$$J = J_{L} - J_{0}\left\lbrack \exp\left( \frac{V}{V_{t}} \right) - 1 \right\rbrack$$
$$E_{G}\left( T \right) = E_{G}\left( 0 \right) - \frac{\alpha T^{2}}{T + \beta}$$
$$E_{G}\left( T \right) = \ E_{B} - a_{B}\left\lbrack 1 + \frac{2}{\left( e^{\frac{\Theta}{T}} - 1 \right)} \right\rbrack$$
$$E_{G}\left( T \right) = E_{G}\left( 0 \right) + BT + CT^{2}$$
$$E_{G}\left( T \right) = \ E_{B}(0) - \frac{\alpha\Theta}{2}\left\lbrack \sqrt[p]{1 + \left( \frac{2T}{\Theta} \right)^{p}} - 1 \right\rbrack$$
$$E_{G}^{\text{AB}} = \text{xE}_{G}^{B} + E_{G}^{A}\left( 1 - x \right) - C\left( 1 - x \right)x$$
$$E_{G,X}^{\text{AB}} = \text{xE}_{G,X}^{B} + E_{G,X}^{A}\left( 1 - x \right) - C_{X}\left( 1 - x \right)x$$
$$E_{G,L}^{\text{AB}} = \text{xE}_{G,L}^{B} + E_{G,L}^{A}\left( 1 - x \right) - C_{L}\left( 1 - x \right)x$$
$$E_{G,\Gamma}^{\text{AB}} = \text{xE}_{G,\Gamma}^{B} + E_{G,\Gamma}^{A}\left( 1 - x \right) - C_{\Gamma}\left( 1 - x \right)x$$
$$a_{}^{\text{AB}} = \text{xa}_{}^{B} + a_{}^{A}\left( 1 - x \right) - C\left( 1 - x \right)x$$
$$\text{CBO}_{\text{AB}} = \chi_{A} - \chi_{B}$$
$$m_{e,\ \text{DOS}}^{*} = \ M_{C}^{\frac{2}{3}}\left( {m_{l}^{*}m_{t}^{*}m}_{t}^{*} \right)^{\frac{1}{3}}$$
$$m_{e,\ \text{cond}}^{*} = \ \frac{3}{\left( \frac{1}{m_{l}^{*}} + \frac{1}{m_{t}^{*}} + \frac{1}{m_{t}^{*}} \right)}$$
$$m_{h,\ \text{DOS}}^{*} = \ \left\lbrack {m_{\text{hh}}^{*}}^{\frac{3}{2}} + {m_{\text{lh}}^{*}}^{\frac{3}{2}} + \left( m_{\text{so}}^{*}e^{\frac{- \mathrm{\Delta}}{\text{kT}}} \right)^{\frac{3}{2}} \right\rbrack^{\frac{2}{3}}$$
$$m_{h,\ \text{cond}}^{*} = \ \frac{3}{\left( \frac{1}{m_{\text{hh}}^{*}} + \frac{1}{m_{\text{lh}}^{*}} + \frac{1}{m_{\text{so}}^{*}} \right)}$$
$$N_{V} = 2\left( \frac{2\pi m_{h}^{*}k_{B}T}{h^{2}} \right)^{\frac{3}{2}}$$
$$N_{C} = 2\left( \frac{2\pi m_{e}^{*}k_{B}T}{h^{2}} \right)^{\frac{3}{2}}$$
$$n_{i}^{2} = N_{C}N_{V}e^{\frac{- E_{G}}{\text{kT}}}$$
$$n_{i} = 9.15 \times 10^{10}\left( \frac{T}{300} \right)^{2}e^{\frac{- 0.5928}{\text{kT}}}$$
$$v_{d} = \text{μE}$$
$$\mu = \ \frac{q\overline{\tau}}{m^{*}}$$
$$\mu = \mu_{\min} + \frac{\mu_{\max} - \mu_{\min}}{1 + \left( \frac{N}{N_{r}} \right)^{\alpha}}$$
$$\frac{1}{\tau_{\text{eff}}} = \frac{1}{\tau_{\text{Auger}}} + \frac{1}{\tau_{\text{radiative}}} + \frac{1}{\tau_{\text{SRH}}} + \frac{1}{\tau_{\text{Surf}}}$$
$$U_{\text{rad}} = Bnp$$
$$U \equiv \frac{\mathrm{\Delta}n}{\tau_{}}$$
$$U_{\text{rad}} = B\left( np - n_{i}^{2} \right)$$
$$U_{\text{rad}} \equiv \frac{\mathrm{\Delta}n}{\tau_{\text{Rad}}} = B\left( np - n_{i}^{2} \right)$$
$$\tau_{\text{Rad}} = \frac{1}{B\left( \left( n_{0} + p_{0} \right) + \ \Delta n \right)}$$
$$\tau_{\text{Rad}} = \frac{1}{BN_{D}^{}}\ $$
$$\tau_{\text{Rad}} = \frac{1}{BN_{A}^{}}$$
$$U_{\text{Auger}} = C_{n}n\left( \text{np} - n_{i}^{2} \right) + C_{p}p\left( \text{np} - n_{i}^{2} \right)$$
$$U_{\text{Auger}} \cong C_{n}n^{2}p + C_{p}p^{2}n$$
$$\backslash nU_{\text{Auger}} \equiv \frac{\mathrm{\Delta}n}{\tau_{\text{Auger}}}$$
$$\tau_{\text{Auger}} = \frac{1}{C_{p}\left( {n_{0}^{2} + 2n}_{0}\Delta n + {\Delta n}^{2} \right) + C_{n}\left( {p_{0}^{2} + 2p}_{0}\Delta n + {\Delta n}^{2} \right)}$$
$$\tau_{\text{Auger}} = \frac{1}{C_{p}N_{D}^{2}}$$
$$\tau_{\text{Auger}} = \frac{1}{C_{n}N_{A}^{2}}$$
$$\frac{\mathrm{\Delta}n}{\tau_{\text{Rad}}} = B\left( \left( n_{0} + \Delta n \right)\left( p_{0} + \Delta n \right) - n_{i}^{2} \right)$$
$$\frac{\mathrm{\Delta}n}{\tau_{\text{Rad}}} = B\left( n_{0}p_{0} + \Delta n\left( n_{0} + p_{0} \right) + \ \Delta n2 - n_{i}^{2} \right)$$
$$\frac{\mathrm{\Delta}n}{\tau_{\text{Rad}}} = B\left( \Delta n\left( n_{0} + p_{0} \right) + \ \Delta n2 \right)$$
$$\frac{1}{\tau_{\text{Rad}}} = B\left( \left( n_{0} + p_{0} \right) + \ \Delta n \right)$$