The admittance measurements of a hetero-junction can be used to derive the density of the interfacial state in the hetero-junction. Hence, prediction conductance via frequency is very useful for comprehension of the admittance of a hetero-junction using a mathematical strategy. From the observations on the curve of the frequencydependent conductance of the hetero-junction an analytic model with four-parameters was developed that relates conductance to frequency; the theoretical results agree quite well with the experimental data. The model shows potential for a variety of applications including different electronic devices. The model is a practical tool that can be readily used for assessing the electronic behaviors of a hetero-junction and is scientifically justifiable. In addition, the mathematical bridge to link the density of the interfacial state of the(pyronine-B)/p-Si structure to energy implies a good route to discuses the density of the interfacial state of interfaces. The admittance measurements of a hetero-junction can be used to derive the density of the interfacial state in the hetero-junction. From the observations on the curve of the frequency dependent conduct of the hetero-junction an analytic model with four-parameters was developed that were conductance to frequency; the theoretical results agree quite well with the experimental data. The model shows potential for a variety of applications including The model is a practical tool that can be readily used for assessing the electronic behaviors of a hetero-junction and is scientifically justifiable. In addition, the mathematical bridge to link the density of the interfacial state of the (pyronine-B ) / p-Si structure to energy implies a good route to discuses the density of the interfacial state of interfaces.