3.1.8 Temperature Effects

$T = \$temperature + DTEMP \qquad (3.101)$

The functional form of temperature dependence of parameters fall in two categories:

Type A:

$PARAM[T] = PARAM[L] \cdot [1 \pm PARAM_T \cdot (T - TNOM)] \qquad (3.102)$

Type B:

$PARAM[T] = PARAM[L] \pm PARAM_T \cdot (T - TNOM) \qquad (3.103)$

where $PARAM_T$ is a model temperature coefficient. BSIM-CMG allows users the option to change the functional form of temperature dependence of a group of selected parameters via temperature selector switch $TEMPMOD$.

$TEMPMOD = 0$ is the default temperature dependence of the parameter expressed in the following equations. Selecting $TEMPMOD = 1$ changes the Type A functional forms to Type B for following parameters: $UC$, $ETA0$, $ETA0R$, $ETAMOB$, $VSAT$, $VSAT1$, $VSATR$, $VSATCV$, $RSDR$, $RDDR$, $PTWG$, $PTWGR$, $K0$, $K1S1$, $K0S1$, $K1$, $K1SAT$, $A1$, $A2$, $AIGBINV$, $AIGBACC$, $AIGC$, $AIGS$, $AIGD$, $BGIDL$, $BGISL$, $ALPHA0$, $ALPHA1$, $ALPHAII0$, $ALPHAII1$, $CJS$, $CJD$, $CJSWS$, $CJSWD$, $CJSWGS$, $CJSWGD$, $PBS$, $PBD$, $PBSWS$, $PBSWD$, $PBSWGS$, $PBSWGD$.

$E_{g,TNOM} = BG0SUB - \dfrac{TBGASUB \cdot TNOM^2}{TNOM + TBGBSUB} \qquad (3.104)$

$E_g = BG0SUB - \dfrac{TBGASUB \cdot T^2}{T + TBGBSUB} \qquad (3.105)$

$n_i = NI0SUB \cdot { \Big( \dfrac{T}{300.15} \Big)}^{\tfrac{3}{2}} \cdot exp \Big( \dfrac{BG0SUB \cdot q}{2 k \cdot 300.15} - \dfrac{E_g \cdot q}{2 k \cdot T} \Big) \qquad (3.106)$

$N_c = NC0SUB \cdot { \Big( \dfrac{T}{300.15} \Big)}^{\tfrac{3}{2}} \qquad (3.107)$

$\Theta_{SS} = 1 + TSS_i \cdot (T - TNOM) \qquad (3.108)$

$V_{bi} = \dfrac{kT}{q} \cdot ln \Big( \dfrac{NSD \cdot NBODY_i[N]}{n_i^2} \Big) \qquad (3.109)$

$\Phi_B = \dfrac{kT}{q} \cdot ln \Big( \dfrac{NBODY_i[N]}{n_i} \Big) \qquad (3.110)$

$\Delta V_{th,temp} = \Big( KT1 + \dfrac{KT1L}{L_{eff}} \Big) \cdot \Big( \dfrac{T}{TNOM} - 1 \Big)\qquad (3.111)$

$ETA0(T) = ETA0 \cdot [1 - TETA0 \cdot (T - TNOM)] \qquad (3.112)$

$ETA0R(T) = ETA0R \cdot [1 - TETA0R \cdot (T - TNOM)] \qquad (3.113)$

$\mu_0(T) = U0[L, N] \cdot \Big( \dfrac{T}{TNOM} \Big)^{UTE_i} + UTL_i \cdot (T - TNOM) \qquad (3.114)$

$ETAMOB(T) = ETAMOB_i \cdot [1 + EMOBT_i \cdot (T - TNOM)] \qquad (3.115)$

$UA(T) = UA[L] + UA1_i \cdot (T - TNOM) \qquad (3.116)$

$UC(T) = UC_i \cdot [1 + UC1_i \cdot (T - TNOM)] \qquad (3.117)$

$UD(T) = UD[L] \cdot \Big( \dfrac{T}{TNOM} \Big)^{UD1_i} \qquad (3.118)$

$UCS(T) = UCS_i \cdot \Big( \dfrac{T}{TNOM} \Big)^{UCSTE_i} \qquad (3.119)$

$VSAT(T) = VSAT[L, N] \cdot [1 - AT \cdot (T - TNOM)] \qquad (3.120)$

$VSAT1(T) = VSAT1[L, N] \cdot [1 - AT \cdot (T - TNOM)] \qquad (3.121)$

$VSAT1R(T) = VSAT1R[L, N] \cdot [1 - AT \cdot (T - TNOM)] \qquad (3.122)$

$VSATCV(T) = VSATCV[L] \cdot [1 - ATCV \cdot (T - TNOM)] \qquad (3.123)$

$PTWG(T) = PTWG[L] \cdot [1 - PTWGT \cdot (T - TNOM)] \qquad (3.124)$

$PTWGR(T) = PTWGR[L] \cdot [1 - PTWGT \cdot (T - TNOM)] \qquad (3.125)$

$\begin{cases} MEXP(T) = MEXP[L] \cdot \Big[ 1 + TMEXP \cdot (T - TNOM) \Big] &\text{if } ASYMMOD = 0 \\ MEXPR(T) = MEXPR[L] \cdot \Big[ 1 + TMEXPR \cdot (T - TNOM) \Big] &\text{if } ASYMMOD = 1 \end{cases}$

$(3.126)$

$BETA0(T) = BETA0_i \cdot \Big( \dfrac{T}{TNOM} \Big)^{IIT} \qquad (3.127)$

$SII0(T) = SII0_i \cdot \Big[ 1 + TII \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big] \qquad (3.128)$

$K0(T) = K0_i + K01_i \cdot (T - TNOM) \qquad (3.129)$

$K1(T) = K1_i + K11_i \cdot (T - TNOM) \qquad (3.130)$

$K0SI(T) = K0SI_i + K0SI1_i \cdot (T - TNOM) \qquad (3.131)$

$K1SI(T) = K1SI_i + K1SI1_i \cdot (T - TNOM) \qquad (3.132)$

$K1SAT(T) = K1SAT_i + K1SAT1_i \cdot (T - TNOM) \qquad (3.133)$

$A1(T) = A1_i + A11_i \cdot (T - TNOM) \qquad (3.134)$

$A2(T) = A2_i + A21_i \cdot (T - TNOM) \qquad (3.135)$

$AIGBINV(T) = AIGBINV_i + AIGBINV1_i \cdot (T - TNOM) \qquad (3.136)$

$AIGBACC(T) = AIGBACC_i + AIGBACC1_i \cdot (T - TNOM) \qquad (3.137)$

$AIGC(T) = AIGC_i + AIGC1_i \cdot (T - TNOM) \qquad (3.138)$

$AIGS(T) = AIGS_i + AIGS1_i \cdot (T - TNOM) \qquad (3.139)$

$AIGD(T) = AIGD_i + AIGD1_i \cdot (T - TNOM) \qquad (3.140)$

$BGIDL(T) = BGIDL_i \cdot [1 + TGIDL \cdot (T - TNOM)] \qquad (3.141)$

$BGISL(T) = BGISL_i \cdot [1 + TGIDL \cdot (T - TNOM)] \qquad (3.142)$

$ALPHA0(T) = ALPHA0_i + ALPHA01_i \cdot (T - TNOM) \qquad (3.143)$

$ALPHA1(T) = ALPHA1_i + ALPHA11_i \cdot (T - TNOM) \qquad (3.144)$

$ALPHAII0(T) = ALPHAII0_i + ALPHAII01_i \cdot (T - TNOM) \qquad (3.145)$

$ALPHAII1(T) = ALPHAII1_i + ALPHAII11_i \cdot (T - TNOM) \qquad (3.146)$

$RDSWMIN(T) = RDSWMIN \cdot [1 + PRT \cdot (T - TNOM)] \qquad (3.147)$

$RDSW(T) = RDSW[L] \cdot [1 + PRT \cdot (T - TNOM)] \qquad (3.148)$

$RSWMIN(T) = RSWMIN \cdot [1 + PRT \cdot (T - TNOM)] \qquad (3.149)$

$RDWMIN(T) = RDWMIN \cdot [1 + PRT \cdot (T - TNOM)] \qquad (3.150)$

$RSW(T) = RSW[L] \cdot [1 + PRT \cdot (T - TNOM)] \qquad (3.151)$

$RDW(T) = RDW[L] \cdot [1 + PRT \cdot (T - TNOM)] \qquad (3.152)$

$RSDR(T) = RSDR \cdot [1 + TRSDR \cdot (T - TNOM)] \qquad (3.153)$

$RSDRR(T) = RSDRR \cdot [1 + TRSDR \cdot (T - TNOM)] \qquad (3.154)$

$RDDR(T) = RDDR \cdot [1 + TRDDR \cdot (T - TNOM)] \qquad (3.155)$

$RDDRR(T) = RDDRR \cdot [1 + TRDDR \cdot (T - TNOM)] \qquad (3.156)$

$R_{s,geo}(T) = R_{s,geo} \cdot [1 + PRT \cdot (T - TNOM)] \qquad (3.157)$

$R_{d,geo}(T) = R_{d,geo} \cdot [1 + PRT \cdot (T - TNOM)] \qquad (3.158)$

$I_{gtemp} = \Big( \dfrac{T}{TNOM} \Big)^{IGT_i} \qquad (3.159)$

$T_{3s} = exp \Big[ \dfrac{1}{NJS} \cdot \Big( \dfrac{q E_{g,TNOM}}{k \cdot TNOM} - \dfrac{q E_g}{k T} + XTIS \cdot ln \Big( \dfrac{T}{TNOM} \Big) \Big) \Big] \qquad (3.160)$

$J_{ss}(T) = JSS \cdot T_{3s} \qquad (3.161)$

$J_{ssws}(T) = JSWS \cdot T_{3s} \qquad (3.162)$

$J_{sswgs}(T) = JSWGS \cdot T_{3s} \qquad (3.163)$

$T_{3d} = exp \Big[ \dfrac{1}{NJD} \cdot \Big( \dfrac{q E_{g,TNOM}}{k \cdot TNOM} - \dfrac{q E_g}{k T} + XTID \cdot ln \Big( \dfrac{T}{TNOM} \Big) \Big) \Big] \qquad \qquad (3.164)$

$J_{sd}(T) = JSD \cdot T_{3d} \qquad (3.165)$

$J_{sswd}(T) = JSWD \cdot T_{3d} \qquad (3.166)$

$J_{sswgd}(T) = JSWGD \cdot T_{3d} \qquad (3.167)$

$J_{tss}(T) = JTSS \cdot exp \Big[ \Big( \dfrac{1}{kT/q} \Big) \cdot \Big( E_{g,TNOM} \cdot XTSS \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big) \Big] \qquad (3.168)$

$J_{tsd}(T) = JTSD \cdot exp \Big[ \Big( \dfrac{1}{kT/q} \Big) \cdot \Big( E_{g,TNOM} \cdot XTSD \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big) \Big] \qquad (3.169)$

$J_{tssws}(T) = JTSSWS \times exp \Big[ \Big( \dfrac{1}{kT/q} \Big) \cdot \Big( E_{g,TNOM} \cdot XTSSWS \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big) \Big]$

$(3.170)$

$J_{tsswd}(T) = JTSSWD \times exp \Big[ \Big( \dfrac{1}{kT/q} \Big) \cdot \Big( E_{g,TNOM} \cdot XTSSWD \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big) \Big]$

$(3.171)$

$\begin{aligned} J_{tsswgs}(T) &= JTSSWGS \times \Big( 1 + \sqrt{JTWEFF/W_{eff0}} \Big) \\ &\times exp \Big[ \Big( \dfrac{1}{kT/q} \Big) \cdot \Big( E_{g,TNOM} \cdot XTSSWGS \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big) \Big] \end{aligned}$

$(3.172)$

$\begin{aligned} J_{tsswgd}(T) &= JTSSWGD \times \Big( 1 + \sqrt{JTWEFF/W_{eff0}} \Big) \\ &\times exp \Big[ \Big( \dfrac{1}{kT/q} \Big) \cdot \Big( E_{g,TNOM} \cdot XTSSWGD \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big) \Big] \end{aligned}$

$(3.173)$

$NJTS(T) = NJTS \cdot \Big[ 1 + TNJTS \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big] \qquad (3.174)$

$NJTSD(T) = NJTSD \cdot \Big[ 1 + TNJTSD \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big] \qquad (3.175)$

$NJTSSW(T) = NJTSSW \cdot \Big[ 1 + TNJTSSW \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big] \qquad (3.176)$

$NJTSSWD(T) = NJTSSWD \cdot \Big[ 1 + TNJTSSWD \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big] \qquad (3.177)$

$NJTSSWG(T) = NJTSSW \cdot \Big[ 1 + TNJTSSWG \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big] \qquad (3.178)$

$NJTSSWGD(T) = NJTSSWGD \cdot \Big[ 1 + TNJTSSWGD \cdot \Big( \dfrac{T}{TNOM} - 1 \Big) \Big] \qquad (3.179)$

$CJS(T) = CJS \cdot [1 + TCJ \cdot (T - TNOM)] \qquad (3.180)$

$CJD(T) = CJD \cdot [1 + TCJ \cdot (T - TNOM)] \qquad (3.181)$

$CJSWS(T) = CJSWS \cdot [1 + TCJSW \cdot (T - TNOM)] \qquad (3.182)$

$CJSWD(T) = CJSWD \cdot [1 + TCJSW \cdot (T - TNOM)] \qquad (3.183)$

$CJSWGS(T) = CJSWGS \cdot [1 + TCJSWG \cdot (T - TNOM)] \qquad (3.184)$

$CJSWGD(T) = CJSWGD \cdot [1 + TCJSWG \cdot (T - TNOM)] \qquad (3.185)$

$PBS(T) = PBS(TNOM) - TPB \cdot (T - TNOM) \qquad (3.186)$

$PBD(T) = PBD(TNOM) - TPB \cdot (T - TNOM) \qquad (3.187)$

$PBSWS(T) = PBSWS(TNOM) - TPBSW \cdot (T - TNOM) \qquad (3.188)$

$PBSWD(T) = PBSWD(TNOM) - TPBSW \cdot (T - TNOM) \qquad (3.189)$

$PBSWGS(T) = PBSWGS(TNOM) - TPBSWG \cdot (T - TNOM) \qquad (3.190)$

$PBSWGD(T) = PBSWGD(TNOM) - TPBSWG \cdot (T - TNOM) \qquad (3.191)$