Resonant boron acceptor states in semiconducting diamond

High-excited discrete states of boron hydrogenlike acceptors in crystalline diamond have been measured by temperature-dependent infrared absorption spectroscopy. We distinguish the boron resonant states in diamond crystals from the localized boron states in the band gap by differentiating the impurity transitions within state continua of the valence light- and heavy-hole subbands on the basis of their relative oscillator strengths, specific selection rules, and temperature dependences. Constraints on the boron binding energy and spin-orbit splitting of the valence band have been derived by analysis of the structure of the infrared absorption spectra of boron-doped diamond, in particular by a comparison with boron spectra in other semiconductors with a diamond lattice.

Figure 1

Schematic presentation of the valence subbands (lh, hh, SO); localized and resonant (RS) impurity states of a boron acceptor in diamond (a), (b). The subband's bottoms are shown as having parabolic dispersion; see the text for further details. The solid arrows are experimentally observed impurity transitions.

Figure 2

Absorption spectra of boron doped and undoped semiconductors at 5 K [only transitions from the ground $1{{\mathrm{\Gamma }}_8}^{+}$ ($p_{3/2}$) state are shown]: (a) diamond, (b) silicon, and (c) germanium samples, scaled by an $\sim {\mathrm{Ry}}^{*2}$ factor. The right part of each plot shows spectral regions where transitions into the resonant states are expected. A few excited boron states corresponding to the most intense impurity lines are marked for Si and Ge. The tag SO indicates the spectral region in the vicinity of the ($E_{\mathrm{B}}+\mathrm{SO}$) energy.

Figure 3

Typical absorption spectra of boron doped (sample CB2) and undoped diamond (C0) at different lattice temperatures: at $T\sim 5\mathrm{K}$ only boron transitions from the acceptor ground state $1{{\mathrm{\Gamma }}_8}^{+}$ ($p_{3/2}$) are present, while at $T>20\mathrm{K}$ additional transitions from the SO ground state $1{{\mathrm{\Gamma }}_7}^{+}$ ($p_{1/2}$) occur. Note the enhanced strengths of discrete transitions with the photon energy above 371 meV at elevated temperatures. The scales of optical density (OD) for the left and right parts of the absorption spectra are different. For clarity, the spectra are shifted vertically.

Figure 4

Spectrally resolved discrete transitions in the vicinity of the valence-band edge in the absorption spectra of boron doped diamond (CB2 sample); amplitudes are given in optical densities (OD) and shifted for clarity: (violet) absorption spectrum OD ($\hslash \omega -{\mathrm{\Delta }}_{\mathrm{B}}$) taken at 5 K; (pink) absorption spectrum at 20 K OD ($\hslash \omega -{\mathrm{\Delta }}_{\mathrm{B}}$), shifted by ${\mathrm{\Delta }}_{\mathrm{B}}$, so that the ${8^{+}}_{3/2}\to S$ and ${7^{+}}_{1/2}\to S$ transition series in the same excited boron state are spectrally matched. Vertical arrows indicate the positions of the boron transitions ($\to S^{*}$) with the abnormally enhanced strengths at $T>20\mathrm{K}$. The dashed line shows the approximate boron impurity to the ${8^{+}}_{3/2}\to p_{3/2}$ band continuum absorption spectrum.

Figure 5

Cross-section of several samples with different boron (natural isotopic content ${}^{\mathrm{nat}}\mathrm{B}$ and isotopically enriched ${}^{11}\mathrm{B}$) concentrations in the vicinity of the boron binding energy at $T=5\mathrm{K}$. The model of the ionization cross-section for a hydrogenlike acceptor yields a value of the ionization energy $E_{\mathrm{B}}\ge 371\left(1\right)\mathrm{meV}$ for a boron center in diamond.