PH YSICA L RE VIE% B VOLUME 13, NUMBER 12 15 JUNE 1976 O~& proyerties of hexagons& boron nitride A. Zunger~ Department of Theoretical Physics, Soreq Nuclear Research Centre, Yavne, Israel and Department of Chemistry, Tel Aviv University, Tel Aviv, Israel A. Katzir Department of Solid State Physics, Soreq Nuclear Research Centre, Yavne, Israel A. Halperin The Racah Institute of Physics, The Hebrew University, Jerusalem, Israel (Received 16 June 1975) Optical absorption, reflectivity, and photoconductivity in the near-uv range (1950-3200 A) of a thin film of hexagonal boron nitride were measured. The m»~ absorption peak was observed at 6. 2 eV. A sharp fall at abeet 5.8 eV was attributed to the direct band gap. The temperature dependence of the band gap was found to be less than 4 X 10 ' eV/X. Self-consistent tight-binding band-structure calculations were performed on a twe4imensiona1 hexagonal crystal model, using H~miltonian matrix elements calculated by semiempirical LCAO (linear combination of atomic orbitals) methods. The calculated value for the band gap of hexagonal SN was in reasonably good agreement with the experimental value obtained in the present work, as well as with values reported earlier from electron-energy-loss and photoelectron-emission measurements. The calculations also predicted a very small change in the band gap with temperature, in agreement with the experimental observations. I. INTRODUCTION Hexagonal boron nitride is very similar to graphite. The band structure of graphite has been investigated extensively, and a great deal of theoretical work (mostly recent) has also been done on hexagonaL boron nitride. ' ' Still, the cal- culated theoretical values for the direct optical band gap Ee in hexagonal boron nitride are quite scattered and range between E, = 2. 45 eV (Hef. 4} and 5. 4 eV (Hef. 2). Many workers have attempted to determine E, experimentally. The experimental methods used were soft-x-ray photoemission, electron spectros- copy, ~ electron . energy loss, ' optical reQection, 9' and optical absorption in thin films. 4 The ex- perimental values found for E, range between 3. 6 eV (Hef. 6} and 5. 9 eV (Hef. 15). From reQectance measurements on hexagonal- boron-nitride powders, Larach and Shrader con- cluded that E~& 5. 5, and Chayke' found that reQectivity increases at energies higher than 4. 1 eV. The latter also observed another prominent peak at 6. 2 eV. Determination of E~ by optical-absorption mea- surements of hexagonal-boron-nitride films was carried out by Band and Roberts ' who gave the value E~=3. 8 eV, by Noreika and Francombe's who obtained E, =4. 9-5. 2 eV, by Baronian who obtained E~ = 5. 9 eV, and by Zupan and Kolar'4 who gave the value E, =4. 3 eV. It should be noted that all the absorption measurements, except those by Saronian, were taken on comparatively thick films (&6000 A}, which limited the range of the measurements to energies below 5. 5 eV. In the present work we report results of optical measurements of hexagonal BN in the range 3. 9- 6. 4 eV, and give band-structure calculations on the same crystal. The experimental values are shown to agree well with the calculated ones. II. EXPERIMENTAL RESULTS Our measurements were carried out on thin hexagonal BN films grown by Baronian~s on quartz substrates, using chemical vapor deposition. The films were polycrystalline, with their optical axis perpendicular to the substrate. We report here results obtained on a film of thickness d =680 + 50 A, as determined interferometrically. Optical-absorption measurements were carried out with a Cary 14-R spectrophotometer. The samples were mounted in an optical cryostat pro- vided with a heater, which permitted measure- ments at various temperatures in the range 4. 2- 700 K. BeQection measurements were carried out at normal incidence and room temperature, in a system constructed by Naveh. " Photoconductivity measurements were also per- formed on the same film, using two evaporated aluminum electrodes. The space between the electrodes was illuminated with monochromatic light obtained from a stabilized high-pressure xenon lamp in conjunction with a Hilger D-285 monochromator. The observed photocurrent was very weak, even with widely opened monochromator slits, which decreased the accuracy of the mea- 13