How to identify semiconductor parameters for spice model?
To the original question, it is rare to see all the necessary parameters for a device in the data sheet, particularly transistors. Some diode manufacturers do put all the necessary parameters in the datasheet.

The model file is here for the MOSFET (and it includes all the necessary parameters).

Just in case the link goes stale, here is the model:

There is a list of MOSFET parameters here as used in SPICE.

    .SUBCKT irfz44n 1 2 3
**************************************
*      Model Generated by MODPEX     *
*Copyright(c) Symmetry Design Systems*
*         All Rights Reserved        *
*    UNPUBLISHED LICENSED SOFTWARE   *
*   Contains Proprietary Information *
*      Which is The Property of      *
*     SYMMETRY OR ITS LICENSORS      *
*Commercial Use or Resale Restricted *
*   by Symmetry License Agreement    *
**************************************
* Model generated on Apr 24, 96
* Model format: SPICE3
* Symmetry POWER MOS Model (Version 1.0)
* External Node Designations
* Node 1 -&gt; Drain
* Node 2 -&gt; Gate
* Node 3 -&gt; Source
M1 9 7 8 8 MM L=100u W=100u
* Default values used in MM:
* The voltage-dependent capacitances are
* not included. Other default values are:
*   RS=0 RD=0 LD=0 CBD=0 CBS=0 CGBO=0
.MODEL MM NMOS LEVEL=1 IS=1e-32
+VTO=3.56214 LAMBDA=0 KP=39.3974
+CGSO=1.25255e-05 CGDO=2.2826e-07
RS 8 3 0.0133305
D1 3 1 MD
.MODEL MD D IS=9.64635e-13 RS=0.00967689 N=1.01377 BV=55
+IBV=0.00025 EG=1.08658 XTI=2.9994 TT=1e-07
+CJO=1.39353e-09 VJ=0.5 M=0.42532 FC=0.5
RDS 3 1 2.2e+06
RD 9 1 0.0001
RG 2 7 2.20235
D2 4 5 MD1
* Default values used in MD1:
*   RS=0 EG=1.11 XTI=3.0 TT=0
*   BV=infinite IBV=1mA
.MODEL MD1 D IS=1e-32 N=50
+CJO=1.52875e-09 VJ=0.5 M=0.584414 FC=1e-08
D3 0 5 MD2
* Default values used in MD2:
*   EG=1.11 XTI=3.0 TT=0 CJO=0
*   BV=infinite IBV=1mA
.MODEL MD2 D IS=1e-10 N=0.408752 RS=3e-06
RL 5 10 1
FI2 7 9 VFI2 -1
VFI2 4 0 0
EV16 10 0 9 7 1
CAP 11 10 2.06741e-09
FI1 7 9 VFI1 -1
VFI1 11 6 0
RCAP 6 10 1
D4 0 6 MD3
* Default values used in MD3:
*   EG=1.11 XTI=3.0 TT=0 CJO=0
*   RS=0 BV=infinite IBV=1mA
.MODEL MD3 D IS=1e-10 N=0.408752
.ENDS


The schottky model is here, and again, in case the link goes stale:

*SRC=MBR1560CT;DI_MBR1560CT;Diodes;Si;  60.0V  15.0A  5.00ns   Diodes Inc. Schottky - One element of device
.MODEL DI_MBR1560CT D  ( IS=11.3u RS=2.64m BV=60.0 IBV=25.0u
+ CJO=530p  M=0.333 N=1.87 TT=7.20n )