Surface State Capture Cross-Section at the Interface between Silicon and Hafnium Oxide

The interfacial properties between silicon and hafnium oxide (HfO 2 ) are explored by the gated-diode method and the subthreshold measurement. The density of interface-trapped charges, the current induced by surface defect centers, the surface recombination velocity, and the surface state capture cross-section are obtained in this work. Among the interfacial properties, the surface state capture cross-section is approximately constant even if the postdeposition annealing condition is changed. This effective capture cross-section of surface states is about 2.4 × 10−15 cm, which may be an inherent nature in the HfO 2 /Si interface.


Introduction
Hafnium oxide (HfO 2 ) has emerged recently as an essential dielectric material in the semiconductor industry, currently being used in logic gate stacks [1] and considered a promising candidate for resistance switching memory devices [2,3] as well as surface passivation of advanced Si solar cells [4,5].Therefore, the determination of surface state capture crosssection at the interface between silicon and hafnium oxide is of great importance for the semiconductor industry, the photovoltaic industry, and the scientific community.The known characteristics of HfO 2 thin films include a large band gap (∼6 eV) [6], a relatively high dielectric constant (>20) [7], an acceptable breakdown strength (>4 MV/cm) [7], excellent thermodynamic stability [8], and an effective mass of carrier transportation [9].In this work, the interface characteristics of the interface-trapped charge density ( it ), the interface-trapped charge density per area and energy ( it ), the effective capture cross-section (  ) of surface states, the surface recombination velocity (  ), and the minority carrier lifetime ( FI J ) are identified.The typically electrical measurements of current-voltage (-) and capacitance-voltage (-) characteristics were performed on the Al/HfO 2 /p-Si metal-oxide-semiconductor (MOS) capacitors and metal-oxide-semiconductor field-effect transistors (MOSFETs).Both gated-diode method [10,11] and subthreshold measurement [12] were applied to evaluate the capture cross-section of interface states for the HfO 2gated MOSFETs.The gated-diode method is a simple way to accurately identify the interfacial characteristics using only a sweeping dc gate voltage, which was introduced in 1966 by Grove and Fitzgerald [10] to determine the surface-state density in MOS structures.According to the gated-diode measurements, the surface recombination velocity and the minority carrier lifetime ( FI J ) in the field-induced depletion region were extracted.In addition, the interface-trapped charge density per area and energy ( it ) was determined by using the device subthreshold measurement.Consequently, the effective capture cross-section of surface states was determined to be about 2.4 × 10 −15 cm 2 by the combination of gated-diode and device subthreshold measurements.

Experiment
Here, (100) -type silicon wafers (1-5 Ω-cm) were used as the starting material.Following the standard cleaning procedures, a 500 nm SiO 2 film was grown on silicon wafers by wet oxidation.The source and drain windows were defined by wet etching and doped by phosphorous diffusion.The HfO 2 films were deposited by RF magnetron sputtering in argon ambient at room temperature.The flow rate of argon was 13.5 standard cubic centimeters per minute (sccm).The total pressure during deposition was 20

Results and Discussion
The drastic irregularity of the oxide/Si interface should introduce a large amount of density of states into the forbidden gap near the interface.The interface state may cause the charge trapping and lead to the device instability as well as the degradation of subthreshold swing, off-state current, carrier mobility, and oxide reliability.Charge carriers can be trapped or captured while they come to the physical vicinity of the center of the interface state.The capture cross-section (  ) of the center is a measure of how close the carrier has to come to the center to be captured.In this work, the gateddiode method is used to identify the interface-trapped charge density ( it ), the surface recombination velocity (  ), and the minority carrier lifetime ( FI J ) in the field-induced depletion region for the nMOSFET devices using HfO 2 gate dielectrics annealed at 500 ∘ C. The test structure described by Grove and Fitzgerald to investigate surface properties in MOS structures is identical to a MOSFET without or with an unconnected source region.In this work, the gated-diode measurement was made using a floating source and a grounded substrate on MOSFET structures, as shown in Figure 1(a).The drain is reversely biased with respect to the substrate (  =  DB ).
According to the theory of gated-diode method, the reverse current of - junctions (  ) is a function of the gate bias (  ).The   -  characteristics may exhibit three distinct regions [10], as indicated in Figure 1(b).The reverse current of - junctions comes from the generation of electron-hole pairs at generation-recombination centers in the depletion region at room temperature.Hence, the magnitude of reverse current depends on the density of such centers and the volume of the depletion region.As the volume of the depletion region in gated diodes depends on the gate voltage, reverse current also depends on the gate voltage.The HfO 2 /silicon interface is in the accumulation mode when   is less than the flat band voltage  FB , and the reverse diode current originates from the generation-recombination centers in the depletion region of the metallurgical junction ( gen,MJ ).When  FB <   <   (where   is the threshold voltage), the field-induced junction is depleted, and the rapid increase in the reverse diode current is caused by the generation of electron-hole pairs at the generation-combination centers of the surface region ( gen, ) and the field-induced junction depletion region ( gen,FI J ).At   >   , the field-induced junction is in the inversion mode and the reverse diode current is reduced by the filling of the interface-trapped charge states by the minority carriers.The magnitude of the reverse diode current is the sum of the generation currents in the depletion volume of the field-induced junction and in that of the metallurgical junction.Based on the Shockley-Read-Hall theory for the single-level centers [10], the equations for the gated-diode are written as follows [13][14][15]: where   = 9.65 × 10 9 cm −3 is the intrinsic carrier concentration in silicon [12];  MJ represents the area of the metallurgical junction;   = 1.9 × 10 −5 cm −2 is the gate area;   is the surface recombination velocity;   is the effective capture cross-section area;  th = 10 7 cm/s is the thermal velocity;  bi is the built-in potential of the - junction;   is the quasi-Fermi potential of the majority carriers of the substrate;  is the width of the depletion region of the metallurgical junction;  ,max is the maximum width of the surface depletion region;  0,FI J is the minority carrier lifetime in the field-induced depletion region;  it is the interfacetrapped charge density (i.e., density of the single-level surface generation-recombination centers per unit area);  it is the interface-trapped charge density per area and energy (i.e., the density of uniformly distributed surface generationrecombination centers per unit area and energy); and  MJ ,   , and  FI J are the generation and recombination rates of carriers per unit volume in the depletion regions of the metallurgical, the surface region, and field-induced region, respectively.
Figure 2 shows the reverse diode current   versus   for the HfO 2 gated-diodes at   = 2V.Through the gated diode method, the surface recombination velocity (  ) and the minority carrier lifetime ( FI J ) in the field-induced depletion region can be extracted.For HfO 2 films annealed in N 2 /O 2 ,   and  FI J are determined to be 4.1 × 10 3 cm/s and 16 ns.On the other hand, for HfO 2 films annealed in N 2 ,   and  FI J are determined to be 8.9 × 10 3 cm/s and 22 ns.Obviously, the reverse diode current of nMOSFETs for HfO 2 annealed at 500 ∘ C in N 2 /O 2 is smaller than that annealed in N 2 .The reduction in reverse current may be attributed to the decrease in oxygen vacancy related defects [16][17][18][19] in HfO 2 .The oxygen vacancy is one type of trapping centers and is easily formed in HfO 2 due to the transportation of oxygen atoms from HfO 2 into Si [18,19].During the thermal treatment of PDA in N 2 /O 2 ambient, the oxygen atoms can Gate voltage (V)  diffuse into the HfO 2 films to partially passivate the existing oxygen vacancies.Hence, the reverse diode current can be reduced by N 2 /O 2 annealing.Figure 3 shows the  DS - GS characteristics.The  on / off ratio is larger than 10 6 at   = 0.05 V, indicating that the nMOSFETs with amorphous HfO 2 gate dielectrics have a good current switch capability.The subthreshold swings (  ) for the HfO 2 gate dielectrics annealed at 500 ∘ C in N 2 and N 2 /O 2 are about 85.1 and 76.4 mV/dec, respectively.According to Figure 3, the density of interface traps per area and energy ( it ) can be determined from the subthreshold swing measurement, because   is expressed as 2.3(/)[1 + (  +  it )/ ox ] [12], where   is the depletion-layer capacitance,  it is the capacitance associated with the interface traps, Figure 4 shows the channel electron mobility versus the effective electric field.The effective surface field ( eff ) and effective channel mobility ( eff ) can be expressed as  eff = (0.5 inv +  )/ Si and  = ( DS / DS )(/)/ inv , respectively, where  inv is the inversion layer charge,   is the bulk depletion layer charge, and  Si is the dielectric constant of Si.The linear approximation of  inv ,  inv =  ox ( GS −  ), is used in evaluating the mobility.The rest of the symbols have been defined earlier.The maximum channel electron mobility for the HfO 2 annealed in N 2 /O 2 and N 2 was determined to be 102 and 43 cm 2 /V s, respectively.Evidently the HfO 2 film annealed in N 2 shows lower channel electron mobility than the film annealed in N 2 /O 2 condition.In addition, the HfO 2 device has a lowered mobility as compared to a universal mobility curve in SiO 2 MOSFETs [20].The lowered mobility may come from the larger surface states which cause the increased interface charge scattering [21].
Table 1 lists the capture cross-sections of surface states (  ) at the interface between silicon and oxides, for example, SiO 2 , ZrO 2 , Al 2 O 3 , CeO 2 , and HfO 2 [22][23][24][25][26][27][28][29].For SiO 2 , the   value is 1-4 × 10 −16 cm 2 [22][23][24] which is smaller than those of high-k dielectrics.For CeO 2 , the   value is around 9 × 10 −15 cm 2 even if the adopted measurement method is different [27,28].In this work, the experimental results show that the HfO 2 films annealed in N 2 /O 2 have lower interface state density ( it ) and higher channel electron mobility (  ) compared to the HfO 2 films annealed in N 2 .Although the different PDA conditions lead to the different values of  it and   , the same   for HfO 2 deposited by rf magnetron sputtering is obtained to be around 2.4 × 10 −15 cm 2 .This finding may suggest that the capture crosssection of surface states for some thin film deposition method may be an inherent nature at the interface between silicon and hafnium oxide.It is worthy to note that the capture crosssection of surface states may be influenced by the factors of environment temperature, film thickness, film deposition method, and especially surface preparation of Si substrate prior to HfO 2 deposition.

Conclusions
The electrical properties at the HfO 2 /Si interface are investigated by the gated-diode method and the subthreshold measurement.Although the HfO 2 films annealed in N 2 /O 2 result in lower interface state density and higher channel electron mobility compared to the HfO 2 films annealed in N 2 , the determined surface state capture cross-section at the HfO 2 /Si interface is the same.This suggests that the surface state capture cross-section may be an inherent nature at the interface between silicon and hafnium oxide.

Figure 2 :
Figure 2: Reverse diode current   of the HfO 2 gated diode versus gate voltage   at   = 2 V.   is the reverse bias of the  + region of the metallurgical junction.

Figure 3 :
Figure 3:  DS - GS characteristics of nMOSFETs fabricated with HfO 2 gate dielectrics annealed in N 2 and N 2 /O 2 at 500 ∘ C for 60 s.
mtorr.The refractive Advances in Materials Science and Engineering Cross-sectional diagram of an HfO 2 gated diode.(b) Effect of the depletion region on the reverse current   of the gated diode at various gate voltages given a fixed reverse drain voltage   .
impedance analyzer.All the measurements were performed under dark condition.Based on the high-frequency (1 MHz) - measurements for the MOS capacitors, the effective dielectric constant of HfO 2 films annealed at 500 ∘ C in N 2 or N 2 /O 2 was evaluated as 18.9 or 19.3, respectively (not shown here).In this work, the relatively large devices were chosen to avoid the short channel effects which may cause the distortion in analysis of surface state capture cross-section.The channel width () is 100 m and the channel length () is 19 m.

Table 1 :
Capture cross-section of surface states at the oxide/Si interface.Figure 4: Channel electron mobility versus effective surface field for the HfO 2 MOSFETs annealed at 500 ∘ C for 60 s in N 2 and N 2 /O 2 .and ox is the dielectric capacitance.The determined  it is about 4.6 × 10 12 and 2.1 × 10 12 cm −2 -eV −1 for HfO 2 annealed at 500 ∘ C in N 2 and N 2 /O 2 , respectively.Once  it is determined,   and  it can be extracted using (4).For HfO 2 annealed in N 2 ,   and  it are extracted to be about 2.4 × 10 −15 cm 2 and 3.7 × 10 11 cm −2 , respectively; for HfO 2 annealed in N 2 /O 2 ,   and  it are extracted to be 2.4 × 10 −15 cm 2 and 1.7 × 10 11 cm −2 , respectively.It is worthy of note that the same   value is obtained for HfO 2 annealed both in N 2 and in N 2 /O 2 .This finding may imply that the capture cross-section of surface states is an inherent nature at the HfO 2 /Si interface.The universal constant of surface state capture cross-section is around 2.4 × 10 −15 cm 2 .