def plot_power_factor_mu(self, temp=600, output='eig',
                             relaxation_time=1e-14, xlim=None):
        """
        Plot the power factor in function of Fermi level. Semi-log plot

        Args:
            temp: the temperature
            xlim: a list of min and max fermi energy by default (0, and band
                gap)
            tau: A relaxation time in s. By default none and the plot is by
               units of relaxation time

        Returns:
            a matplotlib object
        """
        import matplotlib.pyplot as plt
        plt.figure(figsize=(9, 7))
        pf = self._bz.get_power_factor(relaxation_time=relaxation_time,
                                       output=output, doping_levels=False)[
            temp]
        plt.semilogy(self._bz.mu_steps, pf, linewidth=3.0)
        self._plot_bg_limits()
        self._plot_doping(temp)
        if output == 'eig':
            plt.legend(['PF$_1$', 'PF$_2$', 'PF$_3$'])
        if xlim is None:
            plt.xlim(-0.5, self._bz.gap + 0.5)
        else:
            plt.xlim(xlim)
        plt.ylabel("Power factor, ($\\mu$W/(mK$^2$))", fontsize=30.0)
        plt.xlabel("E-E$_f$ (eV)", fontsize=30.0)
        plt.xticks(fontsize=25)
        plt.yticks(fontsize=25)
        plt.tight_layout()
        return plt