Photoacoustic Spectroscopy of Surface Defects States of Semiconductor Samples 1) M.Maliński, 2) J.Zakrzewski, 2) F.Firszt 1) Department of Electronics and Computer Science TU of Koszalin, Poland 2) Instytut Fizyki UMK Toruń, Poland

ABSTRACT This paper presents both theoretical and experimental issues connected with measurements and numerical analysis of the microphone amplitude and phase photoacoustic spectra of semiconductor samples with defects states located on their surfaces. The analytical model of surface states in semiconductors is described and the results of computations are compared with experimental amplitude and phase spectra for Zn Be Se crystal samples. This paper shows the significance of the phase spectra for the proper interpretation of the PA (photoacoustic) results.

INTRODUCTION Poulet Ouzafe model - a thermally thick sample, front experimental configuration, volume absorption approach It was applied for numerical analysis of amplitude PA spectra of several semiconductor samples such as: ZnSe 1-x Te x, Zn 1-x Be x Se, CdS x Se 1-x or Cd 1-x Mn x Te The phase PA spectra were presented for Zn 1-x Be x Se, Zn 1-x-y Mg y Be x Se or CdTe samples

SAMPLE DESCRIPTION Zn 1-x Be x Se crystals were grown by the high pressure, high temperature Bridgeman method Samples were cut in the form of parallel plates of the thickness l=0.1 cm Samples were mechanically polished and chemically etched Two groups of samples were investigated: as grown and annealed in Zn vapour at 1230 C

DESCRIPTION OF THE MODEL Computations of the PA spectra in the surface states model were performed with two spatial temperature distributions for the volume absorption below the energy gap value: T U (x, f, E, R,  U (E), , l) for the surface absorption below the energy gap value: T S (x, f, E, R,  S (E), , l, d) x is the spatial distribution, f is the frequency of modulation, E is the energy of absorbed photons, R –thermal reflection coeff. between the sample and the backing,  U/S (E) are the optical abssorption coeff. formulae given by, d is the thickness of the surface layer.

DESCRIPTION OF THE MODEL

The PA signal in a microphone detection its amplitude and phase are given by formulae :

SCHEMATIC DIAGRAM OF A SAMPLE

EXPERIMENTAL RESULTS Amplitude and phase PA spectra of Zn Be Se sample at f=25 Hz. Circles are experimental results, thick dashed lines are theoretical curves computed in the model of the volume absorption, thick solid lines are theoretical curves in the proposed model with the contribution of the surface absorption.

OPTICAL PARAMETERS From the fitting procedure the optical parameters of the absorption bands can be determined: Eg=2.75 eV,  U =80cm -1  U =0.50,  S =58 cm -1,  S =0.01,  =0.03 cm 2 /s

Urbach edge The optical absorption bands for the Urbach edge tail U and the surface absorption band S were in the form:

OPTICAL ABSORPTION COEFF. BANDS Optical absorption coefficient spectra of the surface and Urbach edge tail absorption regions – dashed and solid lines respectively Sum of the optical absorption coefficient spectra S+U

THEORETICAL CURVES PA spectra for  S =1 cm -1 (solid),  S =30 cm -1 (dashed),  S =100 cm -1 (dadot), f=25 Hz.

EXPERIMENTAL RESULTS Photoacoustic spectra of the Zn Be Se sample but measured at f= 15 Hz. Circles are experimental values, dashed and solid lines are theoretical curves in the volume and surface absorption models. Fitting was performed for the same set of optical parameters.

Zn 0.79 Be 0.21 Se (x=0.21) Parameters: Eg=3.03 eV, l=0.1 cm, f=15 Hz,  U =150 cm -1,  U =0.40,,  S =58 cm -1,  S =0.01,  =0.03 cm 2 /s.

Zn 0.79 Be 0.21 Se (x=0.21) Parameters: Eg=3.03 eV, l=0.1 cm, f=42 Hz,  U =150 cm -1,  U =0.40,,  S =98 cm -1,  S =0.005,  =0.03 cm 2 /s.

Zn 0.79 Be 0.21 Se (x=0.086) Parameters: Eg=2.86 eV, l=0.1 cm, f=42 Hz,  U =150 cm -1,  U =0.65,  S =58 cm -1,  S =0.01,  =0.03 cm 2 /s.

CONCLUSIONS Computations and fittings presented here show that for the proper determination and interpretation of the optical absorption coefficient spectra of semiconductors the numerical analysis of both amplitude and phase spectra is necessary. The phase PA spectra bring information about the type of absorption ie. volume or surface. As a consequence it results that it is not possible to compute the optical absorption spectrum in the region of low absorption only from the amplitude PA spectrum. The surface optical absorption band, being the result of the presence of surface states, is connected with the surface quality of semiconductor samples and the measurement of the phase PA spectra can be a good test for its determination. Energy gap value increase of the semiconductors Zn 1-x Be x Se with the concentration of Be was observed: x= eV, x= eV, x= eV. Increase of the PA phase for low absorption region with the increase of the frequency of modulation indicates also that the thermal diffusivity of the surface layer is smaller than the rest of the crystal.