215 , and  217  now vary as a function of the main operating voltage applied between first electrode  201  and second electrode  202  and a main 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.” Each defect type moves in the direction of a corresponding electrode, at a different velocity. The particular time required by a defect type to reach a particular boundary layer, associated with an electrode after application of the main operating voltage, from the starting position is referred to as characteristic time x. Localized defect states  235  each have same average effective distance a 0    210 . 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 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 0 , and undergo changes in barrier height Δϕ i  due to the defect types that accumulate there, which in the further temporal profile result in a maximum change in barrier height δΦ i . The defect types in each case create a different change in barrier height ΔΦ i . 
       FIG. 3C  shows semiconductor component  200  at a third point in time t 2  subsequent to second point in time. 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 i  there. A critical barrier height ϕ crit  is reached at one of boundary layers  202  or  203  at a fourth point in time t 3  subsequent to the third point in time. As is apparent from  FIG. 3D , 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 crit  is exceeded. This is followed by even further local dielectric breakdowns  225  under continuing load at t&gt;t crit , which ultimately results in complete destruction of semiconductor component  200 .