Charge Pumping Under Spin Resonance in $\mathrm{Si}(100)$ Metal-Oxide-Semiconductor Transistors

Gate-pulse-induced recombination, known as charge pumping (CP), is a fundamental carrier recombination process, and has been utilized as a method for analyzing the electrical properties of defects (or dangling bonds) at the transistor interfaces, which is now recognized to be a well-matured and conventional method. Nevertheless, neither the origin (the bonding configuration) of the defects responsible for the CP nor their detailed recombination sequence has been clarified yet for Si metal-oxide-semiconductor (MOS) interfaces. In order to address these problems, we investigate the CP under spin resonance conditions at temperatures ranging from 27 to 300 K in $\mathrm{Si}(100)$ n type MOS transistors. We obtain evidence that ${\mathrm{P}}_{\mathrm{b}0}$ and E′ centers, the two major dangling bonds at (and near) the $\mathrm{Si}(100)$ interface, participate in the CP recombination process. We also show that the spin-dependent CP process is explained by the formation of electron-electron spin pairs, which, in turn, reveals that the CP via ${\mathrm{P}}_{\mathrm{b}0}$ and E′ centers is inherently a two-electron process.

Figure 1

Setup for the CP and CP EDMR. (a) Setup for the CP. Dashed arrows show the electron flow between the source and drain and the substrate via the interface defects (red cross marks). The parameters of the gate pulse are defined in the inset of the figure, where ΔV, Δt, and V_base are the amplitude, the rise or fall time, and the base voltage of the pulse, respectively. The duty cycle of the pulse is fixed at 50% for all measurements. (b) CP sequence. Electrons (closed circles) are captured by the defect states in the rise step of the pulse (left), and then the trapped electrons recombine with valence-band holes (open circles) in the fall step (right). The electron (hole) emission, which is the competing process against the recombination (electron capture) process, is indicated by the dotted arrow. E_c and E_v are the edges of the conduction and valence band, respectively. Note that the diagram is drawn by assuming one-electron capture or recombination model, implicitly assumed in the literature. On the other hand, we here propose a two-electron CP process, see Fig. 7. (c) Setup for CP EDMR. A MOSFET is mounted on the sample holder and inserted into the cylindrical cavity of the ESR system. Arrow B shows the static magnetic field, while the arrows B_μw and E_μw show the microwave magnetic and electric fields, respectively.

Figure 2

CP characteristics. (a) Temperature dependence of the CP current I_CP as a function of the base voltage V_base of the pulse. (b) The maximum value I_CP,max and area density N_it of the interface defects estimated from the I_CP,max. Inset shows the range of the energy levels of the defects that can contribute to the CP current.

Figure 3

CP EDMR characteristics. (a) Output (differential) spectrum measured at 27 K with the magnetic field B parallel to the [100] direction (B||[100]). Parameters for the CP gate pulse are f = 5 kHz, ΔV = 4 V, and Δt = 30 µs. V_base is fixed at −5 V, at which the I_CP is maximum (= 80 nA) as shown by the arrow in the inset. (b) Integrated spectrum. Thin solid black curve is the experimental data. This curve is deconvoluted into three Voigt functions for ${\mathrm{P}}_{\mathrm{b}0}$ (red line), E′ (green), and SS (blue). Their sum is shown by the dotted black curve.

Figure 4

Rotation-angle dependence of CP EDMR signals. (a),(b) Output and integrated spectra for five rotation angles ranging from φ = 0° (B||[100]) to 90° (B||[011]). Parameters for the CP gate pulse are the same as those for Fig. 3 (f = 5 kHz, ΔV = 4 V, Δt = 30 µs, and V_base = −5 V). In (b), thin solid black curves are the experimental data, and they are deconvoluted into Voigt functions for ${\mathrm{P}}_{\mathrm{b}0}$ (red lines), E′ (green line), and SS (blue line). Their sums are shown by the dotted black curves. (c) Rotation-angle dependence of the g values. Dots are the g values extracted from the experimental data, while the curves are the theoretically predicted ones. Red, green, and blue dots and curves are, respectively, for ${\mathrm{P}}_{\mathrm{b}0}$, E′, and SS.

Figure 5

Pulse-frequency dependence of the CP EDMR signals. (a) Integrated spectra (black lines) for gate pulse f ranging from 3 to 5 kHz with B||[100], each of which is deconvoluted into three Voigt functions for ${\mathrm{P}}_{\mathrm{b}0}$ (red), E′ (green), and SS (blue). Except for f, the pulse parameters are the same as those of the data shown in Fig. 3 (ΔV = 4 V, Δt = 30 µs, and V_base = −5 V). (b) Peak height of the Voigt function for ${\mathrm{P}}_{\mathrm{b}0}$ (red), E′ (green), and SS (blue) as a function of f. I_CP,max (black circles) is also plotted.

Figure 6

Temperature dependence of the CP EDMR signals. (a) Integrated spectra ΔI_CP for temperatures T = 27, 60, and 300 K with B||[100]. Each spectrum (black line) is deconvoluted into three Voigt functions, each of which is assigned to ${\mathrm{P}}_{\mathrm{b}0}$(red), E′(green), and SS(blue). Data for T = 60 and 300 K are respectively expanded to the vertical direction by 13 and 56 times for clarity. CP pulse parameters are the same as those of the data shown in Fig. 3 (f = 5 kHz, ΔV = 4 V, Δt = 30 µs, and V_base = −5 V). In the inset of each graph, the shaded area and bold line indicate the energy range for the CP and the energy level for the CP EDMR, respectively. (b) ΔI_CP as a function of T for ${\mathrm{P}}_{\mathrm{b}0}$ (red) and E′ (green) centers. (c) ΔI_CP as a function of T for SS. Inset in (c) shows the ratio R of ΔI_CP(SS) to the sum of ΔI_CP(${\mathrm{P}}_{\mathrm{b}0}$) and ΔI_CP(E′) as a function of T. In (b) and (c), two vertical dotted lines define three temperature regions (T $\lesssim$ 40 K, 40 K $\lesssim$ T $\lesssim$ 80 K, and T $\gtrsim$ 80 K).

Figure 7

Proposed model of the CP process. (a) Two types of electron-electron spin pairs, off-site (left), and on-site pairs (right), are dominantly formed at low and high temperatures, respectively. The triplet and/or singlet intermediate pairs are forbidden or allowed to make a transition to the ground states. (b) CP process via ${\mathrm{P}}_{\mathrm{b}0}$ and E′ centers. Steps b2 and b3 are relevant to the present CP EDMR signals.

Figure 8

Injected-charge dependence of defect density N_it. For the FN stress, the negatively high voltage fixed at −30 V is applied to the gate, which corresponds to the electric field of −10 MV/cm applied to the oxide. N_it is estimated from the CP method at room temperature (RT). The red circles mark the N_it’s for Tr. A and Tr. B. The cross shows the breakdown point (N_it ∼ 1.5 × 10¹¹ cm⁻²). The dashed line is a guide for the eye.

Figure 9

CP EDMR characteristics of MOSFETs with different amounts of the injected charges. Integrated spectra for Tr. A (left panel) and Tr. B (right) measured at T = 27 K with B||[100]. Parameters for the gate pulse are f = 5 kHz, ΔV = 4 V, and Δt = 30 µs. The black curves are the experimental data. Three peaks in each panel are decomposed using the Voigt function, each of which is assigned to the signal from ${\mathrm{P}}_{\mathrm{b}0}$ (red), E′ (green), and SS (blue). The defect density N_it for Tr. A is twice as large as that for Tr. B. The vertical axis for Tr. B is enlarged two times.

Figure 10

CP EDMR characteristics of MOSFETs FN stressed under different bias polarities. Integrated spectra for Tr. A (left panel) and Tr. C (right) measured at T = 27 K with B||[100]. Parameters for the gate pulse are f = 5 kHz, ΔV = 4 V, and Δt = 30 µs. The black curves are the experimental data. Three peaks in each panel are decomposed using the Voigt function, each of which is assigned to the signal from ${\mathrm{P}}_{\mathrm{b}0}$ (red), E′ (green), and SS (blue). Values shown in the figure are the relative intensities (relative peak heights) with that for the SS set at 1.00.