450 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



Page 



VII. A Note on the Effective Bandwidth 480 



VIII. Saturation Effects 482 



IX. Acknowledgement 483 



I. INTRODUCTION 



Within the past few years the field of paramagnetic resonance ab- 

 sorption has become an important tool in physical and chemical re- 

 search. In manj^ ways its usefulness is limited by the sensitivity of the 

 experimental set up. A typical example is the study of semiconductors 

 in which case one would like to investigate as small a number of impuri- 

 ties as possible. It is the purpose of this paper to analyze the sensitivity 

 limits of several experimental set ups under different operating condi- 

 tions. This was done in the hope that an understanding of these limita- 

 tions would put one in a better position to design a high sensitivity 

 electron spin resonance equipment. In the last section the performance 

 of the different experimental arrangements is tested. The agreement 

 obtained with the predicted performance proves the essential validitj' 

 of the analysis. This paper is primarily for experimental phj'sicists con- 

 fronted with the problem of setting up a high sensitivity spectrometer. 



II. GENERAL BACKGROUND 



We will not consider here the detailed theory of the resonance phe- 

 nomenon but consider this part of the problem only from a phenomeno- 

 logical point of view. When a paramagnetic sample is placed into an RF 

 field of amplitude Hi of a frecjuency w at right angles to which there is a 

 dc magnetic field Ho , magnetic dipole transitions will be induced in the 

 neighborhood of the resonance condition 



/ico = gmo (1) 



where g is the spectroscopic splitting factor, h is Planck's constant and 

 /3 is the Bohr magneton. As a result of these transitions power will be 

 absorbed from the microwave field Hi . This power absorption is asso- 

 ciated with the imaginary part of the RF susceptibility x" ■ The trans- 

 mitted (or reflected) Hi will also experience a phase shift which is 

 associated with the real part of the RF susceptibility x'- The sensitivity 

 of the setup is then determined by how small a power absorption (or 

 phase shift) one is able to detect when going through a resonance 



III. Q CHANGES ASSOCIATED WITH THE ABSORPTION 



The average power absorbed per unit \olume of a paramagnetic 

 sample is 



P = ^o^HiY (2) 



