Electron emission from deep traps in ${\mathrm{HfO}}_2$ under thermal and optical excitation

The ratio between the energies of optical and thermal ionization depends on the defect nature and the strength of the interaction of trapped electrons with phonons. Knowing this ratio for a certain type of defect allows one to predict, e.g., thermal emission energies from the optically measured values. We present the results of direct empirical extraction of the ratio between optical and thermal electron emission energies for ${\mathrm{HfO}}_2$ bulk electron traps combined with theoretical analysis of the physical mechanism of electron transitions from the trapped state to the mobility edge. We show that, by applying different excitation mechanisms, we affect the same deep traps inside the ${\mathrm{HfO}}_2$ band gap; i.e., these traps are both optically and thermally active and are likely to have similar nature. The extracted empirical optical/thermal ionization energy ratio of $2.2\pm 0.3$ is in good agreement with the polaronic nature of the probed electron traps, as shown by the results of theoretical calculations. Our results provide experimental and theoretical methodologies for consistently linking thermal and optical ionization energies of electron traps and describing their distributions in the band gap of amorphous oxides, and can help improve modeling frameworks for reliability issues related to oxide traps.

Figure 1

Schematics of electron transitions during (a) thermal detrapping, and (b) optical EPDS experiments performed on $n\text{-Si}/{\mathrm{SiO}}_2/{\mathrm{HfO}}_2/\mathrm{Au}$ structures. Blue circles represent electrons; the ribbon near the ${\mathrm{HfO}}_2$ CB indicates the existence of partially localized electronic states and the position of ME. The vertical colored arrows show the corresponding electron emission processes, while the gray horizontal arrows illustrate possible escape paths for electrons excited into ${\mathrm{HfO}}_2$ CB or ME.

Figure 2

(a) CV curves before/after electron injection and variable relaxation time. The inset illustrates how $V_{\mathrm{FB}}$ is extracted via the voltage inflection point method on the example of the initial state before electron injection. (b) Linear-log plot of $V_{\mathrm{FB}}$ relaxation in the dark at zero bias from the as-charged state (black squares, left axis). The error bars indicate the standard deviation across $\sim 60$ samples. Dashed lines indicate relaxation time of 48 hours (blue) and $\sim 2$ weeks (green). The red circles show the estimated thermal activation energy of trapped electrons on the corresponding timescale (right axis).

Figure 3

Impact of variable relaxation time on the results of EPDS experiments as measured on identically processed $n\text{-Si}/5\text{-nm} {\mathrm{SiO}}_2/20\text{-nm} {\mathrm{HfO}}_2/15\text{-nm}$ Au samples subjected to charge injection at $+14\mathrm{V}$. Panel (a) shows $V_{\mathrm{FB}}$ variation on the charged samples versus photon energy of incident illumination; panel (b) plots the corresponding SCD values for each energy interval. The detrapping peak at 2.25 eV photon energy is affected the most by the relaxation time variation, suggesting that the time constant of the thermal emission of electrons from this energy level at room temperature is comparable to the relaxation times used in the experiment.

Figure 4

Charge loss (in %) due to photodepopulation at zero bias versus the photon energy (black symbols) as measured on 4 equally processed $n\text{-Si}/5\text{-nm} {\mathrm{SiO}}_2/20\text{-nm} {\mathrm{HfO}}_2/15\text{-nm}$ Au samples subjected to charge injection at $+14\mathrm{V}$ and long relaxation in the dark. The gray area marks the photon energy range (above $\approx 3.1\mathrm{eV}$) where EPDS accuracy decreases significantly. Red and green dashed lines illustrate the average percentage of trapped charge lost after heating at $100{}^{\circ }\mathrm{C}$ and $200{}^{\circ }\mathrm{C}$, respectively, for 90 min, and the corresponding colored area illustrates the estimation error for the set of several samples.

Figure 5

Reference SCD spectra measured on several unheated $n\text{-Si}/5\text{-nm} {\mathrm{SiO}}_2/20\text{-nm} {\mathrm{HfO}}_2/15\text{-nm}$ Au samples. Solid lines with open symbols and dashed lines with filled symbols represent charged and uncharged samples, respectively.

Figure 6

SCD versus photon energy plots at different bias applied during sample illumination: $+2\mathrm{V}$ (a) and 0 V (b), from the samples heated to $70{}^{\circ }\mathrm{C}$ (purple), $100{}^{\circ }\mathrm{C}$ (red), $150{}^{\circ }\mathrm{C}$ (blue), or $200{}^{\circ }\mathrm{C}$ (green) as compared to the reference unheated samples (black). The charging and photodepopulation conditions are indicated in the table on both panels.

Figure 7

Averaged SCD versus photon energy plots (in color) from the samples heated for 1.5 hours without “floating” electrode condition with (a) variable bias during heating at $70{}^{\circ }\mathrm{C}$ and (b) heated at variable temperature, $70{}^{\circ }\mathrm{C}$ or $100{}^{\circ }\mathrm{C}$, while keeping $+3\mathrm{V}$ applied to the top electrode. The reference EPDS spectrum is shown in black on each panel. The experimental conditions are listed in the table on each panel.

Figure 8

An example of the local atomic configuration of electron traps in $a\text{−}{\mathrm{HfO}}_2$. (a) shows a self-trapped electron in the bulk of $a\text{−}{\mathrm{HfO}}_2$. (b) is the $V_{\text{O}}^{-}$ defect, which is an extra electron trapped in a neutral oxygen vacancy. Cyan spheres indicate Hf ions; red spheres indicate O ions. The blue surface is an isosurface of the spin density of the trapped electron.

Figure 9

Plots of the local PEC for electron capture into a trap state, in the single effective harmonic mode approximation. (a) Local PEC for capture of an electron from the BCB state. (b) Local PEC for capture of an electron from a CB state at the ME. The effective coordinate is defined so that $\mathrm{\Delta }{Q}_{\text{eff}}=0$ in the defect-free configuration and $\mathrm{\Delta }{Q}_{\text{eff}}=1$ for the ground state of the trapped electron.