An error analysis of maximum-entropy mobility spectrum of electrical carriers in semiconductor

Abstract

A new approach for mobility spectrum analysis is developed to characterize an electrical transport of multi-carrier material. The technique is a numerical method based on the Bayesian statistics and maximum entropy principle including a Markov chain Monte Carlo algorithm. The mobility spectrum is calculated from the magnetic-field-dependent resistivity and Hall coefficient data and from which the number of carrier species, mobility, and carrier concentration are extracted. This technique is feasible to infer the positive and additive spectrum from a discrete, limited, and noisy data. This calculation technique allows the effect of experimental noise on the calculated mobility spectrum to be examined and the uncertainty of solution is estimated. Testing on the synthetic data shows that the order of magnitude of the uncertainty in solution is consistent with the noise level in measured data. The stability of calculation depends on the error level, the maximum magnetic field strength in data collection, the number of data points used in calculation, and adjustable parameters in the algorithm. The technique is applied to the electrical transport of p-Ge/Si0.4 Ge0.6 heterostructure in the temperature range of 200-300 K. Two hole species are found as expected with electron-like species in the background. The high conductivity carier species is expected to be a two-dimensional hole gas in Ge-layer having a high mobility of 2,500 sq.cm V-1s-1 at room temperature. The lower mobility carrier is expected to come from the boron-doped layer and is found to have a mobility of 800 sq.cm V-1s-1 at room temperature.